many-worlds interpretation of quantum theory...

MANY-WORLDS INTERPRETATION OFQUANTUM THEORY AND MESOSCOPIC

ANTHROPIC PRINCIPLE

A.Yu. Kamenshchik

Dipartimento di Fisica and INFN,

Via Irnerio 46, 40126 Bologna, Italy

L.D. Landau Institute for Theoretical Physics of the

Russian Academy of Sciences, Moscow, Russia

and

O.V. Teryaev

Joint Institute for Nuclear Research, Dubna, Russia

(Received 28 June 2008; accepted 14 July 2008)

Abstract

We suggest to combine the Anthropic Principle with Many-Worlds Interpretation of Quantum Theory. Realizing the mul-tiplicity of worlds it provides an opportunity of explanation ofsome important events which are assumed to be extremely im-probable. The Mesoscopic Anthropic Principle suggested hereis aimed to explain appearance of such events which are neces-sary for emergence of Life and Mind. It is complementary toCosmological Anthropic Principle explaining the fine tuningof fundamental constants. We briefly discuss various possibleapplications of Mesoscopic Anthropic Principle including the

Concepts of Physics, Vol. V, No. 4(2008)DOI: 10.2478/v10005-007-0045-4

575

Solar Eclipses and assembling of complex molecules. Besides,we address the problem of Time’s Arrow in the framework ofMany-World Interpretation. We suggest the recipe for disen-tangling of quantities defined by fundamental physical lawsand by an anthropic selection.

576 Concepts of Physics, Vol. V, No. 4 (2008)

Many-worlds interpretation of quantum theory ...

1 Introduction

The anthropic principle (AP) was proposed long ago [1, 2, 3, 4, 5]but recently it got a strong boost (see e.g. [6, 7]) connected withthe development of cosmology [8] and string theory [9]. The generalidea of AP consists in the statement that existence of the (human)observer imposes important restrictions on the basic laws and funda-mental physical constants. As soon as these restrictions happen to beof tantamaunt importance, the required values of physical constantsappear to be extremely improbable. This smallness of probabilitycould be compensated by the huge number of universes constitutingMultiverse. Under this term one should understand a complicatedobject which may be formed by the process of the ramification ofthe spatial structure of the universe due to the effects of spontaneoussymmetry breaking producing inflationary expansion of the patchesof spacetime. Such an opportunity is inherent in the chaotic inflationmodels [10].

Another source of multiversity is the existence of the so calledstring landscape which means that the fundamental superstring the-ory contains a huge amount of vacuum states, each of those may leadto quite different universes with different physics.

Here we would like to discuss yet another source of multiplicityopening the possibility of further extension of applicability of AP. Itcorresponds to many-worlds interpretation of quantum theory [11].As soon as this multiplicity does not lead to the change of funda-mental cosntants we are dealing with what we call ”Mesoscopic” AP,corresponding to the scales intermediate between cosmological andmicroscopic ones.

The structure of the paper is the following: The second sectionis devoted to a brief review of the basic ideas of the many-worldsinterpretation of quantum mechanics; in the third section we discussbranching of worlds understood in the sense of the defactorizationof the wave function and the problem of the preferred basis; in thefourth section we consider the important problem of irreversibilityand appearance of the arrow of time in terms of the many-worlds in-terpretation; the fifth sections deals with the definition of the Meso-scopic Anthropic Principle and its simplest applications to planetarysystems; in the sixth section we treat biological evolution in termsof variety of options provided by the quantum evolution; in the last

Concepts of Physics, Vol. V, No. 4 (2008) 577

A.Yu. Kamenshchik and O.V. Teryaev

section we discuss the main results and suggest some criteria for dis-entangling of quantities defined by fundamental physical laws and byan anthropic selection.

2 Many-worlds interpretation of quantum mechan-ics

The many-worlds interpretation (MWI) of quantum mechanicswas suggested by H. Everett in 1957 [12] and its invention was mo-tivated by two factors. One of them was intensively discussed sincethe moment of creation of quantum mechanics: it is the problemof reconciliation between two processes present in the theory - dy-namical evolution in accordance with the Schrodinger equation andthe reduction of wave packet, responsible for an observation of theunique outcome of quantum measurement when the quantum staterepresents a superposition of the corresponding eigenstates. In themost popular Copenhagen interpretation of quantum mechanics sucha coexistence of these two processes was provided by the separationof the so called classical realm, which in some versions was connectedeven with the presence of conscious observer. Thus the desire of get-ting rid of the ambiguity connected with the wave packet reductionpostulate and having a unique quantum description of Nature stimu-lated the creation of MWI. In the framework of MWI the Schrodingerevolution is the only process, the principle of superposition is applica-ble to all the states including macroscopic ones and all the outcomesof any measurement-like processes are realized simultaneously but indifferent “parallel universes”. The very essence of the many-worldsinterpretation can be expressed by one simple formula we are aboutto derive. Let us consider the wave function of a system, containingtwo subsystems (say, an object and a device), whose wave functionsare respectively |Φ〉 and Ψ〉 and let us the process of ithe interactionbetween these two subsystems is described by a unitary operator U .The result of action of this operator can be represented as

U |Φ〉0Ψ〉i = |Φ〉iΨ〉i. (1)

Here the state |Ψ〉i is a quantum state of the object correspondingto a definite outcome of the experiment, while |Φ〉0 is an initial state



of the measuring device. Now, let the initial state of the object bedescribed by a superposition of quantum states:

|Ψ〉 =∑

i

ci|Ψ〉i. (2)

That superposition principle immediately leads to

U |Φ〉0Ψ〉 = U |Φ〉0∑

i

ci|Ψ〉i =∑

i

ci|Φ〉iΨ〉i. (3)

Here |Φ〉i describes the state of the measuring device, which has foundthe quantum object in the state |Ψ〉i. The superposition (3) containsmore than one term, while one sees only one outcome of measurement.The reduction of the wave packet postulate solves this puzzle byintroducing another process eliminating in a non-deterministic wayall the terms in the right-hand side of Eq. (3) but one. The MWIinstead says that all the terms of the superposition are realized butin different universes.

The MWI looks the most consistent between interpretations ofquantum theory, because it ultimately reduces the number of pos-tulates. Moreover, one of the proponents of MWI B.S. DeWitt saysthat in the framework of it the mathematical formalism of the theorygives itself its interpretation [13].

Now, let us turn to second motivation for MWI. In quantum cos-mology there is no external observer and hence, no, classical realm.Thus, MWI matches quite well the quantum cosmology.

The many-worlds interpretation with its branching of universesapparently opens a magnificient opportunities for the application ofthe AP. This possibility was practically overlooked in the literature(see, however [14]).

3 Branching of Worlds and the preferred basis

The opportunity to extract non-trivial physical consequences inthe context of MWI is based on the treating of the branching ofworlds as an objective process. However, inevitable question arises:decomposing the wave function of the universe one should choose acertain basis. The result of the decomposition essentially depends



on it. Thus, the so called problem of the choice of the preferred ba-sis arises [15] The essence of the problem can be easily formulatedconsidering the same example of a quantum system consisting of twosubsystems. Let us emphasize that now we would like to undertakea consideration of a general case without particular reference to ar-tificial measuring devices and quantum objects (for a moment weconsider this division of a system into subsystems as granted). Theonly essential characteristics of the branching process is the defactor-ization of the wave function. That means that if at the initial momentthe wave function of the system under consideration was representedby the direct product of the wave functions of the subsystems

|Ψ〉 = |φ〉|χ〉 (4)

then after an interaction between the subsystems it becomes∑i

ci|φ〉i|χ〉i, (5)

where more than one coefficient ci is differentt from zero. Apparentlythe decomposition (5) can be done in various manners. As soon aseach term is associated with a separate universe, the unique prescrip-tion for the construction of such a superposition should be fixed. Webelieve that the correct choice of the preferred basis is the so calledSchmidt or bi-orthogonal basis. This basis is formed by eigenvectorsof both the density matrices of the subsystems of the quantum systemunder consideration. These density matrices are defined as

ρI = TrII |Ψ〉〈Ψ|, (6)

ρII = TrI |Ψ〉〈Ψ|. (7)

Remarkably, the eigenvalues of the density matrices coincide andhence the number of non-zero eigenvalues is the same, in spite ofthe fact that the corresponding Hilbert spaces can be very different.

ρI |φn〉 = λn|φn〉, (8)

ρII |χn〉 = λn|χn〉, (9)

Consequently, the wave function is decomposed as

|Ψ〉 =∑

α√

λn|φn〉|χn〉. (10)



The bi-orthogonal basis was first used at the dawn of quantummechanics by E. Schrodinger [16] for study of correlations betweenquantum systems and was applied to MWI in [17, 18]. Recently,this basis is actively used for measuring of degree of entanglement,in particular, in relation to quantum computing [19]. The expansionwith respect to eigenvectors of spin density matrix and density matrixpositivity was also used in hadronic physics and non-perturbativeQCD [20, 21].

We believe that the bi-orthogonal basis being defined by the fixingof the decomposition of the system into subsystems have a fundamen-tal character and determines the worlds which result from the defac-torization process. However, the subdivision of the system onto sub-systems which implies the branching of the worlds should satisfy somereasonable criteria which we are not ready to formalize at the mo-ment (see, however [22] for analysis of some relatively simple cases).One can say, that the decomposition into the subsystems should besuch that the corresponding preferred basis were rather stable. Forexample, when one treats a quantum mechanical expreriment of theStern-Gerlach type, it is natural to consider the measuring device andthe atom as subsystems.

4 Time‘s arrow

The formalism of the many-world interpretation of quantum the-ory permits to reformulate the problem of a direction of time in avery transparent way. Indeed, the basic dynamics equations are in-variant with respect to the operation of time reflection, while themacroscopic phenomena shows the irreversibility or the presence ofthe arrow of time. One of the quantitative manifestations of thesephenomena is the growth of the von Neumann entropy [23]

S = −Tr(ρ ln ρ) = −∑

i

λi lnλi ≡∑

i

Si. (11)

where the last equality introduces, in the context of MWI the notionof relative entropies of branches. This entropy is minimal and equalto zero for a pure quantum state. Usually, the presence of the arrowof time is connected with the existence of some additional constraintson the solutions of fundamental equations. For example, choosing an



initial state as a state with low value of entropy, one naturally seesits growth. We make an observation that the branching process inthe MWI naturally produces the states with a smaller initial relativeentropy (that is calculated by taking into account only one branch).In other words, after the measurement-like act of branching a newbranch is in factorized quantum state and the density matrices of allits subsystems correspond to pure quantum states. This does notcontradict to the increase of entropy in the standard (Copenhagen)treatment of quantum measurement. In the latter case one is deal-ing after the measurement with the classical statistical mixture of avarious outcomes producing increase of entropy which can be mea-sured experimentally. At the same time in MWI the process of mea-surement (defactorization of the wave function) naturally implies theinclrease of entropy, but after the identification of an outcome of mea-surement, when the defactorization of the wave function is completed,the relative entropy (related to the branch where we live) becomesequal to Si. Forgeting about other branches, which is equivalent tothe reduction of wave packet in the Copenhagen interpretation, corre-sponds to rescaling λ → 1 and Si → SR;SR(t0) = 0, where SR is theredefined entropy after the branching happened at time t0 Thus, rel-ative entropy of each branch is always growing, SR

i (t) > SRi (0) = 0,

so is Si and the usual measurable entropy of classical statistical mix-ture which is just the sum (11) of the entropies of the branches. Notethat this nullification of relative entropy does not involve the distantregions of Universe which are the same for all the branches.

Thus, MWI provides another manifestation of the effect of bound-ary conditions which is present in any explanation of irreversibility.The example of such boundary conditions is, say, the correlationsweakening in the BBGKI chain of equations leading to the appear-ance of irreversibility. In another approach, when deriving [24] the ir-reversible master equation from the reversible Kolmogorov-Chapmanequation is is sufficient[25] to assume the existence of the initial con-ditions in the past. The role of boundary effects for the irreversibilityof field theory evolution equations implying the ”scale arrow” , analo-gous to time’s arrow, is discussed in [25, 21]. In turn, the irreversibil-ity with respect to time reflection in field theory may appear eitherbecause of T(or CP) violation at the fundamental level or becauseof its simulation by imaginary phases of scattering amplitudes. The



latter crucially depend on the sign of iε in the Feynman propagatorswhich is imposed by the causal boundary conditions for Green func-tions. This effect is giving rise to T-odd spin asymmetries [26] beingthe subject of intensive theoretical and experimental studies.

In the actual case of MWI the choice of boundary conditionscorresponds to the choice of factorized wave function in the past,rather than in the future. However, as MWI may be consideredas ”self-interpretation” of the mathematical formalism of quantumtheory [13], the suggested approach may explain the fundamentalphenomenon of Arrrow of Time in a similar manner.

5 Planetary Coincidences and Mesoscopic Anthro-pic Principle

It is usually believed that the suitable values of fundamental con-stants are sufficient for emergence of stars, planetary systems andall the astrophysical objects required for apperance of life. However,there are a number of observations pointing to the special, privileged,role of the Solar system (see e.g. [27]). All the values describing thisprivileged position cannot involve the fine-tuning of neither constantsof elementary particle physics nor cosmology. Therefore we call sucha coincidences the mesoscopic anthropic coincidences and the relatedselection the Mesoscopic Anthropic Principle (MAP).

The first natural opportunity to find the priviliged values of plan-etary characteristics is to explore the vast number of galaxies stars,and planets in our Universe [28]. Note, that the necessity of thislarge number provides a sort of answer for one line of possible criti-cism of AP suggesting that the existence of such a large Universe ishardly necessary for the life on the Earth, this argument being bestexpressed by S. Hawking who was saying that ”our Solar system iscertainly a prerequisite for our existence, But there does not seemany necessity for other galaxies to exist”.

At the same time, the selection among the large number of distantastrophysical objects does not seem sufficient if some fine-tuned valueof mesoscopic parameter is required. For this aim the small changes ofthe relevant parameter within the required range are important. Thisis exactly what happens in the chaotic inflation or stringy landscape



and allows for a fine tuning of fundamental constants 1.As a possible solution of this problem we suggest the MWI is a

source of small variations of mesoscopic planetary constants in differ-ent worlds. We assume that the measurement-like quantum interac-tions leading to the branching occur all the time independently of thepresence of (conscious) observer and produce the planetary systemsin parallel Everett worlds whose parameters differ by small amount.

The example of planetary fine-tuning is provided by Solar eclipsesrequiring the coincidences of angular sizes of Sun and Moon, as seenfrom the Earth. There is currently no explanation of this coincidence,apart from teleological arguments [27]. At the same time, this coinci-dence would be explained if the eclipse were necessary for some stageof the emergence of life. This does not seem completely impossible,although there is no evidences in favour of such a relation. One possi-bility is the emergence of life due to photochemical reaction requiringthe shadowing of strong ultraviolet radiation of the Sun but presenceof the radiation of Solar Corona. Should such or similar scenario findthe experimental support (which is possible, at least in principle) thiswould mean also the support of MAP and the role of MWI.

6 Mesoscopic Anthropic Principle and BiologicalEvolution

In turn, even suitable planetary environment and emergence ofprimitive life does not, contrary to popular wisdom, leads to theappearance of its complex forms. The Darwinian evolution is anadaptive one [29] and explains the arising of the complex structuresif they provide the evolutionary advantages. At the same time, theappearance of complex structures, which does not lead to immediateevolutionary success, including the Human beings is not trivial toexplain. The production of complexity in the process of the type ofrandom walk may be explained [30] only if this complexity is relativelylow. The random walk in that case is limited by zero complexitybarrier and produces its increase. The further evolutionary processexplains the progress of most numerous species, like insects, but notthe apperance of complex and rare ones. Therefore, the origin of

1Such a small changes of some parameter constitute, in fact, the cornerstoneof Darwinian natural selection, see also the next section



humans, being the most popular success of originals theory of Darwinand Wallace, remains out of scope of its modern version.

The natural way to explain the appearance of very complex andimprobable structures is provided by MWI. This opportunity wasrecently explored by J. McFadden [31] in the case of the earliest stageof biological evolution, where he expresses the revolutionary idea thatthe first life appears only in one of innumerous Everett worlds

However, the author dislikes the immediate consequences of hishypothesis which he absolutely correctly deduces: namely, that ex-traterrestrial life, and therefore, intelligence does not exist (note thesame hypothesis was suggested for different reasons by I.S. Shklovsky[32]) and that life cannot be created in the laboratory

To overcome these obstacles he suggests the another use of quan-tum theory to explain the improbable event, namely, the inverse Zenoeffect. However, we do not consider this opportunity as plausible.

Indeed, he considers as a model of improbable event the passageof light through the vertically and horizontally polarized lenses whilethe insertion of extra lenses between them increase the probability.

This case, however, deals with low-dimensional system when thesmall probability is achieved due to a sort of fine-tuning (mutualorthogonality of lenses). At the same time, the low probability oftransition leading to first self-replicator is due to large dimension ofcorresponding Hilbert space. More quantitatively, if one has two wavefunctions (normalized vectors in a Hilbert space) one of which |i〉,corresponds to initial ”single amino acid arginine” [31] while, second,|f〉, corresponds to the emerged self-replicator. The typical (average)value of the square of their scalar product, related to a transitionprobability is

< |〈i|f〉|2 >=1N

, (12)

where N is a dimension of the Hilbert space defined by the num-ber of participating elements. Now, if one produce some quantummeasurement, the scale of this quantity clearly remains the same.The only way to increase these probabilities by dense series of mea-surements would be to arrange them in some particular way definedby the initial and final states. The appearance of such a specialmeasurement-like process is not easier to explain than the occurrenceof small-probability quantum transition. At the same time, some



random measurements will not substantially increase the probability(12), contrary to the case of polarized lenses, when the specially or-ganized low probability may be increased by a generic measurement.

Therefore, we do not consider inverse quantum Zeno effect as acandidate for the explanation of low probability events necessary forlife emergence and come back to the initial suggestion of McFaddenabout the use of MWI.

Moreover, we suggest to extend this mechanism to all the stagesof biological evolution. Indeed, the original suggestion of [31] is tolimit the field of applicability of quantum effects to the microbilogicalscale [33] when the entanglement between cell and its environmentis essential, while for the multi-cell structures quantum effects wereconsidered [31] unimportant.

Contrary to that, we suggest that all the mutations in the courseof biological evolution are the quantum measurent-like processes sothat all their different outcomes are realized in different branches.The increasing of complexity now has purely random character, sothat only in few parallel worlds the biological evolution produces moreand more complex species.

All the parallel worlds emerging due to mutation differ only bysmall variations in the mutating organism. This feature is commonwith a standard (neo)Darwinian paradygm. What is different fromit is that all the versions of this variation are realized in differentparallel Everett worlds. This naturally implies the increase of com-plexity in some of them just by random process. In our opinion, thissolves the fundamental problem of the extremely law probability oflife emergence and evolution to the mosty complex forms, includingourselves.

There are a number of fundamental facts which, to our opinion, donot contradict to or even support this hypothesis. These are ”punc-tuated equilibrium” (evolution proceeds by sudden bursts followedby long ”stasis” periods), ”Out of Africa” theory [34] ( appearance ofall humans from a single family), ”Mitochondrial Eve” (identifyinga common female anchestor, being the support of previous theory),”irreversibility of the brain formation” (once emerged brain neverreduced in the course of evolution) etc.

We have no opportunity of detailed discussions and just mentionthat all these facts may be understood as emerging from improbable



rare events of quantum measurement type, so that all of their out-comes are realized in parallel worlds. We are just lucky inhabitantsof one of the most ”pleasant” of them.

7 Discussion and Conclusions

In this article we have tried to explore the possible relation be-tween Anthropic Principle and Many-World Interpretation of Quan-tum Theory. The key moment is the possibility to multiply the realityto such an extent that very special events like emergence of Life be-come quite possible.

The important feature of this process is the smallness of differ-ences between various parallel Everett worlds This allows to scan allthe possible values of required parameters which is essentially sim-ilar to the arguments justifying Darwinian natural selection. Theonly, albeit crucial difference is that selection occurs not in the dif-ferent moments of time like Darwinian one, but in the different par-allel worlds, or, mathematically speaking, in the different regions ofHilbert space. Such a resemblance to the Darwinian evolution maybe explored for other known mechanisms of generation of variety ofoptions (like string landscape or eternal chaotic inflation) in order toseparate the ”physical” predictions from the effects of ”environment”[6] or ”scanning” [7] which we are about to suggest.

Indeed, if some physical constant should be fine-tuned for theemergence of life it is very unlikely that it is completely defined byunderlying physics (cf. [35]) and selection process of Darwinian typewas likely to contribute. At the same, the physics should rather leadto the establishing of general framework and more robust constraints(see, for example, Ref. [36], where in the framework of the Euclideanquantum gravity some constraints on possible values of the effectivecosmological constant were found) which may be a starting point forsubsequent fine-tuning by anthropic selection.

In the case of the Many-World Interpretation such a selectionallows to fine-tune various parameters which are not amongst the ba-sic constants of theory of fundamental interactions, including gravityand elementary particle physics. This is because the branching dueto the Many-Worlds interpretation occurs when all the fundamentalconstants are already fixed and therefore they are the same in all



the Everett parallel worlds. We suggested to use the term ”Meso-scopic Anthropic Principle” for description of anthropic selection inthe branching process.

We considered two possible fields of applicability of MesoscopicAnthropic Principle, namely, planetary coincidences and biologicalevolution.

In both cases the small differences generated by branching allowto explain the coincidences which is very difficult to do otherwise.As an example we consider the coincidence of angular sizes of Sunand Moon responsible for the Solar eclipses. This coincidence maybe achieved by small steps during branching, and anthropic selectionmay choose it to be realized in our Universe if eclipses played any rolein the life emergence. This hypothesis may be checked , in principle,opening an opportunity for indirect tests of Anthropic Principle.

The other important problem is the arising of complexity duringbilogical evolution, including such extreme cases as Life itself andMind. We suggest that crucial role is played the Many-Worlds inter-pretation, so that extremely small probability is fully compensatedby enormous number of trials.

No we are ready to take an hazard to try to give the crudestestimate of number of the Everett worlds produced up to the presentmoment. We first assume that it is the Planck constant ~ whichselects the measurement-like interactions leading to defactorization.Now, for dimensional reasons when determining the number of worldsit should be divided by some constant with the dimension of action orphase space, characterizing the whole Universe. The emerging ratio isrelated to the ratio of the Planck time tP and the age of the UniverseT . Therefore, we expect that the number of worlds N is

N = f

(T

tP

). (13)

where f is some growing function which we allow to range from lin-ear to exponential (the latter qualitatively supported by the chaincharacter of branching while there is no reason for appearance of log-arithmic function, also growing) which leads to N ranging from 1060

to 101060. Especially the last number seems to be fairly huge in order

to accommodate all the unlikely events leading to modern picture ofLife.



Summing up, we consider the Anthropic Principle combined withthe multiple opportunities opened also by the Many-Worlds interpre-tation of quantum theory, as new exciting field of physics and othernatural sciences, rather than dull alternative to them.

Acknowledgment

O.T. is grateful to Cariplo Science Foundation for support duringhis stay at the University of Insubria (Como) and to the Departmentof Physics and Mathematics of this University for kind hospitality.This work was partially supported by RFBR Grants N 06-02-16215and 07-02-91557 and by LSS-1157.2006.2.

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Comment onMANY-WORLDS INTERPRETATION OFQUANTUM THEORY AND MESOSCOPIC

ANTHROPIC PRINCIPLE

Michael B. Mensky

P.N.Lebedev Physical Institute,

53 Leninsky prosp., 119991 Moscow, Russia

1. The authors of the reviewed paper, A. Yu. Kamenshchik andO. V. Teryaev, consider Many-Worlds Interpretation (MWI) of quan-tum mechanics in connection with anthropic principle. Combiningthe anthropic principle with Many-Worlds Interpretation, they at-tempt to explain why some coincidences necessary for emergence oflife are actually observed although probabilities of these coincidencesmay be estimated as negligible.

The main step in the argument of the authors is the assumptionthat the variety of worlds appearing in MWI (Everett’s worlds) maybe dealt with, in the framework of anthropic principle, in the sameway as the variety of real universes forming the Multiverse in somecosmological models (for example in inflationary models) is used.Considering the Everett’s worlds differing from each other on theastrophysical rather than cosmological scale, the authors define whatthey call Mesoscopic Anthropic Principle (MAP).

As an example of applying MAP, the coincidence of angular sizes


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of Sun and Moon responsible for the Solar eclipses is considered.Another example is arising complexity during biological evolution.In the latter case the role of high complexity for life is evident, butit is not clear how one may explain the process of gradual increasingcomplexity if each step in this process has no evident preference forlife. The authors suggest that MWI may supply an explanation inthis case. In the first example (coincidence of angular sizes of Sunand Moon) the role of the coincidence for life is not evident but “doesnot seem completely impossible”.

The general scheme of reasoning is the following. In the courseof branching (due to measurement-like interactions) of our world theenormous variety of worlds arise, most of them inconvenient for life,but “we are just lucky inhabitants of one of the most “pleasant” ofthem”.

2. MWI is very popular now and is extensively discussed from var-ious viewpoints. The proposal of A. Yu. Kamenshchik and O. V. Tery-aev who consider this concept in its connection with life is evidentlyinteresting. Yet it needs to be clarified in some points and comparedwith close approaches.

In order to discuss Everett’s worlds in their relation to the phe-nomenon of life, it is very important to make quite clear i) how theseworlds are defined and ii) what is a status of each “world”.

The first question is solved in the paper on the basis of the so-called Schmidt basis. This is a pure mathematical definition, of coursepossible but hardly sufficiently justified in the present context. Atleast it should be explicitly discussed what would change in case ofanother definition of “worlds” or why another definition is inappro-priate for the tasks of the authors. There is no such a discussion inthe paper.

The second question (in fact connected with the solution of thefirst one) is more important, but it is also not discussed in the paper.After a quantum state is decomposed (with the help of the Schmidtbasis or in another way), the resulting components are called “worlds”without any explanation of what does this mean. These “worlds” areformally dealt with just as the real material worlds (e.g. those formingMultiverse in cosmological models) are. All considerations, typicalfor the anthropic principle, are applied to the Everett’s worlds justas they might be applied to the set of material worlds. It is evident


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that correctness of such an approach has to be justified (we believethat the approach is correct but needs more deep analysis).

Recall that different Everett’s worlds (for example those with aliveand dead Schroedinger cat) are not different material worlds but onlycomponents in the superposition presenting the state of a single quan-tum material world. The set of all Everett’s worlds (alternative statesof our world) may be called Alterverse to distinguish it from Multi-verse, a set of material worlds (this terminology was proposed bythe present author and supported in A.A. Shatskii, I.D. Novikov andN.S. Kardashev, Physics-Uspekhi 51, No.5, 2008).

Since the Everett’s worlds are not material, the question ariseswhether the whole “many-worlds representation” of the events isobjective or not. The following phrase in the paper turns out tobe doubtful: “The opportunity to extract non-trivial physical con-sequences in the context of MWI is based on the treating of thebranching of worlds as an objective process”.

To our mind, the above-mentioned questions stay unanswered be-cause the authors attempt to treat as completely objective those pro-cesses which actually include subjective elements. In case of quan-tum measurement, subjective is the notion of “observation” or “ob-server”. In case of anthropic principle, subjective is the very conceptof life. The discussion proposed in the reviewed paper would be morecomplete if the (actually unavoidable) concept of consciousness beincluded in this discussion in an explicit way.

We do not think that the results obtained in the paper of A. Yu. Ka-menshchik and O. V. Teryaev should be considered incorrect until alldifficult questions are answered. The approach accepted by the au-thors is to make as many conclusions as it is possible without solvingand even posing further questions. This tactic is right and almost un-avoidable. However, now one has to pose and try to solve all the restquestions. This will allow one to understand the already obtainedresults on a deeper level.

It is curious that even first steps on this way (first of all explicitinclusion of the notion of consciousness) give interesting analoguesthat might point out to further prospects.

3. An attempt to elaborate MWI on the basis of explicit con-sideration of the phenomenon of consciousness has recently been per-formed in the following series of papers: Michael B. Mensky, Physics-


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Uspekhi 43, 585-600 (2000); 48, 389-409 (2005); 50, 397-407 (2007);Optics and Spectroscopy 103, 461-467 (2007); NeuroQuantology Vol5, No 4, 363-376 (2007). The approach developed in these paperswas called Extended Everett’s Concept (EEC). It shows that the for-malism of MWI includes in itself not only its own interpretation butalso the principal features of the phenomenon of consciousness and,more generally, phenomenon of life.

The principal points of EEC are that i) “explicit” consciousness isnothing else than ability of living beings to perceive classical alterna-tives (Everett’s worlds) separately from each other; ii) “implicit” con-sciousness (accomplished in the regime when the explicit conscious-ness is turned off) has access to all alternatives and compares themwith each other; iii) returning to the “explicit” form, the conscious-ness may influence on what alternative it will find itself in, increasingprobabilities of favorable alternatives.

In the framework of EEC, the “practically impossible” (havingnegligible probabilities) events may with great probability happen inthe sphere of life if they are favorable for life. Such situations werecalled “probabilistic miracles”. Many well known but not explainedfacts in the sphere of life turn out to be quite clear from this point ofview. First of all this is the very phenomenon of life, the miracle oflife: survival of living beings and conservation, or even improvement,of the quality of life (for example support of health).

The “probabilistic miracles” predicted in the framework of EECare closely connected with the anthropic principle, although are moregeneral. One of the above-cited papers (Physics-Uspekhi 2007) is astenograph of the author’s talk given on the occasion of the V.L.Ginz-burg’s jubilee. In the course of the discussion after the talk (page 405of the paper), the first question and the answer to it were as follows:

Question (Al’tshuler B L): The talk creates a nostal-gic feeling. Indeed, in 1947, Literaturnaya Gazeta [theLiterature News- paper] published a large article whereVitalii Lazarevich Ginzburg was accused of ‘blatant ideal-ism’. As to my question, it is: just before this talk, ValeriiAnatol’evich Rubakov spoke about the anthropic princi-ple and the multiplicity of worlds; he said that there canbe infinitely many worlds. Is this multiplicity of worldsin the framework of the anthropic principle related to the


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multiplicity of Everett’s worlds?Mensky: This relation was not discussed in the talk

by Rubakov but it suggests itself. It also exists in theoriginal Everett interpretation but even more so in theExtended Everett Concept. It is assumed in the EECthat consciousness can choose alternatives that are mostfavorable for life (more precisely, increase the probabilitythat the consciousness perceives one of the favorable al-ternatives). This can be called the active version of theanthropic principle. But I would also like to touch uponthe first part of Boris Al’tshuler’s comment. Indeed, ‘theages meet’ here. Our scientific community is too conser-vative (much more conservative than the scientific com-munity abroad). In the late 1940s, one could be cursedhere for quantum mechanics. Now, no one is cursed forquantum mechanics. But for the things like those I wasspeaking about, one is still cursed.

In another paper (NeuroQuantology 2007, page 375) this has beenexpressed in a more definite way (in terms of the special mathematicaloperation of postcorrection):

Let us make finally one more remark demonstratinghow natural for living systems is the evolution law (1) in-cluding postcorrection. This law is, in its spirit, very sim-ilar to what is called anthropic principle. The anthropicprinciple explains “fine tuning” of the parameters of ourworld by the fact that in case of any other set of the pa-rameters organic life would not be feasible and thereforeno humans could exist to observe this world. The princi-ple of life, formulated as the ability of the living systemto postcorrect its state to provide its survival, suggests infact something quite similar, even in a softer variant.

In order to explain this, we have to underline oncemore that the postcorrection describes selecting those sce-narios which remain in the sphere of life. The rest sce-narios do not disappear. They are real as well (includedin the complete description of the quantum world), butthey are excluded from the sphere of life, therefore are un-


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observable. This means that no observer can watch these“unfavorable for life” scenarios. The “sphere of life” issuch an image of our world which can be observed. Ifjust this image (i.e. not “the whole world” but only “thesphere of life”) is taken as a starting point for construct-ing evolution law, then the result of the construction willnecessarily be the evolution including postcorrection.

Thus, postcorrection in the evolution of living matter(of the sphere of life) does not need even to be postu-lated. Instead, it may be derived from the (generalized)anthropic principle. Non-living matter satisfies the con-ventional quantum-mechanical causal evolution law. Evo-lution of the living matter (of the sphere of life) simplyby definition should include postcorrection.

4. The coincidences mentioned in the paper of A. Yu. Kamen-shchik and O. V. Teryaev may be considered as special cases of theanthropic principle formulated in terms of the operation of postcor-rection. These coincidences may also be considered to be examples of“probabilistic miracles”. Of course, in this case only primitive classof probabilistic miracles is meant, available for the simple forms oflife.

The miracle in this case is connected only with the very primitivefeature of life, namely, survival. The miracle is survival in the con-ditions which cause death with high probability. Being primitive inits structure, the phenomenon is in this case very important, it is themiracle of life.

Being connected with only primitive forms of life, the probabilisticmiracle taking place in the examples considered by A. Yu. Kamen-shchik and O. V. Teryaev may seem to be purely objective. In fact itis on the border between objective and subjective. This makes theseexamples especially interesting. They may shed light on the phe-nomenon of emergence of life. In any case they give hint of new waysfor further developing EEC and similar theories connecting quantummechanics with the phenomenon of life.


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