Quantum mechanics and realityBryce S. DeWitt

Citation: 23, 9, 30 (1970); doi: 10.1063/1.3022331View online: http://dx.doi.org/10.1063/1.3022331View Table of Contents: http://physicstoday.scitation.org/toc/pto/23/9Published by the American Institute of Physics

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Quantum mechanicsand realityCould the solution tothedilemma ofindeterminism be a universe in which all possible outcomesof an experiment actually occur?

Bryce S. DeWitt

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Despite its enormous practical success,quantum theory is so contrary to intui-tion that, even after 45 years, the ex-perts themselves still do not all agreewhat to make of it. The area of dis-agreement centers primarily around theproblem of describing observations.Formally, the result of a measurementis a superposition of vectors, each repre-senting the quantity being observed ashaving one of its possible values. Thequestion that has to be answered is howthis superposition can be reconciledwith the fact that in practice we onlyobserve one value. How is the measur-ing instrument prodded into making upits mind which value it has observed?

Of the three main proposals for solv-ing this dilemma, I shall focus on onethat pictures the universe as continuallysplitting into a multiplicity of mutuallyunobservable but equally real worlds,in each one of which a measurementdoes give a definite result. Althoughthis proposal leads to a bizarre worldview, it may be the most satisfyinganswer yet advanced.

Quantum theory of measurementIn its simplest form the quantum

theory of measurement considers a worldcomposed of just two dynamical en-tities, a system and an apparatus. Bothare subject to quantum-mechanicalBryce DeWitt is professor of physics atthe University of North Carolina.

laws, and hence one may form a com-bined state vector that can be expandedin terms of an orthonormal set of basisvectors

s,A) = \s)\A) (1)

where s is an eigenvalue of some systemobservable and A is an eigenvalue ofsome apparatus observable. (Additionallabels have been suppressed for sim-plicity. ) The Cartesian product struc-ture of equation 1 reflects an implicitassumption that, under appropriate con-ditions, such as the absence of coupling,the system and apparatus can act as ifthey are isolated, independent and dis-tinguishable. It is also convenient toassume that the eigenvalue ,s rangesover a discrete set while the eigenvalueA ranges over a continuum.

Suppose that the state of the world atsome initial instant is represented by anormalized vector of the form

|*o) = |^)|*) (2)where |i//) refers to the system and |$)to the apparatus. In such a state thesystem and apparatus are said to be"uncorrelated." For the apparatus tolearn something about the system thetwo must be coupled together for a cer-tain period, so that their combined statewill not retain the form of equation 2as time passes. The final result of thecoupling will be described by the actionof a certain unitary operator U

| ) (3) -Because the apparatus observes the •*

system and not vice versa, we mustchoose a coupling operator U that re-flects this separation of function. Let SiU have the following action on the basisvectors defined in equation 1 (or on i>some similar basis):

U\s,A) = \s,A+gs) = \s)\A+gs) (4)

Here, g is a coupling constant, whichmay be assumed to be adjustable. Ifthe initial state of the system were \s)and that of the apparatus were [A) thenthis coupling would be said to result inan "observation," by the apparatus, thatthe system observable has the value s.This observation or "measurement,would be regarded as "stored" in theapparatus "memory" by virtue of thepermanent shift from \A) to \A + gs)in the apparatus state vector.

Is this definition adequate?This particular choice for U, essen-

tially formulated by John von Neu-mann,1 is frequently criticized because itis not sufficiently general and because itartificially delimits the concept ofmeasurement. Some writers2 have alsoinsisted that the process described byequation 4 merely prepares the systemand that the measurement is not com-plete until a more complicated piece ofapparatus observes the outcome of the ^preparation.

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30 PHYSICS TODAY / SEPTEMBER 1970

Schrodinger's cat. The animal trapped in a room together with a Geiger counter and a hammer,which, upon discharge of the counter, smashes a flask af prussic acid. The counter contains a traceof radioactive material—just enough that in one hour there is a 50% chance one of the nuclei willdecay and therefore an equal chance the cat will be poisoned. At the end of the hour the total wavefunction for the system will have a form in which the living cat and the dead cat are mixed in equalportions. Schrbdinger felt that the wave mechanics that led to this paradox presented an unaccept-able description of reality. However, Everett, Wheeler and Graham's interpretation of quantum me-chanics pictures the cats as inhabiting two simultaneous, noninteracting, but equally real worlds.

It is perfectly true that laboratorymeasurements are much more compli-cated than that described by equation4 and often involve interactions that donot establish precise correlations be-tween pairs of observables such as s andA. However, apart from such noncor-relative interactions, every laboratorymeasurement consists of one or moresequences of interactions, each essen-tially of the von Neumann type.Although it is only the results of thefinal interactions with the recording de-vices that we usually regard as beingstored, each von Neumann-type "ap-paratus" in every sequence leading to afinal interaction may itself be said topossess a memory, at least momentarily.This memory differs in no fundamentalway from that of the sophisticated auto-maton (apparatus-plus-memory se-quence) at the end of the line. It is theelementary component that must be un-derstood if we are to understand quan-tum mechanics itself.

In his original analysis of the measure-ment process,1 von Neumann assumedthat the coupling between system andapparatus leaves the system observables undisturbed. Most of his conclusionswould have remained unaffected had heremoved this restriction, and we are notmaking such an assumption here. Al-though measurements of the nondisturb-fflg type do exist, more frequently theobservable suffers a change. It can

nevertheless be shown3 that if suitabledevices are used, such as the compensa-tion devices introduced by Niels Bohrand Leon Rosenfeld in their analysis ofelectromagnetic-field measurements.4

the apparatus can record what the valueof the system observable would havebeen without the coupling. For thisreason, we work in a modified versionof the so-called "interaction picture." inwhich only that part of the state vectorthat refers to the apparatus changes dur-ing the coupling interval.

If the coupling is known, the hypo-thetical undisturbed system observablemay be expressed in terms of the actualdynamical variables of system plus ap-paratus. Hence, the operator of whichthis observable is an eigenvalue is notitself hypothetical, and no inconsistencywill arise if we take it to be the right-hand side of equation 4.

Infinite regressionConsider now what happens to the

initial state vector in equation 2 as aresult of the measurement process ofequation 4. Using the orthonormalityand assumed completeness of the basisvectors, we easily find that

$[.<-]•> = f\A + gs)$(A)dA (7)

$(A) = (.41*) (8)

The final state vector in equation 5 doesnot represent the system observable ashaving any unique value—unless, ofcourse, i/<> happens to be one of thebasis vectors Is). Rather it is a linearsuperposition of vectors [s)|*[s]), eachof which represents the system observ-able as having assumed one of its pos-sible values and the apparatus as havingobserved that value. For each possi-bility the observation will be a goodone, that is, capable of distinguishingadjacent values of s, provided

±A «gAs (9)

where A* is the spacing between ad-jacent values and AA is the variance inA about its mean value relative to thedistribution function '<t>(A)-\ Underthese conditions we have

.vhere

= (s\t)

(5)

(6)

= *„ (10)

In other words, the wave function ofthe apparatus takes the form of a packetthat is initially single but subsequentlysplits, as a result of the coupling to thesystem, into a multitude of mutuallyorthogonal packets, one for each valueof s.

Here the controversies over the inter-pretation of quantum mechanics start.For most people, a state like that ofequation 5 does not represent the actual

PHYSICS TODAY /SEPTEMBER 1970 31

occurrence of an observation. They con-ceive the apparatus to have entered akind of schizophrenic state in which itis unable to decide what value it hasfound for the system observable. Atthe same time they can not deny that thecoupling chosen between system andapparatus would, in the classical theory,have led to a definite outcome. Theytherefore face a crisis. How can theyprod the apparatus into making up itsmind?

The usual suggestion is to introduce asecond apparatus to get at the factssimply by looking at the first apparatusto see what it has recorded. But ananalysis carried out along the above linesquickly shows that the second apparatusperforms no better than the first. It toogoes into a state of schizophrenia. Thesame thing happens with a third ap-paratus, and a fourth, and so on. Thischain, known as "von Neumann'scatastrophe of infinite regression," onlymakes the crisis worse.

Change the rules

There are essentially three distinctways of getting out of the crisis. Thefirst is to change the rules of the gameby changing the theory, the object be-ing to break von Neumann's infinitechain. Eugene Wigner is the most dis-tinguished proponent of this method.Taking a remarkably anthropocentricstand, he proposes that the entry of themeasurement signal into the conscious-ness of an observer is what triggers thedecision and breaks the chain.3 Cer-tainly the chain had better be brokenat this point, as the human brain isusually where laboratory-measurementsequences terminate. One is remindedof the sign that used to stand on Presi-dent Truman's desk: "The buck stopshere."

Wigner does not indulge in merehandwaving; he actually sketches a pos-sible mathematical description of theconversion from a pure to a mixed state,which might come about as a result ofthe grossly nonlinear departures fromthe normal Schrodinger equation that hebelieves must occur when conscious

beings enter the picture. He also pro-poses that a search be made for unusualeffects of consciousness acting on mat-ter.5

Another proponent of the change-the-rules method is David Bohm.0'7 UnlikeWigner, who does not wish to changethe theory below the level of conscious-ness, Bohm and his school want tochange the foundations so that even thefirst apparatus is cured of its schizo-phrenia. This they do by introducingso-called "hidden variables." Whateverelse may be said of hidden-variabletheories, it must be admitted that theydo what they are supposed to. Thefirst such theory" in fact worked toowell; there was no way of distinguish-ing it experimentally from conventionalquantum mechanics. More recent hid-den-variable theories are susceptible topossible experimental verification (ordisproof) .7

The Copenhagen collapseThe second method of escaping the

von Neumann catastrophe is to acceptthe so-called "conventional," or "Copen-hagen," interpretation of quantummechanics. (Reference 8 contains aselected list of papers on this topic.)In speaking of the adherents of this in-terpretation it is important to distinguishthe active adherents from the rest, andto realize that even most textbook au-thors are not included among theformer. If a poll were conductedamong physicists, the majority wouldprofess membership in the conventional-ist camp, just as most Americans wouldclaim to believe in the Bill of Rights,whether they had ever read it or not.The great difficulty in dealing with theactivists in this camp is that they toochange the rules of the game but, unlikeWigner and Bohm, pretend that theydon't.

According to the Copenhagen inter-pretation of quantum mechanics, when-ever a state vector attains a form likethat in equation 5 it immediately col-lapses. The wave function, instead ofconsisting of a multitude of packets, re-duces to a single packet, and the vector

:."

j) reduces to a corresponding element $]is)|$[s] of the superposition. To which ,;element of the superposition it reduces •:one can not say. One instead assigns aprobability distribution to the possible ',outcomes, with weights given by

w. = \c\2 (11)

The collapse of the state vector and 'the assignment of statistical weights donot follow from the Schrodinger equa-tion, which generates the operator U(equation 4). They are consequencesof an external a priori metaphysics, ;',which is allowed to intervene at this ^point and suspend the Schrodingerequation, or rather replace the boundary ?conditions on its solution by those ofthe collapsed state vector. Bohm and ;Wigner try to construct explicit mech- *anisms for bringing about the collapse,but the conventionalists claim that itdoes not matter how the state vector iscollapsed. To them the state vector :

does not represent reality but only analgorithm for making statistical predic- :

tions. In fact, if the measurement in-volves a von Neumann chain they are -even willing to leave the state vectoruncollapsed over an arbitrary number of - - 'links, just so long as it is treated ascollapsed somewhere along the line.

The Copenhagen view promotes theimpression that the collapse of the state dvector, and even the state vector itself, vis all in the mind. If this impression iscorrect, then what becomes of reality? -;How can one treat so cavalierly theobjective world that obviously exists allaround us? Einstein, who opposed tchis death the metaphysical solution oithe Copenhagen school, must surely •,have expressed himself thus in his mo-ments of private indignation over the'-Sieoremquantum theory. I am convinced thai . ithese sentiments also underlie much oi ^the current dissatisfaction with the con^ventional interpretation of quantunmechanics.

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Historical interpretationsThis problem of the physical inter .

pretation of the quantum theory hauntecits earliest designers. In 1925 am ' l

32

'The buck stops here." Wigner's solution to the dilemma of the schizophrenic apparatus is to clair i ' %that the entry of the measurement signal into the consciousness of a human observer triggers th^'infidecision as to which of the possible outcomes is observed—that is, whether the cat is alive or deac./ H i

PHYSICS TODAY/SEPTEMBER 1970

1926 Werner Heisenberg had just suc-ceeded in breaking the quantum theoryfrom its moorings to the old quantumrules. Through the work of Max Born,Pascual Jordan, Erwin Schrodinger, P.A. M. Dirac and Heisenberg himself,this theory soon acquired a fully de-veloped mathematical formalism. Thechallenge then arose of elucidating thephysical interpretation of this formalismindependently of anything that hadgone on before.

Heisenberg attempted to meet thischallenge by inventing numerousthought experiments, each of whichwas subjected to the question: "Canit be described by the formalism?" Heconjectured that the set of experimentsfor which the answer is "yes" is identi-cal to the set permitted by nature."To put the question in its most ex-treme form in each case meant describ-ing the complete experiment, includingthe measuring apparatus itself, inquantum-mechanical terms.

At this point Bohr entered the pictureand deflected Heisenberg somewhatfrom his original program. Bohr con-vinced Heisenberg and most otherphysicists that quantum mechanics hasno meaning in the absence of a classicalrealm capable of unambiguously record-ing the results of observations. Themixture of metaphysics with physics,which this notion entailed, led to thealmost universal belief that the chiefissues of interpretation are epistemo-logical rather than ontological: Thequantum realm must be viewed as akind of ghostly world whose symbols,such as the wave function, representpotentiality rather than reality.

The EWG metatheorem

What if we forgot all metaphysicalideas and started over again at thepoint where Heisenberg found himselffa 1925? Of course we can not forgeteverything; we will inevitably use 45years of hindsight in attempting to re-structure our interpretation of quantummechanics. Let us nevertheless tryt̂o take the mathematical formalism

of quantum mechanics as it stands with-out adding anything to it'to deny the existence of a separateclassical realmt̂o assert that the state vector never

collapses.In other words, what if we assert that

to formalism is all, that nothing elseis needed? Can we get away with it?The answer is that we can. The proof'f this assertion was first given in 1957»y Hugh Everett10 with the encourage-ment of John Wheeler11 and has beensubsequently elaborated by R. Neil]Graham.12 It constitutes the third wayof getting out of the crisis posed bytlle catastrophe of infinite regression.

Everett, Wheeler and GrahamW postulate that the real world,

or any isolated part of it one may wishfor the moment to regard as the world,is faithfully represented solely by thefollowing mathematical objects: a vec-tor in a Hilbert space; a set of dy-namical equations (derived from avariational principle) for a set of opera-tors that act on the Hilbert space, and aset of commutation relations for theoperators (derived from the Poissonbrackets of the classical theory by thequantization rule, where classical ana-logs exist). Only one additional postu-late is then needed to give physicalmeaning to the mathematics. This isthe postulate of complexity: The worldmust be sufficiently complicated thatit be decomposable into systems andapparatuses.

Without drawing on any externalmetaphysics or mathematics other thanthe standard rules of logic, EWG areable, from these postulates, to provethe following metatheorem: Themathematical formalism of tJie quantumtheory is capable of yielding its own in-terpretation. To prove this meta-theorem, EWG must answer two ques-tions :• How can the conventional probabilityinterpretation of quantum mechanicsemerge from the formalism itself?• How can any correspondence withreality be achieved if the state vectornever collapses?

Absolute chance

Before giving the answers to thesequestions, let us note that the conven-tional interpretation of quantum me-chanics confuses two concepts that reallyought to be kept distinct—probability asit relates to quantum mechanics andprobability as it is understood in sta-tistical mechanics. Quantum mechan-ics is a theory that attempts to de-scribe in mathematical language a worldin which chance is not a measure of ourignorance but is absolute. It shouldinevitably lead to states, like that ofequation 5, that undergo multiple fis-sion, corresponding to the many pos-sible outcomes of a given measurement.Such behavior is built into the formal-ism. However, precisely because quan-tum-mechanical chance is not a mea-sure of our ignorance, we ought not totamper with the state vector merely be-cause we acquire new information as aresult of a measurement.

The obstacle to taking such a loftyview of things, of course, is that itforces us to believe in the reality ofall the simultaneous worlds representedin the superposition described by equa-tion 5, in each of which the measure-ment has yielded a different outcome.Nevertheless, this is precisely whatEWG would have us believe. Accord-ing to them the real universe is faithfullyrepresented by a state vector similar to

that in equation 5 but of vastly greatercomplexity. This universe is constantlysplitting into a stupendous number ofbranches, all resulting from the measure-mentlike interactions between its myr-iads of components. Moreover, everyquantum transition taking place onevery star, in every galaxy, in every re-mote corner of the universe is splittingour local world on earth into myriads ofcopies of itself.

A splitting universe

I still recall vividly the shock I ex-perienced on first encountering thismultiworld concept. The idea of 10100+slightly imperfect copies of oneself allconstantly splitting into further copies,which ultimately become unrecogniz-able, is not easy to reconcile with com-mon sense. Here is schizophrenia witha vengeance. How pale in comparisonis the mental state of the imaginaryfriend, described by Wigner,5 who ishanging in suspended animation be-tween only two possible outcomes of aquantum measurement. Here we mustsurely protest. None of us feels likeWigner's friend. We do not split intwo, let alone into 10100+! To thisEWG reply: To the extent that wecan be regarded simply as automataand hence on a par with ordinarymeasuring apparatuses, the laws ofquantum mechanics do not allow us tofeel tlie splits.

A good way to prove this assertion isto begin by asking what would happen,in the case of the measurement de-scribed earlier by equations 4 and 5,if one introduced a second apparatusthat not only looks at the memorybank of the first apparatus but alsocarries out an independent direct checkon the value of the system observable.If the splitting of the universe is to beunobservable the results had betteragree.

The couplings necessary to ac-complish the desired measurements arereadily set up. The final result is asfollows (see reference 13): The statevector at the end of the coupling in-terval again takes the form of a linearsuperposition of vectors, each of whichrepresents the system observable ashaving assumed one of its possiblevalues. Although the value variesfrom one element of the superpositionto another, not only do both apparatuseswithin a given element observe thevalue appropriate to that element, butalso, by straightforward communication,they agree that the results of their ob-servations are identical. The splittinginto branches is thus unobserved.

Probability interpretation

We must still discuss the questionsof the coefficients c,. in equations 6 and7. EWG give no a priori interpretationto these coefficients. In order to find

PHYSICS TODAY / SEPTEMBER 1970 33

The Copenhagen collapse. This interpretation pictures the total wave function as collapsing to one -state of the superposition and assigns a probability that the wave function will collapse to a givenstate. Only for repetition on an ensemble of cats would live and dead cats be equally real.

-

an interpretation they introduce an ap-paratus that makes repeated measure-ments on an ensemble of identical sys-tems in identical states. The initialstate then has the form

where

for all i

(12)

(13)

and the successive measurements aredescribed in terms of basis vectors

\si)\st)...\AUAl...) (14)

If the apparatus observes each systemexactly once, in sequence, then the nthmeasurement is represented by a unitarytransition of the form

\sl)\si)...\AuA,, 4n + gsm. . . ) (15)

After N measurements the state vec-tor in equation 12 is changed to

(16)

where

. .\AX + gsuA» + .as?,. . .)

$(AuAz. . .) (17)

i(.AltA». . .) = (Ai,A2. . . |<J>) (18)

Although every system is initially inexactly the same state as every other,the apparatus does not generally recorda sequence of identical values for thesystem observable, even within a singleelement of the superposition of equation16. Each memory sequence Si,s2, . . .Sy yields a certain distribution of pos-sible values for the system observable,and each distribution may be subjectedto a statistical analysis. The first andsimplest part of such an analysis is thecalculation of the relative frequencyfunction of the distribution:

f(s;s1...sfr) = - £«„„

Let us introduce the function

(19)

(20)

where the iv's are any positive numbersthat add up to unity. This is the firstof a hierarchy of functions that measurethe degree to which the sequence .s, . . .•sv deviates from a random sequencewith weights wa. Let us choose for theiv's the numbers defined in equation11, and let us introduce an arbitrarilysmall positive number e. We shall callthe sequence sx . . . ,sv "first random" ifS(v, . . . Sjr) < c and "non-first-ran-dom" otherwise.

Suppose now we remove from thesuperposition of equation 16 all thoseelements for which the apparatus mem-ory sequence is non-first-random. De-note the result by |*x

e) . This vectorhas the remarkable property that it dif-fers negligibly from |*.v) in the limitN —* co . More precisely,

Lim = 0

for all t > 0 (21)

A proof will be found in reference 13.A similar result is obtained if | ^ e )

is redefined by excluding, in addition,elements of the superposition whosememory sequences fail to meet anyfinite combination of the infinity ofother requirements for a random se-quence. The conventional probabilityinterpretation of quantum mechanicsthus emerges from the formalism it-self. .Nonrandom memory sequences inequation 16 are of measure zero in theHilbert space, in the limit as N goes toinfinity. Each automaton in the super-position sees the world obeying thefamiliar statistical quantum laws. How-ever, there exists no outside agency thatcan designate which branch of the

superposition is to be regarded as thereal world. All are equally real, andyet each is unaware of the others.These conclusions obviously admit ofimmediate extension to the world ofcosmology. Its state vector is like atree with an enormous number ofbranches. Each branch corresponds toa possible universe-as-we-actually-see-it.

Maverick worlds

The alert reader may now object thatthe above argument is circular, that inorder to derive the physical probabilityinterpretation of quantum mechanics,based on sequences of observations, wehave introduced a nonphijsical prob-ability concept, namely that of themeasure of a subspace in Hilbert space.This concept is alien to experimentalphysics because it involves many ele-ments of the superposition at once, andhence many simultaneous worlds, thatare supposed to be unaware of one an-other.

The problem that this objection raisesis like many that have arisen in thelong history of probability theory. Actu-ally, EWG do not in the end excludeany element of the superposition. Allthe worlds are there, even those inwhich everything goes wrong and allthe statistical laws break down. Thesituation is no different from that whichwe face in ordinary statistical mechanics.If the initial conditions were right, theuniverse-as-we-see-it could be a place inwhich heat sometimes flows from coldbodies to hot. We can perhaps arguethat in those branches in which the uni-verse makes a habit of misbehaving inthis way, life fails to evolve; so no intel-ligent automata are around to beamazed by it.

It is also possible that maverickworlds are simply absent from the grandsuperposition. This could be the case ifordinary three-space is compact andthe universe is finite. The wave func-

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« ID t|

N to n

filto

34 PHYSICS TODAY / SEPTEMBER 1970

tfon of a tinite universe must itself con-tain only a finite number of branches.It simply may not have enough finestructure to accommodate maverickworlds. The extreme smallness of theportion of Hilbert space that suchworlds would have to occupy becomesobvious when one compares the lengthof a Poincare cycle, for even a smallportion of the universe, to a typicalcosmological time scale.

Questions of practicality

The concept of a universal wavefunction leads to important questionsregarding the practical application ofthe quantum-mechanical formalism. IfI am part of the universe, how does ithappen that I am able, without runninginto inconsistencies, to include as muchor as little as I like of the real world ofcosmology in my state vector? Whyshould I be so fortunate as to be able, inpractice, to avoid dealing with the statevector of the universe?

The answer to these questions is to befound in the statistical implications ofsequences of measurements of the kindthat led us to the state vector of equa-tion 16. Consider one of the memorysequences in this state vector. Thismemory sequence defines an averagevalue for the system observable, givenby

s

If the sequence is random, as it is in-creasingly likely to be when N becomeslarge, this average will differ only byan amount of order e from the average

(s) = £ «". (23)s

But the latter average may also be ex-pressed in the form

(s) = (<p\s\>p) (24)

where |i//) is the initial state vector ofany one of the identical systems ands is the operator of which the s's are theeigenvalues. In this form the basisvectors \s) do not appear. Had wechosen to introduce a different appara-tus, designed to measure some observ-able r not equal to s, a sequence of re-peated measurements would haveyielded in this case an average approxi-mately equal to

{r) = <^|r|^) (25)

In terms of the basis vectors \s) thisaverage is given by

(r) = V C*(S\T\S%> (26)s,s'

Now suppose that we first measure sand then perform a statistical analysis°n r. We introduce a second apparatusthat performs a sequence of observationsOn a set of identical two-componentsystems all in identical states given by

the vector |*j) of equation 5. Each ofthe latter systems is composed of oneof the original systems together with anapparatus that has just measured theobservable s. In view of the packetorthogonality relations, given by equa-tion 10, we shall find for the averageof r in this case

The averages in equations 26 and 27are generally not equal. In equation27, the measurement of s, which thefirst apparatus has performed, has de-stroyed the quantum interference effectsthat are still present in equation 26.Thus the elements of the superpositionin equation 5 may be treated as ifthey were members of a statistical en-semble.

This result is what allows us, in prac-tice, to collapse the state vector aftera measurement has occurred, and touse the techniques of ordinary statisticalmechanics, in which we change theboundary conditions upon receipt ofnew information. It is also what permitsus to introduce systems having welldefined initial states, without at thesame time introducing the apparatusesthat prepared the systems in those states.In brief, it is what allows us to startat any point in any branch of the uni-versal state vector without worryingabout previous or simultaneousbranches.

We may, in principle, restore the in-terference effects of equation 26 bybringing the apparatus packets backtogether again. But then the correla-tions between system and apparatus aredestroyed, the apparatus memory iswiped out and no measurement results.If one attempts to maintain the correla-tions by sneaking in a second apparatusto "have a look" before the packets arebrought back together, then the statevector of the second apparatus must beintroduced, and the separation of itspackets will destroy the interferenceeffects.

Final assessmentClearly the EWG view of quantum

mechanics leads to experimental pre-dictions identical with those of theCopenhagen view. This, of course, isits major weakness. Like the originalBohm theory6 it can never receive op-erational support in the laboratory. Noexperiment can reveal the existence ofthe "other worlds" in a superpositionlike that in equations 5 and 6. How-ever, the EWG theory does have thepedagogical merit of bringing most ofthe fundamental issues of measurementtheory clearly into the foreground, andhence of providing a useful frameworkfor discussion.

Moreover a decision between the two

interpretations may ultimately be madeon grounds other than direct laboratoryexperimentation. For example, in thevery early moments of the universe,during the cosmological "Big Bang,"the universal wave function may havepossessed an overall coherence as yetunimpaired by condensation into non-interfering branches. Such initial co-herence may have testable implicationsfor cosmology.

Finally, the EWG interpretation ofquantum mechanics has an importantcontribution to make to the philosophyof science. By showing that formalismalone is sufficient to generate interpre-tation, it has breathed new life into theold idea of a direct correspondence be-tween formalism and reality. Thereality implied here is admittedly biz-arre. To anyone who is awestruck bythe vastness of the presently knownuniverse, the view from where Everett,Wheeler and Graham sit is truly im-pressive. Yet it is a completely causalview, which even Einstein might haveaccepted. At any rate, it has a betterclaim than most to be the natural endproduct of the interpretation programbegun by Heisenberg in 1925.

References1. J. von Neumann, Mathematical Foun-

dations of Quantum Mechanics, Prince-ton University Press, Princeton (1955).

2. H. Margenau, Phil. Sci. 4, 337 (1937);PHYSICS TODAY 7, no. 10, 6 (1954).

3. B. S. DeWitt, Dynamical Theory ofGroups and Fields, Gordon and Breach,New York (1965), pp. 16-29.

4. N. Bohr, L. Rosenfeld, Kgl. DanskeVidenskab. Selskab, Mat.-Fys. Medd.12, no. 8 (1933).

5. E. P. Wigner, "Remarks on the Mind-Body Question," in The ScientistSpeculates (I. J. Good, ed), WilliamHeinemann Ltd, London (1961). Re-printed in E. P. Wigner, Symmetriesand Reflections, Indiana UniversityPress, Bloomington (1967).

6. D. Bohm, Phys. Rev. 85, 166 and 180(1952); 87, 389 (1952); 89, 319 and458 (1953).

7. D. Bohm, J. Bub, Rev. Mod. Phys. 38,453 and 470 (1966).

8. A. Petersen, Quantum Physics and thePhilosophical Tradition, MIT Press,Cambridge (1968).

9. W. Heisenberg, "Quantum Theory andIts Interpretation," in Niels Bohr (S.Rozental, ed), North Holland, Wiley,New York (1967).

10. H. Everett III, Rev. Mod. Phys. 29,454 (1957).

11. J. A. Wheeler, Rev. Mod. Phys. 29,463 (1957).

12. R. N. Graham, PhD thesis, Universityof North Carolina (in preparation).

13. B. S. DeWitt, "The Everett-WheelerInterpretation of Quantum Mechanics,"in Battelle Rencontres, 1967 Lecturesin Mathematics and Physics (C. De-Witt, J. A. Wheeler, eds), W. A. Ben-jamin Inc., New York (1968). •

PHYSICS TODAY /SEPTEMBER 1970 35