The Gravitational Constant: Generalized Gravitational Theories and Experiments

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Series II: Mathematics, Physics and Chemistry - Vol. 141

The Gravitational Constant: Generalized Gravitational Theories and Experiments

edited by

Venzo de Sabbata University of Bologna, Italy

George T. Gillies University of Virginia, U.S.A.

and

Vitaly N. Melnikov Moscow University, Russia

Springer Science+Business Media, LLC

Proceedings of the NATO Advanced Study Institute on The Gravitational Constant: Generalized Gravitational Theories and Experiments Erice, Italy April3Q-May 10, 2003

A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN 978-1-4020-1956-2 ISBN 978-1-4020-2242-5 (eBook) DOI 10.1007/978-1-4020-2242-5

Published by Kluwer Academic Publishers, P.O. Box 17, 3300 M Dordrecht, The Netherlands.

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All Rights Reserved © 2004 Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2004 Softcover reprint of the hardcover 1 st edition 2004 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

CONTENTS

Preface ..................................................... vii

Welcome ...................................................... ix

Memorial day: Peter G. Bergmann ............................ xiii

Screening and Absorption of Gravitation in Pre-Relativistic and Relativistic Theories .................... 1

Horst-Heino von Borzeszkowski, T. Chrobok and Hans-Jurgen Treder

Conformal Frames and D-Dimensional Gravity ................... 39 Kirill A.Bronnikov and Vitaly N.Melnikov

Graviton Exchange and the Gravitational Constant ............. 65 Michael J.Clark

Some base for Quantum Gravity .. : ............................. 81 Venzo de Sabbata and Luca Ronchetti

Brane-inspired models in Gravitation and Cosmology .......... 113 Dmitri Gal'tsov

Experimental test of a Time-Temperature formulation of the Uncertainty Principle ................................ 139

George T.Gillies and S.W.Allison

The Newtonian Gravitational Constant: Present Status and Directions for future Research .......................... 149

George T.Gillies and C.S.Unnikrishnan

Toward testing the Fundamental physics by SNIa data ......... 157 Wlodzimierz Godlowski, Marek Szydlowski and Wojciech czaja

Investigation of Schmutzer's Exact External spherically Symmetric Static solution for a Central Body within the framework of the 5-Dimensional Projective Unified Field theory ...................................................... 193

Alexander Gorbatsievich

On exact solutions in Multidimensional Gravity with antisymmetric forms ......................................... 205

Vladimir D.Ivashchuk

50 Gravity and the discrepant G measurements ................ 233 Jean-Paul Mbelek

v

vi

2-component cosmological models with perfect fluid and scalar field: exact solutions ........................... 247

Vitaly N.Melnikov and V.R.Gravilov

Constraints on Non-Newtonian Gravity from recent Casimir Force measurements .................................. 269

Vladimir M.Mostepanenko

Searching for Scalar-Tensor Gravity with Lunar Laser Ranging ......................................... 289

Kenneth Nordtvedt

Is a hypothetical Long Range Spin Interaction Observable with a Laboratory Detector? ..................... 313

Rogers C.Ritter and George T.Gillies

Prospects for a Space-Based determination of G wi th an error below 1 PPM .................................... 331

Alvin J.Sanders and George T.Gillies

Projective Unified Field Theory revisited and adapted to the new measured values (WMAP). New results refer to approximate static interior and exterior solution of a spherically symmetric perfect fluid sphere with applications to celestial bodies, Einstein effects with particular treatment of the perihelion shift of Mercury including the quadrupole moment of the sun ............................ 341

Ernst Schmutzer

The Interface of Quantum Mechanics and Gravity .............. 381 C.S.Unnikrishnan

Quaternionic Program ........................................ 395 Alexander P.Yefremov

Subject Index ............................................... 411

PREFACE

This XVIII Course of the International School of Gravitation

and Cosmology held in Erice from April 30 to May 10, 2003, has

been very successful and has provided an up-to-date

understanding of the progress and current problems on the

Gravitational constant both on "Generalized Gravitational

Theories and Experiments" either in Laboratory with Casimir

force measurements, or in space at solar system distances and

in Cosmological observations.

We have had a qualified participation of more than fifty ASI

research-workers on different fields (theoretical and

experimental physicists, astrophysicists, astronomers,

cosmologists from a variety of backgrounds, mathematicians)

coming from various NATO and partner NATO countries (as, for

instance, Belarius, Bulgaria, France, Germany, Israel, Italy,

Kyrgyzistan, Latvia, Norway, Poland, Russia, Turkey, U.K.,

USA) .

We had lectures on different aspects of the state and

prediction of unified theories of the physical interactions

including gravitation as a cardinal link, on the role of

experimental gravitation and observational cosmology in

discriminating between them, on the problem of precise

measurements and stability of fundamental physical constants in

space and time, and of the gravitational

particular.

constant in

Thus we have had timely lectures in recent advances in unified

and scalar-tensor theories, theories in diverse dimensions and

their observational windows, gravitational experiments in

space, rotational and torsional effects in gravity, basic

problems in cosmology, early universe as an arena for testing

unified models; basis for Quantum Gravity, brane-inspired

models in Gravitation and Cosmology.

vii

viii

Moreover we have considered cosmological variations of G,

absorption and screening in prerelativistic and relativistic

theories, constraints of Non-Newtonian Gravity from the recent

Casimir Force measurements. Search for scalar-tensor Gravi ty

with Lunar laser ranging. Special attention has been paid to

the increasing role of fundamental gravitational experiments in

space, the role of basic standards and determination of

cosmological parameters, prediction of 5-dimensional projective

unified field theory on cosmological, astrophysical and quantum

effects, long range spin interaction, space-based determination

of G, interface of quantum mechanics and gravity, Quaternion

program.

Besides the theoretical aspect, a large part of the Course was

devoted to the examination of laboratory experiments and space

experiments for the measurement of big G and tests of the

equivalence principle including the measurement of big G using

a superconductor gravimeter.

We wish to thank all the lecturers and seminar speakers who did

some much time to make the School successful, and all

participants for contributing to the very scientific and human

atmosphere.

Venzo de Sabbata

(Director of the School)

Erice, 1 May 2003

WELCOME

Only some points before the Gillies lecture

It is a pleasure to welcome you all at this eighteenth

Course of the International School of Cosmology and Gravitation.

The Director of Ettore Majorana Center for Scientific

Culture Professor Antonino Zichichi, who cannot be present at this

moment, (maybe he will come some days) has entrusted me with the

welcome address on his behalf.

I thank all lecturers, who have accepted our

invitations to come to Erice to give lectures (whitout any

renumeration, as is usual in this School), from their different

points of view, on the problem of Gravitational constant.

As you know from the poster, we will present different

aspects of the state and predictions of unified theories of

physical interactions including gravitation as a cardinal link,

the role of experimental gravitation and observational bosmology

in discriminating between them, the problem of precise measurement

and stability of fundamental physical constants in space and time,

the gravitational constant in particular, the basis for non

Newtonian gravity, the constraints on non Newtonian gravity from

the recent Casimir force measurements, gravity and non locality,

neutrinos and gravitation, absorption and screening in

ix

x

relativistic theories, temporal and spatial dependence of

empirical gravitational constant, charges and fundamental

constants in unified theory, torsional effects in gravity,

observational windows of extra dimensions and unified models,

searching for scalar-tensor gravity with lunar laser ranging,

motions of a precise torsion pendulum, early universe as an

arena for testing unified models, 5-dimensional projective

unified field theory for cosmological astrophysical and quantum

effects, cosmic microwave background anysotropy as test of

variability of fundamental constants and so on.

I thank all lecturers also, because they accepted

as far as they were able, to be present the whole time

and to participate in all discussions, which certainly

will arise among all participants.

In fact this is one of the important tasks of these Courses.

As perhaps many participants already know, because they were

present in previous Courses, the atmosphere of the School is

very friendly, and exchanges of ideas can occur quite freely

among all participants including lecturers.

So we will have a very broad spectrum of subjects, of which

at first sight each has sufficient material to constitute a Course

by itself. We have considered it more important to exhibit the

various theories that attempt to give some answer to the many

problem that we have in our hands and to exchange information

on the latest developments discussing future prospects.

Xl

I really hope that this Course with all these different topics

serves to make some further progress on this fascinating subject.

Before asking Professor Gillies to address the meeting, some few

points regarding the organization of the lectures:

as you can see from the tentative time-table, we will have five

lectures each day, three in the morning and two in the afternoon

(with a break, both in the morning and in the afternoon,

for coffee). Every lecture will last no more than fifty minutes,

and after every lecture there will be a few minutes of discussion.

For lunch and dinner you can choose any of the restaurants

approwed for the School (you will see the list near the entrance),

signing a list marked "Cosmology" after every meal and

either "lunch" or "dinner". You have to pay only for beverages.

Now, before that Professor Gillies will address the meeting,

we like to commemorate Peter G.Bergmann.

Peter G.Bergmann (24 March 1915 - 19 October 2002)

Erice, 1 May 2003

Memorial day

Peter was native of Germany: he left the Germany of Hitler in

1933 and completed his doctorate (theoretical Physics) in Prague

1936. Worked with Einstein in Princeton 1936-1941 on unitary field

theories. After world war II became a professor at Syracuse

University in 1947. He was also connected with New York University

Co-founder of International Committee on General Relativity

and Gravitation (1959), and of the International Society on

General Relativity and Gravitation (1973). Author of several books

and of numerous articles. Many lectures, summer Schools, meetings

throughout the world.

In Italy: Sestriere 1958 Erice 1975, 1977, 1979, 1982, 1985,

Napoli 1983, 1984, Bologna 1984.

This is a bare curriculum that he give to me in 1985, hand

written. You can have this manuscript if you like.

Now every people know how deep were and are the works of Bergmann

on general relativity and in developing Einstein theory of

gravitation starting from the remote 1936 when he went from Prague

to the Princeton Institute for Advanced Study to work with

Einstein. In fact Peter come to Prague in 1933 as a refugee from

Hitler's Germany where as a Jew he could not have completed his

academic training. He had read some scientific publications of

Einstein and suddenly he realizes that just this kind of

xiii

xiv

theoretical research he would like to do. So he wrote to Einstein

asking to accept him as a collaborator (but he wrote at a wrong

address). As after one month there was no reply, he wrote again

enclosing a copy of a dissertation. This time he received an

answer in which Einstein wrote that he would be glad tJ talk with

him. At that time Bergmann was unaware that Einstein in the

meantime had written to Prof.Philipp Frank (the Director of the

Institute of Theoretical Physics in Prague) asking him about

Bergmann. So when Bergmann arrived in Princeton he began to work

with Einstein. He in fact worked with Einstein from 1936 to 1941

at the Institute for Advanced Study in Princeton in an attempt to

provide a geometrical unified field theory of gravitation and

electromagnetism. Within this period he wrote two article

together: A.Einstein and P.G.Bergmann in Ann.Math. 12, 65 (1938);

and A.Einstein, V.Bargmann and P.G.Bergmann in Th. von Karman

anniversary volume 212 (1941)

In 1942, Bergmann published the book "Introduction to the Theory

of Relativity" which included a foreword by Albert Einstein. This

book is a reference for the subject, ei ther as a textbook for

classroom use or for individual study. Einstein said in his

foreword: "Bergmann's book seems to me to satisfy a definite need.

much effort has gone into making this book logically and

pedagogically satisfactory and Bergmann ha? spent many hours with

me which were devoted to this end". Einstein said also in this

foreword that if general relativity has played a rather modest

role in the correlation of empirical facts and has contributed

very little to understanding of quantum phenomena (was the year

1942) it is quite possible that some of the results of the

general

nature

relativity such as general covariance of

to and

difficulties

processes.

their non-linearity may

encountered at present

help

in atomic

xv

the lavls of

overcome the

and nuclear

Many of the important works of Peter Bergmann are in fact

concerned with the quantization of field theories which are

covariant with respect to general coordinate transformations. As

to these points, Bergmann's article "General Relativity" in the

volume V of the "Encyclopaedia of Physics" was a pionier work.

Of course we cannot go through all the Bergmann's works but, as we

have said, we like to mention the great contribution that he has

made to the School of Cosmology and Gravitation in Erice from its

inception in 1974: being ever present and always discussing every

argument in great depth, always coming to the point and clarifying

every aspects of the problem under discussion. For instance in the

sixth Course of the School (1979) he discussed "the fading world

point" which deals with the nature of space-time and of its

elements, the world points. Other important discussions were on

the "uni tary field theories", during the eighth Course in 1983

where he discussed various unitary theories such as Kaluza-Klein,

scalar-tensor theories and projective theories. During the ninth

Course (1985) devoted to "Topological properties of space-time"

and during the tenth Course of Schoo,l in 1987 devoted to

"Gravi tational Measurements" Bergmann discussed 'griilvi tation at

spatial infinity' and the 'observables in general relativity'

where he showed in a very elegant way the profound difference of

the notion of observable in general relati vi ty from the

corresponding concept in special relativity (or in Newtonian

physics).

XVI

So Bergmann really has been the centre, the fulcrum of all

discussions in all the Courses of our International School of

Cosmology and Gravitation. We like to remember also that from the

early fifties onwards, one of the main goals and challenging tasks

for Bergmann was the quantization of the gravitational field. The

difficulties which he faced and solved in dealing with the full

non~linear properties of Einstein'stheory and with

non~perturbative approaches

collaborators investigated

were enormous.

the canonical

Bergmann and his

(i.e. Hamiltonian)

formalism of classical and quantum covariant field theories.

These covariant field theories of general type of the theory of

relativity are brought into the canonical form and then quantized.

These works are of the year 1948 and 1949 [Phys.Rev. 12, 680

(1949) and (with Johanna H.M.Brunings) Rev.Mod.Phys.n, 480

(1949)], and constitute the basis of the modern researches in this

field. They are followed by other important works [Phys.Rev.iU,

1018 (1951) with James L.Anderson] on the constraints in covariant

field theories and the application to the cases of gauge and

coordinate invariance specializing the problem by assuming a

quadratic lagrangian in the differentiated quantities; moreover a

beautiful work on 'Spin and Angular Momentum in G.R.' [Phys.Rev . .fi2., 400 (1953)] in presence of a semiclassical Dirac field.The problem

of origin of constraints is considered alsp in another important

work with Irwin Goldberg [Phys.Rev. 98, 531 (1954)] where there is

analyzed the group~theoretical significance of the Dirac bracket

in order to prepare the ground for the utilization of the Dirac

bracket for the quantization of generally covariant theories.

XVll

Once again we cannot describe all of Bergmann work here but we

would like to stress the fact that Bergmann clarified and made

profound contributions in the different quantization programs

based on the canonical formalism. As Bergmann himself said, "the

resul ting theory would give us answers to such questions as the

nature of a fully quantized geometry of space-time , the role of

world points in this geometry, the 'softening-up of the light

cone', and the effect of this not only on the divergences

associated with the gravitational field but with all other fields

as well".

Really Peter Gabriel Bergmann is admirable both as scientist and

as a man of great culture and humanity.

All people in Erice remember for ever his extraordinary

presence together with his wife Margot.

One of the most precious aspect of Peter was his entire kindness as

a human being. He was always courteous and gentle, always, in

every, every, circunstance.

As professor Komar said (Art Komar and his wife Alice were

very close to him and they had liked to be present during that

ceremony but were prevented for some health disease) Peter must be

remembered not only as a brillant physicist but also for his great

and total kindness.

But now I like to give a good new: through Professor Komar I

know that just before to the death he knew that the American

xviii

Physical Society awarded their first medal ever for gravitational

reseaech. This medal was awarded jointly to Peter G.Bergmann and

John A.Wheeler. So Peter was told about the joint award and knew

that he had been awarded this honour he so well deserved, just a

short while before the bad fall that he took from which he never

regained consciousness.

As a little homage of our School to Peter, we propose to dedicate

from now all the future Courses to Bergmann calling our School

THE INTERNATIONAL SCHOOL OF COSMOLOGY AND GRAVITATION

"PETER G.bERGMANN"

Now I invite all of you to a minute of silence.

Now let me to give a last comment: Peter was very sensible to the

problem of peace: in fact in the years '75 and '77, (at that time,

if I remember well, he was the President of the International

Committee of General Relativity and Gravitation) Peter gave the

best, during the Course of our School with Mercier (the secretary

of the International Society of General Relativity and

Gravitation) Hehl, Schmutzer, Rosen, Ivanenko, Sokolov, to

reunite, to unify again the International Committee that was

broken for Some political reason, and he was successtul. r~ay be

that Professor Schmutzer likes to give' some words on that

argument.

Words in commemoration of Peter G. Bergmann

Much was said and has still to be said to pay tribute to Peter G. Bergmann's scientific work and his influence on younger generations of physicists. Allow me to add here some short, very personal sentences. also on behalf of my colleagues forming till 1991 the Potsdam-Babelsberg group ofre1ativists founded by Hans-JUrgen Treder.

Peter Bergmann had a great influence on my colleagues' and my education and later scien­tific work. As to his books and papers that had the greatest fascination for us, I want to men­tion the text book "Introduction to the Theory of Relativity" , the article "General Re1ati vity" in volume V of the "Encyclopedia of Physics" and the pioneering works on the quantization of generally covariant field theories.

Aside from Peter Bergmann's substantial impact on theoretical physics and his great role as a teacher, there is still another aspect that was most important to us. Peter Bergmann will be remembered by us for his lasting friendly support of our Potsdam-Babelsberg gfC'Up which helped us to join the international community of relativists and to take part in its work over decades.

Before 1989, Peter Bergmann and his wife Margot were several times guests of our insti­tute, the Einstein Laboratory for Theoretical Physics. Vividly I remember the stimulating dis­cussions on physics. culture and politics in the Einstein house in Caputh (at that time a part of our institute), at which Peter Bergmann and his wife stayed, and later discussions during the Courses on Cosmology and Gravitation here in Erice. With sincere gratitude, we also recall that. after the unification of Germany in 1990, when - to say it in Peter's own words - the situation throughout the academic institutions of the former GDR was grim, he together with Venzo de Sabbata and Antonio Zichichi became very active to reach that we could continue our scientific work.

Although Peter Bergmann was compelled by the Nazis to leave Germany, he was ready to help many colleagues in Germany after the Second World War, in West and East. I think that by Peter's attitude and friendship we were strengthened in our efforts to do our best to prevent that the outrageous German history repeats.

Those who had the privilege of knowing Peter personally will always remember his kind­ness. modesty and integrity. We shall miss him.

Horst-Heino v. Borzeszkowski Technical University Berlin, Institute of Theoretical Physics

xix

xx

Some History of the Career of Prof Peter G. Bergmann

After coming to the United States in 1936, Dr. Bergmann joined Albert Einstein

at the Institute for Advanced Studies in Princeton, New Jersey. His contemporaries who

also worked with Einstein included Leopold lnfeld, Valentine Bargman, and others.

Among the papers Bergmann published during this time was "On a Generalization of

Kaluza's Theory of Electricity," Annals of Mathematics, Vol. 39, No.3, p. 683 (July

1938), with Einstein as the co-author.

In 1941, following his time at the Institute, Bergmann joined the faculty of Black

Mountain College, near Ashville, North Carolina. Although the college no longer exists,

it is remembered as an interesting experiment in higher education in the United States. It

was founded in 1933 and included among its faculty several artists, writers and thinkers

who were prominent in their fields at the time. Einstein was a member of the College's

Board of Advisors. During his one year term there, Bergmann was the only faculty

member specializing in physics. The college had a very informal class structure and it

sought to introduce the students to many kinds of innovations, both scholastically and

architecturally, including the first construction and use of Buck minster Fuller's Geodesic

Dome.

Immediately after his time at Black Mountain, Bergmann moved to Lehigh

University in Pennsylvania, where he joined the facuIty of the Department of Physics.

He was with them full time for a period of two years and then began to spend an

increasing fraction of his time on war-related research during the period from 1944 to

1946. While at Lehigh, he made a lasting impression on several of the undergraduates

xxi

attending college there, including Lee Iacocca, who is familiar to many for his terms as

President ofFord Motor Co. and Chrysler Motors, Inc. in the U.S. In fact, in his

autobiography, Iacocca mentions some anecdotes about his various interactions with

Bergmann.

It was also during this time that Bergmann's famous book, "Introduction to the

Theory of Relativity," was published by Prentice-Hall, Inc., New York (1946). Einstein

wrote a brief Foreword for this book, and in it he included the comment, "This book

gives an exhaustive treatment of the main features of the theory of relativity which. is not

only systematic and logically complete, but also presents adequately its empirical basis."

It is hard to imagine how one could receive any greater praise for his efforts than these

words offered by Einstein himself.

The bulk of Bergmann's career, from 1947 to 1982, was spent at Syracuse

University in New York. He founded the Relativity Group at Syracuse and worked with

many faculty and students there over the years. Much of his effort there was focused on

attempts to reconcile quantum mechanics with gravity via the introduction of a quantized

theory of gravity. He and many others hoped that such a step would help lead towards

the creation of a unified field theory, which of course was the great quest already begun

during his time with Einstein. Characteristic of his publications in those days was his

paper with 1. Goldberg, "Dirac Bracket Transformations in Phase Space," published in

the Physical Review, Vol. 98, No.2, p. 531 (April 15, 1955).

During his years at Syracuse, and thereafter during his retirement appointment at

New York University, Bergmann maintained a heavy involvement in gravitational

physics and especially in the international aspects of promoting research in it. He did this

XXll

by lending his support and credibility to many different scientific conferences on general

relativity, including the Texas Symposia on Relativistic Astrophysics, the International

Conferences on General Relativity and Gravitation ("GRG" Conferences), and of course

the International Schools of Cosmology and Gravitation held at the Ettore Majorana

Centre in Erice, Italy. He was a tireless traveler to such conferences, and was often

accompanied by his wife Margot.

It is extremely fitting that just prior to his death at the age of 87, he and John

Wheeler were jointly awarded the inaugural Einstein Prize in Gravitational Physics,

granted under the auspices of the American Physical Society. Indeed, as the citation of

the award says, he has been an " ... inspiration to genpr!ltions of researchers in general

relativity."

Dear colleagues,

We heard a lot already here about the outstanding scientist and a man of wonderful human features and great culture, about Peter Gabriel Bergmann. That is why I will dwell upon only on my personal feelings from meetings and contacts with Peter's scientific works.

My first personal meeting with Prof. Peter Bergmann was here in Erice in 1987 at the 10th course of the International School of Cosmology and Gravitation "Gravitational Measurements, Fundamental Interactions and Constants", of which I was a director. After that course the'new area appeared - gravitational relativistic metrology, which influenced very much a f1ll1her development of precise space-time measurements, gravitational wave detectors networks, studies of fundamental physical constants. role of gravity in unified models etc. Peter presented a very nice and enlightening talk on "Observables in General Relativity", which was well received by the audience.

Of course, my knowledge of his works dates to more earlier times, when we studied relativistic theory of gravitation and problems of inter-relations between general relativity and quantum fenomena in particular. First of all. I had to mention his book "Introduction to the Theory of Relativity" (with the foreword of Albert Einstein) as a good book used by many relativists. but what was even more important to us in the end of sixties and later, was his contributions to quan1ization of covariant field theories, canonical formalism of classical and quantum field theories, Dirac brackets etc.

It was a time when these problems were intensively studied in Russia due to pioneering works of K.P. Staniukovich. D.O. Ivanenko. M.A. Markov and later ofYa.B. Zeldovich. A.D. Sakharov and their colleagues and students. which became famous afterwards also.

In our group created by Prof. Staniukovich in the Russian (USSR) State Committee for Standards we started these investigations in 1967, inspired by ideas of unification of micro and macro-world fen omena in such important lie Ids as particle-like exact solutions of self-consistent systems of fields including gravitational one, quantum cosmology with fields and the cosmological constant, quantization of fields in a given gravitational background, self-consistent treatment of quantum effects in cosmology. quantization of the gravitational field itself etc. Many fundamental works were done in this group by such well known now scientists as Profs. Yu.N. Barabanenkov, V.A. Belinski, K.A.Bronnikov. M.B. Mensky, G.A.Vilkovysky. V.D.lvashchuk, V.R.Gavrilov etc. And in all these studies we used many results of Peter Bergmann. J. Wheeler. Bryce Dewitt and other outstanding scientists.

After 1987 I was here in Erice at practically all courses as a lecturer and this year as one of directors. And Peter was here at all courses except maybe one. I was always impressed by his encyclopedic and profound knowledge, his clear and up-to-date lectures, his friendly attitude_ soft and gallant manners. Usually we say in Russian that he was a very intelligent man. I am not sure that it is a proper word in English. but those who know Russian or. at any rate are familiar with the great Russian literature of the 19th century (I mean Tolstoi. Dostoevsky. Chekhov, Turgenev and others) may understand me properly.

Peter is not with us now. it is a very unusual situation here after many years of the working of this school. but I think the fact. that ll'OI11 now on the Erice school led by Prof. Venzo de Sabbata will be called as "Peter Bergmann School of Cosmology and Gravitation". is a good commemoration for him. I wish a big success to this course and many-many courses in future! Thank you.

Prof Vitaly N. Melnikov. Co-director of the I Sth course. President of the Russian Gravitational Society.

Erice. May 9. 2003.

xxiii

In commemoration of Peter Gabriel Bergmann - famous scientist and good friend

Born in 1915 in Berlin, he started his university studies already in the age of 16 at the Technische Hochschule in Dresden, where he registered both for chemistry and physics laboratory exercises. Two semesters later he moved to Freiburg (Breisgau) to attend the lectures of Gustav Mie who then did research on Einstein's General Relativity Theory. After having escaped Nazi terror he continu.ed his studies in physics at the Charles University in Prague, where he finished his doctorate in 1936.

In that same year he moved to the Institute for Advanced Study in Princeton, collaborating with Albert Einstein on the attempt to develop a geometrical unified field theory of gravitation and electromagnetism - the well-known aim of research of the late Einstein. During the following ten years he published two common papers in this field: Einstein and Bergmann (1938), Einstein, Bargmann and Bergmann (1942). About 20 years later, when Peter Bergmann and I met first in 1962 at the Jablonna Conference on General Relativity and Gravitation (near Warsaw), we had a discussion in context with my own research on projective relativity theory. Bergmann told me that then in Princeton he investigated an attempt to generalize this type of theory, as P. Jordan did it later in 1945: In a discussion with Einstein he asked him for a common publication, but Einstein refused. At least at that time Einstein did not believe in a 5-dimensional structure of such a new theory intended ..

Already at Jablonna we both Peter and I spontaneously became friends: He an expelled German and r a German of the younger generation totally condemning Nazism. I was strongly impressed by this great human attitude of Peter, in particular also insofar as I knew of the Nazi crimes that happened to the family of Peter's wife Margot.

After the International Conference on General Relativity and Gravitation in Copenhagen in July 1971, when Peter became president ofthe corresponding society and I a member ofthe International Committee of this society, we both met for several committee meetings etc., particularly also in Erice/Sicily in COlU1ection with the Schools on General Relativity and Gravitation organized by V. de Sabbata. At the GR8-conference at Waterloo in 1977 it was decided by this committee that the next GR9-conference should1ake place in lena (then in the German Democratic Republic) under my leadership. In context with the politically very complicated situation under the conditions of the Cold War it was necessary for me to have a permanent contact with Peter, since he was the president of the society. Peter helped me always in many consultation always, when the emerging problems seemed to be unsolvable.

Peter's idea of having the GR9-conference to Jena based on different reasons: One important point of performing this conference on German soil was the fact that Einstein developed his General Relativity Theory in Berlin 1915. Another argument resulted from the fact of the existence of the Iron Curtain preventing the getting-together of scientist from the east and the west who had contact by mail but never met personally. Last but not least, in lena existed a rather strong reIati vity group that I had founded in 1957. I had to promi se to the International Committee to do all I could making sure that participants from all countries, particularly from Chile, Israel, South Africa, Taiwan and South Korea obtained entrance visas without political interference. Further, after the assassination ofthe Israel athletes during the Olympic Summer Games in Munich in 1972, T had to take care of the security of the participants, particularly

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from Israel. Through very difficult negotiations with my superior authorities I could meet these very strong conditions posed to me by the committee.

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I succeeded and the conference with 830 participants from 51 countries took place successfully in July 1980, running in a good scientific and humane climate. I was strongly supported by the Secretary of the Local Organisational Committee, R. Collier. Peter Bergmann's personality gave me much energy and strong mental help. He was not only an outstanding scientist but also a man with great political foresight - on behalf of the international relativity community in the terrible political situation of the Cold War. I have to thank him much for ever!

Ernst Schmutzer, Jena

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Bergmann with Einstein

Bergmann with Einstein and Bargmann (from the left: Bargmann, Einstein, Bergmann) at Princeton University

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During the memorial day in Erice: Gillies, Schmutzer, de Sabbata, Borzeszkowski and Melnikov

de Sabbata, Bergmann and Datta

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Bergmann and de Sabbata

de Sabbata and Bergmann in Erice