My Double Unveiled

Advances in Consciousness Research

Advances in Consciousness Research provides a forum for scholars from different scientific disciplines and fields of knowledge who study consciousness in its multifaceted aspects. Thus the Series will include (but not be limited to)

the various areas of cognitive science, including cognitive psychology, linguis­

tics, brain science and philosophy. The orientation of the Series is toward developing new interdisciplinary and integrative approaches for the investiga­tion, description and theory of consciousness, as well as the practical conse­

quences of this research for the individual and society.

Series A: Theory and Method. Contributions to the development of theory and method in the study of consciousness.

Editor

Maxim I. Stamenov Bulgarian Academy of Sciences

Editorial Board

David Chalmers, University of Arizona

Gordon G. Globus, University of California at Irvine

Ray Jackendoff, Brandeis University

ChristofKoch, California Institute of Technology

Stephen Kosslyn, Harvard University

Earl Mac Cormac, Duke University

George Mandler, University of California at San Diego

John R. Searle, University of California at Berkeley

Petra Stoerig, Universitiit Dusseldorf

Francisco Varela, C.R.E.A., Ecole Polytechnique, Paris

Volume32

My Double Unveiled: The dissipative quantum model of brain

by Giuseppe Vitiello

My Double Unveiled

The dissipative quantum model of brain

Giuseppe Vitiello Universita di Salerno, Italy

John Benjamins Publishing Company Amsterdam/ Philadelphia

The paper used in this publication meets the minimum requirements of American National Standard for Information Sciences - Permanence of Paper for Printed Library Materials, ANSI z39 .48-1984.

Library of Congress Cataloging-in-Publication Data

Vitiello, Giuseppe My double unveiled : the dissipative quantum model of brain I Giuseppe Vitiello.

p. em. (Advances in Consciousness Research, ISSN 1381-589X ; v. 32) Includes bibliographical references and index.

L Brain--Mathematical models. 2. Quantum theory. 3. Consciousness--Mathematical models. L Title. IL Series.

QP376 V545 2001 612 8011--dc21 2001035806 ISBN 90 272 51525 (Eur.) / 1 58811 076 1 (US) (pb; alk. paper)

© 2001- John Benjamins B.V. No part of this book may be reproduced in any form, by print, photoprint, microfilm, or any other means, without written permission from the publisher.

John Benjamins Publishing Co. · P.O. Box 36224 · 1020 ME Amsterdam · The Netherlands John Benjamins North America · P.O. Box 27519 · Philadelphia PA 19118-0519 · USA

a Marina

Table of contents

Foreword XI

Acknowledgments XVII

CHAPTER 1

Structure and function 1

1.1 Naturalism and Science 2

1.2 A motivation for the quantum model of brain 5

1.3 Quantum Mechanics? 9

1.4 Structure and function n

1.5 Classical or quantum? 14

1.6 Quantum Mechanics and Quantum Field Theory 17

CHAPTER 2

Macroscopic variables and microscopic dynamics 21

2.1 Macroscopic variables and microscopic dynamics 22

2.2 Dynamical fields and phenomenological fields 23

2.3 The perturbative scheme 25

2.4 Symmetry and order: A dynamical problem 28

2. 5 Collective modes, coherence and order 31

2.6 Self-focusing propagation oflong range interaction fields 34

2.7 Nonlinear dynamics and soliton solutions 37

CHAPTER 3 The living phase of matter

3.1 Living matter physics 42

3.2 Frohlich coherent excitations 43

3-3 Phenomenology [ 45

3-4 Davydov soliton 47

3·5 The Quantum Field Theory approach 51

41

VIII Table of contents

3.6 Charge and discharge regimes 53

3·7 Electromagnetic field and cytoskeleton 57

3.8 Phenomenology II 58

3·9 Thermal effects 61

CHAPTER4

The quantum model of brain

4.1 Brain and physics of many-body problems 68

4.2 Natural brain and artificial brain 70

4-3 External stimuli and brain states 72

4-4 Memory recording and memory recollection 75

4·5 Memory and non-equilibrium phase transitions 78

4.6 Brain as a mixed system So

4·7 Open problems and experimental issues 83

CHAPTER 5

Quantum brain dynamics 87

5.1 The physical image of corticon and symmetron 88

5.2 Intracellular quantum signals 89

5·3 Pribram's holonomic brain theory 93

5·4 Microtubules and the electromagnetic field 96

5.5 Cell-to-cell signaling and tissue functional differentiation 99

CHAPTER 6

Dissipation and memory

6.1 The brain is an open system 104

6.2 Now you know it!... 106

6.3 Quantum dissipation 108

6.4 Dissipative quantum brain dynamics 111

6. 5 Life-time and hierarchy of memory 115

6.6 Collective modes on neural nets 117

CHAPTER 7

103

Dissipation and consciousness 123

7.1 Brain and consciousness 124

7.2 Toward a Science of Consciousness? 125

7·3 Modeling consciousness 128

7-4 Three properties of consciousness 131

7·5 Life-time and localizability of correlated domains 134

7.6 Mind the gap! 137

7-7 My Double, Myself 140

Table of contents IX

References 147

Index 159

Foreword

I remember one morning towards the end of May, sitting in my office at the

Physics Department in Edmonton, I was looking through the window at the

brilliant scenery of green trees flourishing in the spring. It was in 1978 and I was visiting the University of Alberta, invited by Hiroomi Umezawa. I was strug­

gling with a difficult problem in quantum field theory, the quantization of the

matter field in curved space-time. At that moment I did not know how to proceed with my problem, I felt lost. Thus I was looking through the window as

searching for something, for some signal coming from somewhere, for some

sort of miraculous help able to suggest to me how to overcome the point where

I was stuck. At a certain moment, however, mentally running away from the

problem I had to solve, I suddenly felt surprised by the rich variety of plants and

trees! Of course, since high school I knew that there is a great variety of plants

and trees, and also of any other kind ofliving beings. In fact I had to memorize

unlimited lists of complicated and strange names for my study of botanic and biology. However, in that moment I felt that "understanding, the richness of

forms and species presented to us by Nature was a formidable problem, very

difficult, if ever possible, to be solved in terms of "scientific, knowledge. So,

looking outside through the window, instead of help for my quantization

problem, I got one much more difficult problem. That morning, however, I put

it immediately aside with the justification that it was not my problem. Biologists

should think about it. In any case, the thought that everything is encoded in the

DNA was quite consoling to me.

The window in my office was exactly in front of my desk, so looking outside

was unavoidable for me (also because there was not much progress in the solution of my quantization puzzle ... ). Thus, the problem of ((understanding,

the richness of the forms in living matter came to my mind again and the fact

that everything is written in the ordered molecular patterns of the DNA was no

more consoling to me. The question indeed then became: "\t\lhat is the dynami­

cal mechanism generating ordered patterns?, I was no more able to turn down

that problem by shifting it to my friends in biology. Their heavy job is to

xn Foreword

analyze and to list in all possible details the molecular components of living

matter and see how they fit together. The genome project which is pursued these days all around the world is the best example of such a tremendous effort.

Even biological engineering does not deal with the generation of ordering. Molecular engineers can do almost everything today. But they are only engi­neers. One cannot ask them questions about the dynamic generation of the

ordering. Such kinds of questions are a trouble to be charged to physicists. So that window in my office was "my" trouble. I realized in one moment what my teacher of physics at high school meant when he was stressing the distinction between naturalism and science: naturalism is necessary to the progress of

science, which means that without those lists of names and catalogs of proper­

ties I had to memorize, you cannot even think of making any progress in knowledge. But naturalism is not sufficient. It is only phenomenology. Sooner

or later you will have a window in your office and then you will ask questions about the "dynamics", questions which naturalism cannot answer. Of course, also asking questions about the dynamics is a necessary but not sufficient

condition for making science. So you need both, phenomenology and dynam­ics. This is much similar to what the Italian writer Italo Calvino describes in his book "Le citta' invisibili" (The invisible towns). He writes that Marco Polo describes a bridge stone by stone. Then the Kublai Kan asks: ''Which one is the

stone that sustains the bridge?''. Polo: "The bridge is not sustained by one specific stone, but by the line of the arch formed by the stones". Kublai Kan remains silent, reflecting upon those words. Then he says: "Why are you telling me about the stones? I only care about the arch", and Polo: "Without stones

there is no arch".

Fortunately, the subject of my doctoral thesis, a work done under Ume­zawa's supervision when he was at Milwaukee in Wisconsin, has been just the problem of the dynamic generation of the order, that Umezawa and his collaborators in the middle of the 1960s called the problem of the dynamical

rearrangement of symmetry. That study, however, was applied to the physics of elementary particles and of condensed matter, not to biological systems. The most intriguing aspect of the mechanism of spontaneous breakdown of symmetry which manifests in the dynamical rearrangement of symmetry is the change of scale, from microscopic to macroscopic. And this is possible since

dynamical consistency requires the existence of collective modes, whose coherent behavior manifests itself as a property of the system as a whole, as a macroscopic quantum system. Could this scenario possibly apply to living

matter? Before those days in Edmonton I never thought I would dare to apply

Foreword XIII

quantum field theory to such complicated stuff as living matter. In Edmonton,

during the long discussions with Umezawa, continuing some time at his home, late at night, I was very careful in not revealing to him anything about my

window and those strange thoughts of mine about ordering in living matter. However, with my pleasure, during one of those discussions Umezawa told me about two papers he wrote between 1976 and 1977 in collaboration with Yasushi Takahashi and lain Stuart on brain and memory, developing the earlier work by Umezawa and Ricciardi of 1967. I was surprised by the fact that he told me

about those papers talking in the most natural way, as he used to do for any other subject in Physics, without revealing any need of justifications for search­

ing in a territory not traditionally explored by physicists. This was a lesson to me, afraid to trespass sacred borders ... Still today, however, I feel embarrassed in telling colleagues who are physicists of certain interests of mine ...

A few years later, I met at a conference on nonlinear dynamical systems, in Leece, on the Adriatic sea in South Italy, Emilio Del Giudice (whom I knew for a long time; he had taught me elementary particle physics when I was an

undergraduate student at Naples University), Marziale Milani and Silvia Doglia. Later, working with these people in Milan, I also collaborated with Giuliano Preparata, who I already had occasion to meet in the past. I must thank these people since I started to do some work in the dynamical rearrangement of

symmetry in Living matter. I had also the great pleasure to meet and discuss with Alexander Davydov at a conference in Copenhagen. On several occasions

I met Herbert Frohlich and have discussed with him quantum coherence in living systems, enjoying his brightness and his teaching. The quantum field theory approach to living matter, which still needs a lot of work, is the result of the collaboration with these people. The results on the water electric dipole dynamics and coherence obtained in setting up the quantum field theory

approach to living matter have turned out to be essential tools in the search in

the 1990s for the quantum model of brain. The work by Frohlich and Davydov was also inspiring for Kunio Yasue and Mari Jibu in their studies on Umezawa's quantum brain model. Jibu and Yasue's work gives a concrete physical body to

the abstract formulation of the quantum model of brain and sets the founda­tions of quantum brain dynamics.

Mario Rasetti, during one of his visits to Salerno, in the early 1990s, told me about a paper by Feshbach and Tikochinsky where the quantization of the damped harmonic oscillator, a prototype of dissipative systems, was presented.

The central idea of the paper is «doubling" of degrees of freedom in order to account for the loss of energy due to dissipation. The «doubled" system

XIV Foreword

represents the environment where the energy lost by the system goes. The smart

point is that the doubled system is the exact copy of the original one, with the only (not trivial!) difference that it is an amplified oscillator, while the original

one is a damped oscillator. The authors, however, recognize in that paper that their result is not mathematically acceptable, since dissipation breaks down the Hilbert space structure. The hamiltonian system looked very familiar to me: it is very similar to the quantum field theory at finite temperature developed by Takahashi and Umezawa in the middle of 1970s. Thus, we decided to see if the

result of Feshbach and Tikochinsky could be "repaired". In a paper with Celeghini (with whom we were already working on some problem in group theory) we found that, provided one operates in the framework of quantum field theory (not of quantum mechanics as in the paper by Feshbach and

Tikochinsky), the canonical quantization of dissipative systems along the line proposed by Feshbach and Tikochinsky is mathematically consistent. Where is the miracle? It is in the fact that in quantum field theory there are infinitely many states of minimum energy (the vacua) which are, however, different among

themselves in their physical properties. This does not happen in quantum

mechanics where the minimum energy states are all physically equivalent. In the typical nonlinear wandering in search of something, the results in the

quantization of dissipative systems together with the ones on the coherent

dynamics ofliving matter obtained in the 1980s brought me to think of an open

problem in the quantum model of brain, the problem of the too small memory capacity. In the model, every time some information is memorized, it is overprinted on the previously recorded one. I felt that if I could justify the use of

dissipative formalism in the brain model, I could solve the overprinting problem. And it was easy to justify that! The brain is an .. open" system, always interacting with its environment from which it gets any sort of information. Getting an information produces an irreversible change in the brain state: Now

you know it! ... Which means that once you come to know something, you are

no longer the same person! Thus the brain evolution is intrinsically irreversible and dissipative formalism must be applied. By considering dissipation I have shown that a solution can be found for the overprinting problem. Pleasant surprises came along with that. The first has to do with the arrow of time, which we always experience pointing toward the future. This is built into the dissi­pative model and, unexpectedly, is related to the possibility of having a huge

memory capacity. There is then a more realistic view on the formation of coherent domains, with the consequent hierarchy of memories in terms of their localization and life time. The possibility of forgetting (not present in the

Foreword xv

original model), of having association, but also confusion of memories and so

on, a series of phenomena belonging to our daily experience, also were ex­

plained by the model.

Another surprise is in the meaning that the doubled degrees of freedom may acquire in the brain model framework: the brain dissipative dynamics

implies a copy, a «double" of the brain. Mathematically and physically speaking

one «needs" such a double for internal consistency, this is quite clear and it

suggests to me that a hint could be there for the understanding of consciousness

mechanisms.

This book is the story of the search summarized above. Let me say it is the

story of the disclosure of my Double. The book, like the research in which I am involved, is not complete, there is still much ahead. I am glad of that. I prefer

books which are open to developments, which open discussions, rather than

dogmatically closing them. Also the different chapters are not closed on themselves. Sometimes I have purposely repeated the same concept in different

chapters, sometimes to stress its relevance, sometimes to look at it from a

different perspective. Always my first concern has been the clarity of the

exposition. I apologize if my effort has not always been successful. I have not used any mathematical formalism, even if sometimes I have suffered for not

sharing with the reader the beauty of the mathematics. However, most of the

concepts and statements have a mathematical counterpart published in the

quoted literature. I am quite proud of this. The book's main subject is about the dissipative quantum model of brain and its possible implications for conscious­

ness studies. However, the dissipative model is so intricately rooted in the

general frame of my research activity, that I could not avoid to outline the

skeleton of such a frame. In fact, a pleasant aspect in my story is the continuous interplay between the research in subjects specific to the physics of elementary

particles and of condensed matter and the research on the basic dynamics in

biology and brain functioning. This continuous flow of exchanges between the two sectors produces the satisfying feeling of the unity of knowledge, which I

hope the reader can share with me.

September, 2000

Acknowledgments

When Maxim Stamenov invited me to write a book on the dissipative quantum

model of brain [thought that after all it would not be a very heavy job. Some­thing like assembling several papers. It has been not so. [had to elaborate a completely new way for presenting and organizing the matter. J had to work hard to translate in understandable and faithful words the mathematical results.

And I had to fight also with my broken English. But all of it has been worth­while. I do not know how the readers will accept this book. To me it has been a good occasion to clarify to myself many questions. For this and for his advice, comments and criticisms I am very much grateful to Maxim. Without the continuous assistance, the comments, the corrections, and the sharp criticisms

of Gordon Globus this book would not be as it is. Many and special thanks go therefore to Gordon. I also thank him for his enthusiastic reactions to some of the parts of the book. This will be a successful book if other readers will react in the same way.

Since this book is the story of a search, its writing could not be done

without the teachings, the contributions and the help of many people. I will just mention a few of them and I apologize for not mentioning all the others. Let me first express my gratitude to Hiroomi Umezawa who taught me how to dig out the physical meaning from the richness of the mathematics of quantum fields. Umezawa has a special place in the development of modern physics. He has also

a special place in my scientific formation. My activity has fully grown out from his teachings. I am also very grateful to Francesco Guerra for his constant guidance since the years of my undergraduate studies.

A very special place in the development of the ideas on living matter

discussed in this book is the one of Emilio Del Giudice. He is the one who has really taken over and developed the line of thought of Herbert Frohlich. I am very grateful to him and to Silvia Doglia and Marziale Milani. The time spent working together has been always very enjoyable, stimulating and fruitful. I am also very grateful to the late Giuliano Preparata. Unfortunately, he left us in

April 2000. Giuliano's contribution to elementary particle physics and to

XVIII Acknowledgments

condensed matter physics is outstanding. His premature departure is a loss for

Physics. He gave a very personal touch to the understanding of many problems and a special contribution to the theory of coherent domains.

Of course, I will never forget the discussion with Alexander Davydov and the ones with Herbert Frohlich. For them, like for Umezawa, there were no frontiers: There is no high energy physics, many body physics, living matter physics. Physics is only one. I think of them when I have to recover from meeting a certain kind of colleagues unable to see beyond their own nose.

Therefore I judge myself being very lucky in meeting and working with Mario Rasetti. He has disclosed to me the elegance and the powerfulness of algebraic

and statistical methods in a wide range of applications. I am also grateful to Giorgio Parisi for his help and encouragement in pursuing the search in living matter physics. A warm, special thanks to Yasushi Takahashi for the many

enlightening discussions and suggestions. I have always been impressed by the sharpness of his comments. I express also my gratitude to the late lain Stuart and to Sydney Webb for the many stimulating discussions on the subtleties of

the experiments in biology and neuro-physiology. [ am grateful to Hideki Matsumoto, Chenu V. Srinivasan, Enrico Celeghini, Gerard Huth, Felix Gutmann, Eliano Pessa, Cyril Smith, Rosario Viglione, Alan Widom, Yogi Srivastava for fruitful collaboration lasting over years.

Mari Jibu and Kunio Yasue have given a special contribution to the development of the quantum brain model. I thank them for all I have learned

from their work and for their friendship. Meeting Karl Pribram was a very fortunate event for me. When Umezawa was talking of the brain model he was always mentioning Pribram. When [ met Karl I understood why it was so. My gratitude goes also to Walter Freeman. We met just a few times. but I received a lot from him. I am also grateful to Subhash Kak, Stuart Hameroff, Alwyn

Scott, Jack Tuszyilski and Giuliana Adamo for many discussions and conversa­tions. Certainly a special thank you goes to my students. [ never told them before now, but [ usually get from them more than they get from me. So I am grateful to all of them and in a special way to the grown up ones, Massimo

Blasone, Elvira Graziano and Alfredo Iorio. Special thanks to Eleonora Alfinito. Without her collaboration some recent developments in the dissipative model could not be achieved. Also many warm thanks to Gabriella Campi for her suggestions and her friendship.

Of course, I will never be grateful enough to my wife Marina and to my

daughters Manuela and Chiara for their patience and for creating that peaceful atmosphere necessary for my study and my writing.

CHAPTER 1

Structure and function

In physical systems made by a large number of basic constituents one can

observe collective properties which find their origin in the microscopic quan­

tum dynamics. In this chapter the question is discussed whether certain macroscopic features of brain, and in genera] of biological systems, also may be described in terms of collective modes born out of the microscopic quantum dynamics. Differences between Quantum Mechanics and Quantum Field Theory are pointed out. The distinction between structure and function appears to be dissolved in the unifying view of Quantum Field Theory.

1.1 Naturalism and Science 2

1.2 A motivation for the quantum model of brain 5

1.3 Quantum Mechanics? 9

1.4 Structure and function n

1.5 Classical or quantum? 14

1.6 Quantum Mechanics and Quantum Field Theory 17

2 My Double Unveiled

1.1 Naturalism and Science

In 1967 Luigi Maria Ricciardi and Hiroomi Umezawa proposed a mathematical

model for the brain based on Quantum Field Theory ( QFT). The title of their paper was «Brain and physics of many body problems" (Ricciardi and Umezawa 1967). This book is about that model and its more recent developments.

Karl Pribram in the 1960's also proposed that memory could be modeled as a hologram in quantum optics (Pribram 1971, 1991), and independently from

these developments, in 1968, Herbert Frohlich published the paper «Long range coherence and energy storage in biological systems" (Frohlich 1968; see also

Frohlich 1977, 1980), where the concepts and formalism of quantum theories also were applied. In 1976 Alexander S. Davydov and N.l. Kislukha (1976) pointed out that the great efficiency of energy transfer over long distances on

muscle fibers could only be the result of nonlinear quantum dynamics (Davydov 1978-1991).

The tentative strategy of applying quantum theories to living matter actually starts very soon after the birth of Quantum Mechanics (QM). Quan­

tum phenomena present so peculiar and so new, unexpected aspects with

respect to the conception of the world based on classical physics that the temptation to look at living systems from the QM perspective has been early on very strong.

When in 1944 Schrodinger wrote his book YVhat is life? (Schrodinger 1944)

the state of the art in biology was not the one we are used to today. In many respects (many more than today!) living matter was a real mystery. Living

systems appear to be open, far from equilibrium systems. Nevertheless, they present stable functional properties, space and time ordering, and at same time great capability to respond to external stimuli and to accommodate to quite different environmental conditions.

Certainly, to scientists it was dear that chemistry had to play the main role

in the understanding ofliving matter. There was, however, a diffuse belief that, beyond chemistry, some sort of force had to underlie the life phenomena. Most probably, the newly born quantum physicists thought that a key to studying the

forces ruling living phenomena could be found in the wonderful world of QM. After all, the same chemistry was enormously benefited by the QM princi­

ples: a quantum key had been found to explain the Periodic Table of the

Elements. Such a key is the Pauli principle which dictates how electrons fill up the electronic shells in the atoms (Landau and Lifshitz 1958). And the Pauli

principle is a truly quantum principle. Moreover, the motion of the electrons in

Structure and function 3

their shells and the molecular quantum structure was also described in terms of

QM, and this made it possible to understand the phenomenology of many chemical reactions.

Q M thus led to a unifying understanding of many facts previously described

by chemistry. Quantum physicists did not, however, substitute for their chemist colleagues in their work. The physicists were (and are) exploring only the

dynamics underlying the rich phenomenology studied by the chemists, who were (and are) continuing their specific work. A flux of continuous exchange of knowledge goes on between the two scientific communities. Both, chemists and physicists, have however a deeper insight into the atomic and molecular world

after the discovery of QM. In a similar fashion the hope and the wishes are that

a deeper insight into the life phenomena may also be reached by the joint efforts, although specific in their own tools and methods, of physics and biology.

In order to better understand the line of thought out of which the quantum model of brain was originated, it is useful to comment, in this chapter and in a

couple of the following ones, on some general features of quantum theories and of their role in the understanding of natural phenomena.

In this connection, the interplay between QM and chemistry mentioned above is very interesting in many respects. One of these has to do with the different perspectives from which Science studies natural phenomena. Among

these perspectives there is the one I will here denote as the "naturalistic" or the "phenomenological" perspective.

The first, fundamental step in the knowledge of Nature belongs to the naturalistic perspective. It has to do with the recognition of the great variety of

phenomena, of species, of samples presented to us by Nature. It has to do with "looking around ourselves" making up classifications, catalogs, lists, grouping similar entities into families; pointing out differences among elements belong­ing to the same family or to different families; in brief, collecting data, finding

relations among them, working out statistics. Our precious inheritance of scientific "memories", our encyclopedic archives of detailed facts about Nature comes from such a hard and smart effort, patiently carried on over the past centuries.

Natural sciences always have in themselves such a naturalistic perspective. They also have, however, another perspective, which I will call the "dynamical"

perspective. This dynamical perspective has to do with the study of the forces and of the changes, or the evolution, in space and in time. This is the perspective

from which the scientist tries to reach a unifying picture of the many data and catalogs and different properties observed in the naturalistic phase of the research.

4 My Double Unveiled

Especially, from such a dynamical perspective, he tries to make up mathe­matical models in terms of evolution equations, which I will globally refer to as the dynamics, underlying the rich phenomenology collected in his observations.

In this phase of the research, sometimes a certain amount of simplification of the data is also introduced with the task, not to neglect their intricacy but to let relations among them be manifested with more clarity. A falling body (the apple!) and the Moon looking at us from the sky would be (and are) classified as completely different phenomena by naturalists. However, the study of the forces involved, of their dynamics, reveals that both of them are ruled by the gravitation law: a deeper unifying level of knowledge is thus reached by joining the naturalistic perspective with the dynamical one.

The dynamics provides that level of knowledge which I simply denote as the understanding of the descriptive level of knowledge accumulated in the naturalis­tic phase. Thus scientific knowledge is only reached when both levels, the naturalistic level and the dynamical one, are fully explored. In this way Science provides its dynamical description of Nature.

Here I am not pretending to discuss any issue of a philosophical nature related to the theory of the knowledge; I only use words like understanding and descriptive in the limited sense explained above.

What I am saying here is indeed quite obvious. Nevertheless, some time had to pass by and many difficulties had to be smoothed out before people would be convinced that collecting data and making catalogs and classifications were not

enough: it was and it is a necessary but not sufficient step to knowledge. Still today, there are some who, impressed by the large quantity and by the beauty of the data collected in some sector of natural sciences, remain confused by such a richness and mistakenly consider the necessary naturalistic perspective to be also a sufficient one. I should add that such a confusion between "necessary and sufficient" is today often favored by the advent of extremely sophisticated technological gadgets used in research and, among those, especially computers. These are extraordinary machines which greatly improve our tools in the investigation of natural phenomena, and our computational power has been extremely enhanced by their use. Nevertheless, "quantity", once more, is not enough! A naturalist with a computer is still only a naturalist.

It is therefore worthwhile to stress once more that only by supplementing the necessary but not sufficient naturalistic approach with the dynamical perspective is scientific knowledge of Nature reached, and it is such a joint effort that makes Science so powerful in practical applications.

Structure and function 5

These applications are of course possible even by mastering the pheno­

menological data alone. However, it is an undeniable fact that technological progress is greatly more effective and rapid when the basic dynamics in play is

discovered. Certainly, fishermen and seamen were building and using their boats with much benefit and developing much skill in navigation since a very long time before the discovery of Archimedes law which explains why some­

thing is floating and something else is sinking. Nevertheless, building and using boats became a science, besides being an "art, as it already was, and the progress in navigation has been greatly boosted only after the "forces, involved in the

floating phenomenon started to be revealed.

1.2 A motivation for the quantum model of brain

It has to he pointed out that the naturalistic and the dynamical phases are not

necessarily separate phases of knowledge. Very often they coexist and/or mix

together in an intricate way, as every scientist knows by direct experience. VVhat one can say is that sometimes one of the two phases proceeds for some

reason more speedily than the other one. For example, in the case of chemistry one had to wait centuries before the dynamics underlying the enormous

amount of phenomenological data could be successfully formulated by QM. It is possible that the time is now ripe to shed some light also on the dynamics underlying the large amount of knowledge accumulated by molecular biology

in the naturalistic phase.

Moving from such a hope Frohlich observed that, although great energy and many valuable efforts have been put into play in biochemistry, nevertheless the question still remains open of how order and efficiency arise in living

systems, and then coexist with random fluctuations in biochemical processes.

Living matter presents several levels of spatial organization (cells, tissues and other ordered domains), time ordering (sequentially ordered chains of chemical reactions), functional organization (functional differentiation among different parts and compartments, hierarchical and temporal sequences of functions).

Thus, from one side, there is the high level of space and time ordering, and the high and stable functional efficiency; on the other side, there is the randomness of kinematics which rules any chemical reaction. As a matter of fact, the question of how order, efficiency and functional stability arise in living systems also was a motivation for Erwin Schrodinger (Schrodinger 1944).

It is well known that macroscopic laws exhibiting ordering and regularities in the behavior of ensembles oflarge number of entities, say atoms or molecules,

6 My Double Unveiled

are predicted by statistical mechanics. The most common example is the one of

the regular flow of a certain substance, diluted, e.g., in water, from regions

where the concentration is higher to regions where the concentration is smaller (diffusion). Such a regularity only concerns the macroscopic behavior of the diluted substance, since at a microscopic level each of its component particles moves in a completely random way with displacements in any arbitrary

direction, not necessarily or preferentially in the direction of the flow. Such a

flow direction arises because of the large number of particles, and in this sense it characterizes the macroscopic behavior of the diluted substance. If one would

make the observation solely of the motion of the single component particle, it would be impossible to predict the flow direction. So diffusion is an ordered

phenomenon of statistical origin. Many observed ordered patterns and phe­nomena are known to be of statistical origin and the accuracy of the ordering increases as the number of the elementary components increases (specifically, a measure of the percentage of how many particles "deviate from the regular or ordered behavior", namely the relative error goes as the inverse of the square root of the number of the components). Since living systems are made by a

large number of particles, statistical regularities may well emerge in their macroscopic phenomenology.

Schrodinger however points out that such an order, better, in his words,

such "regularities only in the average" (Schrodinger 1944, p. 78) emerging from the "statistical mechanisms" is not enough to explain the "enigmatic biological stability" (ibid. p. 47). Pretending to explain the biological functional stability

in terms of the regularities of statistical origin would be the "classical physicist's expectation" that "far from being trivial, is wrong" (ibid. p. 19).

Schrodinger calls it the "naive physicist" answer and he argues that it is wrong since there is biological evidence (he refers to hereditary phenomena) which shows that very small groups of atoms, "much too small to display exact

statistical laws" (ibid. p.20), have control of observable large scale features, very

sharply and strictly determined, of the organism. According to Schrodinger it is of not much value to trace back the "enigmatic biological stability" to the

"equally enigmatic chemical stability". According to him, this is the point where the "Quantum Mechanics evidence" enters into play: namely, by explaining the

stability of configurations of a small number of atoms, which has no explana­tion in classical physics, QM explains the stability of certain biological features.

Although the data available to Schrodinger may have even drastically changed due to the enormous progress of molecular biology, this progress in

fact supports his arguments on the "smallness" of the number of the atoms

Structure and function 7

controlling the system macroscopic features in a highly stable way; in such a

respect, the most striking example is the one of the DNA: its strict and stable atomic ordering has been widely recognized to have a determinant role in the

biological macroscopic organization. My intention here is not to discuss the details ofSchrodinger arguments. As

I will try to explain in this book, the question of using quantum theory in the study of some biological features is a complex and difficult question which leads us even farther than Schrodinger conclusions. Rather, I want here to call

attention to Schrodinger's distinction (Schrodinger 1944, p. 80) between ordering generated by the "statistical mechanisms" and ordering generated by "dynamical" quantum (necessarily quantum!) interactions among the atoms and the molecules. (Actually Schrodinger refers to "an interesting little paper" by Max Planck on the topic "The dynamical and the statistical type oflaw.")

Molecular biology has collected so many successes; we know so much about so many components of biological systems; so many mechanisms and chemical functions have been discovered to be at work in living matter. The question is

now how to put together all these data so to derive the complex behavior of the whole system.

Biological systems are made by a large number of components and explain­ing the collective behavior of an ensemble of a large number of elementary

components is the objective of Statistical Mechanics. In the case of neural components, Hopfield (Hopfield 1982) asked whether stability of memory and

other macroscopic properties of neural nets are also derivable as collective phenomena and emergent properties. The methods of classical Statistical Mechanics have been shown to be very powerful tools in answering Hopfield's question (Amit 1989; Mezard, Parisi and Virasoro 1987). However, I will not

discuss these classical statistical methods in this book. I will discuss quantum

collective modes of dynamical origin on which the quantum model of brain is based. The available tool, experimentally tested, to study collective modes of quantum origin in many-body physics is QFT. The statistical mechanics content of QFT is on the other hand very rich, so that, to stress it, one can talk

in some circumstances of statistical field theory (Parisi 1988). In any case, in the study of living matter Schrodinger's distinction between

the "two ways of producing orderliness" (Schrodinger 1944, p. 80) appears to be of crucial relevance: ordering generated by the "statistical mechanisms" and

ordering generated by "dynamical" quantum interactions.

Time ordering and functional stability in living systems manifest themselves as pathways of biochemical reactions sequentially interlocked. Even by resorting

8 My Double Unveiled

to the regularity emerging from statistical mechanics one crucial problem of molecular biology is that such pathways cannot be expected to occur in a random chemical environment (in this connection see Pokorny 2000a). Common experience is that even the simplest chemical reaction pathway, once embedded in a random chemical environment, soon collapses. Chemical efficiency and functional stability to the degree observed in living matter, i.e. not as "regularity only in the average" (Schrodinger 1944), seem to be out of reach of any probabilistic approach solely based on microscopic random kinematics.

Although highly sophisticated probabilistic methods have been developed, it is still a matter of belief that out of a purely random kinematics there may arise with high probability a unique, time ordered sequence of chemical reactions as the one required by the macroscopic history of the system. It is a fact that there is no available computation or even abstract proof which shows how to obtain the characteristic chemical efficiency and stability of living matter by resorting uniquely to statistical concepts.

Similar difficulties arise with the understanding of the generation of order in space, resulting in organized domains and tissues of the living systems. Understanding how and why cells are assembled in tissues is certainly an urgent task in biology and medicine in order to understand and possibly to prevent the opposite situation, namely the evolution of a tissue into a cancer.

Also in this case, the failure of any model solely based on random chemical kinematics, or even on short range forces assembling cells one-by-one, is obvious. And, unfortunately, basic dynamical laws ruling cell ordering in tissue are not yet known.

The high efficiency in protein folding with its very short time scale also seems not to be understandable in terms of classical kinematics. A quantum process must be at work so as to optimize, by shortening it, the time needed to realize the effective folding through the spanning of all possible allowed configurations (Pain 1994).

Classical statistical mechanics and short range forces of molecular biology, although necessary, do not therefore seem to be completely adequate tools. It appears to be necessary to supplement them with a further step so to include underlying quantum dynamical features. In Schrodinger words: "it needs no poetical imagination but only clear and sober scientific reflection to recognize that we are here obviously faced with events whose regular and lawful unfolding is guided by a "mechanism" entirely different from the "probability mecha­nism" of physics" (Schrodinger 1944, p. 79). As in chemistry at the beginning of

Structure and function 9

this century, also in modern molecular biology a step forward must be made with the help of modern quantum theories describing the intricate nonlinearity of the elementary component interactions.

On a similar line of thought, Ricciardi and Umezawa ( 1967) observed that in the case of the natural brain, any modeling of its functioning cannot rely on the knowledge of the behavior of any single neuron. They thought that it is in fact pure optimism to hope to determine the numerical values for the coupling coefficients and the thresholds of all neurons by means of anatomical or physiological methods. Moreover, the behavior of any single neuron should not be significant for functioning of the whole brain, otherwise a higher and higher degree of malfunctioning should be observed as some of the neurons die. Due to the brain metabolism constituent biomolecules undergo chemical changes and disassembly in a relatively short span of time (a couple of weeks). They are then replaced by new ones in a sort of "turn over,. This clearly excludes that the high stability of brain functions, e.g. of memory, over a long period of time could be explained in terms of specific, localized arrangements ofbiomolecules. Observations (Pribram 1971, 1991; Greenfield 1997a,b; Freeman 1990, 1996, 2000) show, on the contrary, that a long range correlation appears in the brain as a response to external stimuli. Thus Ricciardi and Umezawa proposed their QFT model for the brain.

1.3 Quantum Mechanics?

Sometimes QM is the object of misunderstandings. Sometimes among non­physicists (let me be kind with physicists!) there is either strong faith in QM, or strong opposition against it. In many cases there is among people a sort of strong expectation, as if with a "mystery, (the QM mysteries!) one would be able to solve other "mysteries, (the brain and consciousness mysteries!). Such dogmatic attitudes are of course very dangerous to Science and must be carefully avoided. The path to understanding implies going up and down

through the three stages of "feeling, or intuition (sentire), comprehension (comprendere), detailed knowledge of facts (sapere) (Gramsci 1932; see also

Kamefuchi 1996 for the analysis of Gramsci's stages in the research activity). Dogmatism and sinking into mysteries open the doors to irrationalism, to the magic vision of the world which is the first enemy to fight if one wants to reach the scientific knowledge.

10 My Double Unveiled

First, let me stress that QM, by itself, is not the object of my discussion.

Certainly there are many problems in the interpretation of specific aspects of QM which are of great epistemological and philosophical interest. However,

here such problems are not the object of my discussion. This should be quite clear, since sometimes the discussion about brain modeling or about conscious­ness are mixed up with arguments of specific interest to QM, or to its interpre­tation, or to its formulation, and a great confusion is the net result. Therefore, although it is not only interesting, but certainly necessary to study questions

related to the foundations of QM, these are not the object of my discussion. It should be also observed that interpretative or other open problems in

QM absolutely do not interfere or diminish the great successes of QM in practical applications. And, although it could appear philosophically unsatisfac­tory, fitting the data and predicting phenomena on the basis of a dynamical

scheme is all that is required from a physical theory point of view. Of course, theories are always to be modified or even dismissed if compari­

son with experiments so requires. This is why one does not need to "believe" in QM and also why there is no need to be "against" it. There is no place for

dogmatic attitudes, in one way or the other. All that is required is that "it works,. And QM does work in a large number of practical applications in solid

state physics, electronics, chemistry, etc. with extraordinary success. QM is not

a mystery, from this perspective. It is an undeniable fact that our every day (real!) life strongly depends on those successful applications of QM. The photo­

electric cell controlling our elevator door, or the laser beam reading out the music of our compact disc, or the computer we use, have nothing counter­intuitive: they work quite well. That's it. So there is no need to defend or to oppose to QM. When and/or where it does not work we modify it or chose another, if necessary completely different, theoretical scheme.

On the other hand, the fact that QM is so successful in applications, by itself does not justify the use of QM in brain studies. The success of QM in applica­tions is not a sufficient reason to apply it to the study of the brain. As a matter of fact, as I will argue below and in the course of this book, QM does not

provide the proper mathematical formalism to study living matter and the brain. It appears that the proper mathematical formalism is that of QFT.

In the following and in the course of this book I will try to clarify why quantum and why fields are necessary ingredients to be used in a dynamical

model for the brain and for living matter in general. In the next chapter I will also discuss one more crucial dynamical feature: nonlinearity. Nonlinear dynamical models are of great relevance for a large class of phenomena, at the

Structure and function n

classical as well at the quantum level. For the moment, let me concentrate on

the quantum field aspect.

I start my discussion in the next section by resorting to an example in condensed matter physics.

1.4 Structure and function

In Physics it is not enough to investigate what things are "made of'. Listing elementary" constituents" is a crucial, necessary step, but it is only one step (the

naturalistic level). We want to know not only what things are made of, but also

"how all of it works": we are interested also in the dynamics. In short: we are

interested in structure and in function. To a physicist, having a detailed list of constituents does not mean to know enough about the system under study.

The study of the structure of matter is not simply making up a catalog of the

elementary constituents of matter; it is knowledge of the evolution in space and in time of the elementary constituents and of their interactions (the forces), viz., the knowledge of the dynamics and of its phenomenology. Thus when we physicists say "matter", we do not even think of the mere collection of elemen­tary constituents; we always refer to the full dynamical description of matter. This is what we mean by the dynamical understanding of Nature, the vision of

the world in movement. After all, what I am saying is again quite simple: everybody agrees indeed that studying the Naples phone book does not mean

knowing the city of Naples. In most physical systems the interplay among the elementary constituents

and their interactions is so intricate that it is not even possible to make a complete list of the constituents without knowing how they work all together in

the system. As we will see, the same concept of constituent is meaningless outside the dynamical knowledge of the system. The possibility of a clear definition of structure (the constituents) and of function (how they behave) is

thus reduced down to the point that we can no longer make a sharp distinction between them (Vitiello 1997, 1998).

In the example I am going to present the notions of structure and function indeed merge each into the other. And for that the quantum aspect of the

formalism is crucial. The example is that of the crystal. There are other exam­ples, such as the ferro magnets, the superconductors, and in general, any system presenting some kind of ordered patterns. I like the example of the crystal because it is quite intuitive and it can be qualitatively exposed and understood.

12 My Double Unveiled

Let me make clear that I am going to discuss the crystal not because it is

comparable to a living system. Absolutely not. As we will see, in living matter as well as in crystals ordering is dynamically generated. Apart from such a feature,

living matter and crystals are deeply different systems. The only reason I discuss the crystal is that it provides a relatively simple example of dynamical mecha­nisms described by QFT. I am not interested here in properties of some specific

crystal system. My only interest is in discussing the dynamical generation of order and the merging of structure and function.

In illustrating my example I will use some words and some concepts which I will introduce in more detail in Chapter 2. I apologize for this to those readers who are not familiar with these concepts. One possibility for them is to assume the wanderer attitude: "Let me see where this road leads. Let me keep in mind

that unknown profile of the landscape. Maybe later on I will realize what it is ... ".

As is well known, when atoms (or molecules) of some kind sit in some lattice sites we have a crystal. The lattice is a specific geometric arrangement with a characteristic lattice length; I am thinking of a very simple situation

which is enough for what I want to say. The crystal lattice may be deformed in several ways under the action of specific, external boundary conditions. Different phases are associated to different lattice deformation states. An extreme lattice deformation is one where the lattice is actually destroyed, e.g. by melting the crystal at high temperature. Once the crystal is broken (melted),

one is left with the constituent atoms. So the atoms may be in the crystal phase or, e.g. after melting at high temperature, in the gaseous phase. We can think of these phases as the functions of our structure (the atoms): the physical proper­

ties and behaviors of the system are manifestly different in each of these phases

and thus we can talk of the crystal function and of the gaseous function. In the crystal phase one may experimentally study the scattering of, say,

neutrons on phonons. The atoms in the crystal sites are continuously vibrating,

and these vibrations manifest in the form of elastic waves which propagate all over the crystal. The vibrating atoms interact among themselves by means of the

elastic waves and are thus correlated by them over large distances. It is such a long range correlation which keeps the atoms in the crystal ordering. The elastic waves can be mathematically described as fields and the phonons are the quanta of these elastic fields (or waves) (Anderson 1984; Umezawa 1993; Wolfe 1998).

The phonons are true particles living in the crystal. We observe them indeed in the scattering with neutrons. As a matter of fact, they are the same thing as the elastic waves. In quantum theory, to any wave can be associated a correspond­ing "quantum" which behaves as particle; in this way "wave description" and

Structure and function 13

"particle description" become complementary descriptions (Landau and Lifshitz

1958). Thus phonons propagate over the whole system as the elastic waves do

and therefore act as long range correlation among the atoms (for this reason they are also called collective modes). The atoms in the crystal do not behave anymore as free atoms. They are "trapped", like in a net, by the Long range correlation mediated by the phonons. The phonons (or the elastic waves) are in

fact the messengers exchanged by the atoms and are responsible for holding the atoms in their lattice sites in a stable configuration (Umezawa, Matsumoto and Tachiki 1982; Umezawa 1993; Anderson 1984).

Thus we are led to conclude that the list of the crystal constituents includes not only the atoms but also the phonons. Including only the atoms, the list of the constituents is not complete! However, when one destroys the crystal one is left only with the atoms; one does not find the phonons! They disappear! Thus the phonons are "confined" to exist only "inside" the bulk crystal.

On the other hand, if one wants to reconstruct the crystal in its stable configuration after having broken it, the atoms one was left with are not enough: one must supplement with the long range correlation fields (or quanta of the elastic waves, the phonons) which tells the atoms to sit in the special lattice one wants (cubic or whatever). One needs, in short, to supplement the

ordering information which was lost when the crystal was destroyed. Exactly such an ordering information (the crystal function) is "dynamical­

ly" realized in the phonon particles (structure). Thus, the phonon particle only exists (but really exists!) as long as the crystal exists, and vice-versa. The

function of being a crystal is identified with the particle structure! The reader can object: "But how it can happen that the stable ordering

information (the crystal function) is dynamically realized in the phonon particles (structure)?" This is the point indeed where the quantum aspect of the

theory is essential. Such a thing cannot happen in a classical theory. It cannot happen in a nonlinear dynamical theory as far as it is a classical theory. Non­

linearity plays its role, but the theory must be a quantum theory. No way out. Most of the following Chapter 2 will be devoted to illustrating such kinds of

phenomena. Here I only remark that the description of the crystal in terms of phonons has nothing to do with the "mysteries of quantum theories". It is a

mathematically well formulated, experimentally well tested physical theory (Umezawa, Matsumoto and Tachiki 1982; Umezawa 1993; Anderson 1984).

From the crystal example it is dear that "matter, is not simply a list of

constituents, it is not simply a lot of phenomenological data and statistics. Matter is also the dynamics. The attempt of making a "complete, list of

14 My Double Unveiled

constituents is hopeless and meaningless outside the dynamical perspective: ... a mere phone book is not enough and we now know that it cannot even be complete without the dynamics. This is what experiments tell us.

Moreover, there is no hope of building up a stable crystal without the long

range correlation mediated by the phonons: if you try to fix up atom by atom in their lattice sites, holding them by hooks, you will never get the coherent orchestra of vibrating atoms playing the crystal function. In that case, you would only be like one of those extremely patient and skillful Swiss watch-makers who in the past centuries, by mechanically assembling together a lot of wheels and levers and hooks, were building beautiful puppets able to simulate many human movements, but no more than that. Of course, one can also get results of practical interest by treating the crystal as an-body problem. If, however, one wants to go beyond the phenomenological approach, then he must realize that the crystal is not the output of the assembling atoms by short range forces (hooks). On the contrary, it is the macroscopic manifestation of the long range correlation among the atoms born out of the microscopic quantum dynamics.

1.5 Classical or quantum?

But the crystal, is it a classical system or a quantum system? It is both! It is a macroscopic quantum system. In a trivial sense, any physical system is a quan­tum system since it is made by atoms which are quantum objects. But this is a trivial statement, indeed, and it is not in such a trivial sense, that the crystal is a quantum system.

As I said, you cannot think of the crystal without thinking of the phonons. These are quantum particles and the system property of being a crystal is identified with them. It is therefore the macroscopic property of being a crystal that finds its identification in the quantum phonon mode: although the crystal

property is a classically observable property, it can only be described in terms of

quantum dynamics.

\Vhat one means by saying that the crystal is a macroscopic quantum system is that large scale properties of such a system cannot be explained without recourse to quantum dynamical mechanisms. Therefore, those physical properties of the crystal, specific to the nature of being a crystal, appear to be "classical" not because the Planck constant his taken to be zero, but exactly because his not zero, i.e. because the quantum dynamics is at work. The crystal is thus at the same time a classical system and a quantum system.

Structure and function 15

If you want you can put this in different words: quantum theory is not

restricted to the explanation of microscopic phenomena (Umezawa 1993). The crystal is only one of the many examples to which such a conclusion applies. [

do not think I am far wrong if I state that this conclusion is one of the most important achievements of modern Physics.

To better understand this point, [ recall that the phonons are boson particles. This means that as many of them as one wants can be put in the same state with the same quantum numbers, e.g. same energy, same momentum, etc.

Since they are massless, their lowest energy state is a zero energy state. Therefore we can collect a large number of phonons in the system lowest energy state (the

ground state) without changing its energy: it will remain the system ground state, even with a very large number of phonons condensed in it. Since they have

the same quantum numbers we say that they are coherently condensed in the ground state. Needless to say, this is also the root of the crystal ordering and of its stability. Let me observe that at a classical level it would be impossible that the state of the ordered crystal has the same energy of (is degenerate to) the state

without ordering (where there are no phonons condensed in it). This can

happen because we are considering the quantum mechanism of condensation of massless quanta. It is such a mechanism which allows the existence of crystals, ferromagnets, superconductors, superfluids, and other ordered

quantum systems, which are in fact ordered and at the same time highly stable systems. Their high stability would not be allowed by classical laws of thermo­dynamics: they are macroscopic quantum systems, indeed.

In order to identify the phonon properties of the system ground state (thus the system crystal property) one does not need to monitor the quantum numbers of all the condensed phonons since, as just said, these quantum numbers are coherently the same for all the phonons. This means that it is not the small scale observations which are needed in order to identify the crystal

state: it is here that the transition to large macroscopic scale is made possible.

This happens just because of the coherence of the crystal state. Stated in different words, the phonons are collective modes of the system.

On the other hand, since a large number of them is condensed in the ground state, small fluctuations in their number due to quantum excitation processes are irrelevant to the system's macroscopic behavior: thus we reach the well known statement that a system behaves classically when quantum fluctua­

tions are irrelevant. As we shal1 see, however, the sense of such a statement is not that the Planck constant is zero for the classical system, but that the ratio between the quantum fluctuations and the condensate phonon number is

16 My Double Unveiled

negligible (Umezawa, Matsumoto and Tachiki 1982; De Concini and Vitiello

1976). If the Planck constant would be taken to be zero, there would be no

condensate (which is a quantum effect) and the whole picture would collapse.

Of course, a careful analysis would require us to consider many more details

in the above reasoning. However, I will not discuss them to make the story

short. Nevertheless, there are a couple of further points which deserve to be

mentioned.

The first is that the coherent condensation often proceeds through the

formation of coherent domains. The minimum size of these domains is called

the coherence length. Only at a further stage, the domain boundaries may open

so that domains merge into larger coherent regions and the transition to the ordered state in this way occurs. This means that order can only appear on a

scale larger than the coherence length: order is an "intrinsically diffused"

property of quantum origin. Another point is the interaction of a classical system with a quantum

system. This is a crucial question in QM, which still waits a full understanding.

All the measurement problematic (the measuring apparatus is typically a

classical system) in QM has to do with such a question. In the case of macro­

scopic quantum systems, say of the crystal, we see that a classical probe may

interact with the quantum modes which macroscopically manifest themselves

in the coherent crystal structure. The crystal atoms act as a whole (as a crystal

indeed) since they are trapped by the long range correlation like in a net, and

cannot behave anymore as free atoms. In this way the classical probe interacts

with such a macroscopic "net" (the crystal collective modes). This ''channel of

communication" between the classical world and the quantum phenomena will

be recognized to be relevant in the quantum model of brain.

Of course, there are other examples of macroscopic quantum systems. The

laser is one of these. In that case the quanta of light, the photons, exhibit

coherence in phase (they have the same phase) and thus the laser state is

characterized by a single phase, which therefore appears as a macroscopic

quantum observable.

In QM it is known that phase and number of quantum excitations satisfy

the Heisenberg uncertainty relation. This means that definite value of the phase

(zero uncertainty) implies full (infinite) uncertainty with respect to the num­

ber, and vice-versa. We thus conclude that in the laser beam the photon

number is not exactly determined. In fact the laser state is described as a

coherent (same phase) superposition of states of any photon number (Klauder

and Sudarshan 1968). In such a circumstance, fluctuations in the photon

Structure and function 17

number are irrelevant to the laser macroscopic behavior: you can handle the laser as a classically behaving system; it is indeed a macroscopic quantum system, as is well known.

A beam of normal light (not a laser) does not show coherence in phase since it is a superposition of waves of different phases. Each of these component waves of definite phases can be handled as classical electromagnetic waves. They are represented by a complex field characterized by an amplitude and a phase which satisfy the Maxwell equations. When a beam of normal light of proper frequency impinges on a photoelectric cell, however, its quantum nature is shown: the photoelectric cell, like the one controlling the elevator door, is a simple device which is activated upon quantum interaction with a photon able (i.e. of proper frequency) to excite the electrons in the material of which the cell is made. The cell is not activated if it is not hit by photons of proper frequency (this is why the lift doors do not close if you put your hand on the light beam path). Thus the cell reveals the quantum nature oflight.

Isn't that amazing that next time you use the elevator you can use your classical(!) hand to trigger or not, at your pleasure, a quantum phenomenon

and detect the quantum nature oflight? Light is classical or quantum? The moral is that one must always be very careful in talking about classical

and quantum. Nature, fortunately, is much more rich than we imagine. Playing around with the photoelectric effect got Einstein the Nobel prize in l921.

Further examples of macroscopic quantum systems are superconductors, superfluids, ferromagnets, and in general every system showing an ordered pattern quantum dynamically generated.

1.6 Quantum Mechanics and Quantum Field Theory

We have seen that in the study of the crystal system one must allow for the possibility of the description of several stable "phases" (e.g. the gaseous phase, the crystal phase). These clearly present different physical properties and behaviors. They are therefore said to be physically inequivalent, or also, by using a word to be better explained later on, unitarily inequivalent. Without such a possibility one would not be able to handle the "ordering information".

Stable ordering requires long range correlation among constituents, and this correlation cannot be described by QM. One needs fields. In QM it would never be possible for the system to go from one phase to another (breaking or melting the crystal, or reconstructing it are processes called "phase transitions"). This is

18 My Double Unveiled

the point where the mathematical formalism of QM fails: in QM there is no way to describe physically inequivalent phases. So QM is not adequate to formulate the crystal theory. \\That one needs is QFT, where, instead, there exist many,

physically inequivalent stable phases associated with a given physical system. This is why one needs quantum fields. I will discuss more on this point in the next chapter.

Sometimes, the difference between QM and QFT is not enough appreciat­

ed. Or sometimes QFT is simply ignored. For example, the mechanism by which the quantum superposition in the wavefunction is lost ( decoherence) is mostly considered to signal the limit of applicability of QM, beyond which classical mechanics has to be used. It has been shown (Alfinito, Viglione and Vitiello 2001) that this is not necessarily the case, since there are systems, clearly

ruled by quantum dynamics, where the occurrence of decoherence simply denotes that quantum field theory, not quantum mechanics, has to be applied. So, very often talking of decoherence people simply forgets about the possibility of the QFT dynamical regime, which also exists under proper circumstances. Therefore, I would like to stress that the dynamical generation of ordered states of minimum energy (i.e. ground states presenting long range correlation) is a characteristic feature of QFT, not present in QM. It is then also understandable that somebody, thinking only of what QM may provide, asks for some "more powerful" tools as, for example, those provided by classical nonlinear theories.

Of course, more powerful computers may allow the study of more intricate complexity. The point, however, is that although nonlinearity is absolutely necessary, as we will see in the next chapter, nevertheless it is not sufficient: one needs a quantum theory. In a classical framework, states with long range correlation dynamically built in, i.e. presenting some kind of ordering, cannot be states of minimum energy, as thermodynamics teaches us; so they cannot satisfy the stability condition.

The hope that nonlinearity may reveal unknown phenomena is of course legitimate and I share it, too. In recent decades classical nonlinear dynamical systems have proved to be rich sources of surprising phenomena. However, dogmatic attitudes should be always avoided, also in this case. The crude fact is that there is no nonlinear classical theory describing crystals, superconductors, ferromagnets, etc. On the contrary, the only available theory which describes them and, most important, is in agreement with experiments, is QFT: these systems appear to be macroscopic quantum systems.

I want to add also that, in these systems, vortices, domain walls, dislocations and other" defects" appear. These are extended objects of quantum origin whose

Structure and function 19

behavior, however, manifests classical features: they are described indeed as solutions of nonlinear classical equations. QFT thus provides the basic dynam­ics out of which macroscopic, i.e. classically behaving, systems are generated.

Since the concepts of dynamical generation of order and of constituent particles acting as messengers of the ordering information (like the phonons in the crystal) are very general concepts, the question now can be asked: Do these concepts and the related mathematica] formalism of QFT apply also to living matter and to the brain?

Living matter is no more than matter in the "living phase,. The crysta] is matter in the "inert phase". Certainly the living phase of matter is much more complex than the inert phase; it is in no way comparable to a crystal. However, a world where the basic dynamical laws ruling the physics of matter in the inert phase would not apply also to matter in the living phase would be a really crazy world.

Just as the crystal is the output of the quantum dynamical ordering of the atoms, functional features of the brain, systemic features of living matter, such as ordered patterns, sequentially interlocked chemical reactions, etc., may result

as the output of dynamical laws underlying the rich phenomenology of molecu­lar biology. Again, I stress that crystals and living matter are very different systems and that [ have considered the crystal as an example of dynamical generation of order. Such a mechanism, as I will try to show in the following chapters, could be at work also in living matter.

The natural question then arises of the specificity of living matter with respect to "inert" matter. The dynamical generation of order is a feature which only imposes constraints on general symmetry properties of the dynamics ( cf. Chapter 2) without need to specify its detailed form. Thus, living matter is expected to present a very specific (and complex) dynamical structure. More­over, living systems are also characterized by plasticity, namely they can adapt to many different boundary conditions. The multiplicity of responses of the system to many external inputs or perturbations is eliminated by coherent

responses (functional stability). I will go back to this points several times in the following chapters and we will see that such an adaptive character of living matter is one of its most typical features, and one of the major sources of differentiation with respect to inert matter (on the joint role of complexity and adaptation see also Arecchi (2000)). Living matter appears to be characterized by several organization "levels" and presents an evolution ("story"), which appear impossible to explain simply in terms of structural facts. And here, again, structure and function appear indistinguishable. The idea in the QFT

20 My Double Unveiled

approach to the living phase of matter is to supplement the random kinematics

of biochemistry with a basic dynamics, not to substitute or to eliminate the specificity of the phenomenological analysis and methods of molecular biology.

As already mentioned, other approaches to brain function modeling, mostly classical ones and based on the powerful tools of modern statistical mechanics, will not be considered in this book. These are very successful approaches, especially in connection with modeling of neural nets (Amit 1989; Mezard, Parisi and Virasoro 1987). Computational neuroscience mostly relies on

specific activity of neural cells and of their networks, thus leading to a number of models and simulations of brain activity in terms of neural nets. There is

however an increasing interest in the study of quantum features of network dynamics (Perus 1999; Pessa and Vitiello 1999), either in connection with information processing in biological systems (Hameroff 1987, 1988; Werbos

1992), or in relation to a computational strategy based on the system quantum evolution ("quantum computation"; Feynman 1985; Williams and Clearwater

1998). The line of thought which this books follows is more closely related to

that of quantum computation.

CHAPTER 2

Macroscopic variables and microscopic dynamics

Basic structural aspects of Quantum Field Theory are presented in a qualitative way. The limits of the perturbative scheme are discussed. Order, coherence and collective modes are dynamical manifestations of spontaneous breakdown of symmetry. Long range interaction fields propagate in a self-focusing fashion in ordered medium. The role of nonlinear dynamics is stressed.

2.1 Macroscopic variables and microscopic dynamics 22

2.2 Dynamical fields and phenomenological fields 23

2.3 The perturbative scheme 25

2.4 Symmetry and order: A dynamical problem 28

2.5 Collective modes, coherence and order 31

2.6 Self-focusing propagation of long range interaction fields 34

2.7 Nonlinear dynamics and soliton solutions 37

22 My Double Unveiled

2.1 Macroscopic variables and microscopic dynamics

In Physics as well as in Chemistry and Biology much attention is focused on the problem of the emergence of macroscopic variables out of microscopic dynam­ics. V\lhen the system under study is made up of a large number of elementary constituents its macroscopic state may be characterized by macroscopic variables

such that different values of these variables respectively correspond to different behaviors or phases of the system.

The crystal, which I have briefly discussed in Section 1.4, is one of the most

familiar examples of such a situation. The microscopic quantum dynamics rules the interaction of the constituent atoms. The (emergent) macroscopic variables are, e.g., the density, the stiffness, the electrical conductivity, the magnetic properties, etc. The relevant point is that these are properties of the crystal and not of the individual constituents. We have seen that from the pure collection of atoms one cannot reconstruct the crystal. Something more is needed.

Moreover, the crystal properties may change depending on the tempera­ture. Typically, above certain temperature they may disappear; above a certain (critical) temperature the same crystal may melt. Thus the crystal is recognized to be one of the possible stable phases of the constituent atoms. Above the melting temperature these are, say, in the gaseous phase.

Phases characterized by different values of the macroscopic variables present different physical behaviors or functions. Thus the qualitative functional difference of the phases is quantitatively represented by the different values of the macroscopic variables.

Solid state physics provides many examples of many body systems where macroscopic properties manifest which are not properties of the system's individual constituents (Anderson 1984; Umezawa 1993). This happens under specific dynamical circumstances which are quite well understood in QFT.

It is quite remarkable that QFT provides a quantitative formulation and understanding of the collective behavior of many constituents of a physical system. The long standing conflict between so called reductionism and so called holism thus seems dissolved in the mathematical formalism of QFT. This fact, in my opinion, still awaits full recognition and appreciation by those interested in the gnoseological problematic. But I will not insist more on this point.

As discussed in Chapter L, the statistical mechanisms generating macro­scopic laws of regularity in the behavior of systems of a large number of constitu­ents appear to be insufficient to account for the space and time ordering and for

Macroscopic variables and microscopic dynamics 23

the functionaJ efficiency and stability ofliving matter. These features may find their origin in the dynamical generation of order as described by QFT.

I will introduce in the present chapter a few notions regarding the concep­tual and mathematical structure of QFT. I will not present the mathematical formalism which the interested reader can find in the quoted literature. [ apologize to those readers who are already familiar with QFT for being some­times too crude in the qualitative exposition of some of the aspects ofQFTwhich properly require much more care. It is difficult to translate into words some mathematical subtleties. Nevertheless, I will trymybestto digoutofthemathe­matical formalism its physical implications in the most transparent way, keeping in mind that this book is addressed also to readers who are not mathematicians or physicists. In any case the quoted bibliography should be enough to exhibit the beauty of the mathematics underlying my qualitative presentation.

2.2 Dynamical fields and phenomenological fields

QFT has a very rich structure which allows for the description of dynamical systems over a wide range of energy, from elementary particle physics and cosmology to solid state physics. The systems studied by QFT require the use of fields since they are systems with infinitely many degrees of freedom. Systems of such a kind are also found among those studied by classical physics. For example the state of a fluid, say the water of a river, may be specified by assigning, among other observable data, the velocity monitored at each point of the fluid. The set of such velocity data is an infinite set since there is an infinite number of points one needs to monitor in order to specify the state of the fluid with respect to the velocity: the set of all the velocity data at each point is the velocity field.

In QFT assigning the quantum fields is not enough. One must also specify the set, or space of the physical states in which the system may be observed. The physical states are representable as vectors whose length is well defined. The fields are said to be operator fields, meaning indeed that their mathematical significance is fully specified only when the state space is also assigned. The operator fields are then said to be realized in that state space where they operate (Itzykson and Zuber 1980; Bratteli and Robinson 1979; Umezawa, Matsumoto and Tachiki 1982; Umezawa 1993).

Any quantum experiment or observation can always be schematized as a scattering process, namely a process where one prepares a set of non-interacting

24 My Double Unveiled

particles (free or incoming particles or in-fields) which are then made to collide

at some later time in some space region (space-time region of interaction) out of which the products of the collision are expected to emerge as free (non­

interacting) particles (outgoing particles or out-fields). Correspondingly, one has the in-field and the out-field state space. The interaction region is where the dynamics operates: given the in-fields and the in-states, the dynamics deter­mines the out-fields and the out-states.

The incoming particles and the outgoing ones are well distinguishable and

localizable particles only far away from the interaction region, at a time much before (minus infinity) and much after (plus infinity) the interaction time: in­and out-fields are thus said to be asymptotic fields, and for them the interaction forces are assumed not to operate (switched off). This is a delicate, but impor­

tant, point which I will come back to later on. Here let me point out that in

some cases the interaction cannot be switched off. Thus we may not always identify free, i.e. non-interacting, objects.

Of course, due to the interaction, the outgoing particles are in general

different particles than the incoming ones. For example, the interaction may produce bound states (e.g., the hydrogen atom is a bound state of proton and electron) or other kind of transmutation in the incoming particles. The outgoing particles, in turn, may be used as incoming particles in another

scattering process. Thus there must be a one-to-one correspondence among the in- and the out-state spaces; they are physically equivalent, or, technically

speaking, unitarily equivalent spaces. The only regions accessible to observations are those far away from the

interaction region (when and where the interaction forces can be safely as­

sumed to not operate), i.e., the asymptotic regions (the in- and out-regions). It is so since, at the quantum level, observations performed in the interaction region may drastically interfere with the interacting objects thus changing their nature; this is a typical quantum feature. In contrast, at the classical level we are

well able to observe, e.g., the Moon while it is interactingwith the Earth through the gravitational force, without any fear of interfering with its motion in such a way as to change it. Since in QFT the interaction region is precluded from

observation, one introduces interacting fields, called dynamical or Heisenberg fields, and the dynamics is described in terms of these fields.

The evolution of the system in space-time is described by motion equations (the dynamics) for the Heisenberg fields. The dynamical equations, however, do

not define completely the dynamical problem: one must also specify the space of the states on which the dynamics has to be realized. Only in that case is the

Macroscopic variables and microscopic dynamics 25

dynamical problem well defined. In some sense, by specifying the state space where the dynamics is realized, one specifies the boundary conditions under which the dynamical equations must be solved.

This is a mathematical fact since one works with operator fields and, as said above, these are mathematically meaningful objects only when the state space on which they operate is given. This has a deep physical consequence: it means that the possibility exists that the same dynamical equations for the same set of dynamical fields may be realized in different spaces of states and therefore, depending on the state space one works with, they may produce different dynamical outputs. I will come back again to this important point.

In conclusion, QFT is a "two level" theory (Umezawa 1993; Vitiello 1974): one level is the interaction or dynamical level where the dynamics is specified by assigning the equations for the Heisenberg fields. The other level is the pheno­menological level, the one of the asymptotic fields and of the physical state space directly accessible to observations, which we also call, therefore, the physical level. The equations for this last level are those describing the free propagation of the fields associated with the observed incoming/outgoing particles.

2.3 The perturbative scheme

From the above two level scheme we see that the dynamical problem consists in solving the Heisenberg field equations in such a way that, given the in-fields and

the space of the system states at an initial time, one may predict the out-fields and the system states at a final time (i.e. the system state space at the time much later the interaction time). In order to solve the dynamical problem, the link between the dynamical level and the phenomenological one must be established. Only when such a link is established can one do Physics, since only in that case can one test the dynamical model (i.e. the theoretical apparatus consisting of the set of dynamical equations) with the experimental facts (the observations).

As noted, working with quantum fields is meaningful only when the state space wherein they operate is also specified. Since we are interested in the states which we can observe, and over which we have some sort of control, we chose to solve the equations for the Heisenberg fields in the asymptotic state space (the in- or equivalently the out-state space). Then we have to express the Heisenberg fields in terms of the asymptotic fields which are the ones which operate on the asymptotic state space: in this way the Heisenberg fields, also operate on the asymptotic state space, though indirectly.

26 My Double Unveiled

The expression of the Heisenberg fields in terms of the asymptotic (in- or

out-) fields is called the dynamical map or the Haag expansion. It represents the link between the dynamical level and the phenomenological level we were

searching for. The above two level scheme of phenomenological fields and dynamical

fields strongly relies on the possibility of"switching on and off" the interaction. In other words, the scheme is founded on the assumption that some entities (the particles) may exist as "free,, "non-interacting, objects as long as they do

not collide: They (can) exist "by themselves", as autonomous, non-interacting

entities. I will call it the "ontological hypothesis". The word "ontological"

evokes a lot of philosophical reasoning and schemes, however this should not lead to misunderstandings. I use it only in the above limited sense.

Actually there are interactions which never "go to zero", even when the

interacting objects are separated by a large distance. These never become "free" objects. The electromagnetic and the gravitational forces are of this kind. However, these forces become quite small when interacting bodies are at a large distance, so that one can safely adopt the "approximation" that they are

"switched off' at large distances. In such an approximation the hypothesis that free non-interacting particles exist can be then adopted. Such an approximation actually leads to very accurate theoretical predictions fitting very well experi­mental data, e.g., in Quantum Electrodynamics (which is probably the best theory we have).

In general, one tries to extract dominant contributions to the interaction and considers other, smaller contributions as "perturbations" to the dominant

ones. Then the computation is carried on only by considering dominant contributions and neglecting smaller perturbations. Better approximations are obtained by including more and more perturbative terms.

In some sense the full interaction is split into many terms, each of these

considered as a contributing force. Then one selects dominant forces on the basis of their strength. Weak forces are considered as perturbations on the basis that weak forces generate weak effects. The strength of a force is measured by

the magnitude of the value of the coupling among the interacting objects, the so called coupling constant. Smaller coupling, smaller force, smaller effects. When one talks of free particles, actually one assumes that the coupling constant may be considered to be zero in the asymptotic regions. This is the perturbative scheme (Itzykson and Zuber 1980).

Splitting the full interaction into many, increasingly smaller terms is possible for example when the original coupling constant is a small number

Macroscopic variables and microscopic dynamics 27

(less than one). Then higher powers of such a number are smaller numbers and

one may write the original interaction as a sum of terms which are proportional to increasing powers of the coupling constant, and therefore are smaller and

smaller; in short, one considers expansions in power series of the coupling constants.

Apart from difficulties coming from the proper definition of the pertur­bative series summation (often one has to deal with quantities which are infinite and thus not acceptable), the "perturbative expansion" is impossible

when the original coupling is not a small number (not less than one); in such a case higher power terms will be larger and larger; and then the perturbative scheme cannot be applied. Moreover, the nonlinearity of the interaction may be such that the interaction can never be thought to be switched off (unless

drastically changing the system under study). In those cases the phenomeno­

logical occurrence of free particles is (at the best) in doubt: particles appear to be "confined" by their own interaction, they cannot be observed as "free",

"non-interacting" objects; the quarks in subnuclear physics behave in such a

way for separating distances of the order or larger than the hadron size; they are indeed not observed as free particles.

The conclusion is that one cannot always switch on and off the interaction at one's own pleasure; and it is so not just because of practical difficulties, but

by the substantial reason that the perturbative scheme is not always applicable. This may look quite strange since we commonly believe that we can, at least in principle, apart from practical difficulties, "isolate" something "from all the

rest"; we believe indeed that things, individual objects (including ourselves!)

may or may not interact with other things. This may be true in some approxima­

tion when the perturbative scheme is actually applicable. But in general, "switching off all the interactions" is substantially impossible, and our "believing

it possible" turns out to be only a prejudice, the ontological prejudice, indeed.

The case of the quarks which are not observed as free particles is not an isolated example of "confinement" and of failure of the perturbative scheme. Physics shows to us in fact that there are other cases in which the perturbative scheme cannot be applied. There are systems described by dynamical equations which admit solutions going as the reciprocal l/A. of the coupling constants A. In that cases, the perturbative paradigm, by which weak couplings produce

weak effects, is indeed reversed since the inverse of small couplings are large quantities, and thus smaller couplings give, on the contrary, more robust effects. Included among these cases are the spontaneous breakdown of symme­try in QFT and the so called nonlinear dynamical systems where "soliton"

28 My Double Unveiled

solutions (Scott, Chu and McLaughlin 1973) exist (Itzykson and Zuber 1980;

Umezawa, Matsumoto and Tachiki 1982; Rajaraman 1982). I shall consider these cases in the following sections.

Let me finally remark that the discovery that in proper circumstances one

may extract the dominant contribution to the interaction, and consider other

contributions as perturbations, has been a crucial step in scientific and techno­

logical progress. The discovery of the perturbative method has made possible

quantitative predictions in the study of many phenomena. Today we realize the

practical and conceptual limitations of the perturbative approach; however, it

must be dearly stated that without the perturbative approach, in the study of

wide varieties of phenomena it would have been extremely difficult, if not just

impossible, to extract quantitative information and predictions to compare with

experimental data. On the other hand, the development of non-perturbative

methods to be used in cases where the perturbative approach breaks down has attracted much attention and enormous progress has been achieved in non­

perturbative techniques.

2.4 Symmetry and order: A dynamical problem

Another example of particles, which never "come out" of the bulk of material

"inside, where they are in fact observed, is provided by the phonons in the

crystal, as discussed in Chapter 1. The phonons exist as far as the crystal exists. They are observed by scattering over them an external beam of neutrons;

however, the phonons cannot be "extracted" out of the crystal.

To see what is going on with phonons I have to say something about the spontaneous breakdown of symmetry. To do that I discuss in the following one

more ingredient ofQFT, an essential one, which makes QFT distinct from QM.

As already mentioned in Section 1.6, there are many spaces of the physical

states. These all carry the physical information characterizing the system under

study, including dependence on relevant parameters such as temperature.

Under changes of the physical boundary conditions (induced e.g. by tuning

parameters such as the temperature), the system may undergo phase transition

if brought to a critical dynamical regime, and then relax into the new stable

phase. Accordingly, the physical states of the system, in the new phase, will be

characterized by different values of the observables.

Consider the crystal example. Warming up the crystal above some "critical"

temperature Tc, the crystal will melt and the atomic density will in general

Macroscopic variables and microscopic dynamics 29

change. This also means that crystal ordering is lost in the melting. Another example is a magnet. Above the critical temperature Tc the magnetization of a metal goes to zero, and we have transition to the non-magnetic phase. In this case, the magnetization is the macroscopic observable whose value is a measure of the alignment (ordering) of the magnetic moments of the constituents along the same direction. In general, the macroscopic observable giving a measure of the degree of ordering is called the "order parametee'. Notice that magnetiza­tion, i.e. the order parameter, is a macroscopic variable in the sense that its value is not affected by local fluctuations.

Since in the case of the crystal, as well as in the case of the magnet, the physical properties of the phases are different above and below the critical temperature, the state spaces describing each phase are not physically equivalent to each other. This can be expressed in mathematical language by saying that there does not exist any unitary transformation between state spaces describing different physical phases (the phase above I;; and the phase below Tc in the above examples). One also says that such state spaces are unitarily inequivalent.

Thus we see that one needs unitarily inequivalent spaces in order to describe systems which present different stable phases. One merit of QFT is in fact that it allows infinitely many inequivalent state spaces, also called representations, of the same set of operator fields and of their dynamics. This is the essential ingredient of QFT I was referring to above.

Such a richness of unitary inequivalent state spaces in Q FT is due to the fact that fields imply infinite number of degrees of freedom (or infinite volume), as already observed in Chapter l. On the contrary, if the number of degrees of freedom is finite, as it always happens in QM, then, according to the von Neumann theorem, all the state spaces are unitarily equivalent to each other (von Neumann 1932; Bratteli and Robinson 1979; Umezawa and Vitiello 1985): QM thus only describes systems presenting physically equivalent state spaces, that is only one physical phase. This necessitates using QFT in treating systems with many stable phases ( cf. Section 1.6).

According to what I said in Section 2.2, field equations can be solved only when the physical state space on which fields operate is assigned. For systems with many stable phases such an assignment corresponds to a real choice among physically different situations. This means that the same set of dynamical equations, i.e., the same dynamics, may generate different (physically inequiva­lent) stable phases and different stable symmetry patterns in the same bulk of material (Umezawa 1995; De Concini and Vitiello 1976). For example, the same dynamical equations for the same set of Heisenberg fields carrying a magnetic

30 My Double Unveiled

moment may generate ferromagnetic states with non -zero magnetization (if the system temperature is below T) or non-magnetized states (if above ~) (Shah, Umezawa and Vitiello 1974; Matsumoto et al. 1974; Vitiello 1974).

The magnetic state is symmetric «only" under rotations around the magnetization axis. On the contrary, there is no preferred direction if magneti­zation is zero, and thus the non-magnetic state is symmetric under rotations around any possible direction. In the case of the crystal the different symmetry

patterns are the continuous space translational symmetry for the melted state, corresponding to the fact that the atoms can be in any space position, and the lattice symmetry pattern for the crystal phase, where the atoms can only sit in the lattice sites or move from site to site, translating« only'' by integer multiples of the lattice length.

We see from the above examples that ordering corresponds to the lack of some

symmetry (Vitiello 1975): in the crystal phase atoms cannot move around by continuous spatial translations but «only" by discrete jumps, integer multiples of the lattice length. In the ferromagnetic phase the magnetic moments (or spins) of the constituents cannot rotate freely in any direction but can «only'' point in the same direction (the magnetization direction).

One also says that order arises from the breakdown of symmetry: order means the possibility of making a distinction among things. Symmetry means that things are alike, exchangeable, indistinguishable among themselves. The crystal ordering allows distinguishing lattice sites from any other space point: lattice sites are «special" points in the sense that you find the atoms sitting there, not elsewhere. In the gaseous or in the melted phase any space point is like any other one, in the sense that in any of them you can find an atom. Symmetry thus corresponds to indistinguishable points. In the magnetic ordering, a distinction is made among any possible direction and the magnetization direction. A magnetic needle in the Earth magnetic field makes the compass a useful instrument just because it «points" to the North direction. A non­magnetic needle is useless in that any direction is indistinguishable from any other one. Incidentally, we see that infonnation is associated with ordering and therefore to breakdown of symmetry. Later on I will come back to this point.

The symmetry which gets broken in the creation of observable ordered patterns is the symmetry, or invariance, of the dynamical equations. The group of transformations under which the form of the dynamical equations does not change defines the symmetry properties of the dynamics. Since we have seen that the same set of dynamical equations may describe different orderings, we see that the same original symmetry of the dynamics may be dynamically

Macroscopic variables and microscopic dynamics 31

rearranged in these different observable orderings (Umezawa, Matsumoto and Tachiki 1982; Umezawa 1993; Vitiello 1975).

A unified understanding of many observable ordered patterns is thus reached through the dynamical rearrangement of symmetry: different ordering patterns appear to be different manifestations of the same basic dynamical invariance. This is the phenomenon of the dynamical generation of order.

Notice that the observable ordering is a property (measured by the order parameter) of the system state, i.e., since we are interested in stable configura­tions, of the system state of minimum energy (the vacuum or the ground state). The dynamical invariance is instead related to the field equations. Symmetry is said to be spontaneously broken when the symmetry of the ground state is not the symmetry of the dynamical equations. The word "spontaneous" means that the symmetry of the dynamics can be rearranged in any one of the possible ordering patterns observable at the physical level (in other words, any one of the physical phases can be dynamically realized).

But now, what is the relation between phonons and the crystal ordering? Let me illustrate that in the next section.

2.5 Collective modes, coherence and order

Order is dynamically generated in the mechanism of spontaneous breakdown of symmetry. How does this actually happen?

In Chapter 1 I said that in a crystal the atoms sit in their lattice sites since ordering infonnation is exchanged among them, traveling over the whole system. The atoms are thus correlated among themselves by such an exchange of information over long distances. The atoms are trapped by long range correla­

tion. Order may only be present, indeed, if a large number of elements share the same property (e.g., the property of sitting in equally spaced sites). By saying that ordering is dynamically generated I exactly mean that such a long range correlation is dynamically generated.

This is in fact the content of the Goldstone theorem in QFT (Itzykson and Zuber 1980; Umezawa, Matsumoto and Tachiki 1982). It states that when the system ground state does not have the (continuous) symmetry of the dynamics, then the same dynamics generates a massless boson particle. This is called the Nambu-Goldstone mode, or the Goldstone particle or mode. The Goldstone mode appears to be the dynamical response to the breakdown of the symmetry. It is the carrier of the ordering information and therefore the quantum mediating

32 My Double Unveiled

the long range correlation among the atoms: the Nambu-Goldstone mode is

indeed responsible for the ordering. I am here considering the case in which the Goldstone mode arises as a

bound state of other elementary fields. The Goldstone mode may also be by itself an elementary field. The dynamics then fix its mass to be zero. The conclusions of my discussion do not change if one considers the Goldstone mode to be an elementary field.

In the case of the crystal, the phonon is the Nambu-Goldstone particle

associated with the spontaneous breakdown of the continuous space translat­ional symmetry. The phonon is the quantum of the elastic wave (as noted, in

quantum theory the complementarity principle allows representation of a particle as a wave and vice-versa) through which the atoms "communicate", i.e.,

exchange the ordering information. In the case of the magnet, the Nambu­

Goldstone mode is called the magnon particle or the spin-wave mode. The Goldstone modes are bosons. This means that many of them can

occupy the same state with the same quantum numbers, e.g., the same charge,

the same energy, etc. One also expresses this by saying that bosons may condense in the same state.

The condensation of the bosons is temperature dependent and is controlled by the Bose-Einstein distribution function. At conveniently high temperature, above a certain critical temperature T0 the condensed bosons may "evaporate":

condensation is destroyed and symmetry is restored. We have phase transition to the un-ordered or symmetric phase.

For other kinds of particles, called fermions, one cannot find more than one

of them in a state with the same quantum numbers. This is the content of the

Pauli exclusion principle. Since electrons are fermions, the Pauli principle requires then that electrons occupying the same electronic shell in an atom must necessarily differ among themselves in some quantum number. This

governs the filling up of the electronic shells and accounts for the periodicities

in the Table of the Elements. Since bosons may be found in any number in the same state with exactly

the same quantum numbers, they may generate the phenomenon of coherence. For example, the photons, i.e. the quanta of the electromagnetic waves, which also are bosons, may be organized in laser beams (Klauder and Sudarshan 1968). The coherence of the beam consists in the fact that all the photons in the beam present the same phase, whereas in normal light the phases of the photons

are randomly distributed.

Macroscopic variables and microscopic dynamics 33

In the crystal example, a perfect lattice ordering requires phonons carrying

the same ordering information over the whole bulk of the crystal and therefore the same quantum numbers; the phonons are thus in a coherent state: ordering is

associated with the coherent condensation of the Nambu-Goldstone boson quanta. Since the Goldstone fields are massless their condensation in the ground

state at zero momentum does not add energy to the state. In this way many states of the same (minimum) energy may be obtained, each of them corre­sponding to a different condensate density. We call them degenerate ground

states. Since states of minimum energy are stable states, the stability of the ordering pattern in each of these states is therefore guaranteed. In this way

stability of order is a result of the quantum dynamics. This conclusion relates to the discussion on stability in Chapter l.

Notice that the quantum characterization of the dynamics is crucial. At a

classical level, one cannot obtain ordered states of the same energy as non­ordered ones: creation of order requires expenditure of energy. In QFT sponta­neous breakdown of symmetry allows instead the existence of degenerate

ground states presenting different degree of ordering. They represent physically different, stable phases of the system. In this way we understand the mechanism of spontaneous breakdown of symmetry as the dynamical generation of a multiplicity of stable, ordered states and of coherence.

Since Goldstone modes are massless, they move without inertia and they

span the whole system acting as Long range correlation among the system constituents. For this reason the Goldstone modes are also called the long range correlation quanta, or simply the long range correlations. Thus, the system constituents cannot behave as free elements, but are "trapped" by their own

correlation, and therefore they behave as a "whole,. [n this way the dynamical generation of the correlation, namely the condensation of the corresponding quanta which are the Goldstone modes, determines the system macroscopic

properties. The Goldstone modes are therefore collective modes. Due to coher­ence, the system behaves as a macroscopic quantum system. Ferromagnets, super­conductors, superfluids and crystals are systems of this kind.

Spontaneous breakdown of symmetry in conclusion leads to the generation

of macroscopic, coherent quantum systems and therefore implies the dynamical change of scale, from micro to macro. Macroscopic observables called "order parameters, are thus introduced. The order parameter is a macroscopic variable

in the sense that its value is not affected by local quantum fluctuations. It is remarkable that in spontaneous breakdown of symmetry the order

parameter is expressed in terms of the inverse of the coupling constant: this

34 My Double Unveiled

signals the nonlinear, non-perturbative character of the symmetry breakdown.

It is a clear example of a case where the perturbative approach does not apply: in the case of a small coupling constant, in a first perturbative approximation

one would have been neglecting such small coupling interactions, thus com­pletely missing the "best of the pie", namely the broken symmetry solution, and with it a full rich set of physical behaviors of the system corresponding to the broken symmetry phases. We also learn in this way that the same existence of the unitarily inequivalent representations in QFT is of a non-perturbative

nature, a feature that is non-existent in QM. One more remark regarding the "confinement" of the Goldstone particles,

which are sometimes called quasiparticles for that reason. We have seen that they are dynamically generated when symmetry is broken. If in some way, e.g. by warming up the system, say a crystal, we let it undergo a phase transition

restoring the broken symmetry, then order is destroyed since symmetry is recovered; this means that long range correlation among the atoms is lost, i.e. Goldstone particles are destroyed. This is the reason why they are not found in

the symmetry restored phase. On the other hand, they cannot be extracted out of the ordered system because actually they represent "correlations" and thus, as such they do not exist "by themselves". In this way, as discussed in Chapter 1,

"structure" and "function" become meaningless notions if taken separately. It is extremely interesting that these "conceptual" remarks find their

quantitative formulation in the mathematical formalism of QFT. In a similar

way, it is quite remarkable that the notion of collective behavior of a large number of elements also finds its quantitative formulation as the output of the

microscopic dynamics.

2.6 Self-focusing propagation of long range interaction fields

Until now I have considered only homogeneous boson condensation and I have not considered the role of the so called gauge fields. These are massless Long

range interaction fields. The electromagnetic (em) field is an example of gauge field. The interaction between two particles carrying electric charges consists in

(is mediated by) the exchange of the quantum of the em field, the photon, whose mass is zero and can propagate over long (infinite) distances (the interaction range). Including in the picture long range interaction fields leads us to consider the possibility of generating a finite mass for the gauge field, or, in different words, of confining its propagation to filamentary regions. Non­

homogeneous condensation allows instead for the possibility of creating

Macroscopic variables and microscopic dynamics 35

extended objects of nonlinear (non-perturbative) nature and the creation of finite size coherent domains. In this section I will briefly discuss the filamentary propagation of the long range interaction fields. Extended objects will be considered in the next section.

In the previous sections I have discussed the generation of long range correlation among the system components as a consequence of the spontaneous symmetry breakdown. The quanta which are responsible of such correlation have been named the Nambu-Goldstone quanta. Their condensation with the same quantum numbers in the ground state provides a coherent state. Coher­ence may be thought of as "in phase" oscillations or motion of the system components. This means that the state of the system may be characterized by assigning a single observable, which plays then the role of macroscopic observ­able (the order parameter). Such an "in phase motion" (coherence) among the system components is indeed the manifestation (the consequence) of the fact that the system components are correlated over large distances.

The net result is that the system behaves as a macroscopic (quantum) system, since there is no need to specify the quantum numbers (e.g. the phase) of each component as would be required in a microscopic description. Coher­ence thus allows the transition from the microscopic description scale to the macroscopic description scale ( cf. also Section 1.5).

Let me assume now that the system dynamics possess a phase symmetry. There are two possibilities when considering phase symmetry. In one case one may change the phase of the fields by different amounts in different space points and at different times: we say that the dynamics is symmetric under "local" phase transformations. In such a case the dynamics is also symmetric under changes of the phase which are everywhere and at any time the same, i.e. under "global" phase transformations.

The other case is the one in which the dynamics is invariant only under the just mentioned global phase transformations. Local phase symmetry includes global phase symmetry, but the reverse is not true.

It happens that local phase symmetry requires that some kind of necessarily massless fields must participate in the dynamics. These are the fields which are called the gauge fields and they represent long range interactions among the system constituents. Symmetry requires that they must be massless and there­fore their propagation range extends to infinity (Itzykson and Zuber 1980).

To get an intuitive picture of what is going on, you may consider that if the phases of each component of the system are "locally" changed, i.e. the phase of one component is changed independently of the changes in the phase of other

36 My Double Unveiled

components sitting at different space-time points, a different microscopic arrangement, or configuration of the system, with respect to the phases values of the components, is obtained.

However, one wants (has assumed) that the dynamics should not feel such different microscopic settings (which is the meaning of the symmetry under local phase transformations). The job of the gauge fields is to compensate for the local phase changes in such a way that the dynamics is not affected by such changes: the gauge fields provide a "shielding" or a compensation for the local phase changes. To do that they must involve all the components at once, and thus they must be long range interaction fields spanning the full system, i.e. they must be massless (the propagation range is inversely proportional to the mass). Examples of gauge fields are the electromagnetic field and the weak gauge fields in elementary particle physics. Other gauge fields are the color gauge fields in the quark dynamics.

What happens when phase symmetry is broken and the dynamics thus prescribes a coherence regime to the system components? Notice first that it is only the global phase symmetry which gets broken, since one wants to preserve the symmetry of the ground state under space-time translations: this is equiva­lent to the request that the system behavior should not depend on the reference frame and on the time at which it is observed. Breaking the local phase symme­try, would violate such an obviously necessary request.

Next, a competition is expected between the long range ordering correla­tion arising as a consequence of the symmetry breakdown and the long range interaction mediated by the gauge field. This competition in fact exists and the propagation of the gauge field in the ordered medium may occur according to different regimes: either the gauge field is prevented from penetrating into correlated regions or correlation disappears, at least in some regions, allowing the gauge field to propagate (Anderson 1980; Umezawa, Matsumoto and Tachiki 1982; Del Giudice et al. 1985). Which one of the regimes is actually realized depends on the smaller or greater strength of the gauge field with respect to the strength of the coherent correlation.

If the field strength is not much higher than a threshold, it would penetrate in the medium by "piercing" it: it would be kept confined inside filaments or tubes. The diameter of these regions is controlled by the inverse of a mass factor depending on the strength of the correlation. In the region surrounding the filaments the gauge field is zero and coherence is there preserved. Inside the filament, correlation is destroyed.

The propagation of the gauge field in filamentary regions may be represented

Macroscopic variables and microscopic dynamics 37

in terms of the propagation of a "massive" gauge field: the "obstruction, to its propagation due to the coherent correlation of the medium can be in fact formally represented as a mass acquired by the gauge field. Such an acquired mass introduc­es modifications into the dynamical equations which now admit a "self-focusing" propagation mode for the gauge field. The gauge field is "squeezed" by the coherent correlation into filamentary tubes.

This phenomenon is very general and is commonly observed in solid state physics and in elementary particle physics. It is the so called Anderson-Riggs­Kibble (AHK) mechanism (Anderson 1980; Matsumoto et al. 1975). The Wand the z!l particles in electroweak theory are massive gauge quanta generated through the AHK mechanism. In superconductors, the magnetic field penetration in the core of supercurrent vortex structures, and the related quantization of the magnet­ic flux, is also a manifestation of the AHK mechanism.

Self-focusing or filamentary propagation of the gauge field (the e.m. field in this case) also occurs in nonlinear optics (Konno and Suzuki 1979; Kelley 1965).ln the case considered above, however, the ordering of the medium is the prerequisite of self-focusing and this allows the AHK mechanism to occur also for fields of strength as weak as the one of the medium correlation. In nonlinear optics the medium is in general uncorrelated and the self-focusing efficiency is much lower (Del Giudice et al. 1986, 1991 ).

Finally, in the case where the gauge field strength is much stronger than the medium coherent correlation strength, then the gauge field may completely destroy the medium coherence, or simply "see" the medium as an uncorrelated one. It will then propagate in its usual massless propagation mode.

2.7 Nonlinear dynamics and soliton solutions

A wave of given wavelength is said to be monochromatic. In dispersive media monochromatic waves propagate with phase velocities depending on their wavelength. The phase velocity can be thought as the velocity of a given point in the wave profile (a point of constant phase).

There are excitations, called wave packets, which can be described as superpo­sition of monochromatic waves. A wave packet arises due to constructive interfer­ence of the constituent waves in some limited space region, and negative ( destruc­tive) interference elsewhere. So it appears as an excitation localized in the region of constructive interference.

Since in a dispersive medium waves of different wave-lengths propagate with different velocities, the wave packet spreads out during its propagation

38 My Double Unveiled

through such a medium. It is then difficult to transfer the energy associated

with a wave packet over long distances in a dispersive medium: apart from energy losses due to the interaction of the wave packet with the medium, turned

into vibrations of the medium particles, i.e. into heat, energy spreads out into the medium as the packet spreads out. "When the superposition of solutions of a certain equation is also a solution of that equation, this is said to be a linear equation. Linear equations thus admit wave packets as solutions.

There exist however excitations which do not behave as wave packets, i.e.

cannot be considered as superpositions of monochromatic waves and do not spread out in dispersive media. They are stable excitations localized in a limited

space region and energy is associated with them. These excitations are called solitary waves or solitons and are solutions of classical nonlinear dynamical equations. Due to their stability, solitons are well suited to describe transport of

energy without dissipation (Scott, Chu and McLaughlin 1973; Davydov 1978-1991; Rajaraman 1982).

Although the rigorous definition of soliton refers to stable, finite energy,

localized solutions of so called completely integrable one-dimensional nonlin­

ear equations, in physical applications one generally refers to solitons, or to solitary waves, in a much broader sense, including some realistic feature of the system, such as finite extension, boundary effects, dissipative terms in the interaction, not necessary one-dimensionality, etc., which spoil complete integrability of the nonlinear equations.

By the word soliton one sometimes also means vortices, dislocations and other kinds of extended objects in realistic systems. In these cases, the stability of the soliton, which makes it so interesting, is still much greater than for other kinds of solutions for which the superposition principle can be applied: generally speaking, solitons are localized excitations arising from the balance between

dispersion and nonlinearity, which propagate in a quasi-non-dissipative way. Nonlinearity means that fields are "self-interacting" fields. One can also

think in terms of the field interacting with the "reaction" field generated by

itself (back-reaction field, or self-interaction, indeed). One can then speak of

self-localization since localization arises as one of the effects of nonlinearity, i.e. of the self-interaction.

Solitons provide one example of those cases in which the perturbative approach cannot be applied. In the perturbative approximation one would be able indeed to "linearize" the theory and then proceed by adding successive

perturbative terms as described in Section 2.3. The superposition principle holds indeed when the linearization procedure is applicable. Soliton solutions cannot

Macroscopic variables and microscopic dynamics 39

be found by linearization methods: a soliton solution is a non-perturbative solution. A mathematical treatment shows in fact that the coupling constant enters the solution in a way that cannot be made to go to zero in a mathemati­

cally meaningful way. In other words solitons are incompatible with the ontological prejudice ( cf. Section 2.3): in the soliton theory the fields entering the soliton solutions are never non-interacting fields (Mercaldo, Rabuffo and Vitiello 1981; Manka and Vitiello 1986, 1990; Del Giudice et al. 1988c).

The appearance of solitons is related to breakdown of the homogeneity of the boson condensation, with consequent localization of excitation energy, charge, etc. The QFT for soliton formation in fact describes them as localized Bose condensation of the field quanta: the soliton, which behaves as a solution of classical nonlinear equation, is thus described as the macroscopic envelope of localized quantum condensation.

Another important property of solitons is their topological charge (Umezawa, Matsumoto and Tachiki 1982; Rajaraman 1982). This means that they are described by functions which have definite topological properties. For example, the so called kink soliton is described by the hyperbolic tangent function which is well known to assume opposite values, say -v and +v, at large distances (space infinity) on the left and on the right side of the soliton center, respectively. This denotes a behavior ''topologically non-trivial" and the topo­logical charge is given by the difference 2 v of the two values (the space we are used to live in, on the contrary, presents the same properties at space infinity, independently of the direction we observe it, so its topological charge is zero). The meaning of such a topological property is that the kink "interpolates" between two phases of the system whose «order parameter" is -v and +v, respectively (Mercaldo, Rabuffo and Vitiello 1981; Manka and Vitiello 1986,

1990; Del Giudice et al. 1988c). The kink appears thus in the transition from one phase to the other, it represents the «wall domain" which separates the two phases. The topological charge is a conserved quantity. Since the ground state has zero topological charge, the state with a topologically non-trivial soliton is particularly stable since it cannot decay to the ground state. Such decay would violate the topological charge conservation.

Another example of an extended object with topological charge is the vortex (Umezawa, Matsumoto and Tachiki 1982). This represents a localized domain of condensed bosons with topological charge defined by the number of closed paths or circuits around a region, the core or center of the vortex, where there is no condensate. In such a region there is non-zero flux of some gauge field, of the magnetic field, for example. The magnetic field is then damped so as to be

40 My Double Unveiled

zero everywhere except at the vortex center. In superconductors the magnetic flux in the vortex core is quantized. Flux quantization is not restricted to superconductors, however. It can be shown that it is a general phenomena, related to the appearance of the vortex in condensed matter.

The number of circuits characteristic of the vortex solution is called the winding number. It counts the number of flux quanta trapped in the vortex core. Different values of the winding number classify topologically distinct vortex solutions of the field equations.

Typically, vortices appear during the process of phase transition, e.g. in superfluid helium. Their appearance is also related to the formation of finite size coherent domains, each with a different value of the order parameter: the vortex acts as singular boundary solution ("defect") interpolating among different coherent domains. The study of defect formation during phase transitions is of great interest in condensed matter physics as well in high energy physics and in cosmology (Vitiello 2000b; Bunkov and Godfrin 2000).

The boson condensation often proceeds through the formation of coherent domains. The size of these domains is called the coherence length (which for example in superconductors can be few thousands of Angstroms). The forma­tion of domains can be thus understood as a non-homogeneous boson conden­sation mechanism. When the domain boundaries will open so that domains merge into larger coherent regions, condensation may become homogeneous and the transition to the ordered state on a scale larger than the coherence length will then occur.

Finally, let me recall that the word "soliton" was introduced by Zabusky and Kruskal in 1965 (1965) in connection with the property of nonlinear waves of preserving their shape and velocity after scattering, as particles do in their elastic collisions. Probably, the first observation of solitary waves dates back to 1834, when the naval engineer Scott-Russell observed a particularly stable wave propagating in a canal at Edinburg in Scotland (Scott, Chu and McLaughlin 1973).

The study of solitons is of interest in relation to an extremely large number of phenomena in any branch of Science, including Biology, and there is an exten­sive related theoretical and experimental research activity, including numerical studies and computer simulations, with a rich body of results (Scott, Chu and McLaughlin 1973; Hilborn 1994; Alfinito et al. 1996; Rajaraman 1982; Davydov 1982, 1991 ). Equipped with the notions presented in this chapter, we are now ready to consider in the next chapter the QFT approach to living matter.

CHAPTER 3

The living phase of matter

Boson condensation, coherence and nonlinearity are basic ingredients in the Frohlich model for living systems and in the dynamics ofDavydov solitons on protein chains. In the Quantum Field Theory approach to living matter, the mechanism of spontaneous breakdown of symmetry provides an integrated scheme of Frohlich and Davydov dynamics. Coherent vibrational modes of electric dipoles of water molecules and other biomolecules play a central role in the Quantum Field Theory approach.

3.1 Living matter physics 42

3.2 Frohlich coherent excitations 43

3·3 Phenomenology I 45

3·4 Davydov soliton 47

3·5 The Quantum Field Theory approach 51

3.6 Charge and discharge regimes 53

3-7 Electromagnetic field and cytoskeleton 57

3.8 Phenomenology II 58

3·9 Thermal effects 61

42 My Double Unveiled

3.1 Living matter physics

Theoretical Physics and Biology is the title of one of the last papers by Herbert Frohlich (Frohlich l988a). There he tells that since 1938 he became to be interested in the fact that biological membranes maintain a small electric potential difference of 100m V. Since the cell membrane presents a thickness of 10-6 cm, it means that this potential difference corresponds to an enormous electric field of 105V/cm. Layers of ordinary materials would break down in such a huge field unless special precautions were taken. Moreover, with an elastic constant corresponding to the sound velocity of 105 cm/s, a frequency of 1011Hz for oscillating electrical dipoles is involved, corresponding to oscilla­tions in the millimeter electric waves region.

In that paper Frohlich reminds us that the first Versailles meeting organized by the Institut de la Vie in 1967 also had the title "Theoretical Physics and Biology" and that Ilya Prigogine presented there his ideas about "dissipative structures, (Prigogine 1962; Prigogine and Nicolis 1977). On the other hand, in

those same years, the long range correlation, dynamically generated through the mechanism of symmetry breakdown in QFT, was recognized to be responsible for ordering in superconductors, superfluid helium, and other systems present­ing stable ordered ground states (Anderson 1984; Umezawa, Matsumoto and Tachiki 1982). These developments, together with the recognition of the crucial role of nonlinearity in dynamics, also are at the basis ofHaken's formulation of Synergetics (Haken 1977) and of Davydov's studies of nonlinear molecular dynamics (Davydov 1978-1991).

Stimulated by such developments (to which he also greatly contributed) Frohlich proposed in 1968, "as a working hypothesis, that phase correlations of some kind, coherence, will play a decisive role in the description of biological materials and their activity, (Frohlich 1988a). It is remarkable that in those same years, the dynamical generation of order provided by the spontaneous breakdown of symmetry in QFT also inspired the formulation of the quantum model of the brain. Ricciardi and Umezawa's paper appeared in 1967 (Ricciardi and Umezawa 1967).

Since it will turn out to be useful for a better understanding of more recent developments of the quantum model of the brain, I will summarize in this chapter the main features of the physics for living systems developed along the lines of Frohlich's suggestion. Anticipating a possible conclusion, let me say here that much work is still to be done before producing a full theory ofliving matter. And a lot of experimental work is still needed to find a dear cut test of

The living phase of matter 43

some of the theoretical features which [will discuss below. A close collaboration between theory and experiments is required.

However, I want also to observe that from the confluence of experimental

data it appears that the proposal of the dynamical generation of long range coherent correlation in living matter, even if not yet manifestly supported by a definitive experiment, is far from being contradicted by any observation: on the contrary, it stands up in its full elegance and "necessity,. Although specific models may be not adequate in many respects to describe the experiments and the observations which are carried out, nevertheless the path to be followed has been opened. One of the merits of theoretical physicists is to be able to look at the Moon when somebody points to it, not to his bad- or good -looking finger.

After introducing the Davydov soliton on protein molecular chains (Section 3.4), in this chapter I will also introduce the QFT approach to living matter (Del Giudice, Doglia and Milani 1982; Del Giudice et al. 1983-1988a, 1988c; Del Giudice, Preparata and Vitiello 1988b ), which, moving from the Frohlich and Davydov proposals, presents an integrated scheme of their respective dissipative and conservative dynamical mechanisms.

3.2 Frohlich coherent excitations

As said above, the cell membrane electric field shows that active biological systems have extraordinary dielectric properties, when compared to the ones met in ordinary inert materials. They exhibit stable ordering, as anticipated in Chapter 1. In this respect, it is worthwhile to stress that not only space ordering, to which we are most familiar, should be considered, but also time ordering, as sequentially interlocked chemical reactions. Moreover, although living systems are open, far from equilibrium systems, nevertheless they present high efficien­cy and stable functional activity.

Common experience and detailed observations also show high sensitivity of biological systems to external stimuli of very low intensity. It is known that the sensitivity at low light intensity of the human eye is extremely high. Also, careful measurements show that the sensitivity of some species of fishes to electric signals is so high as to evoke a response to electric fields as low as 10-8V/cm. This might appear quite surprising if compared to the huge electrical field maintained in the cell membranes (Frohlich 1988a).

The above features are among those suggesting that a dynamics underlying the phenomenology of molecular biology is at work. Starting from the fact that

44 My Double Unveiled

the high field in membranes causes strong electric polarization, Frohlich suggested that electrical polarization could indeed be taken as the macroscopic observable corresponding to the order parameter. This means that the oscilla­tions of the electric dipoles (with which any biological molecule and water molecules are endowed), occurring in the millimeter wave region are "in-phase", and therefore coherent, oscillations. Thus the dynamical ordering is actually time ordering, or motional ordering, as Frohlich calls it (Frohlich 1988a).

These are in fact features of the Frohlich model. He shows that for a system of oscillating charges in interaction with a thermal bath or any other source of energy (e.g. light radiation), provided the interaction is nonlinear, one single dipole mode may be excited when the amount of supplied energy is above a given threshold.

In terms of particle description, this is equivalent to saying that a number of quanta, all of them with same definite frequency, are condensed in the system state. The fact that the quanta oscillations manifest in a single polar oscillation mode means that they coherently oscillate (in phase oscillations).

The number of such quanta is temperature dependent and is given by the Bose distribution (cf. Section 2.5). It should be observed that the required nonlinear interaction with an external source of energy will in general also fix the system temperature. When the number of quanta is fixed, the system temperature is determined by the Bose distribution. However, in the case under consideration, the temperature is fixed and the number of quanta is the one required by the Bose distribution. The energy supply must reach the threshold required to excite such a number of quanta. When such a number matches the one corresponding to the given temperature, Bose condensation occurs.

One more feature of the Frohlich model is that the system possesses energy storage capability and, moreover, a resonant answer is possible so that response time of the system to an external energy input is much shorter when the external input frequency matches the polar mode frequency. Since energy may also be supplied by radiation sources, resonant system responses may also follow as effects due to applied radiations.

According to the Frohlich model and its subsequent developments, in addition to the coherent excitation of a single dipolar mode, which implies long range correlation among dipoles (in-phase oscillations), it is also possible to excite metastable highly polar states and limit cycles or Lotka-Volterra oscilla­tions. These limit cycles arise in complex situations, as in periodic enzyme reactions. In these cases frequency selective long range resonant interactions among molecules can also occur. Selective interactions are of course of great

The living phase of matter 45

general interest in biological processes where a specific molecule has to reach another specific molecule sitting in a determined site, e.g. on the cell membrane, with high efficiency. The interested molecules may be distant far away from each

other many order of magnitude larger than the chemical interaction range, and moreover, in between them generally there are many thousands of other, chemically different, molecules. Of course, the random kinematics of molecular biology cannot give a reasonable explanation of the observed high efficiency in the gathering of such molecules under such prohibitive boundary conditions. Note that these are not cases where one can use statistical laws since the observed high efficiency excludes "regularities only in the average" and in any case the number of molecules to interact is "much too small to display exact statistical laws,, to put it in Schrodinger's words (cf. Section 1.2) (Schrodinger 1944).

Excitations of metastable highly polar states are predicted when polar excitation may couple to elastic modes. This has to do with the system softness or plasticity, i.e. its shape adjustments to external stimuli, or even with its own spatial volume adjustments under the inner polar mode dynamics. The possibil­ity of existence for these metastable modes is shown to depend on the material properties of the system, such as its elastic properties, high polarizability, and large coupling between polar and elastic modes. We will see that these modes may be originated on protein molecular chains in a nonlinear dynamical regime, as proposed by Davydov.

3·3 Phenomenology I

There are several phenomenological observations and experiments which may be discussed in the light of the Frohlich model. Careful and extensive series of observations have shown that metabolic activity is affected by non-ionizing and non-thermalizing radiations (Adey 1981, 1988; Smith 1988; Jelinek et al. 1999; Pokorny, Fiala and Vacek 1991). According to the coherent oscillation scheme, external fields may indeed produce effects at the dynamical level and as a

consequence on the biochemical activity. By means of mm wave spectroscopy it has been shown that irradiation of

biological systems induces effects which depend strongly on the frequency of the microwaves. In a certain microwave power range these effects weakly depend on the variations of the power through several order of magnitude. Moreover, significant dependence on exposure time is observed (Devyatkov 1974; Frohlich 1988a). All these features agree with the theoretical predictions.

46 My Double Unveiled

One of the points to be stressed is that Frohlich's theory concerns active

biological systems, which means that experimental tests are to be carried out in vivo, and this of course requires great care in the sample preparation. Synchron­icity in the biological activity of the samples is required, for example, in some kind of experiments. Frequencies and intensities of the spectral Raman lines of bacterial cell population in particular syncronicity conditions have been observed to be strongly time dependent (although there are doubtful aspects on some of Webb's experiments, see Webb 1980) and in the first part of the life cycle no lines appear. A correspondence between the spectroscopic pattern and time ordering of biochemical activity can be registered (Del Giudice et al. 1984).

In the blood coagulation process cells appear to interact at a distance several orders of magnitude greater than the range of chemical forces thus producing rouleaux of red blood cells (erythrocytes) (Rowlands 1988; Paul et al. 1983; Paul, Tuszyflski and Chatterjee 1984). Long range interaction disappears when: a)the cells are depleted by the source of energy, but it is restored when metabol­ic energy is supplied again; b) the cell membrane potential is reduced to zero; c) the cell membrane is disorganized by addition of poisons. The interaction appears to be specific: preferential rouleau formation is observed among cells of the same species when a mixture of different types of cells is examined.

The rouleau formation thus points to the existence of selective long range forces among cells. In the theoretical scheme cells may be described as ordered systems. Two cells separated by a non-ordered region may behave in a way similar to Josephson junctions in superconductivity. An array of cells interact­ing through long range forces may be then understood as an array ofJosephson junctions in a regime of ((phase locking" (coherence). A similar phenomeno­logical situation may occur in yeast cells cultures (Del Giudice et al. 1989). Selective long range coherent interaction among cells of the same type may thus promote their cooperative activity in tissue formation. This could provide a step forward in the understanding of the insurgence of anomalous behavior of cells m cancer.

As observed by Frohlich (Frohlich 1988a), experimental activity may be classified into two types of investigations: one in which the coherent long range correlation concept is used to interpret known biological features, the other one in which experiments are performed in order to exhibit evidence for coherent excitations. In both kind of investigation one crucial problem is the reproduc­ibility of the experiments. In this respect it has been pointed out that the occur­rence of chaotic regimes may play a relevant role due the nonlinear nature of the dynamics (Kaiser 1988). The chaotic regime may strongly affect the response

The living phase of matter 47

of the system in its interaction with external electromagnetic radiation. For a discussion on the biological, geometrical and electronic parameters involved in the detection of the electromagnetic field in biological systems see, e.g., Belyaev 2000, Holzel and Lamprecht 1994, 1995.

Further experimenta] activity which can be quoted in support of the proposed dynamical scheme includes topics such as low intensity, sharp frequency radiation effects on cell growth (Grundler and Keilmann 1983; Grundler et al. 1988; Grundler and Kaiser 1992; Pohl 1980), extremely low frequency electromagnetic fields enhancing the stress response in embryogene­sis of drosophila (Gutzeit 2000), non-thermal effects of extremely high frequen­cy microwaves on chromatin conformation (Belyaev 2000), nonlinear and chaotic dynamical response to external stimuli (Kaiser 1988), nonlinear tunneling at high frequency in biological membranes (Huth, Bond and Tove 1984), coherent nuclear motion in membrane proteins (Vos et al. 1993), existence of metastable excited states (Hasted 1988; Celaschi and Mascarenhas 1977; Mascarenhas 1974, 1975), low-frequency Raman spectra and relaxation time of crystal water (Urabe et al. 1998), weak radiation fields irradiated by metabolically active systems (Li et al. 1983; Popp 1986; Jerman, Berden and Ruzic 1996), nonlinear propagation of coherent waves in ordered molecular monolayers (Huth, Gutmann and Vitiello 1989; Christiansen, Pagano and Vitiello 1991; Christiansen et al. 1992; Bartnik, Blinowska and Tuszyilski 1992), water dynamics (Woutersen and Bakker 1999; Urabe et al. 1998; Watterson 1987), and so on. The interested reader can usefully consult the referenced literature and a collection of selected papers edited by Frohlich (Frohlich 1988b ). An interesting collection of papers reporting recent experiments can be found in Pokorny (2000b) (see also Pokorny and Wu 1998).

3·4 Davydov soliton

Energy transfer on protein molecular chains is one of the key processes in any biological activity.

Living systems are open systems. They are coupled with the environment, exchanging with it energy and matter. Such an exchange is characterized by the fact that living systems are dissipative systems (Prigogine 1962; Prigogine and Nicolis 1977), i.e., they are open systems able to dissipate outwards all (or most of) the incoming energy. In other words, only a small part of the incoming energy is transformed into heat: a "healthy" living system is not thermalized by the incoming energy.

48 My Double Unveiled

The incoming energy is instead converted into chemical energy through chemical reactions occurring at definite times and at definite sites of the biological macromolecules. This energy can be stored and efficiently (i.e. without dissipation which would possibly increase the system temperature) transported over the biomolecular chains, to be finally released in a non­thermalizing dissipative way.

The problem then arises of understanding how such a non-dissipative energy transport may occur and how it may occur over distances much longer than the ones predicted by any dispersion process. This was termed the "bio­energetic crisis" (Davydov 1982). In fact any modeling based on linear (har­monic) vibrational analysis of the involved molecules fails to explain non­dissipative long distance energy transfer.

To better understand the terms of the problem, it is good to recall that chemical energy in the living system is mainly the oxidation energy of organic substances. [n the cells such an energy is stored in the process of phosphoryla­tion, i.e., the synthesis of the adenosine triphosphate (ATP) acid molecule from the adenosine diphosphate (ADP) and phosphoric acid with release of a water

molecule. The ATP molecules then diffuse to sites where energy is utilized. At such sites the reverse reaction occurs, called the hydrolysis of ATP, with release of energy in the presence of water and enzymatic molecules. These intermediate steps are universally utilized in all living organisms, including plants, which use light radiation as energetic input. Due to the size of the involved macro­molecules, the release and the utilization of hydrolysis energy occur in sites apart, at distances of several order of magnitude higher than interatomic distances. Hence the problem arises of the efficient, non-dissipative energy transport over such distances.

The energy released in a single process of hydrolysis is of the order of 0.5 e V,

a too small amount to excite the electronic state of a molecule and only 20 times larger than the average energy of a thermal fluctuation. It suffices, however, to excite molecular vibrations of the carbon-oxygen ( C=O) atomic group (the so called Amide-! group) which only requires 0.21eV. The Amide-I group is incorporated into larger groups, called peptide groups (O=C-N-H), which appear as segments in all protein molecules. lt also carries an electric dipole moment of 0.3 de byes.

Thus one could think that the ATP hydrolysis energy is carried over the protein molecular chains through propagation of the vibrations of the Amide-I groups. This is, however, not possible since the lifetime of vibrations the peptide groups can support is of the order of 1 picosecond; this is too short a

The living phase of matter 49

time to allow vibrations to propagate over distances much larger than the ones

of the peptide group. In 1976 Davydov and Kislukha (1976) entered the scene with the proposal

that nonlinear dynamics in the protein chain may support a soliton wave propagating over the chain, generated by the ATP hydrolysis energy release, and the soliton wave is responsible for the non-dissipative energy transport. This was a very successful proposal, which provoked an extensive theoretical and experimental activity all around the world, including numerical studies and

computer simulations (Hilborn 1994; Alfinito et al. 1996). Proteins are macromolecules oflarge molecular weight, assembled through

the polymerizations of several amino acids. Living matter only uses 20 different types of amino acids, out of the much larger number of existing types. Proteins can assume intricate spatial configurations and can organize into helical

structures, called the a-helices. The peptide groups are connected by hydrogen bonds. The Davydov soliton is modeled as a collective mode propagating over such a protein helical structure.

Protein are present in all the relevant processes in the cell. Their ability to have changeable spatial configurations (softness) makes them responsible for all inter- and intra-cellular motions: they transform chemical energy into mechan­ical energy.

Davydov's theory uses nonlinear, anharmonic coupling among the dipole vibrational field of the peptide group and the phonon field representing the

chain deformation consequent to the dipole vibration. This coupling is a nonlinear coupling since the dipole field interacts with the phonon which is the effect of its own vibrational state (cf. Section 2.7). It is an interaction with its own reaction field. The vibrational dipole field is "trapped" by the deformation

field self-induced on the molecular chain. Such kind of "self-trapping", for

convenient values of the involved parameters (masses, coupling constants, etc.), is enough to counter -act the dispersion involved in the propagation. The "trap, , i.e. the deformed part of the chain, then moves along the chain, i.e. "coherently"

propagates and with it the vibrational dipole quanta confined in it: a "lump" of

coherent vibrational energy thus propagates over the chain without dissipation. The nonlinear excitation, the soliton indeed, is thus a collective mode of the protein chain (Davydov 1978-1991).

It should be stressed that for infinitely long molecular chains solitary waves are stable, i.e. protected against dissipation, since their energy is less than the

energy of wave packets made of a superposition of plane waves (called exci­tatons). Moreover, they move with a velocity less than the longitudinal sound

50 My Double Unveiled

velocity, which means that they cannot decay by emitting phonons. In other words, the soliton deformation does not "split up" into elastic waves (the phonons) spreading out over the chain.

Finally, solitons are "topologically stable" which means that peptide groups on the right of the soliton center have displacements which are different from the ones of the groups on the left. For an infinitely long chain such a distribu­tion of the displacements is a constant of motion. Topological stability has been discussed in Section 2. 7.

Since protein chains do not have infinite length, the soliton in realistic cases is not completely stable. This is not a negative fact, of course, since it means that solitons can be created, i.e. incoming energy may be converted into soliton energy and then transported over the proteins; and they can decay, thus releasing their energy to be utilized by the system or to be finally dissipated outwards as required by the dissipative nature ofliving matter.

Non-complete stability is thus consistent with the "openness" of biological systems. Creation of a soliton, due to its topological properties, can only occur at the end of the protein chain. Moreover, only energy released by chemical reactions, not by electromagnetic radiation, as e.g. light, can excite a soliton. This is so because absorption of radiation by a molecular system does not produce variations in its coordinates. For the same reason the probability for a soliton to emit photons is very small. A soliton formation instead requires molecular vibrations, as explained above, which can be induced by chemical energy release.

We thus see that the ATP hydrolysis energy can excite a soliton at one of the ends of molecular chains. The soliton then propagates along the chain transfer­ring its energy without dissipation, in the most effective way: it is the carrier of the ATP hydrolysis energy. The solution of the "bioenergetic crisis" thus resides in the nonlinear dynamics of the protein molecular structure.

One of the original motivations for developing the solitary dynamics on protein chains was the modeling of the muscle contraction mechanism, which does not find acceptable explanations in terms of molecular biology. The reasons for such a failure are in fact in the energetic balance which cannot be achieved due to the large mass of the involved myosin molecule and to the long distances over which the ATP hydrolysis energy must be efficiently carried. In the soliton model the soliton kinetic energy is used to produce the fiber contraction and its rest energy is then released as heat, with consequent disappearance of the soliton.

The living phase of matter 51

The existence of contractile proteins can also be related to the soliton ability to convert ATP energy into mechanical deformations. These proteins, such as actin, tubulin, etc. are basic constituents of the "cytoskeleton", i.e. the network of filaments which includes microtubules and determines any motion and change in the cell, and where any process is realized through release and transport of ATP hydrolysis energy.

The a-helix structure able to support soliton formation and motion also characterizes transmembrane glycoproteins which determine cellular individu­ality, their adhesion and intercellular interaction. Glycoproteins are coupled to the cells internal microtubules thus providing coupling and signal transfer between the external environment and the cells internal activity (for the relation between Frohlich model and Davydov soliton see Tuszyflski et al. 1984; Tuszynski, Bolterauer and Sataric 1992).

Moreover, solitons may trap electric charges in their motion thus providing a non-dissipative electric current similar to the supercurrent in superconduc­tors. Nonlinear dynamics therefore turns out to be relevant also to such crucial biological processes as charge transfer and ionic exchanges.

In conclusion, nonlinear dynamical solutions play a determinant role in many aspects of the biological activity. The Frohlich model and Davydov soliton represent a big step forward in the formulation of a dynamical scheme for biological process. Even if these specific models turn out to not completely fit the observations, nevertheless they confirm the dynamical origin of the molecular biology phenomenology. It is therefore interesting to explore the possibility of deriving as many conclusions as possible from those theoretical aspects which are model independent. One can then identify those theoretical predictions and features which do not belong to a specific model and as such will not be washed out when experimental findings require changing or dismissing that model. In the next section I therefore present the QFT approach to Living matter which is mainly based on general symmetry properties of the dynamics rather than on specific dynamical modeling.

3·5 The Quantum Field Theory approach

Biological systems present a large number and a wide variety of microscopic components. Molecular biology has been and is very successful in accumulating theoretical and experimental data about each of these components. The macro­scopic behavior of the system, or in other words, the solution to the problem of

52 My Double Unveiled

combining the components into a working, functional scheme, is supposed to follow from the detailed knowledge of each component of the system.

Certainly, in some of their features, living organisms appear to be macro­

scopically fragile, in the sense that their behavior strongly depends on the local arrangement of the elementary components and localized damage or modifica­tion at a microscopic level may result in a drastic modification or destruction of some of the macroscopic functions, or even of the whole system.

From an other side, however, there are features in the macroscopic behavior of biological systems which appear not so strictly related to local variations of microscopic parameters. Undoubtedly, living matter presents macroscopic plasticity, namely it presents macroscopic properties that are independent of a specific microscopic configuration, and sometimes also of the number of the elementary components: as an example, brain functioning is not apparently affected by the death of some of the neurons.

One may then attempt to consider a minimal, but essential, set of macro­scopic requirements for living systems, on the basis of their observable features, to be described as emerging not from a purely statistical microscopic configuration of the components, but from a microscopic dynamical scheme. This is indeed the suggestion coming from Frohlich, Umezawa, Davydov and their collaborators. Following in fact such a suggestion, Emilio Del Giudice, Silvia Doglia, Marziale Milani, Giuliano Preparata and myself have formulated in the 80s the QFf approach to living matter (Del Giudice, Doglia and Milani 1982; Del Giudice et al. 1983-1988a, l988c-1991; Del Giudice, Preparata and Vitiello 1988b).

The bridging between the microscopic and the macroscopic levels allowed by QFT in condensed matter physics is also exploited in the case of living matter. The resulting scheme provides a general theoretical framework where in a natural way many features of the Frohlich model are recovered and where those macroscopic features, such as space and time ordering, dissipativity, and long range correlation, are manifestations of the components' microscopic dynamics. The relevant dynamical mechanism is the spontaneous breakdown of symmetry. Let me illustrate how this happens.

Most of the molecular components ofliving matter carry an electric dipole moment. [n the QFT approach dipole excitations are described by quantum fields, as is customary in many-body physics. The living system is then schema­tized as one or more chains of macromolecules made of weakly bound mono­mers embedded in water.

The living phase of matter 53

We thus have from one side quasi-unidimensional structures, i.e. the macromolecule chains, from the other side the three-dimensional embedding made of water. The dimensionality of these structures plays a relevant role in the picture.

In the case of water, the fields describe molecular (electric) dipole excita­tions and field equations are invariant under rotations of the electric dipoles. In the case of biochains, their chemical structure is such that one may safely assume a lattice periodicity and thus translational invariance with characteristic lattice length may be considered.

Experimental evidence that water surrounding protein molecules shows a net polarization density (the electret state) (Hasted 1988; Celaschi and Mascarenhas 1977; Mascarenhas 1975) suggests that dipole rotational symmetry is spontaneously broken: the electrical polarization density is thus adopted as the system order parameter on a phenomenological basis.

The dynamical scheme has to take into account, however, one of the most relevant macroscopic properties, that of dissipativity: the living system is indeed an open system able to dissipate outwards all the incoming energy. What is required is to understand the actual story of the energy while flowing inside the system: the dissipativity requirement is too general and therefore it must be articulated in terms of actual microscopic processes.

Observation shows that the energy uptake occurs at definite times and sites on the macromolecules by means of chemical reactions. Energy is then trans­ported with great efficiency over long distances and is finally released over a large region. The phenomenology thus shows that energy uptake occurs under very different conditions than energy release. The dynamical regime of energy uptake must be then differentiated from that of the energy release: the general principle of dissipativity must be articulated into a principle of energy charge and discharge (Del Giudice et al. 1985).

Accordingly, the QFT approach provides the theoretical framework for an integrated scheme of the Frohlich dissipative mechanism and of the Davydov conservative one.

3.6 Charge and discharge regimes

On the basis of Davydov's suggestion, it is assumed in the QFT approach that nonlinear dipole waves (solitons) may propagate without dissipation over macromolecular chains. The energy to create a soliton is supplied by ATP

54 My Double Unveiled

metabolic reactions occurring at one of the end-points of the chain. When

traveling on infinite length chains, solitons do not undergo the spreading of familiar wave-packets in quantum mechanics; on finite length chains they,

though more stable than usual wave-packets, have finite life-times. Propagating on biomolecular chains, solitons may trap electric charges

weakly bound to their sites. Soliton motion (and thus charge motion) is quasi­non-dissipative (I consider finite length chains); a superconducting-like current is then originated which may couple to the electromagnetic field of the sur­

rounding water. Soliton propagation also produce mechanical effects on the chain such as deformations, straightening, contractions, etc., which in turn

produce variations of the chain dipole field and consequent additional effects on surrounding water dipoles. The net effect is therefore a coupling of nonlin­ear dynamics of molecular chains with surrounding water dipole dynamics: the

soliton motion thus may trigger spontaneous breakdown of the water dipole rotational symmetry, with consequent emergence of coherent boson condensa­tion and of the water dipole polarization playing the role of the order parameter (as illustrated in Chapter 2) (Del Giudice et al. 1983, 1985).

Summarizing: external (incoherent) energy input ("feeding" the system) induces ATP reactions at one of the macromolecule chain end-points and a solitary wave traveling on the chain is generated. This is a first level of coherent

response of the system (the soliton does have a coherent structure in terms of boson condensation). This phase of the system history is named the "charge regime" or the "Davydov regime". The soliton motion on the chain then may

trigger the breaking of dipole rotational symmetry: as a consequence water is

ordered in the electret state. This is a further level of organization with the appearance oflong range correlation and is called the "discharge regime" or the "Frohlich regime" (Del Giudice et al. 1985).

Owing to the finite length of the chain the soliton decays, releasing its energy

in a non-thermalizing way. Heat propagates indeed in the organized medium (the water electret) in a wave-like fashion and not in a diffusive way. Resonant

intermolecular transfer of vibrational energy has been observed to be very

efficient in liquid water because of dipole-dipole interaction, indeed (Wouter­sen and Bakker 1999). On the other hand, the water electret state has a finite life-time (also due to thermal effects) and therefore, to keep itself organized, the

system needs to be "fed" again. A cyclic sequence of charge and discharge regimes is thus obtained. Any imbalance between the charge and the discharge

regime turns into "pathology" for the system. For example, non-sufficient energy discharge may show up as "stress" in the system, i.e. energy over-charge.

The living phase of matter 55

From what was said above, the life-time of the soliton and of the electret state, the molecular chain elasticity, the water dipole response to electromagnet­ic fields and the temperature effects are all relevant parameters in reaching the desired balance between energy charge and discharge. For example, doping the molecular chain with drug molecules may change the rate of formation of the solitons on the chains or/and their non-dissipative propagation, and so on. Electromagnetic perturbations interfering with the water dipole vibrational modes may as well alter their response to the solitons action, with effects on the water ordering. In the following section I will discuss more on the propagation of electromagnetic fields in the ordered water and on the role of thermal effects.

As discussed in Chapter 2, due to the Goldstone theorem, the breakdown of the dipole rotational symmetry implies the existence of Nambu-Goldstone modes. These are the quanta of dipole vibrational waves and I accordingly will call them dipole wave quanta (dwq). They manifest as long range correlation among molecular dipoles in water and are thus the carrier of the ordering information in water.

Although these dwq are massless in the infinite volume limit, they may develop a non-zero effective mass when boundary effects are considered. In this more realistic case, their condensation in the ground state produces quasi­degenerate states, which have long, but finite, life-time and may be excited with low, but not zero, expense of energy. Their effective non-zero mass sets a threshold under which an external supply of energy cannot excite dwq. In this way the stability of the ordered pattern gets protected against perturbations below the threshold. This mechanism by which stability is protected is named the low energy theorem in QFT. On the other hand, occasional (random) weak (but above threshold) perturbations are recognized to play an important role in the complex behavior ofliving systems (Celeghini 1990).

In conclusion, the dynamical origin of the observed ordered distribution of water molecules surrounding biochains is thus recognized. The Frohlich dipole wave is identified with the Nambu-Goldstone dipole mode. Dissipativity is insured at the macroscopic level as the manifestation of a complex interplay between nonlinear dynamics on uni-dimensional molecular chains and three­dimensional long range correlation in the embedding matrix of water molecules.

The molecular domains where dwq propagate present coherent dipole oscillations with a time scale much shorter (10-14 sec) than the one of short range interaction and therefore are protected against thermalization (Del Giudice, Preparata and Vitiello 1988b ). An explicit analysis of the water dynamics shows phase locking of the dipole field with its own radiative em field:

56 My Double Unveiled

water undergoes the so called "lasering, behavior, in analogy with the known mechanism in laser physics (Del Giudice et al. 1985; Vitiello 1992). Here, the term "laser, should not create confusion, however. It only stresses the crucial

role of coherence in the formation of ordered domains (Preparata L995). In water these have been found to have a size of a few hundred of microns. The analysis of the water dynamics, which started in the frame of the research program on the QFT approach to living matter, has been continued with intense activity beyond that original research program by Emilio Del Giudice, Giuliano Preparata and collaborators, leading to a number of very interesting results (Preparata 1995).

As mentioned above, the realistic finite size effects may imply an effective mass, different from zero, for the Nambu-Goldstone modes. A temperature T may be then associated to such a non-zero mass value. The finite system volume, namely the coherence domain dimensions, in this way gets related to the system temperature (Del Giudice et al. 1985).

Finally, I note that depending on the interactions of the system with the surrounding environment and on possible changes of inner dynamical condi­tions, in each charge-discharge cycle different values of the order parameter (the polarization density) may be realized. The system may thus "live" by spanning in time a full set of quasi-degenerate ground states corresponding to those different values of the order parameter (Del Giudice et al. 1988c). A sequence of differentiated functional behaviors may thus emerge at the macro­scopic level, corresponding to variations in the degree of coherence: a system with just one ground state would be a "dead, system, "crystallized, in its unique

ordered pattern (the living system is not like a crystal! cf. Chapter 1). Until now I have only considered the long range correlation among the

water electric dipoles which is dynamically generated through the mechanism of the spontaneous breakdown of symmetry. Other kinds oflong range forces, like the ones of the electromagnetic interaction, have not been considered so far. As anticipated in full generality in Chapter 2, the effects of the mechanism of symmetry breakdown on the propagation of the electromagnetic (em) field and, vice-versa, of the em field on the ordered state, cannot be neglected. The next Section is devoted to the discussion of such effects.

The living phase of matter 57

3·7 Electromagnetic field and cytoskeleton

In biological systems coherent oscillations of dipoles, charged subgroups on the biomolecular chains, ions, or else non-uniform distributions of concentration of molecular species, resulting in charge distribution gradients, may act as sources of em fields. Inside biological systems there can thus be many sources of em disturbances. Other sources of em disturbances are of course external.

From the discussion presented in Section 2.6 it follows that the propagation of the em field in an ordered medium may occur according to different regimes: either the em field is prevented from penetrating into correlated regions, or correlation disappears allowing the em field to propagate. The two different regimes are realized in correspondence to smaller or greater strength of the em field with respect to the strength of coherent correlation, respectively. If the field strength is not much higher than a threshold, it would penetrate in the medium, but it would be confined inside filaments or tubes, whose diameter is controlled by the inverse of a factor, with mass dimensions, depending on the strength of the correlation. Outside the filament the em field is zero and coherence is preserved. Inside the filament correlation is destroyed. As we have seen in Section 2.6, this controls the magnetic field penetration in superconductors.

In the QFT approach to living matter, the em field is thus allowed to propa­gate only within a network of filaments inside the correlated water medium, provided the strength of the electric disturbances is sufficiently high (Del Giudice et al. 1986). According to the discussion of Chapter 2, this may be described in terms of propagation of a "massive, em field (massive photons) in the correlated medium.

The diameter of the filament in the simplified case of a completely aqueous medium with maximum of polarization may be computed and it turns out to be of the order of 15 nanometers (Del Giudice et al. 1986), which is a figure very near to the inner diameter of micro tubules.

This is an intriguing feature which brings us to the conjecture that the filamentary propagation of the em field in structured water may be at the origin of the formation of the cytoskeleton, namely of that complex structure made of microtubules which pervades the cell and which is so crucially relevant to any metabolic activity. Let me sketch how this can be.

The filamentary propagation of the em field implies the presence of strong field gradients on the side boundary of the filament: the non-zero field trapped into the filament goes rapidly to zero outside the filament. Therefore "gradient

58 My Double Unveiled

forces, emerge which may act on molecules surrounding the filaments by attracting or repelling them. In fact a small change in the involved frequencies may turn an attractive force into a repulsive one. Moreover, such an action is selective since it is of resonant nature: the resonance occurs when the molecule oscillatory characteristic frequency matches the field frequency. The gradient forces thus act selectively on the surrounding molecules according to a well defined resonance pattern (Del Giudice et al. 1986).

The attracted molecules may in turn contribute to a change of the field frequency in the filament, with consequent, say, attraction of molecules of different characteristic oscillatory frequency. The filament thus gets coated by a molecular pattern, which may stabilize into a polymeric structure if the coating molecules may form stable chemical bonds. In this case, it will survive even if the field filament should disappear. Otherwise, it will collapse as soon as the supporting filamentary field vanishes. Such a scheme thus provides a dynamical description of cytoskeleton formation and of its structure.

As a matter of fact, the observed dynamical behavior of the cytoskeleton, with its intricate network, with continuous creation and destruction of branch­es, and with its movements, is a true puzzle to biochemistry (Clegg 1983; Hotani et al. 1992; Engelborghs 1992). Spatial arrangements of microtubules form dissipative structures, which only can be studied in a non-equilibrium dynamics framework (Tabony and Job 1992). Some features in their growth are associated with spatially inhomogeneous concentrations of reactives, which also suggests that gradient forces are brought into action (for a study on dipole­dipole interaction in microtubules see Trpisova and Brown 1998). The QFT approach could then supply an integrated scheme describing these behaviors on a dynamical basis.

3.8 Phenomenology II

It is interesting to list some observed phenomena in the cytoskeleton behavior which may be traced back to the scheme depicted above. Since a small change in the frequencies may turn an attractive force into a repulsive one, modifica­tions in the source of the field (e.g. in the charged subgroup of DNA) may then result, through subsequent changes in the frequencies, in the breakdown of the filament structure. The observed microtubule catastrophes (Mcintosh 1984; Mitchison and Kirschner 1984), i.e. the sudden filament disappearance, may be traced back to this instability against small frequencies fluctuations.

The living phase of matter 59

Longitudinal components in the forces, called radiation pressure forces, may act on the molecules trapped in the filament (Del Giudice et al. 1985 1986). Such forces push the molecules in the direction of the filament. This increases

the probability of polymerizations since the molecules are squeezed together, but it also produces the release of monomers at the end of the filament. Then new monomers could fill the gap produced at the chain beginning. This could be a dynamical explanation for the so called "treadmilling'' (Margolis and Wilson 1981) of the polymer chain.

Most of the chemical activity in the cell is observed to occur on the cyto­skeleton microtubules. According to the above discussion we may have a first primitive insight to the problem of driving time-ordered sequences of chemical reactions: the self-focusing propagation of em field and the resulting selective gradient forces allow the recognition of different molecules at different times. Such a timing is built up out of a definite frequency pattern.

When the strength of the em disturbance is very low, the em field does not propagate at all. [n such a case coherence plays the role of protecting the system from em fields weaker than the correlation strength. This may be an extremely relevant role played by coherence, since it means that chemical activity, in which molecular interactions involve em fields weaker than coherence strength, are protected against unwanted comparable em perturbations from internal as well as from external sources. Coherence acts in such a case as a "filter" which excludes the unwanted, perturbing em fields.

Of course, this may be one of the possible, subtle ways in which the stability of "delicate" biochemical activity (which would soon collapse in a random chemical environment) is insured. Fine tuning of the correlation strength may move up or down the protection threshold for some biomolecular reactions, with corresponding functional changes at macroscopic level. As already noted, tuning of the correlation strength may be obtained through variations of the order parameter as a response of the system to environmental actions or perturbations (Celeghini, Graziano and Vitiello 1990; Del Giudice et al. 1988c). Creation, enhancement or inhibition of functions appear thus as a feedback effect in the system-environment interaction.

Fields of strength stronger than the one of the correlation have disruptive effects on coherence, or, at the best, they "see" the medium as an uncorrelated one. This suggests that coherent structures in biological systems should be probed by weak em fields. On the other hand, it also may shed some light on possible mechanisms by which em radiation may cause damage to biological systems. Clearly, I am referring here not to the commonly studied ionizing

6o My Double Unveiled

radiation damages, but to disruptive and/or negative interference of the em fields with the system microscopic coherence.

Though radiation cannot excite solitons, neither can soliton emit radiation, however, radiation can resonantly interact with solitons, inducing even their decay into metastable excitons. In this way non-dissipative transfer of energy is ruined and the cell life may be accordingly affected. We thus see that the experimental observation of radiation effects on living systems, e.g., the resonant radiation effects of mm electromagnetic waves on the rate of growth of some bacteria, may find an explanation in the microscopic nonlinear dynamics (Kaiser 1988; Grundler et al. 1988; Kremer et al. 1988).

It is known that anesthesia is induced by a large class of molecules (some­times with strong differences in the respective chemical properties) which form hydrogen bonds with proteins thus producing, for example, inhibition of the cells normal functioning. The barbiturate molecules contain the atomic group O=C-N-H which is similar to the peptide group. The molecule of barbiturate attaches to the protein by creating hydrogen bonds with it. In that site where new bonds are created, the protein structure and conformation

change since bonds between peptide groups are destroyed with consequent increase of their separation. This protein deformation induced by its "doping'' with the barbiturate molecule affects the soliton propagation (and/or forma­tion) thus altering the cell life cycle. How such an alteration then manifests itself in the typical anesthesia effects is to be explained on a different ground. In the framework of the quantum brain model it has been proposed that intracellular signal transmission can be based on the dwq mode propagation in water surrounding the cytoskeleton network and the extracellular matrices of neuron and astrocytes in the brain (Jibu and Yasue 1993b; Jibu et al. 1994). The introduction of anesthetic molecules, may then produce defects in the water organization, thus destroying the dwq modes and, consequently, the signal transmission (cf. Chapter 5).

Summarizing, the QFT approach provides a description of living matter which presents several levels of organization (I would say of"languages") which are not simply derivable from structural features of the elementary components. The very same "story" or behavior of the living system, its evolving in time, cannot be solely explained in terms of structural features. A deeper understand­ing of the dynamics is required, which reveals to us the non-separability, or, better, the dynamical unification of structure and function (cf. Section 1.6). The systems observed functional stability is ensured by the system "coherent response" to a multiplicity of external stimuli or perturbations, or also

The living phase of matter 61

back-reaction generated inputs. There are recurrent cycles of system-environ­ment-system interactions consisting in highly nonlinear back-reaction effects which point to a typical self-referential character ofliving system behavior. Let me stress that such a self-referential behavior only exists as an effect of the fact that living systems are open systems. Self-referentiality of the kind observed in living systems absolutely does not mean the "closure" of the system onto itself: contrarily to what could appear at a (naive) first sight, self-referentiality and adaptiveness ofliving systems ( cf. Section 1.6) have the same dynamical root in the QFT approach, namely dissipation.

3·9 Thermal effects

It can be objected that temperature effects may destroy coherence and thus spoil the QFT approach to living system presented above. It can be therefore useful to collect in this section a few comments on this point and see how the question raised by the above objection may be answered.

The first thing to be said is that, as already observed, the molecular domains where dwq propagate present coherent dipole oscillations with a time scale much shorter (10-14 sec) than the one of short range interaction and therefore are protected against thermalization (Del Giudice, Preparata and Vitiello 1988b ). This is an explicit result which by itself should be enough to dissipate any doubt about the persistence of coherence against thermalization. However, I would like to add one more remark on the specific non-perturbative nature of coherence in QFT. As observed in Chapter 2, the quantum dynamics out of which coherence emerges is a non-perturbative dynamics. In particular the quantity which controls coherence is, among other quantities, the reciprocall/A. of the coupling constant A, which means that small couplings may generate very robust coherence. This is the reason why coherence may be triggered and sustained by very low couplings and at the same time it is very stable against external, even strong, perturbations. This appears to be quite paradoxically from the stand point of the "perturbative" approach, where couplings (i.e. forces) are classified as dominant ones, less dominant, and so on according to their decreas­ing strength. Correspondingly, in the perturbative approach we expect that stronger couplings (forces) generate more robust effects. In the non-perturbative dynamics such a situation is in fact reversed: a smaller coupling may produce more robust coherence. In QFT, coherence (ordering) is therefore shielded from

thermalization as far as the effect of temperature is the one of weakening the

62 My Double Unveiled

coupling among the system components. Therefore, if the dynamics is such to generate coherence, then it may persist in the presence of thermalization.

This is not, however, the end of the story. The possibility of having non­perturbative dynamics generally also depends on the values of some of the theory parameters. In general, only if such parameters have values belonging to a certain range, then coherence may be generated. It can happen that these parameters depend on temperature in such a way that for a given temperature (the critical temperature) the parameter values lie outside the range allowing coherence. Then at the critical temperature, and above it, coherence may be lost. We thus see which one is the real mechanism behind the thermalization­coherence question. The above quoted result on the frequency range of the dipole quanta ensures us that the involved parameters depend on temperature in a way that coherence survives at room temperature. The dipole frequency thus sets the "scale" to be used in energy considerations. Of course, all of this does not exclude that you should never put your cat in the oven! ...

The non-perturbative dynamical origin of coherence also explains another apparent paradox in the QFT approach, namely that living matter uses the "incoherent" (information-less) energy input to generate its coherence (order­ing). The possibility of generating ordering and coherence is in fact fully "internal" to the system quantum dynamics (this is what I mean when I say "dynamical" generation of ordering). It does not come from the outside as, e.g.,

in programming a computer. The energy input is only a trigger which starts the chain of events described in the previous sections (the ATP reaction, the soliton generation and so on). Once energy has been used to that aim. it must be released to the outside: the system is a dissipative system. In this connection, it is interesting to recall Schrodinger's remark on "metabolism" (Schrodinger 1944). He reminds us that the word metabolism means "exchange". Now living matter could appear to evade the general law by which physical systems decay to the thermodynamical equilibrium, i.e. to the state of maximum entropy (maximum disorder): in its "life" the biological system keeps avoiding its decay by the continuous effort of maintaining its order, or, in technical words, of lowering its entropy. So, what really does the system exchange with the environ­ment? It does exchange energy, but this exchange is such that the energy input is balanced by the energy output with the overall effect of creating or maintain­ing order, and Schrodinger expresses this continuous balancing by saying that the system exchanges with the environment "negative entropy ". Such an expression has generated much misunderstanding, confusion and a lot of endless discussions. Actually, Schrodinger clarifies very well his thought in the

The living phase of matter 63

"Note to the Chapter 6" of his book (ibid. p. 74). He explains that he uses the words "negative entropy" to let the layman understand that the living system exchanges energy with the environment in such a way to escape the decay to the

thermodynamical equilibrium and to that aim the fact that living systems "give off heat is not accidental, but essential" (ibid. p. 74), which corresponds to the essential requirement of dissipativity in the QFT approach. The extraordinary feature of QFT, which was not yet recognized in Schrodinger time, is the existence of states which are ordered (low entropy) states and "at the same

time" they are states of minimum energy, namely the existence of unitarily inequivalent vacua or ground states. This clarifies that the energy input is not

needed to directly generate and/or sustain ordering. It is only required to trigger the dynamical selection of the ordered vacuum state among the many inequival­ent vacua, selection which, we have learned, corresponds to the spontaneous

breakdown of symmetry mechanism. After that, energy must be released out of the system. Thus we realize that the existence of inequivalent vacua, which is a

specific quantum field theory feature, is in se enough to justify the use of quantum field dynamics in the study of living matter. I feel confident enough

in saying that the existence of these inequivalent vacua may correspond to one of those "other laws of physics" hitherto unknown, which living matter, while not

eluding the "laws of physics" as established to date, is likely to follow (ibid. p. 68). Still today, the ignorance of such a crucial property of QFT, which makes it

essentially different from Quantum Mechanics, is the source of many misun­

derstanding and of many erroneous statements. One further comment on thermal effects is the following. It is known that

heat propagates in an ordered medium in a non-diffusive way; heat waves have

been observed for example in superfluid helium, or in purely crystalline substances and are called second sound waves (Wilks 1967). In contrast with a diffusive propagation, where the energy transfer is achieved through scattering of accelerated particles and the medium temperature consequently increases,

the heat wave produces a coherent oscillation of the medium components, whose frequency is found to depend on the ordering correlation (a very rich source of information on acoustic waves propagating in matter is given in Wolfe 1998). As already mentioned, it has been observed resonant intermolecu­

lar transfer of vibrational energy in liquid water sustained by dipole-dipole

interaction (Woutersen 1999). With reference to the QFT scheme, this means that heat released by, e.g., a chemical reaction occurring on the microtubules will propagate as a wave, in a non-diffusive way, in the water electret and will thus promote electric polarization waves. These in turn may affect the pre-existent

64 My Double Unveiled

ordering correlation. In the new situation different biochemical reactions may be supported, and so on (Del Giudice et al. 1983-1988a): A time ordered sequence of chemical reaction may originate as the cooperative effect of order­

ing, em self-focusing and heat release. This is a result difficult to obtain in a perturbative dynamics, i.e. in a purely random chemical environment.

As a final comment I observe that thermal effects may inhibit or interfere with the formation of solitary waves on protein chains, or also destroy the soliton wave, if already formed. In this respect, I remark that the water struc­tured in the electret state surrounding the protein acts as a "cage, for the

protein component molecules so to reduce their vibrational modes and thus

shields the protein from the environment temperature (the temperature on the protein is then lower than the temperature of the bath outside the electret

coating) (Del Giudice et al. 1985-l988a). In the following chapters I will illustrate the quantum model of brain. The

notions and the comments presented in the present and in the previous chapters will turn out to be very useful for my discussion.

Self-portrait with bird, charcoal on paper 1954 (Pasquale Vitiello, 1912-1962). Private collection.

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CHAPTER 4

The quantum model of brain

The quantum model of brain proposed by Umezawa and Ricciardi is reviewed. The cultural environment in which it was formulated is briefly sketched. The memory model resorting to non-equilibrium phase transitions and the mixed system brain model are also discussed.

4.1 Brain and physics of many-body problems 68

4.2 Natural brain and artificial brain 70

4·3 External stimuli and brain states 72

4·4 Memory recording and memory recollection 75

4·5 Memory and non-equilibrium phase transitions 78

4.6 Brain as a mixed system 8o

4-7 Open problems and experimental issues 83

68 My Double Unveiled

4.1 Brain and physics of many-body problems

The paper Brain and Physics of Many-Body Problems (Ricciardi and Umezawa

1967) was written by Ricciardi and Umezawa between 1966 and 1967, when

Umezawa was still at Istituto di Fisica Teorica in Naples. Soon after he left Naples and went to Wisconsin, at Milwaukee.

The Istituto di Fisica Teorica was founded ten years earlier, in 1957, by

Eduardo Caianiello. In the middle of the 1960s Eduardo Caianiello was pursu­

ing his research on renormalization in field theory. At the same time he was also involved in the mathematical description of nonlinear binary decision elements and neural nets. His neuronic equations in Cybernetics were already well

known. Professor Valentin Braitenberg soon joined the Istituto and his contri­

bution to the establishment of the Division of Cybernetics was essential. Not much later, in 1968, Caianiello founded the Laboratory of Cybernetics at Arco Felice, in the Naples area.

At the Istituto there was a very exciting atmosphere. Many physicists and

mathematicians were visiting and working in Naples. Umezawa was among these. He left the chair of Professor at the University of Tokyo and moved to

Naples in 1963. At the Istituto he was the Leader of the group of Struttura della Materia.

In those years impressive progress was achieved in quantum field theory. As

Robert Marshak says (Marshak 1993 ), it was the "Heroic Period" ( 1960-1975)

of the formulation of the standard model of strong and electroweak interaction. And the Istituto in Naples was sharing such a cultural atmosphere, so dense with events: Caianiello's group was setting up the analytical renormalization scheme; other research groups were involved in group theory and inS-matrix

theory studies; Umezawa was working with his associates L. Leplae and R.N. Sen on spontaneous breakdown of symmetry, a hot subject in those days of discussion on gauge theories. Umezawa writes (Umezawa 1995) that in Naples he started to work on the mathematical formulation of the dynamical rear­

rangement of symmetry after he had an illuminating discussion with Werner Heisenberg at the Max Planck Institute in Munich (Professor Heisenberg delivered the opening lecture for the graduate school of the newly established Istituto in Naples in 1958; he was a good friend of the Istituto). In this formula­tion, essential ingredients are the existence in QFT of infinitely many unitarily

inequivalent representations of the canonical commutation relations, the coherent boson condensation in the ground state and the role of long range correlation in the emergence of observable ordered patterns.

The quantum model of brain 69

The model of brain as a many-body system came to the light in such a

scientific atmosphere, merging Cybernetics with gauge theories. In one of his last papers, dedicated to Eduardo Caianiello, Umezawa writes: "His Institute

was not just an institute of theoretical physics, but included mathematical and experimental section for information and brain science. This gave me a very enjoyable environment. Practically everyday I met theorists and experimental­ists on brain science,. He then adds, "Since I was deeply involved in the subject of order and long range correlation in many-body systems, I naturally asked

myself the question "is there any long range correlation" associated to brain. If there is long range correlation, each constituent of the system should be trapped

by this correlation and its individual behavior should not be freely exhibited and should instead be controlled by the correlation. In that case we do not observe individual cells, but the quasi-cells (in analogy to the term quasi­

particle) ... I intensively discussed this view with L. Ricciardi who was a young (at that time) associate of Eduardo and we published a paper on this subject.,

(Umezawa 1995) It was clear to Umezawa that the mechanism of the dynamical generation of

long range correlation in spontaneous breakdown of symmetry was of such a general validity and so relevant that it could not be "confined" to the domains of particle physics and solid state physics. For the first time physicists had in

their hands the possibility to give a quantitative description of collective modes

for a physical system not on a purely statistical, kinematic basis, but on a dynamical ground.

These collective modes do not describe in fact the collective behavior of an

ensemble of elements of the kind described by Statistical Mechanics. This last

behavior is the one Schrodinger was referring to as being not sufficient to account for the stability and ordering in biological systems (Schrodinger 1944) ( cf. Chapter l).

The collective modes appearing in quantum theory of many-body physics

are not of statistical origin. They are dynamically generated as long range correlation among the system components. For example, the phonon in the crystal is not the cooperative mode of a large number of atoms in the statistical

sense. It is a truly long range interaction mode among the atoms. The ordered patterns observed in crystals, superconductors, superfluids, ferromagnets and other solid state systems are not collective phenomena of statistical origin. They are macroscopic manifestations of the quantum dynamics.

Almost at the same time in which Umezawa and Ricciardi were studying the

brain as a many body system, Herbert Frohlich, independently, but sharing the

70 My Double Unveiled

same cultural excitement of the community of the physicists in those years, also

proposed his model of living matter based on coherent boson condensation (Frohlich 1968).

4.2 Natural brain and artificial brain

Long range correlation in the brain or in living matter was not just a dream of

theoretical physicists. Experimental findings in neurophysiology were confirm­ing the existence of almost simultaneous responses in several regions of the brain to some external stimuli and that these responses could not be explained in terms of single neuron activity (Pribram 1971, 1991). For example, storing and recalling information appear as diffuse, non-local activities of the brain, not

lost even after destructive action on local parts of the brain or after treatments with electric shock or with drugs.

For a long time, Lashley's experimental work was suggesting that "masses of excitations ... within general fields of activity, without regard to particular

nerve cells" (Lashley 1942; Pribram 1991) were involved in the determination ofbehavior. In the middle of the 1960s Karl Pribram, motivated by experimen­tal observations, started to formulate his holographic hypothesis, which subsequently was incorporated in the holonomic brain theory, thus calling into play newly born concepts of Quantum Optics (see also N obili 1985). Informa­

tion appears indeed in such observations to be spatially uniform (Weiss 1986) "in much the way that the information density is uniform in a hologram"

(Freeman 1990, 2000). While the activity of the single neuron is experimentally

observed in form of discrete and stochastic pulse trains and point processes, the "macroscopic" activity of large assembly of neurons appears to be spatially

coherent and highly structured in phase and amplitude (Freeman 1996, 2000). Lashley's question: "What sort of nervous organization might be capable of

responding to a pattern of excitation without limited, specialized paths of conduction?" did of course not exclude that also single neurons and paths of

neurons were involved in the brain activity. Nevertheless, the question was there and still awaits a complete answer. It is, on the other hand, a well known

fact that brain functioning cannot depend too strictly on the functioning of each single neuron since specific activities of the brain manifestly persist in spite

of the continuous changes in the number of living neurons. In the brain metabolic activity constituent macromolecules undergo chemical changes or disassembly within a couple of weeks and are then replaced by new ones.

The quantum model of brain 71

Despite such a continuous molecular "turn over", the brain functions appear to

be highly stable over long period of time. Still in Lashley words, in "all behavior [ ... ] it is the pattern and not the element that counts" (Lashley 1942).

On a different side, the need of machines capable of simulating brain activity for industrial (both military and peaceful) tasks was also pushing in the direction of modeling artificial logical circuits. These are built essentially by assembling one-by-one (artificial) neuron units into complex patterns. This line of research, which as everybody can see has been very successful, has sometimes "inverted" the roles of the "models": The "computer", which was originally

thought to be modeled after the natural brain so as to simulate the brain

functions, has been and is sometimes taken as a model for the understanding and the description of the natural brain.

Naturally, adopting the computer "philosophy" as a model for the natural

brain studies may be a strong "temptation" for any scientist working in brain sciences, and due to the impact of the computers success, this is understand­able. In any case, it is a fact that for the layman the "computer" is the model.

Of course, this creates many misunderstandings and also many difficulties.

The success in the construction of artificial computing machines mistakenly makes many people (not only laymen!) skeptical or simply not very interested in other possibilities different from the view according to which it is enough to

sum up properties of the microscopic units in order to get the systems complex functions. Very often, even in neurosciences, as observed by Pribram (ibid. p. XVI), "tenets based on [ ... ] exclusively bottom-up views are held implicitly and

therefore felt to be fact rather than theory". As I have tried to explain in the previous chapters, this kind of view,

although necessary, is not sufficient to explain certain kind of macroscopic behaviors of the system, unless one adds to it the understanding of the dynam­ics generating collective modes. Typical examples are collective modes in many­

body physics. Referring and in contrast to the artificial machine research program,

Ricciardi and Umezawa write in the Introduction of their paper (Ricciardi and Umezawa 1967): ... "in the case of natural brain, it might be pure optimism to hope to determine the numerical values for the coupling coefficients and the thresholds of all neurons by means of anatomical or physiological methods" ... "many questions immediately arise ... is it essential to know the behavior in

time of any single neuron in order to understand the behavior of natural brain? Probably the answer is negative. The behavior of any single neuron should not be significant for functioning of the whole brain, otherwise a higher and higher

72 My Double Unveiled

degree of malfunctioning should be observed ... ,,. And they conclude that

neither the postulate of the existence of «special" neurons characterized by

exceptionally long life-time, or the postulate of a huge redundancy in the

circuits of the brain, or the existence oflarge dusters of neurons may be of help,

for the simple reason that there is no anatomic or physiological evidence for

such structures.

It is interesting that, in 1982, Hopfield (Hopfield 1982), also starting from the observation that «in many physical systems, the nature of the emergent

collective properties is insensitive to the details inserted in the model. .. ,, and

that «the details of neuro-anatomy and neural function are both myriad and

incompletely known", proposed his seminal model seeking "collective proper­ties that are robust against change in the model details". Of course, the line of

thought promoted by the Hopfield model has gone through the path of the

Statistical Mechanics approach and has collected a great amount of results in neural network modeling (Amit 1989; Mezard, Parisi and Virasoro 1987). As

mentioned in Chapter 1, I will not discuss this line of research in this book.

Starting thus from the observed non-local, diffuse activity of the brain,

Ricciardi and Umezawa proposed that the brain states are characterized by dynamical long range correlation among the constituents. It was then obvious

for them to suppose that the generation of such long range correlation occurs

through the dynamical mechanism of spontaneous breakdown of symmetry: the resulting mathematical model is a QFT model where brain is described as a

macroscopic quantum system.

4·3 External stimuli and brain states

The brain is a system whose phenomenology is extremely rich and complicated,

and therefore it is very hard to produce a unified theoretical scheme aimed to

account for «all" the system observable features. What one does in similar cases

is to try a more general description, where many details of the system behavior

may even be missing, but where some essential requirements have to be satisfied.

One of the most typical features of the brain is its capability of storing

information, for short and for long time periods, and retrieving it. These

activities are certainly related to higher mental functioning. The quantum

model of brain was formulated in order to describe short-term and long-term memory and the brain's capability to recall stored information. These were

considered by Ricciardi and Umezawa some of the necessary requirements to be

The quantum model of brain 73

satisfied by a model for the brain. Moreover, the diffuse, non-local character of

memory activities suggests that they are also good candidates to be described in terms of collective modes of the brain system.

Although it is estimated that in the brain there are about 1010 neurons, interconnected by a myriad of dendritic branches and synaptic connections in an intricate series of neuron nets, and ten times as many glia cells, it appears that memory is not "wired, into individual neuron nets: incoming information seems to involve large regions of brain cells aggregates (Pribram 1971, 1991;

John 1972; Freeman 1990-2000; Greenfield l997a). Another feature of memory activity is the lack of"conscious simultaneous

recall, of several recorded information. Rather, it is often our common experi­ence that once some information has been recalled, another sometimes com­

pletely different information is subsequently recalled, too, in a mechanism of

"association of ideas, through a path or sequence of memories. This suggests that stored information can be recalled according to serial, rather than parallel, processes (Ricciardi and Umezawa 1967).

The above features of memory activity are taken to be experimental evidences on which the quantum brain model is to be based. The formal apparatus of the model is the well founded QFT of many-body physics. The starting point is that the brain is a system in interaction with the external world

from which it receives stimuli carrying information. These stimuli put the brain into states. Let me remark that the introduction of the concept of" state, for the "brain system" is a crucial step in brain modeling. The study of the brain in terms of its states entails considering the ensemble of its constituents; and thus

to focus the attention not on every single one of them, to be linked to its

neighboring in a one-by-one assembling, but on their collective dynamics. Cutting one link, or the death of one of the nodes (neurons), which commonly

occurs in natural brain, would crucially interfere with the good functioning of the "brain system". Even postulating a huge redundancy of such circuits one

should justify how it can happen that functionally equivalent (specialized) circuits are activated. It is quite well known that, apart from structural neural connectivity (which is stationary in time), the functional neural connectivity is quite changeable in time (see e.g. Greenfield l997a) and therefore the notion of "specialized" functional circuitry and of its replacement by equally specialized

alternative connections appears to be in conflict with physiological observa­tions. Paradoxically, the single neuron cell is much more known (and this is mostly welcome!) than the brain as a "system".

74 My Double Unveiled

In many-body physics, states are described by a suitable set of"dynamical variables". The nature of these variables needs not to be analyzed in a first formulation of the model. They are only required to represent certain (very

large) number of entities, essential for producing the different states of the brain. Formally they are associated with the symmetry of the system under certain transformations.

In the usual models of brain the relevant variables are binary variables describing the neurons on/ off activity. However, "we do not intend", Ricciardi

and Umezawa say "to consider necessarily the neurons as the fundamental units of the brain"; this is a clearly heretical standpoint with respect to the "neuron doctrine".

Umezawa writes (Umezawa 1995): "In any material in condensed matter

physics any particular information is carried by certain ordered pattern main­

tained by certain long range correlation mediated by massless quanta. It looked to me that this is the only way to memorize some information; memory is a printed pattern of order supported by long range correlations" ... "In any case

soon after I moved to Naples, I strongly felt that there should be a long range correlation which controls the brain function. If I could know what kind of correlation, I would be able to write down the Hamiltonian, bringing the brain science to the level of condensed matter physics.,,

Of course, stimuli coming to the brain from the external world should be coded and their effects on the brain should persist also after they have ceased;

this means that stimuli should be able to change the state of the brain pre­existing the stimulation into another state where the information has been "printed" in a stable fashion. But this, translated into the language of many­

body physics, means that the state where information is recorded under the action of the stimuli must be a ground state in order to realize the persistence, i.e. the stability, of the recorded information; and that symmetry is broken in

that state in order to allow the coding of the information.

In conclusion, the external stimulus triggers the spontaneous breakdown of symmetry with consequent printing of the information in the ground state.

I will analyze in more detail these steps in the next sections. In order to avoid misunderstanding, I want to stress here that the external stimulus has only the role of selecting one asymmetric (i.e. ordered) ground state among the

infinitely many available ones. Such a ground state is labeled by a specific value of the order parameter, and such a value represents the information content of that state. The external stimulus has no role in the system dynamics, it only

picks out one specific asymmetric state in which the dynamics is realized. The

The quantum model of brain 75

nature of the ordering of the ground state does not depend on the external stimulus, but solely on the system inner dynamics. One might be wondering how it can happen that the brain would decrease its entropy. The answer to such a question relies (cf. Section 3.9) on the extraordinary feature of QFT which is the existence of states which are ordered (low entropy) states and "at the same time" they are states of minimum energy, namely the existence of unitarily inequivalent vacua or ground states. The external input is not needed to directly generate and/or sustain ordering. It is only required to trigger the dynamical selection of the ordered state. The possibility of generating ordering and coherence is fully "internal" to the system quantum dynamics. It does not come from the outside as, e.g., in programming a computer. In a classical framework it would be not possible that ordered states are degenerate to the disordered states, i.e. that ordered states have the same minimum energy as the disordered states. This is a special feature of QFT.

4-4 Memory recording and memory recollection

For the readers convenience it is perhaps useful to recall some facts on sponta­neous breakdown of symmetry in QFT already introduced in previous chapters ( cf. especially Chapter 2).

In QFT the dynamics (i.e. the Lagrangian or the Hamiltonian, or simply the field equations) is in general invariant under some group, say G, of continuous transformations. Spontaneous breakdown of symmetry occurs when the minimum energy state (the ground state or vacuum) of the system is not invariant under the full group G, but under one of its subgroups. Then it can be shown (Anderson 1984; Itzykson and Zuber 1980; Umezawa, Matsumoto and Tachiki 1982) that collective modes, the Nambu-Goldstone boson modes, are dynamically generated. Propagating over the whole system, these modes are the carrier of the ordering information (long range correlation): order manifests itself as a global property dynamically generated. For example, in ferro magnets the magnetic order is a diffused, i.e. macroscopic, system feature of dynamical origin. Ordering is thus achieved by the condensation of collective modes in the ground state.

The invariance of the Hamiltonian under the symmetry group G means that conservation laws of certain physical quantities are satisfied. These conservation laws would be violated by the breakdown of the symmetry in the ground state. It can be shown that the appearance of the Goldstone modes is the dynamical

76 My Double Unveiled

response to the symmetry breakdown, which serves to preserve the conservation

laws (Umezawa, Matsumoto and Tachiki 1982; Umezawa 1993; Vitiello 1974).

As already seen in the crystal example ( cf. Chapter I and 2), the long range

correlation modes are responsible for keeping the ordered pattern; in the crystal

case they keep the atoms trapped in their lattice sites. The long range correla­

tion thus forms a sort of net, extending over all the system volume, which traps

the system components in the ordered pattern. This explain the macroscopic collective behavior of the components as a "whole".

The brain is modeled by Ricciardi and Umezawa by following the above

scheme. Recording of information is represented by coherent condensation of

collective modes in the ground state; in Umezawa's words, "memory is a printed

pattern of order supported by long range correlations" (Umezawa 1995).

Notice that the existence oflong range correlation does not depend on the

specific nature or form of the dynamics, i.e. of the basic interaction among the system constituents, but only on the mechanism of spontaneous symmetry

breakdown. Therefore, as already mentioned, it is possible to avoid specifying

the nature of the basic variables in a preliminary, structural formulation of the

quantum model of the brain. Of course, the price to pay is that the model is too general to lead to quantitative predictions. This limitation has motivated, as we

will see, further, more specific developments of the model. However, the

amount of qualitative features the model can account for, already in its first

general formulation, is remarkable.

Since collective modes are massless bosons, their condensation in the

vacuum does not add energy to it: the stability of the ordering, and therefore of

the registered information, is thus insured. Long-term memory is modeled in

this way. As a footnote to their paper, Ricciardi and Umezawa remark that the

extremely stable type of memory related to the DNA genetic code may also be

explained in terms of boson condensation. It is precisely the stability of the genetic memory which suggested to Schrodinger that Quantum Mechanics

should be used in the study of living systems (Schrodinger 1944). The QFT

description of the DNA crystalline order through boson condensation would

completely fulfill Schrodinger's project since it includes the Quantum Me­

chanics explanation of the chemical bound stability and goes even beyond that

by showing how ordering (i.e. the DNA code) is dynamically generated and

sustained.

The observable specifying the ordered state is called the order parameter. It

is a measure of the condensation of the Nambu-Goldstone modes in the ground

The quantum model of brain 77

state and acts as a macroscopic variable, since the collective modes present

coherent dynamical behavior. Due to coherence the brain appears as a macro­scopic quantum system.

The order parameter is specific to the kind of symmetry of the dynamics and its value is considered to be the code specifying the information printed in that ordered vacuum (recall that the order parameter, is a macroscopic variable in the sense that its value is not affected by local fluctuations). The conclusion

is that stable long range correlation and diffuse, non-local properties, related to a code specifying the system state, are dynamical features of quantum origin: it is in this way that the stable and diffuse, non-local character of memory is

represented in the quantum model; it is derived as a dynamical feature rather than as a property of specific neural nets (which would be critically damaged by

local destructive actions). It may also happen that under the action of external stimuli the brain may

be put into an excited state, i.e. a quasi-stationary state of greater energy than the one of the ground state. Such an excited state also carries collective modes

in their non-minimum energy state. Thus this state also can support recording

some information. However, due to its higher energy such a state and the collective modes are not stable and it will sooner or later decay: short-term memory is then modeled by the condensation oflong range correlation modes

in the excited states. Different types of short-term memory are represented by

different excitation levels in the brain state. Another possibility is the excitation of collective modes out of the ground

state. This brings us to the mechanism of recall of the stored information. In Umezawa's words: "I noticed that this could provide a remarkable mechanism

for memory recollection. Suppose that an ordered pattern was printed on the brain by condensation mechanism in the vacuum which was induced by certain external stimuli. Though an order is stored, brain is not conscious of this because it is in the ground state. However, when a similar external stimulation comes in, it easily excites the massless boson associated with the long range correlation.

Since the boson is massless, any small amount of energy can cause its excitation. During the time of excitation, brain becomes conscious of the stored order (memory). This explains recollection mechanism." (Umezawa 1995).

And it may also explain the above mentioned serial nature of memory recollection. In fact, the decay of an excited state (associated with a certain

information) may occur in several steps through a sequence of intermediate transitions to other excited states oflower energy (each one associated to some other different information); in other words some higher excited state may not

78 My Double Unveiled

decay directly to the lowest energy state, but to some other excited state oflower

energy and so on in a series of transitions. This may then account not only for the serial nature of recalling, but also for the familiar phenomenon of"associa­

tion" of ideas or memories.

Summarizing, the recall process is described as the excitation of Nambu­

Goldstone modes under the action of external stimuli of a nature similar to the

ones producing the memory printing process. When these modes are excited, the brain "consciously feels, (Stuart, Takahashi and Umezawa 1978) the pre­

existing ordered pattern in the ground state. The excited modes have finite life­

time and thus the recall mechanism is a temporary activity of the brain, accord­

ing indeed to our common experience. This also suggests that the capability to be "alert" or "aware" or to keep our "attention" focused on certain subjects

(information) for a short or a long time may have to do with the capability of

the brain to be put into an excited state with short or long life-time. The short-term memory mechanism has been further analyzed in terms of

non-equilibrium phase transitions in the context of the quantum brain model.

I will discuss these and other developments of the quantum model of brain in

the next Sections.

4·5 Memory and non-equilibrium phase transitions

S. Sivakami and V. Srinivasan ( 1983) have observed that besides the short-term memory modeled by Ricciardi and Umezawa, we also experience another kind

of short-term memory, which to be maintained needs continuous or periodic

external agency. In other words, the stored information needs to be constantly brushed up in order not to be forgotten (external stimuli maintained memory).

In the framework of the quantum model of brain, they proposed the non­

equilibrium phase transition model for such a kind of short-term memory.

The original formulation of the Ricciardi and Umezawa model is in fact

based on the equilibrium phase transition mechanism. Information is printed

through boson condensation into the ground state. Such a state is the equilibri­um (stable) state where the brain relaxes once the action of the external input

has ceased. Even in the case of the short-term memory considered in the

previous section, once the input action is terminated and the excited state has

been reached, it is supposed to decay to the equilibrium (ground) state (with

consequent loss of the information).

The quantum model of brain 79

A different situation is the one where the excited state is steadily maintained by the external stimulus which is constantly supplied. This is the case of non­equilibrium phase transition, well known, for example, in laser physics (Klauder and Sudarshan 1968) where the action of an external pump keeps the system in the lasing state which is an excited steady state. When the boson population is greater than a critical value, the transition to the lasing state occurs and the pump role is the one of maintaining the population ofbosons above that critical value, against its otherwise natural decay.

The excited steady state so obtained is also an asymmetric (i.e. ordered) state due to its boson condensate. The density of such a condensate provides the information code, according to the general description of the quantum model. If the external stimulus (the pump) is withdrawn, the excited state decays and memory is lost. Brushing up on a subject thus "refreshes" the memory, i.e. it works against the decay of the corresponding excited state.

Suppose the excited steady state is obtained. It is known that, if the pump is then withdrawn, the steady state life-time is in general longer compared to the life-time of the excited state where the critical boson population has not been reached. This difference may explain why somebody more "familiar" with certain information (a certain phenomenon or circumstance) reacts in a different way than another person who gets that information "for the first time": presumably, in the latter person the critical boson population has not been reached in the corresponding excited state, contrary to the one who had the occasion to reinforce the first stimulus by subsequent ones of the same kind, thus reaching the excited steady state. Training and repetition act thus like the pump pushing up the boson population and keeping it above the critical threshold.

According to observations the level of RNA and of proteins seems to increase with training. This suggests that the RNA level should be related to the level of coherence in the steady state. It has also been observed that inhibitory drugs may lower the RNA level, with memory loss effects. In this case inhibitory drugs act like an external random field destroying the coherence in the steady state (Stuart, Takahashi and Umezawa 1979).

These considerations lead us to the crucial question of the existence and the possible realization of reciprocal interaction between the quantum dynamical level and the phenomenological level where biochemical agents operates. These agents cannot be considered as quantum objects, therefore one should ask how it happens that they couple to the quantum state.

Of course, the question of the reciprocal interaction between the quantum system and the classical world is a central, still unanswered question in the

8o My Double Unveiled

discussion on the foundations of Quantum Mechanics. It is a question of great theoretical and practical interest, and it is the core of the measurement prob­lematic in QM, where the "classical" measurement apparatus has to interact with the quantum system.

Here, as I have already declared in Chapter 1, I do not want to go into discussions on the foundation of QM. I will rather follow the philosophically unacceptable attitude of the physicist searching for the practical solution of his problems, conscious that it may be only a temporary, imperfect, incomplete solution, and therefore ready to dismiss it as soon it will be contradicted by observations.

Let me present in the following section how the practical physicist attitude may be of help in the present case of the brain quantum model. I will follow the path traced by Stuart, Takahashi and Umezawa.

4.6 Brain as a mixed system

In several papers where developments of the quantum model of brain were presented, C.l.}.M. Stuart, Y. Takahashi and H. Umezawa (1978, 1979) observed that any brain model should explain how memory remains stable and well protected within a highly excited system, as indeed the brain is. This is a "stability" in permanent electrochemical activity and in continual response to

external stimulation. As we have seen, experimental evidence of the non -local nature of memory

demands the existence oflong range correlation modes. Furthermore, the high stability of memory demands that such correlation modes must be in the lowest energy state (the ground state), which also guarantees that memory is easily created and readily excited in the recall process. On the other hand, the long range correlation must also be quite robust to be maintained against the constant state of electrodynamical excitation of the brain. At the same time, however, such electrochemical activity must also, of course, be coupled to the correlation modes which are triggered by external stimuli. It is indeed the electrochemical activity observed by neurophysiology that provides (Stuart, Takahashi and Umezawa 1978, 1979) a first response to external stimuli.

The simple way out of the dilemma suggested by Stuart, Takahashi and Umezawa is to model the memory mechanism as a separate mechanism from the electrochemical processes of neuro-synaptic dynamics: the brain is then a "mixed" system involving two separate but interacting levels. The memory level

The quantum model of brain 81

is a quantum dynamical level, the electrochemical activity is at a classical level.

The interaction between the two dynamical levels is possible because of the specificity of the quantum dynamics: the memory state is a macroscopic quan­

tum state due to the coherence of the correlation modes.

We have learned that in many-body physics there are many systems whose

macroscopic properties must be described classically, but they can only be

explained as arising from a quantum dynamics. The crystal, the superconduc­

tors, the superfluids, the ferromagnets, and in general all systems presenting

observable ordered patterns are systems of this kind.

Of course, any physical system is, in a trivial sense, a quantum system since

any system is made by atoms which are quantum objects. But it is not in this

trivial sense, indeed, that the above mentioned systems presenting an ordered pattern are macroscopic quantum systems. The specific, not at all trivial way in

which they appear to be "macroscopic quantum systems" has to do with the dynamical origin of the macroscopic scale out of the microscopic quantum scale

of the components.

The macroscopic scale has to do not only with the large number of constit­

uents assembled in the system (trivial summing up). This is a necessary, but in

our case not sufficient condition. The "emergence" of the macroscopic scale has

to do primarily with the appearance of long range correlation among the

microscopic constituents. Due to such correlation the rate of quantum fluctua­

tions is negligible and the system behaves as a classical one. As mentioned in Section l.S, the ordered state can only appear in a region of size larger than or

equal to the coherence Length: "order is intrinsically diffused" (Stuart, Taka­

hashi and Umezawa 1978). We have seen that long range correlation modes and

their stable coherent condensation in the lowest energy state cannot be under­stood without recourse to quantum dynamics. In this non-trivial sense, then,

"quantum theory is not restricted to the explanation of microscopic phenome­

na" (Stuart, Takahashi and Umezawa 1978).

It is then in such a way that the "classical" behavior of the memory state has

to be expected to emerge out of the microscopic dynamics depicted by the

quantum model of brain. This is the most stringent parallel with the physics of

the many-body problem which gave the title to the original Ricciardi and

Umezawa paper (Ricciardi and Umezawa 1967). The brain is a many-body

system. It is a macroscopic quantum system. In the following (c£ Section 5.5)

I will briefly consider the question of the specificity of the brain system with

respect to other physical systems.

82 My Double Unveiled

Stuart, Takahashi and Umezawa (1978) gave the name of"symmetron" to

the Nambu-Goldstone correlation mode, in order to stress its role of carrier of

the symmetry quantum numbers in the ordering information and that its origin

is due to the spontaneous breakdown of symmetry. On the other hand, they also pointed out that the anatomical representation of the neuronal structure is

meaningful only when associated with description of its modes of action.

Because these are predominantly transmembrane modes, when one tries to

depict the neuron so as to include its functional activity, one should conclude

that "the neuron has no definite spatial boundary" (Stuart, Takahashi and

Umezawa 1978, 1979). The basic quantum variables entering the quantum

model must then represent other elementary entities, distinct from the neuron

and other brain cells which cannot be considered as quantum objects (Ricciardi

and Umezawa 1967; Stuart, Takahashi and Umezawa 1978, 1979). These basic

variables were named "corticons" (Stuart, Takahashi and Umezawa 1978). In conclusion, the dynamical model is specified by the interaction among

the corticon fields which is characterized by a definite invariance under a

certain group of transformations (the dynamics symmetry group). The realiza­

tion of the dynamics may occur in a state symmetric under the same symmetry group, or in a state non-symmetric under that group. In the latter circumstance

we say that symmetry is spontaneously broken, and this occurs under the action

of the external stimulus (carrying the information). The asymmetric state then turns out to be a coherent condensate of symmetron modes. The density of

these condensed modes represents the information code. The state appears

therefore as a classically behaving macroscopic quantum state.

The problem of the coupling between the quantum dynamical level and the

electrochemical level is then reduced to the problem of the coupling of two macroscopic entities. Such a coupling is analogous to the coupling between

classical acoustic waves and phonons in crystals. Acoustic waves are classical

waves; phonons are quantum long range modes. Nevertheless, their coupling is

possible and this is nothing mysterious since, as I have stressed several times,

the macroscopic behavior of the crystal "resides" in the phonon modes, so that

the coupling acoustic waves-phonon is equivalently expressed as the coupling

acoustic wave-crystal (which is a perfectly acceptable coupling from a classical

point of view).

Ricciardi and Umezawa stress in their paper that the long range correlation

modes are truly dynamical modes (i.e. dynamically generated) and they"do not

represent a pure speculative fiction; in fact from their observed properties we

must be able to identify them as realistic entities. In this respect a very urgent

The quantum model of brain 83

and significant problem is to measure the energy spectrum of the long range correlation" (Ricciardi and Umezawa 1967).

The interaction of the externaJ stimulus with the brain is, in conclusion, mediated by the electrochemical response. This response sets the boundary conditions such that symmetry is broken firstly in limited regions (coherence domains) of the size of the coherence length. If enough energy comes into play, the coherence domain boundaries may be broken; the domains then merge into larger ordered regions with the establishment oflong range correlation modes and consequent recording of the information. One could speculate that the observed biochemical activity, related to RNA molecules (cf. Section 4.5), may contribute to reducing the domain surface energy thus promoting domain merging. The dynamics of domain formation is the subject of recent studies (Alfinito and Vitiello 2000b-d) which point to a substantial agreement with physiological observations (Greenfield 1997a). I will go back to these issue in the following chapters.

Once the long range correlation has been established, the system then behaves as a macroscopic quantum system and coupling between the long range modes and electrochemical activity becomes possible. At this stage a weak external stimulus, of a nature similar to the one responsible for the printing, may directly excite the symmetrons and induce the recall mechanism.

4·7 Open problems and experimental issues

The model does fit the original requirements suggested by the neurophysiolog­ical observations of memory nonlocality and stability. However, several problems, even of general relevance, are left open. A few of them are as follows.

As I have said, the interaction between the classical electrochemical level and the quantum dynamical level is reduced to the problem of the interaction between two macroscopic systems, since the quantum level manifests itself as a macroscopic quantum state. Although such an interaction becomes thus possible, nevertheless the nature of the coupling remains unspecified in the model. One reason preventing the specification of such a coupling is that the physical nature of the corticon and of the symmetry of the dynamics are not further analyzed. As a matter of fact, they cannot be theoretically assumed outside any experimental observation, i.e. in the absence of an empirical input.

In the next Chapter we will see how Jibu and Yasue give a concrete physical image to the corticon and symmetron, which also leads to specification of the

84 My Double Unveiled

nature of the dynamics symmetry group. The nature of the coupling between the electrochemical activity and the macroscopic quantum state remains, however, an open problem. Perhaps a possible solution is in the formation of coherent

domains of finite size. I will discuss the formation of such domains in Chapter 6 and 7. However, let me remark here that low-frequency (i.e. long wave length) pulsed electromagnetic fields influence EEG of man (von Klitzing 1995).

Another open problem is that of memory capacity. I have named this problem the overprinting problem. It can be illustrated as follows.

Suppose a specific code corresponding to a specific information has been printed in the vacuum. The brain then sets in that state and successive record­ing of a new, distinct (i.e. of different code) information, under the action of a subsequent external stimulus, is possible only through a new condensation

process, corresponding to the new code. This last condensation will superim­pose itself on the former one (overprinting), thus destroying the first registered information.

Only in this way may the new code be registered. Vacua labeled by different code numbers are accessible only through a sequence of phase transitions from one to another one of them. Then, it will be possible to recall only the last recorded information. This is the problem of memory capacity or overprinting

which arises because in the model there is only one kind of symmetry. Stuart, Takahashi and Umezawa (1978) had realized the existence of this

problem and they proposed that in order to allow the recording of a huge number of different information, the model could be extended so as to present

a huge number of symmetries (a huge number of code classes). This, however, would introduce serious difficulties and spoil the models practical use. In

Chapter 6 I will discuss how the dissipative character of brain dynamics may solve the problem of memory capacity without recourse to the introduction of a huge number of symmetries.

The general formulation of the model does not include the specification of

experimental parameters. This is justified since the main objective has been the recognition of structural aspects of the theory. However, it puts severe limita­tions on its experimental testing, which cannot go beyond qualitative aspects.

In any case, it is beyond any doubt that the existence of ordered patterns cannot be detected within the electrochemical activity. The formation of domain structures should be nevertheless experimentally accessible at the coupling of the electrochemical activity with the quantum dynamics.

This suggests two possibilities. From one side, one should be able to detect

the domain formation at a certain stage of the memorization. On the other side,

The quantum model of brain 85

actions aimed at the destruction of formed domains, or inhibiting domain formation, should turn out to prevent the memory printing process (Stuart, Takahashi and Umezawa 1978). But then we are again facing the first men­tioned open problem: namely, the one of the knowledge of the symmetry of the dynamics, so as to be able to know what kind of ordering characterizes the domains we search for or want to act on. A possible solution to such a problem is discussed in the following chapters (cf. Chapter 5, Sections 6.5 and 7.5).

On the other hand, the quantum model ofbrain, together with the dynami­cal model for microtubule formation proposed in the framework of the QFT approach to living matter (cf. Section 3.7), provides a possible understanding of the dynamic features of neuronal cytoskeleton. As we have seen (Section 3.7),

the coherent condensation ofNambu-Goldstone modes in the system ground state, as the one occurring in the quantum model of brain, is the prerequisite for the self-focusing propagation of the electromagnetic field, out of which, in turn, the microtubule formation originates. Microtubule formation and behavior therefore might be taken as the observable effects, at a molecular level, of the underlying quantum dynamics of the brain. At the moment, besides a very detailed phenomenological description, there is no other theoretical or empirical understanding of the highly dynamical behavior of cytoskeleton and of its formation. It is thus interesting to investigate the relation of memory and cognitive functions in general with neuronal cytoskeleton and dendritic arborization. As a matter of fact, in recent years, a great amount of neuro­physiological observations points to the key role played by microtubules in cognitive functions. This could be considered to support the theoretical scheme of the quantum brain model (Pessa, Penna and Bandinelli 2000). It has been observed that neuro-degenerative disorders producing progressive cognitive impairment are strictly related with drastic alterations of neuronal cytoskeleton. In the Alzheimers disease abnormal filaments (helical filaments) appear in neurons, showing modified configurations in the microtubule associated protein tau (PHF-tau), with consequent modifications in the microtubule network observed in affected neurons (Kidd 1984; Brion 1992). At the same time, in the Alzheimers disease abnormalities in the electroencephalographic coherence patterns are observed (Besthorn et al. 1994), which might signal disturbances in the background correlation between brain regions (i.e. in the coherent Nambu-Goldstone condensation). In Picks dementia, in diffuse Lewy body disease and in corticobasal degeneration, several forms of configurational alterations of neurofilaments are observed in the neurocortex (Dickson et al. 1996). In the Creutzfeld-Jacob disease, antibodies reacting with neurofilaments

86 My Double Unveiled

have been detected (Mitrova and Mayer 1989). Also the cognitive impairment in the Huntingtons disease and in the acquired human immunodeficiency virus type 1 (HIV-1) appears to be related with severe abnormalities in the microtu­bule structures (Walling, Baldassare and Westfal1998; Bukrinskaya 1998).

In the following chapters we will see the central role of microtubules in quantum brain dynamics (Chapter 5), in the dissipative quantum brain dynamics, which predicts that formation of correlated neuronal domains is directly related to degree of" openness" of the brain to the external world (as it

is indeed observed) (Chapters 6 and 7) and in the Hameroff-Penrose conscious­ness modeling (Chapter 7).

Finally, I refer the reader to Section 3.9 for those issues related to the persistence of coherence against thermal effects. As explained there the non­perturbative character of the dynamics out of which coherence emerges also acts as a shield against thermal effects.

Let me also remark that recent criticisms (Tegmark 2000) on the use of the quantum formalism in brain modeling (especially addressed to the Penrose­Hameroff model, cf. Section 7.3) are easily countered since in the quantum

model neither the neurons nor other brain cells are treated as quantum objects (as explicitly stated in Ricciardi and Umezawa 1967; Stuart, Takahashi and Umezawa 1979; and Vitiello 1995). Stuart, Takahashi and Umezawa (1978), with a pleasant sense of humor, have remarked that "it is difficult to consider neurons as quantum objects,. The quantum variables in the quantum model of

brain are basic field variables (the electrical dipole field, cf. Chapter 5) and the brain is described as a macroscopic quantum system (cf. Section 4.6). On the other hand, the mechanism by which the quantum superposition in the wavefunction is lost (decoherence) and which has been invoked in these criticisms, points to the failure of quantum mechanics, not of quantum field theory, in quantum modeling the brain ( c£ Section 1.6). The occurrence of the decoherence mechanism does not necessarily imply that classical physics must be applied. Indeed, it has been shown (Alfinito, Viglione and Vitiello 2001) that decoherence provides an useful criterion to determine as well the limits of applicability of quantum mechanics beyond which quantum field theory has to be used.

CHAPTER 5

Quantum brain dynamics

Developments of the quantum model of brain are presented in this chapter. The corticon and the symmetron modes are identified with the electric dipole vibrational mode of protein macromolecules and with the Nambu-Goldstone mode in the coherent dynamics of water, respectively. The intricate network of the cytoskeleton and of the extracellular matrix of protein filaments supports the propagation of the electric dipole vibrational modes and cooperates in the cell-to-cell communication. The holonomic theory ofPribram is presented.

5.1 The physical image of corticon and symmetron 88

5.2 Intracellular quantum signals 89

5·3 Pribram's holonomic brain theory 93

5·4 Microtubules and the electromagnetic field 96

5·5 Cell-to-cell signaling and tissue functional differentiation 99

88 My Double Unveiled

5.1 The physical image of corticon and symmetron

In the original Ricciardi and Umezawa paper (Ricciardi and Umezawa 1967)

the nature of the symmetry group of the dynamics is not specified. As I have already mentioned, in that paper there was no need to specify it, or to specify the related dynamical variables, because the accent was on the structural part of the theory, namely on the dynamical generation of long range correlation in brain. "Ifl would know what kind of correlation, I would be able to write down the Hamiltonian ... ", writes Umezawa referring to the years in which that paper was conceived (Umezawa 1995).

In subsequent papers, Stuart, Takahashi and Umezawa (1978, 1979)

considered the group of continuous rotations around a given fixed axis (the cylindrical phase transformation group) to be the symmetry group of the dynamics and they explicitly carry out the computations to exhibit the sponta­neously broken symmetry solution. They use such a symmetry group as a simple computational example, without pretending that such a group would be the one at work in realistic cases: "the mathematical model given in this Appendix represents an extreme simplification that was intended ... simply to demonstrate the logical possibility of accounting for the macroscopic properties of memory in terms of known physical principles. In particular, we realize the spin operator model represented here is too simplistic" (Stuart, Takahashi and Umezawa 1978).

They further notice that the specification of the dynamics "cannot be done on purely theoretical grounds, but must depend upon the outcome of experi­ments designed to test which symmetry attributes might undergo phase change leading to domain structures" (Stuart, Takahashi and Umezawa 1978).

The quantum model of brain, in such a stage of development, thus provides "a fairly abstract understanding of fundamental physical processes of the brain on the basis of known physical principles in quantum field theory", and it has "much success in showing the logical possibility of accounting for the stability and non-locality of memory as well as its mechanism" (Jibu and Yasue 1992).

In their report to the Eleventh European Meeting on Cybernetics and System Research, held at the University of Vienna in 1992, Mari Jibu and Kunio Yasue named the quantum model of brain "Quantum Brain Dynamics" (QBD) and, noting that "the system of corticons and bosons has been kept abstract and conceptual,, they discussed the possibility of giving this system a "concrete physical image" (Jibu and Yasue 1992).

Quantum brain dynamics 89

Jibu and Yasue, on the basis of the analysis of the protein filaments span­ning inside and outside of the neurons and astrocytes, assume that the Frohlich and Davydov mechanisms may well provide a concrete physical image of the corticon. They thus take ··a quantum of Frohlich longitudinal electric mode, as a corticon in QBD (Jibu and Yasue 1992). The corticons are thus given the physical image of quanta of Frohlich electric dipole vibrational fields.

Protein filaments inside and outside both neurons and astrocytes are embedded in water. As already discussed ( cf. Chapter 3) in relation to the QFT approach to living matter, the coupling of the electric dipole vibrational quanta on the network of protein filaments with the quanta of the water electric dipole field may produce deformation of the water configuration, and, consequently, breakdown of the symmetry of the water dipole dynamics.

We have seen the rest of the story when we have discussed the QFT approach to the general case ofliving matter: Nambu-Goldstone bosons are then generat­ed and ordered patterns (in-phase dipole oscillations) arise. These bosons have been called the dipole wave quanta ( dwq). The symmetrons of the brain model are identified by Jibu and Yasue with such Nambu-Goldstone bosons.

The Ricciardi and Umezawa model, from one side, and the Davydov soliton theory on a-helices and the Frohlich model, on the other side, were indepen­dently formulated in roughly the same years. The Davydov and Frohlich models, later on incorporated in the QFT approach to living matter, pointed to the description ofliving matter in general, whereas the former was formulated to describe in particular brain functions. The work by Jibu and Yasue shows that these theories actually share the same unifying dynamical view and opens the way to a number of interesting developments.

5.2 Intracellular quantum signals

The identification of the corticon with the quantum of the dipole vibrational field and of the symmetron with the Nambu -Goldstone boson (the dwq) of the water dynamics makes the quantum brain model more concrete and realistic.

Let me remark firstly that the concept of the neuron as processing element with somewhat a fuzzy boundary surface (Stuart, Takahashi and Umezawa 1978, L979) (cf. Chapter 4) plays a crucial role in the Jibu and Yasue analysis. Such a concept allows them to represent the dwq propagating as an intracellular

quantum signal in the whole cell assembly of the brain (Jibu and Yasue 1992-1995; Jibu et al. 1994; Jibu, Yasue and Hagan 1997; Jibu, Pribram and Yasue 1996; see also Jibu 2001b).

90 My Double Unveiled

Physiological observations show that the activity of the brain involves an intricate structure of protein filaments extending inside and outside the neuronal membrane, forming a filamentous web. Such a physical network, intrinsic to the neuron cell and to the extracellular matrix outside the neuron is quite well known in its biochemical structure. The cytoskeletal portion of the network contains mainly tubulin dimers, and the rest is mainly actin and myosin filaments; the extracellular matrix mainly consists of collagen filaments. The connection between the cytoskeleton and the extracellular matrix is made by transmembrane proteins. A common feature to all these protein filaments is that their molecular components possess an electric dipole moment. This means that vibrational dipole waves may propagate on the huge filament network, inside and outside the neuronal membrane, disregarding the mem­brane boundary.

It should be recalled that besides the neurons there are also the astrocytes in the brain. The cytoskeleton structure is also present in these glial cells and it is also connected to the protein filaments of the extracellular matrix. There are ten times more astrocytes than neurons in the brain. Although traditionally the astrocyte cells are not considered relevant to brain functioning (the ((neuron doctrine"), nevertheless from a physical point of view there is no reason to neglect them since the electric dipole properties of their cytoskeleton network are the same as the ones of the neuron cytoskeleton. In conclusion, we have vibrational dipole waves propagating in the brain tissue along the pathway of the huge, intricate protein filamentous web.

The vibrating electric dipoles belong to the atomic and molecular constitu­ents of the proteins, which are quantum objects. We are thus allowed, as usual in quantum theory, to associate to the vibrational dipole waves (or fields) the corresponding quanta (recall that in a quantum theory the wave representation is equivalent to the particle representation in terms of quanta (the comple­mentarity principle)). These quanta (the corticons) thus propagate over the protein network.

Now consider that the full network of protein filaments is embedded in water. The electrical dipole structure of water molecules, as discussed in Chap­ter 3, is also representable in terms of a dipole vibrational field. The water dipole quanta may then be coupled to the corticon quanta propagating along the network. The result of such an interaction is a coherent vibrational mode of the water molecule dipoles. The coherence manifests itself as correlation among the water dipoles over long distances (long with respect to the molecular size): this correlation can be described in terms of correlation waves (or fields), and

Quantum brain dynamics 91

their corpuscular representation in terms of quanta. The Nambu-Goldstone boson or dipole wave quanta (dwq), indeed, are the symmetrons of the quan­tum brain model.

Once the water surrounding the network has been set into the coherent dynamical regime, the interaction among corticons may produce deformations in the water dipole long range correlation, in other words it produces excitation of dwq (symmetrons). The net result is that corticon interaction is mediated by dwq: the dwq act as information carriers, or "signals", exchanged by the

corticons. The information carried by these signals is about the dynamical state of the corticons and about the state of the water dipole correlation, and it is channeled through the bulk of coherent water structure and the filament network: the propagation of such signals is very efficient since the dwq are massless quanta. Efficient propagation means that the information propagation range covers the whole coherent domain without inertia and without distor­tions, which also means that information propagation is stable against decay processes, since it occurs in a state of a very low energy, very near to the lowest energy state (the ground state) of the system (dwq oflowest momentum carry very small amount of energy since they are massless): in other words, the information flux through the system is (almost) persistent. The conclusion is that we have intracellular quantum signal transfer via dwq.

On this basis }ibu and Yasue also propose a possible understanding of the mechanism of anesthesia. Although anesthesia is widely used in surgery and anesthetic practice is quite well developed, its theoretical understanding does not rest on a firm basis, so that it is not clearly understood why anesthetic substances cause anesthesia. According to }ibu and Yasue, anesthetic substances interfere with the intracellular signal transfer by causing defects in the water organization with consequent collapse of the propagation of the symmetron modes, or in other words, breaking up the long range correlation in the system. The onset of anesthesia is thus seen as the consequence of the loss oflong range correlation. This in turn is due to the breaking, caused by the hydrophobic anesthetic molecules, of the hydrogen bonds in water crystalline structures in the vicinity of neurons and astrocytes in general anesthesia and in the vicinity of other cells in local anesthesia. The hydrophilic anesthetic molecules on the other hand may prevent the water ordering by gathering around the electric dipoles of the protein filaments (Jibu and Yasue 1993b).

In conclusion, the physical image of the corticon and of the symmetron rests on the propagation of the dipole vibrational quanta along the protein filaments (also according to the Davydov proposal) and in the surrounding

92 My Double Unveiled

water, and on the spontaneous breakdown of the water dipole rotational symmetry (as in the QFT approach). Thus it provides a unified view of living matter physics and brain dynamics.

Umezawa writes (Umezawa 1995): " ... we realized that the long range correlation of the kind Ricciardi and myself thought cannot be confined to the neural domain; as a matter of fact, we found that the boundary is a fuzzy one". Jibu and Yasue's work is essentially based on such a view and they observe that in fact intracellular quantum signal transfer may "possibly explain the overall existence of a secret network of meridian pathway conduction of Qi in our body, which is the central dogma in the Chinese and Japanese traditional medicine. There, each physiological tissue is tacitly controlled globally by the whole system of intracellular quantum signal transfer via Goldstone bosons propagating along the extremely huge overall network of cytoskeleton and extracellular matrices of all human cells forming the meridian, ( Jibu and Yasue 1993b). The "unknown object called Qi" is identified in this view with the dwq Goldstone boson. An interesting relation between synchronicity and coherent excitation in microtubules and the Jungian archetypes has been made by Insinna (Insinna 1992).

Let me add one more comment on the words secret and tacitly used by Jibu and Yasue in the above remarks on the Qi conduction. The Jibu and Yasue metaphor tacitly controlled reminds me of the absence of inertia in the propaga­tion of the dwq, and thus of the lowest energy level (state) in which it occurs. That the network of meridian pathways is secret means that it cannot be anatomically observed in the body dissection. However, in the living body one may act on the meridian pathway by a convenient procedure, e.g. by acupunc­ture, whose therapeutic effects are now recognized also in western medicine (although no "scientific" justification or explanation exists for it in medicine or molecular biology). Such a metaphor used by Jibu and Yasue could also be applied to phonons in a crystal. According to my discussion in Chapter 1, you may observe the scattering of particles, e.g. neutrons, with the phonons in a crystal; however also the phonons are secret: if you destroy (dissection) the crystal, you do not find the phonons among the resulting "anatomical pieces". This brought us to the conclusion that any distinction between structure and function is meaningless. Perhaps we can also conclude that the "anatomical" search for Qi is meaningless for the same reasons which make meaningless the search of the phonons among the pieces of a broken crystal.

Quantum brain dynamics 93

5·3 Pribram's holonomic brain theory

In the book Brain and Perception Karl Pribram (Pribram 1991) outlines his holonomic brain theory. His starting point is the original question asked by Lashley, since 1942, on the possibility that in neurophysiology something like interference patterns and interference phenomena could arise as an effect of the subjects experiences (Lashley 1942). The question was stimulated by Lashley's work showing the diffuse, non-local nature of brain activity. The intuition that the interference of some kind of waves is going on in the brain activity received a stronger support when holography, whose theoretical study starts with Gabor, since 1946 (Gabor 1946, 1968), became a reality with the discovery of the laser light in the early 1960s (Klauder and Sudarshan 1968; Arecchi et al. 1972). Soon

after that Pribram proposed his holographic hypothesis and then his holonomic brain theory.

Let us see why non-local activity of brain suggests looking for interference phenomena and holography, and what this has to do with the quantum brain dynamics discussed in this chapter.

The interference phenomenon occurs when one sums up two wave distur­bances and goes to look at the resulting wave motion amplitude. Consider two waves, e.g. for simplicity two sinusoidal waves, of the same wavelength traveling with the same speed in the same direction, with or without the same amplitude. Let them be shifted from one another in such a way that the crest (the maxi­mum amplitude) of one of them does not coincide with the crest of the other one. The measure of such a shift in units of the wavelength is called the phase

difference of the waves. A phase difference constant in time thus means that the shift of the waves does not change in time. lf the shift is such that the crests of the two waves almost coincide or they are only a little displaced from each other, the amplitude of the total wave disturbance is the sum of the two crests heights (the amplitudes of the component waves). ln such a case the wave disturbance will be enhanced and one says that the interference is constructive. On the contrary, when the shift (phase difference) is such that the crest of one of the two waves gets located in correspondence, or almost in correspondence, to the minimum of the other wave, the amplitude of the resulting wave distur­bance is equal to the difference between the waves amplitudes (it is almost zero if the waves have equal amplitudes) and the interference is said to be destruc­tive. The amplitude of the resulting wave disturbance is thus controlled by the definite phase difference of the two components waves. Waves propagating with phase difference constant in time are said to be coherent waves. The observation

94 My Double Unveiled

of the resulting wave disturbance amplitude thus provides the information on the phase differences among the constituent waves.

Interference patterns are obtained, for example, when two coherent (i.e. with constant phase difference) beams of light of the same frequency collide at the same point on a screen. In such a case the difference in the traveling paths of the two beams to reach the given point on the screen results in a further phase difference. Different points on the screen thus correspond to different path differences, and therefore to different phase differences. The degree and the nature of the interference (more or less constructive or more or less destructive) will then depend on the positions on the screen where the beams collide. In this way, interference patterns are obtained on the screen. From the degree of "brightness" or "darkness" of the point one may reconstruct the phase difference at that point. One might then use the numbers representing the phase differences among a set of waves to encode some information. Reading out the interference amplitude then corresponds to decoding, i.e. recovering, the original information.

Let me observe that in order to compute the intensity (the "brightness" of a point on the screen) of the resulting wave in the interference phenomena, one must first add the component waves and then square the resulting amplitude. In other words one must follow not the "classical" rule which says "first square and then add", but the prescription which is the basis of the computation in quantum theory: "first add and then square". By following the classical rule one would lose any information on the phase difference ("squaring" means com­puting the modulus square. thus missing the phase factors) which is the crucial ingredient controlling the interference. This also suggests that coherence (which is a necessary condition in order to have interference) would not be seen in a classical computation.

The reason why two beams of natural light do not produce interference patterns on a screen is that the electromagnetic (em) waves of natural light have non-constant phase differences: natural light is not coherent. One must then devise careful settings to observe interference patterns, trying to produce coherent sources of waves, i.e. of waves with constant phase differences for each given frequency. The em waves entering the natural light are generated by excitation and de-excitation processes involving the atoms of the light source. These processes are random, i.e. they do not occur at the same time or within definite, regular intervals of time; atoms behave incoherently, not in a coopera­tive way, like musicians of an orchestra tuning their instruments before the concert starts: they produce something much more near to noise than to music.

Quantum brain dynamics 95

Thus there are random phase differences among the em radiation waves emitted in each atomic process. Since the 1960s, however, it has been possible to build devices able to induce in the atoms of specific materials cooperative emission of em waves. The light coming out from such an "orchestra" is the laser light. Laser light is thus realized from coherent emission of em waves of given frequency. The interference patterns obtained with laser light are called holograms, and the spectacular thing is that once one knows what the pattern looks like in a specific, small region of the hologram, one may reconstruct all the remaining parts of the pattern. This is practically impossible to do with natural light because of the unavoidable fluctuations in the phase differences of the interfering waves. [f one thinks of the holographic pattern as a "picture" of something, then from a small piece of it one may reconstruct the whole picture. The features impressed in a specific region can be recovered by exploring any other region of the picture: the information is not localized in a specific region, it is diffused everywhere in the picture. We have non-local encoding of the information.

It should be now clear to the reader why holography and wave interference are inspiring phenomena in modeling the non-local processes of memory and perception in natural brain. This was the original Pribram proposal. However, many objections were raised against the holographic brain model. An analysis of the objections can be found in the above quoted book by Pribram. There he especially notices that the main difficulty arises when one does not take into account the full setting of the holographic scenario, limiting oneself to consider the space-time picture or description of the phenomenon. Actually one should consider the full complex of space-time and spectral analysis involved in holography, as in fact Gabor originally did.

Interference phenomena and holography are based on the possibility of relating space-time variables and frequencies, i.e. the spectrum, of a wave signal. In mathematics, through the so called Fourier analysis, it is always possible to describe the space-time properties of a signal in terms of its spectrum proper­ties; the signal is in this way represented as the sum of its spectral components, namely of component waves of specified amplitude, frequency and phase. It is therefore crucial to include the spectral domain besides the configurational (i.e. the space-time) domain in the analysis of brain memory processes. The term holonomic, instead of holographic, is then used by Pribram in order to stress such a circumstance: thus holonomic refers to representations in the space of the states defined by both spectral and space-time coordinates. These representations are constrained by dynamical processes. They thus differ from

96 My Double Unveiled

structural representations which are constrained by more permanent con­straints (Pribram 1991).

Properly taking into account the spectral domain also implies limits in the

accuracy of simultaneous measurements of conjugate variables, such as position and momentum, already pointed out by Gabor, and leading to a formalism of the same nature as Quantum Mechanics where the uncertainty relations hold. A further consequence is that in the holonomic theory efficiency processing must be based on the spectral resolution of the signal in a way consistent with the uncertainty relations.

The mathematical formalism developed for the holonomic theory turns out to have even more contact points with the quantum formalism. In fact Yasue, Jibu and Pribram have shown that the neural wave equation, describing the interaction between the polarization oscillation modes of the membrane dendritic network and the charge carriers (ionic bio-plasma), has the same form as the Schrodinger equation in Quantum Mechanics (see the Appendix A in Pribram 1991). It appears in this way that holonomic brain theory and quan­tum brain dynamics have a common root in the neurodynamics of the dendritic network. Moreover, coherent dynamics at the level of cytoskeletal microtubules have further consequences, as we will see in next section.

5·4 Microtubules and the electromagnetic field

In Chapter 2 we have seen that in the ordered medium the electromagnetic (em) field may propagates in filamentary fashion, thus providing a possible mechanism for the cytoskeleton formation. The em field in this way gets confined in the core of the microtubules. There the correlation of the medium disappears and the em field propagate coherently; such a kind of propagation has been called "self-focusing" propagation (cf. Chapters 2 and 3). Moreover, the analysis shows that a delay in the em propagation should be expected, which corresponds to the time needed to reach the energy threshold necessary for the self-focusing propagation regime to occur. It has been suggested (Del Giudice et al. 1986) that such a kind of propagation could account for some interesting experiments on the propagation of light in living tissues (transparency) (Mandoli and Briggs 1982). The study of coherent dynamics in water molecules, treated as a system of electrical dipoles interacting with the quantized em field, has shown the emergence of collective modes with features oflaser-like behav­ior (Del Giudice, Preparata and Vitiello 1988b). The system exhibits frequencies which fall in three distinct bands around 1600, 750 and 400cm-1

, which is in

Quantum brain dynamics 97

acceptable agreement with the observed absorption bands of pure water located at 1640, 580 and 180 cm-1

. Moreover, in the presence of an impurity carrying an electrical dipole (such as protein macromolecules) a permanent electric

polarization emerges which signals the occurrence of ordered structures in domains of a few hundreds of microns in size. It must be stressed that the time scale associated with the coherent interaction is computed to be of the order of 10-14 sec, thus much shorter than times associated with short range interac­tions, and therefore these effects are well protected against thermal fluctuations (Del Giudice, Preparata and Vitiello l988b) (see also Section 3.9).

On the other hand, since 1974 Hameroff (1974) has suggested that, in the understanding of brain activity, one could consider microtubules to be acting as waveguides for photons and holographic information processors. Also considering the coherent excitation of tubulin subunits, he proposed that microtubules could be the basis of computational cellular automata. Further studies have been made by Jibu, Hagan, Hameroff, Pribram and Yasue (1994) who have shown that the dynamics of the water molecules interacting with the em field inside the microtubules is quite similar to the dynamics first consid­ered by Dicke (Dicke 1954) in the study of coherent photon emission without external energy pumping. Such a phenomenon, which is called superradiance, occurs when matter interacting with an em field has a transition from incoher­ent microscopic motion to a coherent and ordered motion which in turn induces a collective emission of coherent photons. These results confirm and extend the above mentioned conclusions on the coherent laser-like dynamics of water: once the collective mode is created in the dynamics of water molecules, coherent emission of pulse modes of the quantized ern field (photons) follows (superradiance). The superradiant solutions have been found for any incoher­ent and disordered initial conditions, thus confirming that coherence is not affected by thermal fluctuations (Jibu et al. 1994).

The generation of photons through superradiance opens new perspectives on the study of holographic phenomena in the dendritic network. [t appears that there is an actual possibility of propagation of optical coherent signals in the microtubule pathway. A suggestive scenario thus opens which adds optical information encoding to the electrochemical information propagating on the neural network. The analysis of the propagation equations shows that propaga­tion of photons in microtubules may occur without damping and losses due to thermalization and other disturbing interactions. In other words, due to nonlinear effects it appears that pulse mode of coherent photons propagate through microtubules as if they were perfectly transparent (Jibu et al. 1994).

98 My Double Unveiled

This phenomenon, well known as a typical nonlinear effect in quantum optics (McCall and Hahn 1967), is termed self-induced transparency.

Superradiance and self-induced transparency are thus dynamical mecha­

nisms which put the cytoskeletal structure of microtubules in a central position for the understanding of the brain activity. In this respect, the observation (Wulf and Featherstone 1957; Franks and Lieb 1982) is most interesting that anesthetic binding within protein hydrophobic regions altered protein-water binding at the protein surface. Such an interference with the water dynamics clearly affects the superradiance and the self-induced transparency phenomena. Moreover, anesthetic substances have been shown to bind to microtubules and at high enough concentrations they cause depolymerization (Allison and Nunn 1968). This finding thus show that coherent microtubules dynamics may play a relevant role in controlling different degrees of awareness and consciousness, and they also support the Jibu and Yasue proposal explaining the anesthesia mechanism (see Section 5.2).

Finally, the existence of distributed patterns of activity in the huge dendritic network has been suggested (Jibu, Pribram and Yasue 1996) to originate from the condensation of the massive em modes generated in the Anderson-Riggs­Kibble mechanism presented in Chapter 2 (see also Chapter 3). In particular, the dendritic perimembranous regions have been studied. The interior of dendritic membranes is hydrophobic and is formed by a fluid matrix of lipids within which protein molecules are embedded. The lipids can move laterally at a rate of2jlm/sec. The protein molecules move about 40 times more slowly, at 50 nm/sec (Shepherd 1988). Some channels of ions through the membrane are also present. The outer layer of the membrane is also composed of phospholipid molecules to which long-branching structures made of carbohydrate molecules are attached. These structures are wiggling through the extracellular space and attract water molecules (Shepherd 1988). Jibu, Pribram and Yasue ( 1996) have proposed that in these extracellular compartments Bose condensation of dipole wave quanta (dwq) (the Nambu-Goldstone bosons generated in the process of water ordering) occurs and ionic charges, such as Ca2+, Na+ and K+, act as the sources of em perturbation waves. Due to the Anderson-Higgs-Kibble mecha­nism these em fields acquire an effective non-zero mass and propagate (in a self-focusing manner) as massive photons. These photons have been termed evanescent photons since their propagation is squeezed to filamentary paths (it is not representable in spherical waves as in the case of Maxwell massless photons). The evanescent photons, together with the dwq, are proposed to be the substrate for the dendritic perimembranous activity.

Quantum brain dynamics 99

In conclusion, the role of microtubules in the cytoskeleton structure of the cell as well as in the dendritic arborization appear to be of primary relevance to the brain activity. The basic mechanism of dipole wave quanta condensation

appears to control the evolution of the intricate structures of microtubules at the level of the brain cells and at the higher level of the dendritic network. On the other hand, external agents may affect the functioning of these intricate structures by interfering with the water dipole dynamics.

Also in other contexts which are not specifically related to Quantum Brain Dynamics, such as the theoretical scenarios proposed by Penrose (1989, 1994) and by Hameroff and Penrose ( 1996a) (see also Hamer off 1998b ), the modeling of brain activity and consciousness is focused on microtubule structures, as I will briefly illustrate in Chapter 7.

5·5 Cell-to-cell signaling and tissue functional differentiation

In Chapter 3 I have reported about the experimental observation that in the blood coagulation process red blood cells (erythrocytes) appear to interact over distances greater than the range of chemical forces thus leading to the forma­tion of cell rouleaux (Rowlands 1988). In other words, the cells communicate, or "see" other cells over long distances. Such a long range interaction disappears when a)the cells are depleted by the source of energy, but it is restored when metabolic energy is supplied again; b) the cell membrane potential is reduced to zero; c) the cell membrane is disorganized by addition of poisons. If we maintain that cell interaction is mediated by the long range correlation modes of the coherent dynamics in the water surrounding the cells, the above actions inhibiting the red blood cell interaction could be actually responsible for the destruction of the coherent domains in water, or they can even prevent the formation of such domains. Of course, long range interaction does not exclude short range chemical interaction. On the contrary, the latter is favored once the cells, correlated by the coherent dwq fields, come to a smaller distance such that chemical bonding becomes possible. In particular, selectivity of chemical bonds may be in this way favored since long range interaction in red blood cells appears to be specific: preferential rouleau formation is in fact observed among cells of same species when a mixture of different types of cells is examined (Rowlands 1988).

The rouleau formation of red blood cells is an example of cell-to-cell interaction over long distance. It suggests that in other situations such a

100 My Double Unveiled

"communication, among cells, mediated by the surrounding water coherent domains, is also possible. Recent observations have in fact shown that resonant intermolecular transfer of vibrational energy in liquid water is particularly efficient due to dipole-dipole interaction, which suggests that water may play an important role in transferring energy between different biomolecules or along extended biological structures (Woutersen and Bakker 1999).

If confirmed, some experimental observations by Albrecht-Buehler (1992) appear to be particularly interesting. They seem to point also to a form of cell­to-cell communication mediated by em signals (in this connection see also Pohl 1980; Gutzeit 2000; and Pokorny 2000). More specifically it seems that the cell may be the source and the receiver of em signals. In these observations, so­called 3T3 cells show ability to locate and approach microscopic sources of pulsed infrared light (of wavelengths between 800 and 900 nm) up to a distance on the order of 50 microns. They produce surface projections (pseudopodia) orienting towards single distant sources. In order to give a theoretical under­standing of such a phenomenon, which remains unexplained in terms of biochemical activity, }ibu, Yasue and Hagan ( 1997) have proposed that the

infrared em waves generated by the microscopic sources act as an energy pump able to trigger the lasering regime in the coherent water surrounding the cell, provided its intensity is above a certain threshold (which in Albrecht-Buehler experiments is on the order of 0.48mW per square em). As I have already explained in this chapter and in Chapter 3, the coupling among the water electric dipole molecules and the em field may generate coherent em modes (photons) oflaser-like nature. The source of infrared light of adequate intensity provides the energy to stimulate the laser-like behavior in the cooperative mode of the water molecules. These coherent laser-like pulses represent the signals, transmitted through the water medium, that the cell receives from the infrared sources. As a response, the cell then produces the pseudopodia trying to reach the light source. Jibu, Yasue and Hagan show how the thermal losses and thermal fluctuations enter into the process of triggering of laser pulses in coherent water domains. They also give a quantitative treatment relating the lasering process to the intensity threshold of the infrared light source. More­over, they show that below such a threshold cell-to-cell communication is still possible and is mediated by the dwq of the intracellular coherent water do­mains, thus confirming the picture of cell communication described above.

One further point may be added to such an analysis, which has to do with the cells reaction upon receiving the signal from the infrared source. As noted above, the cell produces pseudopodia which project themselves towards the

Quantum brain dynamics 101

light source. The formation of these pseudopodia is of a dynamical nature and difficult to understand solely in terms of chemical mechanisms. These chemical mechanisms must be highly efficient and highly selective (in their spatial distribution pointing to the source). In order to achieve such levels of efficiency and selectivity, however, some sort of"wave guide" may be needed. The filamen­tary propagation of the em fields in ordered medium introduced in Chapter 2

and 3 now comes to our aid. In Chapter 3 I have discussed the formation of microtubules as due to the chemical coating of the em field propagating in filamentary fashion in the ordered water domains. The cell pseudopodia projecting themselves towards the light sources could possibly be generated by a similar coating of the em field propagating from the cell to the light source in filamentary self-focusing fashion through the ordered water. In this way, the coherence of the surrounding water again enters into play, this time by helping to channel the cell "reply" to the signal received from the source.

In the case of cell-to-cell interaction the extracellular matrix of micro­tubules may be dynamically generated by the chemical coating of the filamenta­ry network of the em fields which percolate the coherent domains of intracellu­lar water. In this way the intricate pathway of cell interconnections is construct­ed. The different biochemical nature of different tissues may then result in different formation/ depletion times of the extracellular matrix and in different levels of stability/instability of the chemical bonds of the extracellular matrix. In a word, the softness or plasticity of the tissue may be a determinant factor in the insurgence, persistence and dynamical evolution of cell-to-cell signaling. In a given assembly of cells (tissue), those functional properties related to intracellu­lar signaling may be thus affected (regulated or ruined or enhanced) by acting at a biochemical level; or else, functional differentiation in different tissues may be ascribed to their different biochemical nature (different cell species and/ or the presence or the absence of different biomolecules) in the sense that such biochemical differences sustain different dynamical regimes in the extracellular matrix formation and evolution, and in this way different functional properties (associated to intracellular signaling) appear. It should be also remembered that the propagation of electric dipole waves over the extracellular matrix feeds back to water molecule dipoles by acting on their coherent dynamics.

These remarks on the tissue functional differentiation may help in answer­ing the natural question of the different functional behavior of the brain with respect to other tissues. From one side, we reach the unified dynamical scheme for living matter and brain. From the other side, we must provide an account of the specificity ofbrain functioning. From the above remarks we could say that,

102 My Double Unveiled

apart the obvious specificity of the brain cells, in the brain we must expect

much more softness in the tissue, in the sense that the extracellular matrix may

adjust itself much more easily to different regimes of signal transfer with consequent feedback to the water coherent domains. In other tissues we could expect more «crystallized, structures. In other words, brain tissue should respond much more to external stimuli than other tissues, the level of the

response being measured by the rapidity and flexibility in the dynamics of the

microtubules network with consequent feedback to the water coherent dynam­ics. We are thus brought to consider one crucial aspect of the brain system,

namely the fact that it is an open system, permanently interacting with the environment. As we will see in next chapter, the intrinsic dissipative character

of the dynamics will also solve the problem of the memory capacity of the quantum model of brain (mentioned in Section 4.7).

CHAPTER 6

Dissipation and memory

The brain is an open system in permanent interaction with the environment. This implies that quantum brain dynamics must be a dissipative dynamics whose treatment requires the doubling of the system degrees of freedom. Dissipation is shown to play a crucial role in memory processes allowing a huge memory capacity and thus solving the overprinting problem in the quantum brain model. The breakdown of time reversal symmetry, intrinsic to dissipative dynamics, manifests itself as the commonly experienced arrow of time. Some recent work on neural net simulations is also presented.

6.1 The brain is an open system 104

6.2 Now you know it!... 106

6.3 Quantum dissipation 108

6.4 Dissipative quantum brain dynamics 111

6.5 Life-time and hierarchy of memory 115

6.6 Collective modes on neural nets 117

104 My Double Unveiled

6.1 The brain is an open system

Any attempt to formulate a model for the brain cannot avoid considering the

basic fact that the brain is an open system in interaction with the external

world. The quantum model of brain is based on such a basic fact. In the quantum model. indeed. information printing is achieved under the action of external stimuli, which produce the breakdown of the symmetry associated with

the electric dipole vibrational field. The ((openness" of the brain to the external world means that it is perma­

nently coupled to the environment. Of course, this is a feature common to any living system, not specific to the brain system. Any living system exchanges

matter and energy with the environment and such an exchange is essential to its survival. In the QFT approach to living matter we have seen how the energy

feeding of the living system triggers, through the ATP reaction, the nonlinear dynamics on the protein macromolecules with the consequent chain of dynami­cal mechanisms described in Chapter 3. The brain of course is also «living

matter" and as such also falls in the same QFT scheme. It presents several levels

of organization which are not simply derivable from structural features. Its same «story" or evolution in time, cannot be solely explained in terms of structural features. The basic dynamical processes play a key role. The functional specifici­

ty of the brain requires, however, that the brain system must possess much greater capability to «respond" to external inputs. Living matter in general may

be less sensitive and less prompt to respond to external stimuli. As we have seen in the previous chapters, however, the boundary of the brain system is a ((fuzzy boundary" (in Umezawa words) and we could express this by saying that there is a sort of«diffused intelligence" permeating the full body through the intracel­lular signal network. Thus, in a list of "specific properties" of the brain one must include very short reaction times to external stimuli, the highest possible «resolution" power among different stimuli, an enormous capability to «collect experiences", i.e. a very large memory capacity, but also a very efficient "ar­

chive" organization and a very quick memory retrieval. I am certainly not pretending here to give an exhaustive list of the properties required by the

brains functional activity. My only intention is to observe that even from a very rough and short list of properties of the brain system, lets say the more obvious and immediate properties that come to my mind, one unambiguously derives that the brain cannot be treated as an isolated system. Moreover, this same short list also shows that the brain is a system far from the equilibrium (also a

common property of living matter in general).

Dissipation and memory 105

In the above remarks I have been talking of the brain and of living matter

as macroscopic systems. The sensitivity to external stimuli is however to be considered not only as the macroscopic reaction to external inputs. It should be

also possible to investigate the reaction mechanisms at the level of the micro­scopic dynamics. On the theoretical side, this means that the investigative tools must be adequate to treat the microscopic dynamics able to describe the open,

far from equilibrium systems under study. This leads to a series of difficult problems to be solved since quantum theories (Quantum Mechanics and QFT)

have been formulated to study isolated systems. It is not fully understood (apart suggestions coming from Statistical Mechanics) how does it happen that time

flows only in one definite direction for macroscopic systems (all of us have experience of the arrow of time definitely pointing to the future), although

physical laws show no preferred direction for the time flow at a microscopic level; in other words, how does it happen that from the microscopic physical laws, which appear to be preserved in their form under reversal of the time evolution direction (time reversal symmetry), there may emerge at a macro­

scopic level the breakdown of such time reversal symmetry.

On the other hand, the problems to be faced on the experimental side are not easier ones. Systems which are far from equilibrium are difficult systems to test. The prescription of the reproducibility of the experiment, a golden rule of Galileian science, is hard to satisfy for such systems, since it is difficult, if not

impossible, to exactly reproduce the same boundary conditions in different experiments. Sometimes it appears that statistical treatment of the data is not of great help. Moreover, the high sensitivity of biological systems to weak fields

and forces and the non-perturbative, nonlinear character of their microscopic

dynamics require a high level of accuracy in any sort of experimental work. Finally, in the quantum model of brain there is the already mentioned

memory capacity problem, which I have termed the overprinting problem ( cf.

Chapter 4). At first sight, this problem seems to be not related to the fact that the

brain is an open system. One would be tempted to consider the memory storing capacity as a property related to static, structural features of the system, not depending on its relation to other systems or to the environment. It happens to

the contrary that the memory capacity is strictly dependent on the system dissipativity, namely on the fact that the system exchanges energy with the environment. This constitutes the starting point of my analysis in this chapter. The following section is in fact devoted to a very simple, however crucial remark: dissipativity must be included in the quantum model of brain as one of

106 My Double Unveiled

its basic ingredients. Thus I will discuss the extension of the quantum model of

brain and of its developments presented in Chapter 5 to the dissipative dynamics.

6.2 Nowyouknowit! ...

It might be useful to summarize a few aspects of the quantum brain model

introduced in Chapter 4. Let me remind that the observable specifying the

ordered state is called the order parameter and acts as a macroscopic variable for the system. The order parameter is specific for the kind of symmetry

brought into play and may thus be considered as a code specifying the vacuum

or ground state of the system. The value of the order parameter is related to the density of condensed Goldstone bosons in the vacuum and specifies the phase

of the system in relation to the considered symmetry. Code numbers specifying

the phases may be thus organized in classes corresponding to different kinds of dynamical symmetry.

In the quantum model ofbrain the information storage function is repre­

sented by the coding of the ground state through the condensation of the dipole

wave quanta (denoted as dwq and identified with the symmetrons). In such a model only one kind of symmetry is assumed (the dipole rotational symmetry).

Thus there is only one class of code numbers.

Suppose a vacuum of specific code number has been selected by the

printing of a specific information. The brain then sets in that state and no other vacuum state is successively accessible for recording another information,

unless the external stimulus carrying the new information produces a phase

transition in the vacuum specified by the new code number. This will destroy the previously stored information, so we have overprinting. vacua labeled by

different code numbers are accessible only through a sequence of phase

transitions from one to another one of them.

The existence of such a problem of memory capacity was already realized by

Stuart, Takahashi and Umezawa (1978), who admitted that the model was too

simple to allow the recording of a huge number of information data. These

authors then proposed that the model could be extended in such a way as to

present a huge number of symmetries (a huge number of code classes) and «a

realistic model would therefore require a vector space of extremely high

dimensions" (Stuart, Takahashi and Umezawa 1978). Such an extension,

however, would introduce serious difficulties and spoil the models practical use.

I will show that, by taking into account the fact that the brain is an open

Dissipation and memory 107

system, one may reach a solution to the problem of memory capacity which

does not require the introduction of a huge number of symmetries. Even by allowing only one kind of symmetry, infinitely many vacua are accessible to

memory printing in such a way that in a sequential information recording the successive printing of information does not destroy the previously recorded ones: a huge memory capacity is thus achieved (Vitiello 1995). Taking into account the dissipative character of the open brain system, namely its perma­nent energy exchange with the environment, is crucial in reaching such a result.

In the quantum brain model spontaneous breakdown of dipole rotational symmetry is triggered by the coupling of the brain with external stimuli. Here,

however, I want to call attention to the fact that once the dipole rotational symmetry has been broken (and information has thus been recorded), then, as

a consequence, time-reversal symmetry is also broken: Before the information recording process, the brain can in principle be in anyone of the infinitely many

(unitarily inequivalent) vacua. After information has been recorded, the brain state is completely determined and the brain cannot be brought to the state configuration in which it was before the information printing occurred. What

I am saying is nothing but the content of the well known warning .. . NOW you

know it! ... , which tells you that since nowyou know, you are another man, not

the same one as before ... Once you have known, you cannot go back in time (Paci 1965).

Thus, the same fact of getting information introduces the arrow of time into

brain dynamics. Due to the memory printing process, time evolution of the

brain states is intrinsically irreversible. Stated differently, getting information introduces a partition in the time evolution, it introduces the distinction

between the past and the future, a distinction which did not exist before the information recording. This is also the content of the (trivial) observation that "only the past can be recalled": memory printing breaks the time-reversal

symmetry of the brain dynamics and this is another way to express the (obvious) fact that brain is an open, dissipative system coupled with the external world.

For a discussion on the emergence of the arrow of time in brain dynamics in the non-critical string theory see also Mavromatos and Nanopoulos (1995-1998).

Ricciardi and Umezawa (1967) have studied the brain's non-stationary or quasi-stationary states in the stationary approximation, thus avoiding damped oscillations. In the following discussion, on the contrary, I will consider non­

stationary states without using the stationary approximation. In order to do that I have to resort to some results obtained in the study of dissipative quantum systems, which I will do in the next section.

108 My Double Unveiled

6.3 Quantum dissipation

In QFT (but also in Quantum Mechanics) the energy of the system under

study is normally assumed to be a constant of motion. namely one assumes that

the energy is time independent. One makes such an assumption for a very simple reason: essentially because the available quantum formalism is not well suited to treat problems where the energy is dependent on time. This means

that one only studies systems which are isolated from other systems (so that

their energy cannot be exchanged and thus it remains constant in time) or systems that, although not being isolated, can be treated as such in a good

approximation. The formalism available to study energy conserving systems is

called the canonical formalism.

When one cannot consider the system under study as an isolated system (for example because treating it as an isolated system would completely change the problem under study) one has to incorporate in the treatment also the other

systems (which are then thought to constitute the environment) to which the original system is coupled, in such a way that the full set of systems now behaves as a single isolated (dosed) one. At the end of the required computations, one

tries to single out the information regarding the evolution of the original system

by neglecting the changes in the remaining systems. In many cases the nature and the specific details of the coupling of our

system with the environment may be relevant to the specific information one

wants to get about the system evolution. In some cases, the specific details of the

coupling may be very intricate and changeable so that they are difficult to measure and know. Then one may adopt a number of strategies. One of them is to average the effects of the coupling and represent them, at some degree of accuracy, by means of some ((effective" interaction. Another possibility is to take into account the environmental influence on the system by a suitable choice

of the vacuum state (the minimum energy state or ground state). This last strategy, however, is only allowed in QFT where such a choice is actually possible: as we have learned ( cf. Chapter 2), infinitely many unitarily inequival­

ent state spaces (and therefore infinitely many vacua) exist indeed in QFT. The chosen vacuum thus carries the signature of the reciprocal system-environment influence at a given time under given boundary conditions. If one adopts such a strategy, to a change in the system-environment reciprocal influence would

correspond to a change in the choice of the system vacuum: the system ground state story is thus the story of the trade of the system with its environment. The theory should then provide the equations describing the system evolution

Dissipation and memory 109

"through the vacua", each vacuum corresponding to the system ground state at

each time ofits history. The formal (mathematical) description of"transitions" through the vacua is realized via the so-called Bogoliubov transformations

(Takahashi and Umezawa 1975; Umezawa L 993; Vitiello 1995). They constitute a powerful technical tool extremely useful in solid state physics and in particle physics. By means of the Bogoliubov transformations one can move from one vacuum to another one under suitable mathematical constraints.

In conclusion, in order to describe open quantum systems first of all one

needs to use QFT (Quantum Mechanics does not have the many "inequivalent" vacua! ( cf. Chapter 2)). Then one also needs to use the time variable as a label

for the set of ground states of the system (Celeghini, Rasetti and Vitiello 1990): as the time (the label value) changes, the system moves to a "new" (physically

inequivalent) ground state (assuming continuous changes in the boundary

conditions determining the system-environment coupling). Of course, "physi­cally inequivalent" means that the system observables, such as the system energy, assume different values in different inequivalent vacua, as is expected to

happen in the case of open systems.

In some sense, one gets a description for the open systems which is similar to a collection of photograms: each photogram represents the "picture" of our system at a given instant of time (a specific time label value). Putting together

these photograms in "temporal order" one gets a movie, i.e. the story (the evolution) of our open system, which includes the system-environment

interaction effects. The mathematical formalism which realizes the above strategy needs the

formal (i.e. mathematical) representation of the environment, of course. Such a representation must satisfy the requirement that the flux of energy between system and environment must be balanced: the energy lost by the system must

match the energy gained by the environment, and vice-versa. This is the only

condition to be explicitly imposed. All other details of the system-environment interaction may be taken into account by the vacuum structure of the system, in the sense above explained. Then the environment may be represented in the

simplest way one likes, provided the energy flux balance is preserved. One possible choice is to represent the environment as the "time-reversed copy" of the system: time must be reversed since the energy" dissipated" by the system is "gained" by environment. Other representations are also possible, however they may be shown to be equivalent to the one representing the environment as the

"time-reversed copy" of the system. Therefore I will choose such a representa­

tion without loss of generality.

no My Double Unveiled

Summarizing, the system has thus been doubled. The environment is

mathematically represented as the time-reversed image of the system, i.e. as its "double". What the system loses, the environment gains. Such a doubling must

be consistently performed for all the system degrees of freedom and the system vacuum structure at a given time depends on both the sets of the degrees of

freedom, the system degrees of freedom, let me denote them by Ak, and the "doubled" degrees of freedom, say Ak. The suffix k here generically denotes

kinematical variables (e.g. spatial momentum) or intrinsic variables of the fields

fully specifying the field degree of freedom. The structure of the vacuum turns out to be a condensate of couples of Ak and Ak.

I remark that the many particle (the condensate) structure of the vacuum of the system naturally brings us to consider its statistical and thermal proper­

ties. For example, its time evolution is controlled by the entropy function, as it should be since the entropy controls the irreversible time evolution in statistical mechanics. In the next section I will consider the case of the dissipative dynam­

ics for the brain and I will present there other implications of the formalism for dissipative quantum system.

Here, as a final comment, I observe that the formalism for dissipative

systems which uses the doubling of the system degrees of freedom finds very useful applications in many problems of practical interest. from condensed

matter physics to elementary particle physics. Moreover, I would like to stress that the "tilde" or doubled mode is not just a mathematical fiction. It corre­

sponds to a real observable excitation mode (quasiparticle) living in the system as an effect of its interaction with the environment: the couples A,_Ak represent

the correlation modes dynamically created in the system as a response to the system-environment reciprocal influence. It is the interaction between tilde and

non-tilde modes that controls the time evolution of the system. Like other collective modes we have met in the previous chapters also the modes A,_Ak are

confined to live in the system. They vanish as soon as the links between the system and the environment are cut.

Notice that by using the word "representation" I mean that the environ­ment is "mathematically represented" as the time-reversed copy of the system. However, it is clear that corresponding to different subjects (systems) we will have "different" representations of the environment, each of them being indeed

a "copy" of the corresponding subject. Therefore we have that the environment is "subjectively represented" by each subject. I will discuss more on the subjec­tive representation of the world in Section 7.7.

Dissipation and memory 111

6.4 Dissipative quantum brain dynamics

Let me now illustrate in more detail how the quantum dissipation formalism

(Celeghini, Rasetti and Vitiello 1990; Feshbach and Tikochinsky 1977) and the

doubling of the system degrees of freedom permit solving the overprinting problem in the quantum model ofbrain (Vitiello 1995).

Let AK and AK denote the dwq mode and its "doubled mode", respectively.

The A mode is the "time-reversed mirror image" of the A mode and represents

the environment mode. Let W ~ and W AK denote the number of AK modes and

AK modes, respectively. Taking into account dissipativity requires (Vitiello 1995) that the memory

state, identified with the vacuum 10 > 'N' is a condensate of equal number of AK

and AK modes, for any K: such a requirement ensures in fact that the flow of the

energy exchanged between the system and the environment is balanced. Thus, the difference between the number of tilde and non-tilde modes must be zero:

W ~-W A.c = 0, for any K. Note that the label W in the vacuum symbol 10 > 'N

specifies the set of integers { W ~, for any K} which indeed defines the "initial

value" of the condensate, namely the code number associated to the information recorded at time t0 = 0. Note now that the requirement W ~-W AK = 0, for any K,

does not uniquely fix the set {W~, for any K}. Also IO> 'N' with W'={W'~; W'~-W'A.c =0, for any K} ensures the energy flow balance and therefore also

10 > 'N' is an available memory state: it will correspond however to a different code number (i.e. W') and therefore to a different information than the one of

code W. The conclusion is that fixing to zero the difference W ~-W AK = 0, for any K, leaves completely open the choice for the value of the code W. Thus, infinitely many memory (vacuum) states, each one of them corresponding to a different code W, may exist: A huge number of sequentially recorded informa­

tion data may coexist without destructive interference since infinitely many vacua 10 > 'N' for all W, are independently accessible in the sequential recording

process. Recording information of code W' does not necessarily produce destruction of previously printed information of code W t:. W', contrary to the

non-dissipative case. In the dissipative case the "brain (ground) state" may be represented as the collection (or the superposition) of the full set of memory

states 10 > 'N> for all W. In summary, one may think of the brain as a complex system with a huge

number of macroscopic states (the memory states). The degeneracy among the vacua 10 > 'N plays a crucial role in solving the problem of memory capacity. The dissipative dynamics introduces W-coded "replicas" of the system and

112 My Double Unveiled

information printing can be performed in each replica without destructive

interference with previously recorded information in other replicas. In the non­dissipative case the "W-freedom" is missing and consecutive information

printing produces overprinting. Let me remind that there does not exist in the infinite volume limit any

unitary transformation which may transform one vacuum of code W into

another one of code W': this fact, which is a typical feature of QFT, guarantees

that the corresponding printed information data are indeed different or distin­

guishable ones (W is a good code) and that each information printing is also protected against interference from other information printing (absence of

confusion among information data). The effect of finite (realistic) size of the system may however spoil unitary inequivalence. In the case of open systems, in fact, transitions among (would be) unitary inequivalent vacua may occur (phase transitions) for large but finite volume, due to coupling with the external environment. The inclusion of dissipation leads thus to a picture of the system "living over many ground states" (continuously undergoing phase transitions) (Del Giudice et al. 1988c). Note that even very weak (although above a certain threshold) perturbations may drive the system through its macroscopic

configurations (Celeghini, Graziano and Vitiello 1990). In this way, occasional

(random) weak perturbations are recognized to play an important role in the complex behavior of the brain activity. The possibility of transitions among different vacua is a feature of the model which is not completely negative:

smoothing out the exact unitary inequivalence among memory states has the

advantage of allowing the familiar phenomenon of the "association" of memo­ries: once transitions among different memory states are "slightly" allowed the possibility of associations ("following a path of memories") becomes possible.

Of course, these "transitions" should only be allowed up to a certain degree in order to avoid memory "confusion" and difficulties in the process of storing "distinct" informational inputs (Vitiello 1995; Alfinito and Vitiello 2000b-d).

It is interesting to observe that Freeman, on the basis of experimental observa­tions, shows that noisy fluctuations at a microscopic level may have a stabilizing effect on brain activity, noise preventing to fall into some unwanted state

( attractor) and being an essential ingredient of the ground state for the neural chaotic perceptual apparatus (Freeman 1996, 2000; Skarda and Freeman 1987).

According to the original quantum brain model, the recall process is described as the excitation of dwq modes under an external stimulus which is "essentially a replication signal" (Stuart, Takahashi and Umezawa 1978) of the

one responsible for memory printing. When dwq are excited from the vacuum

Dissipation and memory 113

state the brain "consciously feels" (Stuart, Takahashi and Umezawa 1978) the

presence of the condensate pattern in the corresponding coded vacuum. The replication signal thus acts as a probe which "reads" the printed information.

Since the replication signal is represented in terms of A-modes, these modes act in such a reading as the "address" of the information to be recalled. In fact the coded vacuum is a condensate of couples (i.e. of equal number) of A and A modes, one acting as the "hole" (the address) of the other one. One can show indeed that, in the vacuum state, the annihilation of the quantum A corre­sponds to the creation of the quantum A, and vice-versa (Vitiello 1995). Then

the excitation of a quantum A from the vacuum (its annihilation in the vacuum) corresponds to the creation of its "hole" in the vacuum, namely to the creation

of the corresponding A mode, which may indeed occur under the external

replication signal. Incidentally, it is interesting that Stuart, Takahashi and Umezawa use the

words "consciously feels". This may appear disappointing from a philosophical point of view since no further or independent "explanation" of these words is given. Nevertheless, this is exactly what one does in physics: physical processes define by themselves concepts otherwise outside of physical control. Of course,

this does not exclude that other levels of search (e.g. the philosophical level)

may be explored beyond the tasks of the physical investigations. I also observe that the dwq may acquire an effective non-zero mass due to

the effects of the system finite size (Del Giudice et al. 1985; Vitiello 2000a). Such

an effective mass will then act as a threshold for the excitation energy of dwq so

that, in order to trigger the recall process, an energy supply equal or greater than such a threshold is required. When the energy supply is lower than the required threshold a "difficulty in recalling" may be experienced. At the same time, however, the threshold may positively act as a "protection" against

unwanted perturbations (including thermalization) and contributes to the stability of the memory state. In the case of zero threshold any replication signal could excite the recalling and the brain would fall into a state of "continuous flow of memories" (Vitiello 1995).

Finally, I also mention that memory states can be also connected with the squeezed coherent state well known in quantum optics (Stoler 1970; Yuen 1976). In squeezed states the uncertainty, for example, on the position variable, !J.X, may be less than the value it has for a usual coherent state (typically

!J.X2 = %). The Heisenberg uncertainty relation between the position and the conjugate momentum variable is however preserved: !J.X!J.P= %, and thus the

uncertainty on the momentum !J.P must be greater than % in squeezed states.

114 My Double Unveiled

Squeezed states are therefore coherent states with the uncertainty on one of the canonical variables (the position X in the example above) "squeezed" to values

below the quantum uncertainty value: the states are more "sharp, or more "focused'' in such a squeezed variable. The degree of squeezing may be repre­sented by a parameter, the squeezing parameter. Memory states appear to be squeezed states and the squeezing parameter is the memory code (Vitiello 1995). But here I will not insist more on this subject.

Summarizing, Let me stress once more that the process of information printing by itself produces the breakdown of time-reversal symmetry and thus it introduces the arrow of time into brain dynamics (Vitiello 1995, 2001;

Alfinito and Vitiello 2000b-d). The key point is that the resulting dissipative dynamics cannot be worked out without the introduction of the time-reversed

image (the tilde-system) of the original system. As a consequence, energy degeneracy is introduced and the brain ground state may be represented as a collection (or superposition) of infinitely many degenerate vacua or memory states, each of them labeled by a different code number and each of them

independently accessible to information printing (without reciprocal interfer­

ence). Many information storage levels may then coexist thus allowing a huge memory capacity.

Differently stated, the brain system may be viewed as a complex system with

(infinitely) many macroscopic configurations (the memory states). Dissipation,

which is intrinsic to the brain dynamics, is recognized to be the root of such a complexity, namely of the huge memory capacity. Of course, several structural and dynamical levels (the basic level of coherent condensation of dwq, the cellular cytoskeleton level, the neuronal dendritic level, and so on) coexist,

interact among themselves and influence each other's functioning, as already observed in Chapter 5. Dissipation introduces the further richness of the replicas or degenerate vacua at the basic quantum level. The crucial point is that

the different levels of organization are not simply structural features of the brain, their reciprocal interaction and their evolution is intrinsically related to

the basic quantum dissipative dynamics. The brains functional stability is ensured by the systems "coherent response, to the multiplicity of external stimuli. Thus dissipation also seems to suggest a solution to the so called binding problem, namely the understanding of the unitary response and

behavior of apparently separated units and physiological structures of the brain. Let me dose this section with an observation which will turn out to be

useful in the future discussion. As stated above, the doubled degrees of freedom, i.e. the tilde-system, represents the environment and cannot be neglected since

Dissipation and memory 115

the brain is an open system. This means that the tilde-modes can never be eliminated from the brain dynamics. This will lead me to consider some features of the dissipative brain dynamics which might play a role in the study of consciousness mechanisms.

6.5 Life-time and hierarchy of memory

In Chapter 4 I have discussed the life-time of memory states in the quantum model of brain. Let me observe that I am presently considering memory states associated to the ground states and therefore oflong life-time. These states have a finite (although long) life-time because of dissipativity. Then, at some time t=T, conveniently larger than the memory life-time, the memory state 10 > 'N is reduced to the «empty" vacuum 10 > 0 where WK = 0 for all K: the information has been forgotten. At the time t=T the state 10 > 0 is available for recording a new information. In order to not completely forget certain information, one needs to «restore" theW code (Vitiello 1995), namely to «refresh" the memory

by brushing up the subject (external stimuli maintained memory ( Sivakami and Srinivasan 1983)). Thus a familiar feature of memory can find a possible explanation in the dissipative quantum model of brain. Notice also that the quantum model of brain could not explain the mechanism by which some information can be forgotten without considering dissipativity.

As already mentioned, the evolution of the memory state is controlled by the entropy variations: this feature indeed reflects the irreversibility of time evolution (breakdown of time-reversal symmetry) characteristic of dissipative systems, namely the choice of a privileged direction in time evolution (arrow of time). In thermodynamics one can construct a functional called the «free energy" by using the entropy and the energy. Such a quantity is of great practical interest since physical systems evolve in such a way to minimize the free energy. In the present case, the stationary condition for the free energy functional leads to recognizing (Vitiello 1995) the memory state 10( t) > 'N to be a finite temperature state (Takahashi and Umezawa 1975; Umezawa, Matsu­moto and Tachiki 1982). Such a finding is most interesting since it is a direct consequence of the dissipative character of the brain dynamics and it is well known that brain activity is highly sensitive to temperature variations. In this connection, I observe that the ((psychological arrow of time" which emerges in the dissipative brain dynamics turns out to be oriented in the same direction as the «thermodynamical arrow of time", which points in the increasing entropy

116 My Double Unveiled

direction. It is interesting to note that both these arrows, the psychological one and the thermodynamical one, also point in the same direction as the «cosmo­logical arrow of time", defined by the expanding Universe direction (Alfinito and Vitiello 1999-2000d; Alfinito, Manka and Vitiello 2000a) (see e.g. (Hawk­ing and Penrose 1996) ). It is remarkable that the dissipative quantum model of brain let us reach a conclusion about the psychological arrow of time which we commonly experience.

In conclusion, time evolution of the W-coded memory state can be repre­

sented as a trajectory of initial condition W = { W ~} running over the states 10( t) > w, each one minimizing the free energy functional. Also note that in addition to the breakdown of time-reversal (discrete) symmetry, dissipation also implies spontaneous breakdown of time translation (continuous) symme­try, which simply means that the brain system exchanges energy with the environment.

Until now I have considered the frequency associated to each dwq to be independent of time. A more general case may be the one where time depen­dent frequencies are instead considered (Alfinito and Vitiello 2000b-d). This is also more appropriate to a realistic situation where the dipole wave quanta may undergo a number of fluctuating interactions with other quanta and then their characteristic frequency may accordingly change in time. The study of the dissipative model with time dependent frequency leads to a number of interest­ing new features, some of which I will briefly discuss in the following.

The main remark is about the insurgence of a different life-time for the dwq of different momentum k. Modes with longer life-time are the ones with higher momentum. Since the momentum is proportional to the reciprocal of the distance over which the mode can propagate, this means that modes with shorter range of propagation will survive longer. On the contrary, modes with longer range of propagation will decay sooner. The scenario becomes then particularly interesting since this mechanism may produce the formation of ordered domains of finite different sizes with different degree of stability: smaller domains would be the more stable ones. Remember now that the regions over which the dwq propagate are the domains where ordering (i.e. symmetry breakdown) is produced. Thus we arrive at the dynamic formation of a hierarchy (according to their life-time or equivalently to their sizes) of ordered domains. Since in our case «ordering" corresponds to the recording process, we find that the recording of specific information related to dwq of specific momentum k may be «localized" in a domain of size proportional to 11 k, and thus we also have a dynamically generated hierarchy of memories. This

Dissipation and memory 117

might fit some neurophysiological observations by which some specific memo­

ries seem to belong to certain regions of the brain and some other memories seem to have more diffused localization. In Chapter 4 I have discussed the

problem of the long-term memory and short-term memory. Now we see how the

dissipative quantum dynamics leads to a dynamic organization of the memories

in space (i.e. in their domain of localization) and in time (i.e. in their persis­

tence or life-time). In Chapter 7 I will comment on the agreement between the

process of coherent domain formation in the dissipative model and the physio­

logical observation of the formation of the correlated assembly of neurons.

One more remark has to do with the "competition" between the frequency

term and the dissipative term in the dwq equation. Such a competition (i.e. which term dominates over the other one) may result in a smoothing out of the

dissipative term, which may become then even negligible. According to the

discussion in the present chapter, in such a case we should expect a lowering of the memory capacity which could manifest in a sensible "confusion" of

memories, a difficulty in recording different memories as distinct memories, a

difficulty in recalling, namely those "pathologies" arising from the loss of the

many degenerate and inequivalent vacua due to the loss of dissipativity. The competition between the frequency term and the dissipative term in

the dwq equation is controlled by parameters whose values cannot be fixed by

the model dynamics. They have to be given by some external input of biochem­ical nature. [t is quite interesting that the dissipative quantum model contains

such freedom in setting the values for such parameters. Let me recall that

Stuart, Takahashi and Umezawa (1978, 1979) did suggest that the formation of

ordered domains could play a significant role in establishing the bridge between the basic dynamics and the biomolecular phenomenology (cf. Section 4.6). In

the following chapter I will further discuss the formation of finite size domains.

Another direction of research which is pursued at this time is the one of

producing simulations of the dissipative quantum model of brain by means of neural networks. [ will discuss this topic in the following section.

6.6 Collective modes on neural nets

The quantum brain model discussed in the previous sections and chapters at

this juncture provides mainly a theoretical scheme to represent some of the

functions of the natural brain. The problem of testing its accuracy in fitting

specific observations of neurophysiology remains open and much work has yet

118 My Double Unveiled

to be done to find out how its general mathematical framework can accommo­

date the rich phenomenology of molecular biology. On the other hand, compu­tationa] neuroscience mostly relies on specific activity of neural cells and of

their networks, and a number of models and simulations of the brain activity in terms of neural nets exist. More recently, there is also an increasing interest in the study of quantum features of network dynamics, either in connection with information processing in biologica] systems, or in relation to a computational strategy based on the system quantum evolution (quantum computation

( Feynman 1985; Williams and Clearwater 1998)). It is outside the scope of this book to present the state of research in these specific sectors. However, I would like to report here about some recent work (Pessa and Vitiello 1999) aimed at modeling the dissipative quantum model of brain in terms of neural nets. This is a work still in progress, however some results are already available. One

further element of interest in such a work is provided by the fact that, besides the interest in modeling the natural brain, this study leads to modeling the states of neural nets in terms of collective modes with the help of the formalism of Quantum Field Theory. In other words, it shows that a novel conceptual and

formal scheme in neural net modeling may be introduced which is based on simulation of a quantum dynamical evolution (the methods of statistical mechanics and of spin glass theory are not considered here (see Amit 1989; Mezard, Parisi and Virasoro 1987)).

Let me introduce the general theoretical background on which our neural

net is modeled. Consider a three-dimensional set of Ninteracting units (neural units) sitting each one in a space-time site xn, n= 1,2, ... N. Each unit can be in

the state on (1) or off (0). The neural unit activity is characterized by the

amplitude of the emitted pulse and by a phase determined by the emission time. This suggests to us that each unit can be described by a complex doublet field whose two components are associated to the .. inner" degree of freedom u and d, corresponding to on and off, respectively.

At each site xn the field inner variable may assume a well defined value ( u or d). The set of these values for all the sites specifies a microscopic configu­ration of the net. Since we want to model the natural brain, we require that in

full generality the specification of the macroscopic or functional state of the net does not actually require that correspondingly one should have a unique, well definite microscopic configuration where each unit is in a definite u or d state.

Indeed, many distinct microscopic configurations of the component units may correspond to the same functional state of the net.

Dissipation and memory 119

This means that a given (equilibrium) state of the net may be compatible

with fluctuations in the states of the individual component units. Thus the net state is not strictly dependent on the specific state of each individual unit: i.e. we

admit enough plasticity (as contrasted with rigidity) for the net; in other words, the net macroscopic state is the output, or the asymptotic state, emerging from the microscopic dynamics which rules the interaction among the component units. For large number N of component units, such a picture is certainly more

appropriate for the modeling of the natural brain in terms of neural nets. It is well known that the brain functional activity is not strictly related to the activity of each single neuron.

Since a considerable amount of fluctuations is allowed for the states of the individual unit at each site, and thus for the basic field, and since, as a conse­quence, the uncertainty in the identification of the evolution of the state of the unit cannot be eliminated without strongly interfering with it, we are led to assume the basic fields to be quantum fields satisfying quantum dynamical

equations. The global, macroscopic behavior of the net, namely its functional state and

its evolution, can be characterized by a (classical) macroscopic observable, as is usually the case in solid state physics. Such an observable is the order parameter and it is determined by the dynamics of the elementary units and by its symme­

tries (Umezawa, Matsumoto and Tachiki 1982; Itzykson and Zuber 1980). We

have seen that it may be considered as a code specifying the vacuum or ground state (cf. Chapter 4). We then assume that the values of the order parameter, say

Jv[, specify the information content of the net. We define Jvf 1/2I(Nu- Nd)l, with

N = N u + Nd, where N u and N d denote the number of units on and off, respective­ly. In other words, Jvf is a measure of the excess of sites on with respect to the sites off. The state Jvf = 0 is called the "normal state" (void of information content); the " information states" are the ones with Jvf> 0 (different informa­

tion data associated to different non-zero Jvf values). We assume that the neural net may be set into a Jvf> 0 state under the

action of an external input (coupling of the net with the environment). This implies that the interaction among the net units cannot force, by itself, the net into a Jvf> 0 state (i.e. in the absence of external input the net remains in its normal state). This in turn means that, from one side, the basic dynamics

describing the interaction among the units (i.e. the evolution equations for the basic field) must be invariant under the group of rotations acting on the doublet field. On the other side, it also means that the ground state is not

invariant under the full group of rotations. In conclusion, the dynamics is

120 My Double Unveiled

invariant under the full rotation group, but the ground state is not invariant under such a group: this means that we have spontaneous breakdown of rotational symmetry and, consequently, long range correlation modes or collective modes, i.e. the Nambu-Goldstone modes, are dynamically generated.

Since the normal state as well as the information states must be stable states of the net, all of them must be states of minimum energy, i.e. degenerate ground states. Moreover, since a conveniently large (in principle infinite) "memory capacity" is required, we should have many (in principle infinitely many) degenerate ground states.

We also require that the quantum field dynamics be such that it generates asymptotic equilibrium states with negligible fluctuations of YVf. The macro­scopic "memory" state of the neural net indexed by YVf will be then the classical

limit state in the sense of QFT, namely the state for which the fluctuations in the number of the Nambu-Goldstone modes is negligible with respect to the number of modes condensed in it: in other words, it is a coherent state with respect to these modes.

Since the net is an open system and the information storage produces by itself the breakdown of the time-reversal symmetry, we have to consider the QFf for dissipative systems and the consequent doubling of the degrees of freedom, as explained in previous sections. As we have learned, the role of dissipation is crucial in solving the overprinting problem, namely the problem of the net memory capacity. Dissipation implies energy degeneracy and the net ground state may be represented as a superposition of infinitely many degener­ate vacua, or memory states, each of them labeled by a different code number and each of them independently accessible to information storage. Many information "files" may then coexist thus allowing a huge memory capacity.

Moreover, non-unitary equivalence among these vacua acts as a protection against overlap or interference among different information data.

In realistic neural networks, the finiteness of the "volume" (the number of neural units) and possible defect effects may spoil unitary non -equivalence thus leading to information interference and distortions.

The retrieval of information can be described by "reading off' the mirror modes of the same code number of the information to be recalled. As in the dissipative quantum model of brain, these mirror modes are essentially a "replication signal" of the one responsible for memory storage.

The practical implementation of the net described above has been carried out and a number of simulations have been performed. Technical details can be found in the quoted literature. At this stage of the work the net appears to be

Dissipation and memory 121

able to record a sequence of information data without overprinting (i.e. without destruction of previously registered information) and it shows a capability to recall any one of the registered information data (i.e. not simply the last one) under presentation of an external input similar to the one to be recalled.

Thus I can conclude that the classical limit of the dissipative quantum brain dynamics may be simulated by and, at the same time, provides a representation of a neural net characterized by long range correlation among the nets units, and vice-versa. In this way, a link is established between dissipative quantum brain dynamics and neural net dynamics.

Self-portrait, charcoal on paper 1962 (Pasquale Vitiello, 1912-1962). Private collection.

--~---......... ~. ··-· -·-•f l \ ..

'

CHAPTER 7

Dissipation and consciousness

The problem of founding a science of consciousness is briefly discussed and some contributions to consciousness modeling are summarized and briefly commented on. The formation of finite size correlated domains is considered in the framework of the dissipative quantum model of brain and their role in consciousness related mechanisms is discussed. Consciousness appears to be intimately related to dissipation. [ts manifestation as a «second person" acting as the Double of the subject is disclosed.

7.1 Brain and consciousness 124

7.2 Toward a Science of Consciousness? 125

7·3 Modeling consciousness 128

7·4 Three properties of consciousness 131

7·5 Life-time and localizability of correlated domains 134

7.6 Mind the gap! 137

7·7 My Double, Myself 140

124 My Double Unveiled

7.1 Brain and consciousness

The study of "brain and consciousness" certainly provides a striking example of the unity of structure and function. In Chapter 1 I have stressed that the distinction between structure and function appears to be dissolved in the unifying view of quantum field theory. A sharp distinction between the struc­ture, which includes all the system components, and the functions which characterize the system as a whole, cannot be made. Trying to understand consciousness by detaching it from the understanding of the structure (the "brain") most probably will turn out to be a hopeless effort. Vice-versa, the study of the "parts" or components of the brain in the full glory of their details, but abstracting from the functions (consciousness among others) which only emerge from the brain as a whole, is not the study of the brain.

There is, however, the question: Where to start if one wants to know something about consciousness? From the standpoint of a physicist, or of a neurophysiologist, the answer to such a question is rather obvious: "the actual material", "the physical brain" is the only available starting point. How to start? By collecting all possible knowledge about the "parts" and asking questions on their working together, namely on the dynamics which puts them together in a functional whole. [nternational conferences aimed at founding the basis for a Science of Consciousness are periodically held in Tucson since 1994 (Hameroff, Kaszniak and Scott 1996b, 1998a). In 1999 a similar conference was held in Tokyo (Jibu, Della Senta and Yasue 2001a). These conferences have seen the participation of a large number of people with a wide range of cultural and professional backgrounds, from physicists to physicians, from philosophers to biologists, neurophysiologists, psychologists, and so on. My impression is that in these conferences the discussion about consciousness is leading to a discus­sion of the different standpoints from which the consciousness is approached in the different disciplines.

A first effect of these meetings is the attempt to build up a common language or at least agreement on which are the problems or the classes of problems to be faced. Thus, these conferences result in a tentative definition of the problem, rather than of consciousness per se. [will very shortly list some of

the positions which emerge in these discussions on consciousness. Then I will report on some specific models for the emergence of consciousness. My exposition cannot cover, of course, all the models, the hypotheses, the specula­tions. I will only briefly touch some of those proposals which seem to me closer to the line of research presented in the previous chapters, and in doing so I will

Dissipation and consciousness 125

even neglect to quote outstanding voices in the field. I apologize for that.

Finally, I will discuss how the mathematical formalism of the quantum model suggests that consciousness might emerge from dissipation. Moreover, in my

discussion the issues related to the consciousness debate will not be considered from a philosophical point of view. Commenting on the consciousness litera­ture or considering philosophical questions is outside the scope of this book. Even if some of the words [will use could be evocative of a certain philosophical content, they only refer to the limited sense I specify each time for them.

7.2 Toward a Science of Consciousness?

What is the route toward a Science of Consciousness? [s it possible to apply "scientific methods" to the study of consciousness? It is not so simple to answer

such a question. In fact there are many unavoidable prerequisites to be satisfied before saying that one is "making Science". Consciousness is certainly a phenomenon of which everybody has experience. However, this is a personal,

first person experience and does not have the chief property required by the

scientific method, which is objectivity, namely the possibility that a third person

could check it. How might there be accommodated in the scientific methodolo­gy the study of those personal experiences which cannot be observed by any other observer than the experiencing "subject"? For example, how could one ever know qualia, your feeling, say, of "redness" as compared to his feeling of

redness in the presence of a common input? Of course, here I am using words such as qualia, subject, feeling, which would need careful analysis, even asking questions about their meaning, if any. But, as I did already in other parts of this book, I will leave such kind of analysis, which is beyond the scope of this book,

to specialists. It seems to me that there is a "circularity" in the questions which have

arisen in discussions "about" consciousness, in the sense that questions on

aspects apparently distinct merge together, thus pointing to a substantial unity

of the mechanisms related to consciousness. For example, asking what is the nature of consciousness and asking if there is a possibility for its scientific comprehension, or what happens to consciousness when we sleep, or if it is something distinct from emotions, and so on, brings us to a unique substantial core of the problem, whose existence we can feel, but which we are yet not able

to identify. The same terms in which questions are posed sometimes lead us to doubts about their meaning and to the suspicion that they eventually do not

126 My Double Unveiled

make sense at all, that one cannot check if they are true or false (Preti 1957).

Since at the moment there is no such kind of control, one may attempt to "graduate" the problems, e.g. classifying them in two large categories: the easy

problems and the hard problems (Chalmers 1996). Easy problems are those which may find a solution in neuroscience labora­

tories. For example, the problem of finding out how stimuli from the external

world are elaborated by our brain, which neural processes we use to compute distances, recognize patterns, how we translate into words our feelings, and so on. Of course these are not at all "easy, problems, however, neuroscience gives

us a reasonable hope that at some time in the future we will be able to know

about those processes. Hard problems perhaps may roughly all summed up into one very difficult question, namely: what is the nature of the subjective experi­ence of the world? How do external inputs and stimuli become our subjective experiences (such as qualia)?

The emergence of subjectivity appears to be one of the central issues in the

understanding of consciousness. Since Descartes consciousness has been in good part related to "self-consciousness, ( cogito ergo sum), to the Ego reflecting upon itself. Of course, many divergent positions arise in the discussion. However, I do not want to enter into discussions on the consciousness litera­

ture, which is not the subject of this book. With much simplification I will only recall that there are those who deny that there is a hard problem at all, main­

taining that the hard problems will find their solution in terms of chemical transmitters and neuronal activity, that consciousness is only an epiphenome­

non (Dennett 1991). Others believe that consciousness, as well as subjectivity, emerges from the cooperation of a very large number of neuronal cells and do not see any reason to call in a .. new physics" (Churchland 1998; Crick 1994). Some predict that it will be possible to build conscious computers .. .it is only a matter oC'complexity,. There are those who postulate a .. dual" reality, different

from the one studied by Science and to which consciousness belongs, or who propose (Chalmers 1996) that consciousness belongs to a "further" reality to which scientific investigation should be addressed in the future. Others point to the possible relation between quantum mechanisms, such as boson condensa­

tion and long range interactions, and consciousness mechanisms (Marshall 1989; Beck and Eccles 1992).

Globus (1995, 1998, 2001a, 2001b) shifts the focus from consciousness to existence. He proposes that the "matching" of the subject, which for Globus is a nonlocal control, with the external world is not simply an influence of the

input on the subject, it also includes "what the brain brings to the input",

Dissipation and consciousness 127

nonlocal control "situates" for the external reality. World presences in the

matching. Focusing more on brain organization and physiology, Baars (Baars 1997) proposes the "global workspace theory" where consciousness is seen as an

architectural aspect of the brain. Moving on convergent roads Baars, Newman

and Taylor relate consciousness to global effects of coherent information (Baars,

Newman and Taylor 1998). Scott (1995) stresses the role of nonlinear dynamics

in the many level organization of living matter, symbolized with a stairway to

the mind.

One cannot forget about the "actual material", and this also includes the

"conscious subject" and his "conscious experience": the analysis is thus natural­

ly enlarged to include the wide world of the phenomenology studied by

sociology, psychology, psychiatry and medicine (Zohar 1991). Putting the irreducibility of the "lived experience" at the center of the analysis is the core of

the renewed phenomenological approach ofVarela (Varela 1998). His effort to move beyond the opposition of subjective and objective, seeking a "fundamen­

tal correlation", reminds me of a similar effort in the analysis of "time and

relation" pursued by Enzo Paci (1965) always in the realm of the Husserlian

phenomenology. An interesting position from a philosophical standpoint is the one of

purposely not asking whether it is possible to study consciousness, because the

same fact of asking such a question immediately and automatically "postulates"

consciousness as the "object" to be studied (Desideri 1998). This may introduce

a prejudice in the study, since it is not at all clear how consciousness, whose main

apparent characteristic is "subjectiveness", may be classified by logical catego­

ries dealing with "objects". Thus, there is proposed instead an "itinerary" about

and "inside" consciousness. In such an itinerary the search becomes "listening to consciousness" and through such a listening the same search becomes

identification with and therefore knowledge of consciousness (Desideri 1998).

Nevertheless, as Searle (Searle 1992, 1998) reminds us in his "program" for

consciousness study, the problems of reconciling the primary subjective charac­ter of consciousness with the objectivity requirement of Science, of the commu­

nication of the mental world with the physical world, of the qualia ... , and so on,

are still there and await solution. Further discussion of these "founding" questions would keep me far away

from the task of this book, so I will leave them aside. In the following sections

I will briefly introduce some models which point to the role which might be

played by the microtubules and by the neural connections in consciousness

mechanisms.

128 My Double Unveiled

7 ·3 Modeling consciousness

The microtubules play a central role in the process of cell division or mitosis.

They are made up of 13 molecular chains of tubulin arranged so as to form a

hollow tube or channel with water inside it. These polymeric chains are made up of components or units which are called dimers since they present two extreme regions of globular proteins, the alpha tubulin and the beta tubulin.

The dimers present two different states of electric polarization, depending

on whether one electron is displaced in the alpha region or in the beta region. As the electron shifts to one or the other region, a flip in the electric dipole momentum is induced and the dimer exhibits one or another of two different

configurations. Such a process is, of course, a quantum process. The time scale involved in the change of configurations of the dimer is of the order w-u sec.

Stuart Hameroff has pointed out that such a property makes them interesting objects from the point of view of information processing (Hameroff 1987): as is well known, an elementary information may be associated to any artificial or natural device which may take two different configurations (on/off, one/zero,

yes/no). Therefore, one might think that some information may be coded on

dimers. On the other hand, since the cytoskeleton network supports the transport of energy and of electrically charged particles and it is involved in a lot of the biochemical activity, one may conclude that the information coded on

microtubules may play a relevant role in all these activities. In fact, the relevance

of microtubules in memory and cognitive functions has been confirmed by many observations, as I have already reported in Section 4.7. Hameroff suggests that microtubules are able to provide a "computational" activity inside the cell.

In order that such an activity may be a stable one and at once may involve large (with respect to the dimer size) regions on the microtubule, coherence phe­

nomena are necessary and therefore a quantum dynamics is invoked. In recent years proposals have been advanced (Penrose 1989, 1994; Jibu and

Yasue 1995; Hameroff and Penrose 1996a) that consciousness finds, indeed, its root in the activity of the cytoskeleton. A possible hint in such a direction is

provided by the fact that anesthetic substances produce the loss of conscious­ness by interfering with the normal cytoskeleton activity. Even if much is known, a fully understanding of the activity of anesthetic molecules has not yet been reached.

In quantum mechanics, according to the superposition principle, any state

of the system is described as the sum, or superposition, of a set of independent (orthogonal) states. Such a set is called a basis. Each state of the basis contributes

Dissipation and consciousness 129

with a definite weight to the superposition. The modulus square of the weight

gives the probability that the system when observed is found in the state associat­ed to that specific weight. In other words, in quantum mechanics one cannot predict in a definite (i.e. non-probabilistic) way in which state the system will be found when observed; one can only"expect" that the system may be observed in a specified state "with the probability associated to that state". All the

computing in quantum mechanics is about finding out such probabilities. Before and in the absence of any observation or measurement, one can only express the system state as the superposition of the basis states with the respec­tive probability amplitudes. The measurement operation acts as a "filter" or a

"projection operation" singling out the state of the basis in which we observe our system sitting: the observation thus produces the "reduction" of the system (actually of the system wave-function) to one of the states entering the superpo­sition. Contrary to what happens in classical mechanics, no matter how accurate is our knowledge of the dynamics and of the boundary conditions, our

statements about the system state are always in terms of probability expecta­tions. Once the measurement is carried out, the system definitely sits in one of the states of the basis.

It is still a matter of discussion how the quantum system and the measure­ment apparatus, which typically is a classical system, affect each other. In other

words, the quantum/classical interplay which seems to occur in the measure­

ment of quantum systems, is not completely understood. This is the subject of the measurement theory in quantum mechanics. Penrose suggests that a "non­computational" character is involved in such a quantum/classical interplay

characterized by the quantum state reduction process. He also observes that there are indications that the mental activity may also adopt "non-computa­tiona]" strategies. For example, he remarks that in order to find the solution to

certain problems one must adopt computational procedures which "have no end" (for example: finding a number which is not the sum of four squared

numbers), and that to find out if a computational procedure belongs to the class of those which have no end, the mathematician adopts strategies which do not belong to the general definition of"calculus".

In conclusion, according to Penrose, non-computational mental strategies are adopted in finding the solution to certain problems. This amounts to saying

that in general mental activity is not limited to the use of"logical" procedures of calculus. The various "steps" of the calculus are always well defined, at any point

or moment of the computational procedure. The calculus procedure can be described as a system evolving in time, whose "states" are always unambiguously

130 My Double Unveiled

defined, i.e. as a "classical, system. Incidentally, there is today much interest in "quantum computation, {Feynman 1985; Williams and Clearwater 1998), where the "computation procedure" is indeed represented as a quantum system

and the states of the evolution (the steps of the computation) can be represent­ed only probabilistically in terms of the superposition principle.

Summing up, according to Penrose all of this suggests that consciousness might find its origin in the non-computational nature of the quantum state reduction. The brain state is supposed to be characterized by the coherent

collective state of the microtubules. Consciousness arises in the reduction process of such a state under the influence of the gravitational field which acts

as the measuring agent. In order to understand how gravitation enters into play one should

consider that in the microtubules, the quantum state of the dimers implies the

superposition of the two configurations (states) of the dimers and therefore of the gravitational fields associated to the two respective mass distributions. Such a superposition implies an energetic expense with consequent instability for the whole system, which therefore decays to the state of lowest energy. The quan­

tum state is thus "reduced, to a single one of the dimer configurations: con­sciousness is then viewed as the "unambiguous, manifestation of such a definite

component of the system quantum state, as the "act'' of the state reduction. An "orchestrated, reduction {Hameroff and Penrose 1996a) is the one simulta­neously induced on a large number of dimers and microtubules by specific

chemical activation. It is to be observed that consciousness is not the mere result of the brain "complexity,. There is the "new ingredient, of the non­

computational character of the brain activity. There are other somewhat more speculative aspects (proto-conscious

experience, pre-conscious phase, fundamental space-time geometry, free will

etc.) of the Penrose-Hamer off model (Hameroff and Penrose 1996a; Hamer off 1998b) on which here [will not report. A recent criticism {Tegmark 2000) of the use of the quantum formalism can be easily turned down since in the model neurons and microtubules are not considered to be quantum objects (for a

reply to the criticism see also Hagan, Hameroff and Tuszyflski 2000). Of course, the electron oscillation in the dimers is a quantum process. Other objections deal mostly with the ideas, or the philosophy, underlying the model and its genesis. Of course, apart from another series of objections coming from a prejudicial negative attitude with respect to the use of quantum models, there

are aspects of this model which await clarification. For example, there is the question of the dynamics leading to coherent and relatively stable domains of

Dissipation and consciousness 131

microtubules, or also to an extended giant dendritic network behaving as a

whole system. Here there might be at work a mechanism like the one studied in the framework of the quantum brain model where the system of microtubules

behaves as a macroscopic quantum system. Let me turn now to the discussion of some physiological aspects of the brain

which might play a role in the understanding of consciousness mechanisms.

7 ·4 Three properties of consciousness

Together with Schrodinger, a physicist or a neuroscientist would ask the ques­

tion: What kind of material process is directly associated with consciousness? (Schrodinger 1944). Thus, for a physicist or a neuroscientist the starting point to investigate consciousness is the physical brain. But "where" in the brain? In

which one of its regions should one look in order to find some special tissue or neuronal circuit or anything special out of which the "function" of conscious­

ness comes out? In one of her papers, which here I will closely follow, Susan

Greenfield (1997a) starts her discussion on the issue of consciousness by

considering such a question. The problem of the "location" of functions in the brain is a recurring

problem in neuroscience. However, although the search of the location of

functions such as memory, vision and other functions relating to the external world, has been carried on for a long time, such functions have not been found to be related to respective single brain regions. Neuroscientists now know from laboratory observations that several brain regions act cooperatively and simulta­neously, as a connected whole (Lashley 1942; Pribram 1991; Freeman 2000; Greenfield 1997a, b), in performing functions of the brain which relate it to the

outside world. Information appears spatially uniform "in much the way that the information density is uniform in a hologram" (Freeman 1990) ( cf. Section 4.2).

On the basis of such experimental observations, it has been suggested (Crick and Koch 1990; Greenfield 1997a) that the same would also be the case for

consciousness, so that there would be no specific neuronal circuits or neuronal populations committed to consciousness generation. Thus, a first property of consciousness, consistent with these physiological observations is the one of being "spatially multiple" and "temporally unitary" (Greenfield 1997a).

But consciousness, according to Greenfield, also appears to be a continuum

and it derives from a specific stimulus. The property of being a continuum means that consciousness grows as the brain develops: consciousness is not "all

132 My Double Unveiled

or none", it is more "like a dimmer switch that grows as the brain does" (Green­field 1997a, 1998). The manifestation of consciousness in different degrees (as values in a continuous scale) is not only referred to different beings (animals

versus humans) or to different stages of the growth (children versus adults), but also to different moments of ones mental experience, perhaps consequent to some external action. Apparently there is no lower bound to consciousness (Edelman, however, would exclude "lower" animals (1987, 1989)).

On the other hand, it is a common experience that one is always conscious

of something, never of nothing and not of everything at once. Incidentally, such a serial character of consciousness experiences is also shared by memory storing

and recalling and, as an experimental acquisition of neurophysiology, was also an inspiring hint for the quantum brain modeling (Ricciardi and Umezawa 1967). This is the content of the third property of consciousness. One is always

conscious of" some kind of focus, epicen tre or trigger" (Greenfield 1997 a, 1998). Which ones are the physiological features which may possibly support these

last two properties of consciousness? In order to answer to such a question, one should consider that the brain presents an extremely dense network of connec­

tions between the neurons (ranging from 10 to 100,000 connections between each of the 100 billion brain cells) and that a distinction has to be made between structural or anatomical connectivity, which is quite stable (quasi­stationary), and functional or effective connectivity, which, on the contrary, may be highly dynamic with modulation times of the order of hundreds of

milliseconds. The dynamic cooperativity of neurons is sustained by such an intricate net of connections: neural cooperativity is thus an emergent property of neurons which could not be inferred by single neuron observation (Aertsen and Gerstein 1991; Freeman 1990-2000). Observations also show that the connectivity of non-specialized neurons grows as the brain develops and relates

to the external world. The growth of the connectivity is observed to be related

to brain age, with training in performing certain operations and in general with the brains experience in relating to its environment. For example, the produc­tion of a large quantity of tubulin is observed in the visual cortex of baby rats

when they first open their eyes (starting of the critical learning activity). Such a production decreases when the critical learning activity is over ( Cronley-Dillon, Carden and Birks 1974). Moreover, the plasticity of the functional neural connections, the fact that they are not "hard wired" (Zheng et al. 1994) but

dynamical, implies that the brain can learn, it is an "adaptive, system, able to

perform a large and rich spectrum of activities within a wide range of change­able boundary conditions. In this respect, it is quite interesting that already

Dissipation and consciousness 133

Schrodinger was associating consciousness to learning, namely to the ability of

adapting to external conditions (Schrodinger 1944).

The connected domains of neurons thus change in time by assembling and disassembling, and recruiting time by time a different number of neurons. The

Libet experiments (Libet et al. 1979) show that under the external stimulus a

(relatively) restricted number of neurons are first recruited in the brain

response. Such a response was dearly recorded by electroencephalogram, but

the subject did not report any conscious feeling of the stimulus at this stage. Only after 500 milliseconds or so, when the instrumentation recorded the neural

activity spreading over a much larger region of the brain, did the subject report

"the feeling" of the external stimulus. The set of neurons firstly responding to the external stimulus, which act as a quite robust "seed" for the connection spread­

ing (as a "stone thrown in a puddle" generating spreading rings of waves on the

water surface, in the Greenfield picture), may physically represent the epicentre. This is a pre-conscious stage. Consciousness sets in with the observed time­

delay, when the larger assembly of correlated neurons is formed. The emergence

of consciousness is thus described by this growing population of neurons,

gradually recruited in about half a second. Also Hobson (Hobson 1998) notices that the "level" of consciousness changes as a function of neuronal activation

around a "focus" triggered by an input and its "form" is related to the activity

of modulatory neurotransmitters. As stressed by Freeman, while the activity of

the single neuron is experimentally observed in form of a discrete and stochastic pulse train and point processes, the "macroscopic" activity of a large assembly

of neurons, spatially coherent and highly structured in phase and amplitudes,

appears to evolve in time continuously (Freeman 1996) ( cf. Section 4.2). The

continuous, experience-related, formation of neural connectivity supports the

view of consciousness as a continuum.

The dynamics of the connection formation is such that the same number of

neurons are never correlated in exactly the same extent in exactly the same way. Thus one never has the same consciousness. The physical property which can

sustain such a scenario is the modulation of the neuronal activity. And this may

be obtained by means of some chemical messengers able to influence the degree

of sensibility of the neurons to a certain input signal. Such chemicals do exist and

they do seem to have rapid access to a large group of cells. Their action does not

produce the cell excitation, but makes it more receptive to the recruiting signal

from the epicentre. These chemicals thus "cooperate" to the enlargement of the

connected neural domain starting from the epicentre. Apparently, these chemi­

cals are indeed the target of those drugs (such as prozac, amphetamine, LSD)

134 My Double Unveiled

which are known to modify our consciousness states. According to the degree of the action of such chemicals on a specific neuron cell, it is recruited or not in the connected assembly. Consciousness is triggered when this assembly is

sufficiently extended. Greenfield admits that there is no indication at the moment of what "sufficiently" means, of how many neurons should be in­volved to trigger consciousness. However, she stresses that the critical factor is not qualitative (nothing "special,, specialized neurons are not required to exist), but quantitative.

In conclusion, "consciousness is spatially multiple, yet effectively single at one time. It is an emergent property of non-specialized groups of neurons that are continuously variable with respect to an epicentre" (Greenfield 1997a).

Greenfield then goes on to consider what could be the effects of too small or too large neural correlated domains. Before considering these cases, I will

consider in the next section a few more results of the dissipative quantum model which appear to fit particularly well with the physiological observations mentioned above.

7·5 Life-time and localizability of correlated domains

In the quantum model of brain memory recording is obtained by condensation

of the electric dipole wave quanta ( dwq) in the system ground state. In the non­

dissipative case the memory states are thus stable states (infinitely long-lived states): there is no possibility to forget. On the contrary, in the dissipative case the memory states have finite (although long) life-times. In Section 6.5 we have

also seen that modes with larger momentum k live longer than modes with smaller momentum. It can be also shown that modes of given momentum can

be stored only in a time span whose length is specific for that momentum. For given k, the corresponding time span useful for the recording process (the ability of memory storing) grows with the growth of the number oflinks, say n, which the system is able to make with the external world: the more the system is "open" to the external world (the more there are links), the longer is the time span available to interact (and thus memorize) with the environment (high

ability oflearning). Notice that such a time span is the time interval in which the interaction can occur (the interaction time does not necessarily last for the full interval). Thus, if this time span is longer, the interaction probability with

the external world is higher. Moreover, the ability in memory storing also turns out to depend on the brain internal parameters, which may represent subjective

Dissipation and consciousness 135

attitudes (such as the biochemical specificity of the subject). The ability for

information recording thus may be different under different circumstances, at different ages, and so on. In any case, a higher or lower degree of openness

(measured by n) to the external world may produce a better or worse ability in learning, respectively (Alfinito and Vitiello 2000b--d). In this connection let me recall that changes in the system-environment coupling act at the basic dynami­calleve] by pushing the system to a different ground state, which in turn reflects into a change of the system evolution ( cf. Section 6.3) ending up, at a higher

level, into a rearrangement or formation or depletion of the neuronal connec­tions. Of course, as already said in Section 7.1, here and in the following I do not attach any philosophical content to the expression "external world". It is only used in a mathematical and physical sense: there are two interacting physical systems, the brain and the external world (whatever it is, for a philo­

sophical discussion of"external world" in quantum brain dynamics see Globus 1998, 2001a).

It is to be remarked that a threshold, say k, exists for the k modes, namely

only modes with momentum larger than k may be recorded. Such a kind of "sensibility" to external stimuli depends on the internal parameters. On the other hand, for given values of these parameters, the threshold k may decrease

as the number oflinks with the external world grows. A consequence of the existence of the threshold on k is that it excludes

modes of wave-length greater than the cut-off value 1/k, for any given nat a

given time t. Thus, correlated domains of sizes less or equal to 11 k are involved in the memory recording, and such a cut -off shrinks in time for a given n. On the other hand, a growth of n opposes such a shrinking. Infinitely long wave­

lengths (infinite volume limit) are thus actually precluded and at a given time

t transitions through different vacua (which would be unitarily inequivalent in the infinite volume limit) are possible. Thus we see how the processes of "association of memories" and of "confusion" of memories (see Sections 6.4 and 6.5) may occur and how "fixation" or "trapping" in some specific memory

state is avoided. In conclusion, more persistent memory codes (with a spectrum more

populated by the higher k components) are also more "localized" than shorter

term memory codes (with a spectrum more populated by the smaller k compo­nents). We thus reach a «graded" non-locality for memories depending on the

number of links n and on the spectrum of their k components, which is also related to their life-time or persistence. Since k is the momentum of the dwq excitations, it is expected that, for given n, the "more impressive" is the external

136 My Double Unveiled

stimulus (i.e. the stronger is the coupling with the external world) the greater is

the number of high k momentum excitations produced in the brain and, consequently, the more "focused" is the "locus" of the memory.

I observe that the model provides a first understanding of how opposite features, such as "non-locality" from one side and "localization" from the other side, may even coexist, in the sense that they are not mutually incompatible in a rigid and definitive way. Rather they correspond, in a much less naive scheme, to different dynamical regimes, continuously merging one into the other, in

dependence on the behavior of well specified variables and parameters. The results presented above appear to fit well with the physiological observations, mentioned in the previous section, which show that the more the brain relates to external objects, the more neuronal connected domains will form. Since the description of such physiological findings was not planned at the beginning of

the model formulation, this fitting has actually the flavor of predictivity. This makes the model quite appealing.

As mentioned, functional connections are observed to be highly dynamical.

They may quickly change and new configurations of connections may be

formed extending over a domain including a larger or a smaller number of neurons. Also such a picture may find its description in our model. Let me indeed recall that the electromagnetic (em) field propagates in a self-focusing

fashion in ordered domains, thus producing a highly dynamic net of filaments (see Section 3.7). Such a mechanism has been proposed to be at the basis of the

dynamical processes of assembly and disassembly of microtubules and it can also model the neuronal connection formation and their highly dynamic

assembly and disassembly. The prerequisite, in the quantum model, for the connection formation is the dynamical generation of domains of correlated dwq. As seen above, the size and the life-time of these domains appear to

depend on the number oflinks that the brain sets with its environment and on

internal parameters, in agreement with the observed plasticity of the brain. It is interesting that physiological observations show that the recruitment of

neurons in correlated domains occurs not in a process of" one cell to another

one at a time", as in the traditional view of neuronal communication through electrical signals, but "all at once over an ever larger group" and is mediated by "a chemical, than can bias large number of neurons to be activated simulta­

neously" (Greenfield 1997a). The emergence of such a simultaneous coherent cooperativity among neurons is exactly what the dissipative quantum model predicts. The quantum model provides the dynamical ground which manifests in simultaneous neuronal activation under the "recruiting signal". The further,

Dissipation and consciousness 137

necessary step forward to be made is to disclose how the underlying dynamics

controls the details of the chemical scenario.

I finally observe that as an effect of the "dying" at different times of differ­

ent k modes, the spectral structure of a specific memory code may be "corrupt­

ed", thus allowing for more or less severe memory "deformations". These

"defects" in the memory codes may be repaired, or at least circumvented, by

resorting indeed to the possibility of associations of memories, or paths through

memories (which our model predicts), which we commonly experience when

we try to "reconstruct" some weakened memory, appearing to us initially as a

vague, fuzzy memory, which however we might succeed to make dear again by

going "from memory to memory".

7.6 Mind the gap!

The dwq acquires a non-zero effective mass due to the finite size of the correlat­

ed domain (cf. Section 6.4). Such a mass acts as a protection threshold against

unwanted perturbations since an expense of energy above that threshold is

required in order to excite dwq. The non-zero effective mass produces "inertia"

in the dwq propagation through the finite size domain and therefore a time­

delay in setting long range correlation. This fits with Libets observation on the

time-delay of the neuron recruitment in a correlated assembly and it may

describe the dynamical spreading of the modulatory chemicals. We have seen

that the finite size of the correlated domains also leads to possible associations

or even to confusion of memories. But let me consider, following Greenfield

(Greenfield 1997a), what is the scenario in extreme cases.

Consider first the case of the very small neuronal assembly. This can occur

when the epicentre is so weak (the external driving stimulus is not so strong)

that a large number of neurons cannot be excited in a collective mode. In the

quantum model this corresponds to having very few "links" interlaced with the

external world, and in this model we expect sudden shifts from one vacuum

(one memory) to another one (another memory) of the too small correlated

domain, a typical situation of"confusion". When one is dreaming the external

inputs are not so strong, the number oflinks with the external world is in fact

really small. Since the EEG of a dreaming subject turns out to be similar to

when the subject is awake, some (low) degree of consciousness may be attached

to the dreaming activity. It is the case of "fragile, little bits of consciousness"

(Greenfield 1997a), I would say of very short and unstable permanence in one

138 My Double Unveiled

single vacuum of the correlated domain, with sudden transitions to other vacua;

in fact in dreams we experience sudden change of scenarios, of facts, we feel flooded by a rapid succession of emotions. It would be interesting to study

other cases of an extreme low number oflinks with the external world such as in autism and coma states.

In the dissipative model high momenta (in the spectrum of the memory code) are associated with small domains. Then it might be that what is really "surviving" into the low "level of consciousness" (Hobson 1998) associated to

dreams (what we actually dream about) are indeed those "pieces" of informa­

tion corresponding to these high momenta, which, having also a longer life­time, are left out as relics of information codes. These deformed or corrupted information codes might even be felt in the dream with the flavor of new, never lived situations, as not belonging to our past, in that intricate blend or mix,

between dream and thought (Scalzone and Zontini 1998), we experience in dreaming, presenting sometimes an obscure core, as the center of a vortex, which Freud has called the "dream navel" (Freud 1900).

Another cause of too small neuronal assembly may be in the weak neuronal recruitment; in other words, in the low level of connectivity. Physiology tells us that this is the case of the brain with a low level of relation and experience with the external world. These are also the cases where the dissipative model predicts small correlation lengths (correlated domains of small size) due to lack oflinks to the outside world, or else a low coherence in the correlation so that the self­

focusing propagation of the em field (out of which neuronal connections may be generated) is inhibited. Typically, in such cases the subject appears to be easily "distracted" from a certain object by another upcoming sensory input. He can be emotionally taken by a new scenario, apparently dominated by any epicentre triggered from the outside.

Similarly, during activities where very strong signals come up in a rapid

succession the subject appears dominated by the incessant succession of the inputs. The arousal level of the subject, his emotional involvement, may be then very high. The modulatory chemicals, able to make the neuronal cells receptive

to the recruitment signal, produce many competitive domains in so short a time that none of them has really enough time to expand to the size required to put attention on something. In the quantum model such an inflation of different external inputs would correspond to a null information "in the average", and

thus it would produce no symmetry breakdown at all, and in turn no formation

of extended correlated domains. When the formation of such domains is inhibited the system cannot produce a "coherent response" to the external

Dissipation and consciousness 139

concurrent stimuli and the subject is dominated by them. His functional

stability is lost (cf. Section 3.7). Laboratory observations show that cognitive impairments, such as defects in learning and memory, are observed to be

related to the amount of reduction in the dendritic microtubule associated protein MAP-2 and to the selective destruction of of neurona] microtubules caused by colchicine (Kudo et al. 1990; Bensimon and Chernat 1991). On the other hand, sabeluzole, which is a memory enhancing drug, increases fast axonal transport in microtubules (Geerts 1992).

Let me observe that the impossibility of the formation of a correlated domain of a convenient size and the consequent impossibility of singling out

one specific vacuum could be thought to be analogous to the impossibility of the reduction of the system state in the Penrose-Hamer off model.

Even the feeling of pain, with the pain threshold that may change in

dependence on our biorhythms throughout the day, may be interpreted in terms of neuronal assembly (Greenfield 1997a). In this case drugs such as morphine may reduce the extension of the connected domains and give the sensation of reduced pain. It is intriguing that in dreams, where correlated

domains are small, the reported experience is that pain is absent (on the contrary, in dreams we can experience nightmares where we feel at the mercy of uncontrollable forces). An interesting question to ask is then about the nature of the mechanisms activated by acupuncture when applied to control (to reduce) the feeling of pain. This sends us back to our discussions in Chapter 5

on the intracellular signal transport in the quantum model and on anesthesia. In the literature is also reported the finding in schizophrenia of specific

alterations in two microtubule associated proteins, MAP-2 and MAP-S. These contribute to the establishment and maintenance of neuronal polarity, and thus to the signal transduction in the related dendrites. Their alterations thus reflects

on the functionality of the neuronal correlation (Arnold et al. 1991 ).

What can be the phenomenology in the opposite case of abnormally large neuronal assembly? The dissipative model would predict a more strict inequi­valence among the vacua, namely a stronger resistance in switching from one to

another one of them, an inclination to "fixations", to be trapped in one of the vacua and to remain fixed on the information, image or idea, there coded. This is also expected on physiologica] grounds, where, in the absence of competing epicenters, the subject is expected to show a strong continuity, a perseverance in what he has come to think. Such a sort of control on the incoming change­

able stimuli will make the world appear to him as remote, distant, grey, as in clinical depression cases where the patient appears unable to get emotionally

140 My Double Unveiled

involved, "the opposite of the glowing bright colors of the childs perspective, (Greenfield 1997a).

Of course, the "normal, situation is the one where many factors come in

and concur in determining the size of the connected domains in an highly dynamical regime. This results in a continuously varying degree of conscious­ness, in the familiar experience of our changeable degree of attention, of our

changeable ability in registering or not a specific informational input among many impinging on our senses, and so on. This is why warnings such as the popular "Mind the gap!, in the London tube are needed. In the quantum model the capability to be "alert, or "aware, or to keep our "attention, focused on a

certain subject for a short or a long time is determined by the life-time of the excited dwq (cf. Section 4.4). Since modes with longer life-time are the ones with higher momentum, we expect that the stronger is the coupling (pay

attention, please!) with the external world, the better and longer we can keep alert. It is also interesting that external stimuli modulated in rhythms in space (visual rhythms) as well as in time (musical rhythms) appear to play a relevant

role in cognitive sciences experiments (Olivetti Belardinelli 1986). Awareness

and perception of rhythms appear to live on the same psychological edge.

7·7 My double, Myself

I will introduce in this section some suggestions which are directly prompted by

the mathematical formalism of the dissipative quantum model.

The mathematical and physical meaning of the tilde-system is to describe the environment to which the brain is permanently coupled (linked). Since the brain is intrinsically an open system, the tilde-system can never be neglected ( cf.

Section 6.4). The tilde-modes thus might play a role as well in the unconscious brain activity. This may provide an answer to the question "as whether sym­metron modes would be required to account for unconscious brain activity,

(Stuart, Takahashi and Umezawa 1978, 1979). As already observed, the tilde­

modes might tell us something about that fuzzy region between fragile con­sciousness and the obscure unconscious core of the dream activity.

The mathematical form of the coupling of A with A describes nonlinear dynamical features of the A system. Technically speaking the nonlinearity of the

dynamics describes a self-interaction or back-reaction process for the A system (Vitiello 1995). A thus plays a role in such self-coupling or "self-recognition,

processes. Again, here I need to stress that the word "self' is only used in the limited sense of mathematical nonlinearity (coupling of the A system with itself).

Dissipation and consciousness 141

The A system is the "mirror in time'' image, or the "time-reversed copy" of the

A system. It actually duplicates the A system, it is the A systems Double and since it can never be eliminated, the A system can never be separated from its Double. The role of the A modes in the self-interaction processes leads me to

conjecture that the tilde-system is actually involved in consciousness mecha­nisms (Vitiello 1995-2001). Thus the overall mathematical structure of the

model and in particular the specific dissipative character of the dynamics strongly point to consciousness as a "time mirror", as a "reflection in time"

which manifests as nonlinear coupling or dialogue (Desideri 1998) with the inseparable own Double (Vitiello 1997, 2000a, 2001). In some sense, the

unavoidable coupling with the external world is "internalized" in the dialectic, permanent relation with the Double.

The "doubling" of the self is actually a very old literary metaphor. Plautus invention of the "doubling" of Sosia in his comedy Amphitruo (Plautus, 189 B.C.), or even the falling in love of Narcissus with himself mediated by his "reflection" in the water, are famous examples of such a metaphoric use of the

"doubling ". On the other hand, in the ancient Vedic tradition (Kak 1996),

consciousness also flows between two poles: an identity of self and an identity

with the processes of the Universe. It is quite interesting to me that, although in its limited mathematical meaning previously mentioned, such a doubling plays a crucial role in the dissipative model.

Consciousness seems thus to emerge as a manifestation of the dissipative

dynamics of the brain. In this way, consciousness appears to be not solely charac­terized by a subjective dynamics; its roots, on the contrary, seem to be grounded in the permanent "trade" of the brain (the subject) with the external world, on

the dynamical relation between the system A and its Sosia or Double A, perma­

nently joined (conjugate) to it. I am absolutely not saying that A acts as a mirror of the outside world. On the contrary, consciousness is reached "through" the opening to the external world. The crucial role of dissipation is that self-mirror­ing (in the mathematical sense explained above) is not anymore a "self-trap" (as for Narcissus), the conscious subject cannot be a monad. Consciousness is only

possible if dissipation, openness onto the outside world is allowed. Without the "objective" external world there would be no possibility for the brain to be an open system, and no A system would at all exist. The very same existence of the

external world is the prerequisite for the brain to build up its own "subjective simulation" of the external world, its own representation of the world ( cf.

Section 6.3). Of course, I am here assuming the standpoint of the physicist, not questioning the "existence" and" objectivity" of the external world.

142 My Double Unveiled

It would be interesting to analyze the relation between consciousness as

depicted above by the mathematics of the dissipative model, namely as perma­nent trade between subjective and objective, and the phenomenological search

for the fundamental correlation between subjective and objective in the Varela approach (Varela 1988), from one side, and the matching, the absence of contrast between subjective and objective streams, in Globus' analysis (Globus 1998, 2001a, 2001b).

The informational inputs from the external world are the "images" of the

world. Once they are recorded by A they become the "image" of A: A is the "address" of A (cf. Section 6.4), it is identified with (is a copy of) A. We have

seen that such a process implies a "breakdown,, a "lack" of symmetry: memory as "negation" of the symmetry which makes things indistinguishable among themselves (Vitiello 1997); memory as "non-oblivion,, literally the aATj8ELa, i.e.

the word used by the ancient Greeks to denote the "truth" (Tagliagambe 1995). As already mentioned, the finiteness of the correlated domains implies that

recording memories requires some expense of energy. Thus, unavoidably, we are led to make a "choice,, an "active" selection among the many inputs we

receive: we record only those that we judge worthwhile to expend some energy for, the ones to which we attribute a "value", which involve our "emotion". It

is the specific information received through those selected inputs which then

becomes "our memory", it becomes "our truth" (aATj8Eta, indeed). It is here, in such a map of values, that our memory depicts our "identity" and, since our choice is unavoidable, the emergence of the identity is also a "necessary" event.

In fact, mathematically speaking, in the model the brain state is "identified" by

the collection of the memory codes ( cf. Section 6.4).

Summing up, the subjective representation of the external world in terms of A, at the same time, coincides with the self-representation ("identification")

(recall that A is, in a mathematical sense, the environment and the "copy" of A).

As the brain develops and establishes more links with the environment, extended domains of connected neurons are formed, and "hence, these experi­ence-related connections account, to a certain measure, for your individuality,

your particular fantasies, hopes, and prejudices" (Greenfield 1997a). Observations show that such a connected assembly of neurons does not

need to remain "intransigently hard wired"; on the contrary, plasticity of connectivity appears to characterize the brains functionality. The dissipative model also excludes any rigid "fixation, or "trapping" in certain states, as we

have previously seen. Such a plasticity leaves open the possibility for our per­sonal growth, for our capability to change our view of the world as we develop.

Dissipation and consciousness 143

We are not simply spectators or VICtims of "passive perceptions". "Active

perceptions", our active choices have also a part in our continuous interplay

with the world. Plasticity allows agency, volition and intentionality which have

a non-negligible role in the raising of our consciousness (Nelson 2001).

Pribram remarks (Pribram 2001) that there is always an "attention" content in

the input, an "intention" content in the output, and a "thought" content in the

memory processes and all of it participates in a "vast unconscious processing". Freeman's work points to evidence of synaptic connections that "act as a unified

whole in shaping each intentional action at each moment" (Freeman 1997). Freeman also stresses that brain actually processes meanings rather than

information (it is an obvious fact that information does not automatically imply analysis and understanding, information is necessary, but not sufficient for

comprehension). In Freeman's view meanings are "intended actions", namely

the meaning belongs to (is in) the subject and arises from the "active" percep­

tion of that subject, which includes intentionality. The brain as an adaptive system permanently conjugates the memory of the past, namely the "knowl­

edge" of the causes, which deterministically pushes forward, with the goal­

oriented "activity" of the present, which teleologically attracts to the future

(Caianiello 1981). In the light of Freeman's suggestion, the tilde-modes express

meanings or "meaningful representations" rather than just representations.

The conclusion is that one reaches "an active point of view" of the world

(Desideri 1998; Vitiello 1997), which naturally carries in it the "unfaithfulness"

of subjectivity. But such unfaithfulness is precious. It is exactly in such an unfaithfulness that the map of the values (Freeman meanings) which identify

the subject has to be searched.

The openness to the external world, dissipation, thus implies the capability

of the brain to respond to the external stimuli at each specific instant of time, to be "present", namely to singling out at each specific instant of time one specific

vacuum among those entering the superposition of the brain state. From one

side, openness thus guaranties against the risk of remaining "trapped" in one

single vacuum, without updating the vacuum «choice" to the present time, it guaranties "presence", "conscious feeling" of that specific, "actual" vacuum. On

the other hand, it also avoids blind traveling, running without "looking inside",

over the superposition of memory states which makes the brain state. In the

absence of the healthy or normal state of openness, as seen in Section 7.6, too

small or too large neuronal correlated assembly may turn into "low level of consciousness". The unconscious brain activity may be then related to lack of

openness or to too high level of openness (too many inputs in a too rapid

144 My Double Unveiled

succession), which paradoxically may correspond to "closure", producing too

slow, or even absent, adaptive capability to the present or too high emotional arousal. The dynamics of the correlated domains discussed in the previous

sections again seems to reconcile extreme, apparently opposite situations and conditions. In the dissipative quantum model unconscious brain activity and consciousness appear to be merging dynamical regimes, different modulations in the dialogue with the Double.

It would be interesting to try a first approach to the "hard problems" along

these lines suggested by the mathematical formalism of quantum field theory: how external stimuli and experiences become part of our self. Also interesting would be relating the "doubling" mechanism to the so-called model of con­sciousness with dual-focus in linguistic studies (Stamenov 1997). It is supposed that there are two different attention-controlling systems in the brain/mind

which could perform in a dissociable way. Then one can "think unconsciously or semiconsciously (i.e. think while focusing ones attention on some other mental activity)". Among the main features of the dual-focus system I will only mention that it may explain the performance of both "monitoring and control"

over the execution of mental patterns. This also seems to suggest a sort of self­mirroring as in the dissipative model. Note that dissipation introduces also in the quantum formalism the "notion of loop" (Cordeschi, Tamburrini and Trautteur 1999; Trautteur 1995, 1997), which is commonly found in classical studies of consciousness. The above mentioned self-recognition process

includes reflection loops as well as control loops of the subject -environment interaction. Due to the self-identification process these loops are self-reference loops (Cordeschi, Tamburrini and Trautteur 1999) (cf. also Section 3.7).

Finally, the brain, as described by our model, is at any instant of time (locally in time) in a minimum energy state: the brain state is well "identified"

at any given instant "out of the becoming". Nevertheless, the brain is also fully

immersed in the irreversible history of its changeable states. Such an irrevers­ibility only manifests itself when the brain is considered as isolated from its Double. Only in such a case is the entropy found to increase (Vitiello 1995), and

the arrow of time, its history, becomes manifest. The conscious identity thus emerges at any instant of time, in the "present", as the minimum energy brain state which separates the past from the future, that "point" on the "mirror of

time" where the conjugate images A and A join together. In the absence of such

a mirroring there is neither consciousness of the past nor its projection in the future. The subject identity may only emerge in the dissipative dynamics, in its interplay with the objective external world. Eventually, the intrinsic dissipative

Dissipation and consciousness 145

nature of the brain excludes any model of consciousness centered exclusively on "first person" inner activity. Dissipation manifests itself as a "second person",

the Double or Sosia, to dialogue with.

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Index

A absorption 50, 97

actin 90

adaptive system 19, 132, 143 adenosine triphosphate 48-51, 53,

54, 62, 104 amplitude 17, 70, 93-95, 118

Anderson-Higgs-Kibble mechanism 37, 98

anesthesia 60, 91, 98, 139 arrow of time xiv, 103, 105, 107,

114-116, 144

association of memories xv, 73, 78,

112, 135, 137

B

binding problem 114 blood cells 46, 99

Bogoliubov transformations 109 Bose condensation 15, 39-41, 44,

54, 68,70, 76, 78, 126

Bose-Einstein distribution 32

boundary effects 38, 55

c cell membrane 42, 43, 45, 46, 99

chaos 46, 47, 112

coherence xiii, 2, 15-17, 21, 31-33, 35-37, 41, 42, 46, 56, 57, 59-62,

75, 77, 79, 81, 83, 85, 86, 90, 94,

97, 101, 128, 138 coherence length 16, 40, 81, 83

coherent domains xiv, xviii, 16, 35, 40,84,99-102

coherent response 60, 114, 138

coherent state 33, 35, 113

collective mode xii, 1, 7, 13, 15, 16,

31, 33, 69,71, 73, 75, 76, 77, 96,

110, 118, 120

commutation relations 68

condensation 16, 32-35, 39, 40, 54, 55, 75-77, 81, 84, 85, 98, 99,

106, 114, 134 confusion of memories xv, 112, 117,

135, 137 consciousness xv, 9, 10, 86, 98, 99,

115, 123-128, 130, 131,

132-134, 137, 138, 140-145

corticon 82, 83, 87-91

crystal 11-19,22, 28, 30-34, 56, 69,

76, 81, 82, 92

cytoskeleton 51, 57-60, 85, 87, 90, 92, 96, 99, 114,128

D Davydov vii, xiii, xviii, 2, 38, 40-43,

45, 47-49, 51-54, 89, 91, 149, 157

decoherence 18, 86

degrees of freedom xiii, xv, 23, 29, 103, 110, 111

dendrite 139

Descartes 126 dipole wave quanta 55, 60, 61, 89,

91, 92, 98-100, 106, 111, 112, 113, 114, 116, 117, 134-137,

140 disordered states 75

dissipation xiii, xiv, 38, 48-50, 53,

61, 103, 111, 112, 114, 116, 12~

123, 125, 141, 143, 145

160 Subject index

dissipative system xiv, 4 7, 107, 120 DNA xi, 7, 58,76

domain formation xiv, 16, 40, 56, 83, 84,86, 99, 116, 117, 123, 138, 139

Double xv, 123, 140, 141, 144, 145

doubling of degrees of freedom xiii, 103, llO, 111, 120, 141, 144

dynamical rearrangement of symmetry xii, xiii, 31, 68

E EEG 84, 137 electret 53-55, 63, 64 electric dipole xiii, 44, 48, 53, 56, 87,

89-91, 100, 101, 104, 128, 134 electromagnetic field 36, 47, 54, 55,

57, 84 energy transfer 2, 47, 48, 63 entropy 62, 63, 75, 110, 115, 144 exclusion principle 32

F fermions 32 flux quantization 40 frequency 17, 42, 44, 45, 4 7, 58, 59,

62, 63, 84, 94, 95, 116, 117 Frohlich xiii, xvii, xviii, 2, 5, 41-44,

46, 47, 51-53, 55, 69, 89

G Gabor 93, 95, 96 gauge fields 35, 36 glia cells 73 Goldstone theorem 31, 55 gradient forces 58

H

Heisenberg fields 24, 25, 29 Heisenberg uncertainty 16 Hilbert space xiv hologram 2, 70, 95, 131 holonomic brain theory 70, 87, 93,

96 hydrogen bond 49, 60, 91

I interacting fields 24, 39 interference 37, 60, 93-95, 98, l11,

112, l14, 120

J Josephson junction 46

L laser 10, 16, 17, 32, 56, 79, 93,

95-97, 100 Lashley 70, 71, 93, 131 living matter xi, xii, xiii, xiv, xvii,

xviii, 2, 5, 7, 8, 10, 12, 19, 23, 40-43, 49-52, 56, 57, 60, 62, 63, 70, 85, 89, 92, 101, 104

long range correlation 9, 12-14, 16-18, 31, 33-35, 42, 44, 46, 52, 54-56, 69,70, 72,74, 76, 77, 80, 81, 83, 91, 99, 120, 121, 137

M macroscopic quantum system 17,

83, 86

many body physics xviii Maxwell equations 17 memory capacity xiv, 84, 102-106,

111, l14, 117, 120 memory recording 75-77,83, 84,

106, 107, 111, 115-117, 134,

135, 142 metabolism 9, 62 mirror modes 120 myosm 50, 90

N Nambu-Goldstone boson 31-35,

55, 56, 75, 76, 78,82, 85, R7,89, 91, 92, 98, 106, 120

naturalism xii, 2 neural networks 7, 20, 68, 72, 77,

97, 117-121

neuron doctrine 74

non-perturbative methods 28, 34, 35, 39, 61, 62, 86, 105

nonlocality 83

0 operator fields 23, 29 order parameter 29, 31, 33, 39, 40,

44, 54, 56, 59, 77, 106, 119 ordered state 16, 33, 40, 75, 76, 81,

106 overpnntmg xiv, 84, 103, 105, 106,

111, 112, 120, 121

p

perturbation theory 21, 25-28, 34, 38, 61, 64

phase difference 93-95 phase transformations 35 phase transition 28, 34, 40, 78, 84,

106, 112 phonon 12-15, 19, 28, 31-33, 49,

50, 69,82, 92 photoelectric effect 17 photon 16, 32, 50, 57, 97, 98, lOO

Planck 7 Planck constant 14, 15 plasticity 19, 45, 52, 101, 119, 132,

136, 142, 143 polarization 44, 53, 54, 56, 57, 63,

96, 97, 128

Pribram viii, xviii, 2, 9, 70, 71, 73, 87, 89, 93, 95-98,131, 143, 153, 155, 156

Q

quantum computation 20, 130 quantum dissipation 108, 111

R

random kinematics 8, 20, 45 RNA 79, 83

s Schrodinger 2, 5-8, 45, 62, 63, 69,

76, 96, 131, 133

Subject index 161

self-focusing propagation 34, 59, 85,

96 self-induced transparency 98 self-interaction 38, 140, 141 self-referentiality 61 self-trapping 49 short range forces 8, 14 soliton 37-40, 43, 49-51, 53-55, 60,

62, 64, 89 Sosia 141, 145 spontaneous symmetry breaking xn,

21, 27, 28, 31-33, 35, 41, 42, 52, 54, 56, 63, 68,69, 72, 74-76, 82, 92, 107, 116, 120

squeezed coherent state 113 structure and function 11, 12, 19,

92, 124

superposition principle 38, 128, 130 superradiance 97, 98 symmetron 82, 83, 87-89, 91, 106,

140

T thermal effects 54, 55, 63, 64, 86 thermalization 55, 61, 62, 97, 113 thermodynamics 15, 18, 115 time mirror 141 time reversal 103, 105 time-reversed image 110, 114 tubulin 51, 90, 97, 128, 132

v vacuum state 15, 18, 31, 33, 35, 36,

39, 42, 55, 56, 63, 68, 74-78, 80, 84, 85, 91, 106, 108-115,

118-120, 134-139 von Neumann theorem 29

w water electric dipole 54, 55, 89, 90,

92, 99 wavefunction 18, 86

wavelength 37, 93, 100

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