Quantum mechanics and reality 

Could the solution to the dilemma of indeterminism be a universe in which all possible outcomes
of an experiment actually occur?
Bryce S. DeWitt

Physics Today 23 (9), 30–35 (1970);

https://doi.org/10.1063/1.3022331

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17 May 2024 07:00:09

 - " •

Quantum mechanics
and reality
Could the solution tothedilemma of
indeterminism be a universe in which all possible outcomes
of an experiment actually occur? Won
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Bryce S. DeWitt

17 May 2024 07:00:09

Despite its enormous practical success, laws, and hence one may form a com- | ) (3) -
quantum theory is so contrary to intui- bined state vector that can be expanded Because the apparatus observes the •*
tion that, even after 45 years, the ex- in terms of an orthonormal set of basis system and not vice versa, we must
perts themselves still do not all agree vectors choose a coupling operator U that re-
what to make of it. The area of dis- flects this separation of function. Let Si
agreement centers primarily around the s,A) = \s)\A) (1) U have the following action on the basis
problem of describing observations. where s is an eigenvalue of some system vectors defined in equation 1 (or on i>
Formally, the result of a measurement observable and A is an eigenvalue of some similar basis):
is a superposition of vectors, each repre- some apparatus observable. (Additional
senting the quantity being observed as labels have been suppressed for sim- U\s,A) = \s,A+gs) = \s)\A+gs) (4)
having one of its possible values. The plicity. ) The Cartesian product struc- Here, g is a coupling constant, which
question that has to be answered is how ture of equation 1 reflects an implicit may be assumed to be adjustable. If
this superposition can be reconciled assumption that, under appropriate con- the initial state of the system were \s)
with the fact that in practice we only ditions, such as the absence of coupling, and that of the apparatus were [A) then
observe one value. How is the measur- the system and apparatus can act as if this coupling would be said to result in
ing instrument prodded into making up they are isolated, independent and dis- an "observation," by the apparatus, that
its mind which value it has observed? tinguishable. It is also convenient to the system observable has the value s.
Of the three main proposals for solv- assume that the eigenvalue ,s ranges This observation or "measurement,
ing this dilemma, I shall focus on one over a discrete set while the eigenvalue would be regarded as "stored" in the
that pictures the universe as continually A ranges over a continuum. apparatus "memory" by virtue of the
splitting into a multiplicity of mutually Suppose that the state of the world at permanent shift from \A) to \A + gs)
unobservable but equally real worlds, some initial instant is represented by a in the apparatus state vector.
in each one of which a measurement normalized vector of the form
does give a definite result. Although Is this definition adequate?
this proposal leads to a bizarre world |*o) = |^)|*) (2) This particular choice for U, essen-
view, it may be the most satisfying where |i//) refers to the system and |$) tially formulated by John von Neu- .
ltsi

answer yet advanced. to the apparatus. In such a state the 1

mann, is frequently criticized because it v
system and apparatus are said to be is not sufficiently general and because it , °i
Quantum theory of measurement "uncorrelated." For the apparatus to artificially delimits the concept of
In its simplest form the quantum learn something about the system the measurement. Some writers2 have also
theory of measurement considers a world two must be coupled together for a cer- insisted that the process described by
composed of just two dynamical en- tain period, so that their combined state equation 4 merely prepares the system
tities, a system and an apparatus. Both will not retain the form of equation 2 and that the measurement is not com- ^
are subject to quantum-mechanical as time passes. The final result of the plete until a more complicated piece of
Bryce DeWitt is professor of physics at coupling will be described by the action apparatus observes the outcome of the ^
the University of North Carolina. of a certain unitary operator U preparation.
'• suffe
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 trace
of radioactive material—just enough that in one hour there is a 50% chance one of the nuclei will
decay and therefore an equal chance the cat will be poisoned. At the end of the hour the total wave
function for the system will have a form in which the living cat and the dead cat are mixed in equal
portions. 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.

17 May 2024 07:00:09

3
It is perfectly true that laboratory nevertheless be shown that if suitable $[.<-]•> = f\A + gs)$(A)dA (7)
measurements are much more compli- devices are used, such as the compensa- $(A) = (.41*) (8)
cated than that described by equation tion devices introduced by Niels Bohr
4 and often involve interactions that do and Leon Rosenfeld in their analysis of4 The final state vector in equation 5 does
not establish precise correlations be- electromagnetic-field measurements. not represent the system observable as
tween pairs of observables such as s and the apparatus can record what the value having any unique value—unless, of
A. However, apart from such noncor- of the system observable would have course, i/<> happens to be one of the
relative interactions, every laboratory been without the coupling. For this basis vectors Is). Rather it is a linear
measurement consists of one or more reason, we work in a modified version superposition of vectors [s)|*[s]), each
sequences of interactions, each essen- of the so-called "interaction picture." in of which represents the system observ-
tially of the von Neumann type. which only that part of the state vector able as having assumed one of its pos-
Although it is only the results of the that refers to the apparatus changes dur- sible values and the apparatus as having
final interactions with the recording de- ing the coupling interval. observed that value. For each possi-
vices that we usually regard as being If the coupling is known, the hypo- bility the observation will be a good
stored, each von Neumann-type "ap- thetical undisturbed system observable one, that is, capable of distinguishing
paratus" in every sequence leading to a may be expressed in terms of the actual adjacent values of s, provided
final interaction may itself be said to dynamical variables of system plus ap- ±A «gAs (9)
possess a memory, at least momentarily. paratus. Hence, the operator of which
This memory differs in no fundamental this observable is an eigenvalue is not where A* is the spacing between ad-
way from that of the sophisticated auto- itself hypothetical, and no inconsistency jacent values and AA is the variance in
maton (apparatus-plus-memory se- will arise if we take it to be the right- A about its mean value relative to the
quence) at the end of the line. It is the hand side of equation 4. distribution function '<t>(A)-\ Under
elementary component that must be un- these conditions we have
derstood if we are to understand quan- Infinite regression = *„ (10)
tum mechanics itself. Consider now what happens to the
initial state vector in equation 2 as a In other words, the wave function of
In his original analysis of the measure- the apparatus takes the form of a packet
ment process,1 von Neumann assumed result of the measurement process of that is initially single but subsequently
that the coupling between system and equation 4. Using the orthonormality splits, as a result of the coupling to the
apparatus leaves the system observable and assumed completeness of the basis system, into a multitude of mutually
s
undisturbed. Most of his conclusions vectors, we easily find that orthogonal packets, one for each value
would have remained unaffected had he
(5) of s.
removed this restriction, and we are not
making such an assumption here. Al- Here the controversies over the inter-
though measurements of the nondisturb- pretation of quantum mechanics start.
.vhere For most people, a state like that of
fflg type do exist, more frequently the
observable suffers a change. It can = (s\t) (6) equation 5 does not represent the actual

PHYSICS TODAY /SEPTEMBER 1970 31

 beings enter the picture. He also pro- j) reduces to a corresponding element $]
occurrence of an observation. They con-
poses that a search be made for unusual is)|$[s] of the superposition. To which ,;
ceive the apparatus to have entered a
effects of consciousness acting on mat- element of the superposition it reduces •:
kind of schizophrenic state in which it
one can not say. One instead assigns a
is unable to decide what value it has ter.5
found for the system observable. At probability distribution to the possible ',
Another proponent of the change-the-
the same time they can not deny that the rules method is David Bohm.0'7 Unlike outcomes, with weights given by
coupling chosen between system and Wigner, who does not wish to change w. = \c\2 (11)
apparatus would, in the classical theory, the theory below the level of conscious- :.
have led to a definite outcome. They ness, Bohm and his school want to The collapse of the state vector and '
therefore face a crisis. How can they change the foundations so that even the the assignment of statistical weights do
prod the apparatus into making up its first apparatus is cured of its schizo- not follow from the Schrodinger equa-
mind? phrenia. This they do by introducing tion, which generates the operator U
so-called "hidden variables." Whatever (equation 4). They are consequences
The usual suggestion is to introduce a
else may be said of hidden-variable of an external a priori metaphysics, ;',
second apparatus to get at the facts
theories, it must be admitted that they which is allowed to intervene at this ^
simply by looking at the first apparatus
do what they are supposed to. The point and suspend the Schrodinger
to see what it has recorded. But an
first such theory" in fact worked too equation, or rather replace the boundary ?
analysis carried out along the above lines
well; there was no way of distinguish- conditions on its solution by those of
quickly shows that the second apparatus
ing it experimentally from conventional the collapsed state vector. Bohm and ;
performs no better than the first. It too
quantum mechanics. More recent hid- Wigner try to construct explicit mech- *
goes into a state of schizophrenia. The
den-variable theories are susceptible to anisms for bringing about the collapse,
same thing happens with a third ap-
possible experimental verification (or but the conventionalists claim that it
paratus, and a fourth, and so on. This
disproof) . 7 does not matter how the state vector is
chain, known as "von Neumann's
collapsed. To them the state vector :
catastrophe of infinite regression," only
The Copenhagen collapse does not represent reality but only an
makes the crisis worse.
The second method of escaping the algorithm for making statistical predic- :
Change the rules von Neumann catastrophe is to accept tions. In fact, if the measurement in-
There are essentially three distinct the so-called "conventional," or "Copen- volves a von Neumann chain they are -
ways of getting out of the crisis. The hagen," interpretation of quantum even willing to leave the state vector
first is to change the rules of the game mechanics. (Reference 8 contains a uncollapsed over an arbitrary number of - - '
by changing the theory, the object be- selected list of papers on this topic.) links, just so long as it is treated as
ing to break von Neumann's infinite In speaking of the adherents of this in- collapsed somewhere along the line.
chain. Eugene Wigner is the most dis- terpretation it is important to distinguish The Copenhagen view promotes the
tinguished proponent of this method. the active adherents from the rest, and impression that the collapse of the state d
Taking a remarkably anthropocentric to realize that even most textbook au-

17 May 2024 07:00:09

vector, and even the state vector itself, v
stand, he proposes that the entry of the thors are not included among the is all in the mind. If this impression is
measurement signal into the conscious- former. If a poll were conducted correct, then what becomes of reality? -;
ness of an observer is what triggers the among physicists, the majority would How can one treat so cavalierly the
decision and breaks the chain.3 Cer- profess membership in the conventional- objective world that obviously exists all
tainly the chain had better be broken ist camp, just as most Americans would around us? Einstein, who opposed tc
at this point, as the human brain is claim to believe in the Bill of Rights, his death the metaphysical solution oi
usually where laboratory-measurement whether they had ever read it or not. the Copenhagen school, must surely •,
sequences terminate. One is reminded The great difficulty in dealing with the have expressed himself thus in his mo-
of the sign that used to stand on Presi- activists in this camp is that they too ments of private indignation over the'-Sieorem
dent Truman's desk: "The buck stops change the rules of the game but, unlike quantum theory. I am convinced thai . i
here." Wigner and Bohm, pretend that they these sentiments also underlie much oi ^
Wigner does not indulge in mere don't. the current dissatisfaction with the con^
handwaving; he actually sketches a pos- According to the Copenhagen inter- ventional interpretation of quantun
sible mathematical description of the pretation of quantum mechanics, when- mechanics.
conversion from a pure to a mixed state, ever a state vector attains a form like • "

which might come about as a result of that in equation 5 it immediately col- Historical interpretations
the grossly nonlinear departures from lapses. The wave function, instead of This problem of the physical inter .
the normal Schrodinger equation that he consisting of a multitude of packets, re- pretation of the quantum theory hauntec
believes must occur when conscious duces to a single packet, and the vector its earliest designers. In 1925 am ' l

'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^'infi
decision as to which of the possible outcomes is observed—that is, whether the cat is alive or deac./ H i

32 PHYSICS TODAY/SEPTEMBER 1970

1926 Werner Heisenberg had just suc- or any isolated part of it one may wish that in equation 5 but of vastly greater
ceeded in breaking the quantum theory for the moment to regard as the world, complexity. This universe is constantly
from its moorings to the old quantum is faithfully represented solely by the splitting into a stupendous number of
rules. Through the work of Max Born, following mathematical objects: a vec- branches, all resulting from the measure-
Pascual Jordan, Erwin Schrodinger, P. tor in a Hilbert space; a set of dy- mentlike interactions between its myr-
A. M. Dirac and Heisenberg himself, namical equations (derived from a iads of components. Moreover, every
this theory soon acquired a fully de- variational principle) for a set of opera- quantum transition taking place on
veloped mathematical formalism. The tors that act on the Hilbert space, and a every star, in every galaxy, in every re-
challenge then arose of elucidating the set of commutation relations for the mote corner of the universe is splitting
physical interpretation of this formalism operators (derived from the Poisson our local world on earth into myriads of
independently of anything that had brackets of the classical theory by the copies of itself.
gone on before. quantization rule, where classical ana-
Heisenberg attempted to meet this logs exist). Only one additional postu- A splitting universe
challenge by inventing numerous late is then needed to give physical I still recall vividly the shock I ex-
thought experiments, each of which meaning to the mathematics. This is perienced on first encountering this
was subjected to the question: "Can the postulate of complexity: The world multiworld concept. The idea of 10100+
it be described by the formalism?" He must be sufficiently complicated that slightly imperfect copies of oneself all
conjectured that the set of experiments it be decomposable into systems and constantly splitting into further copies,
for which the answer is "yes" is identi- apparatuses. which ultimately become unrecogniz-
cal to the set permitted by nature." Without drawing on any external able, is not easy to reconcile with com-
To put the question in its most ex- metaphysics or mathematics other than mon sense. Here is schizophrenia with
treme form in each case meant describ- the standard rules of logic, EWG are a vengeance. How pale in comparison
ing the complete experiment, including able, from these postulates, to prove is the mental state of the imaginary
the measuring apparatus itself, in the following metatheorem: The friend, described by Wigner,5 who is
quantum-mechanical terms. mathematical formalism of tJie quantum hanging in suspended animation be-
At this point Bohr entered the picture theory is capable of yielding its own in- tween only two possible outcomes of a
and deflected Heisenberg somewhat terpretation. To prove this meta- quantum measurement. Here we must
from his original program. Bohr con- theorem, EWG must answer two ques- surely protest. None of us feels like
vinced Heisenberg and most other tions : Wigner's friend. We do not split in
physicists that quantum mechanics has • How can the conventional probability two, let alone into 10 100 +! To this
no meaning in the absence of a classical interpretation of quantum mechanics EWG reply: To the extent that we
realm capable of unambiguously record- emerge from the formalism itself? can be regarded simply as automata
ing the results of observations. The • How can any correspondence with and hence on a par with ordinary
mixture of metaphysics with physics, reality be achieved if the state vector measuring apparatuses, the laws of
which this notion entailed, led to the never collapses? quantum mechanics do not allow us to

17 May 2024 07:00:09

almost universal belief that the chief feel tlie splits.
issues of interpretation are epistemo- A good way to prove this assertion is
logical rather than ontological: The Absolute chance to begin by asking what would happen,
quantum realm must be viewed as a Before giving the answers to these in the case of the measurement de-
kind of ghostly world whose symbols, questions, let us note that the conven- scribed earlier by equations 4 and 5,
such as the wave function, represent tional interpretation of quantum me- if one introduced a second apparatus
potentiality rather than reality. chanics confuses two concepts that really that not only looks at the memory
ought to be kept distinct—probability as bank of the first apparatus but also
The EWG metatheorem it relates to quantum mechanics and carries out an independent direct check
What if we forgot all metaphysical probability as it is understood in sta- on the value of the system observable.
ideas and started over again at the tistical mechanics. Quantum mechan- If the splitting of the universe is to be
point where Heisenberg found himself ics is a theory that attempts to de- unobservable the results had better
fa 1925? Of course we can not forget scribe in mathematical language a world agree.
everything; we will inevitably use 45 in which chance is not a measure of our The couplings necessary to ac-
years of hindsight in attempting to re- ignorance but is absolute. It should complish the desired measurements are
structure our interpretation of quantum inevitably lead to states, like that of readily set up. The final result is as
mechanics. Let us nevertheless try equation 5, that undergo multiple fis- follows (see reference 13): The state
^to take the mathematical formalism sion, corresponding to the many pos- vector at the end of the coupling in-
of quantum mechanics as it stands with- sible outcomes of a given measurement. terval again takes the form of a linear
out adding anything to it Such behavior is built into the formal- superposition of vectors, each of which
'to deny the existence of a separate ism. However, precisely because quan- represents the system observable as
classical realm tum-mechanical chance is not a mea- having assumed one of its possible
^to assert that the state vector never sure of our ignorance, we ought not to values. Although the value varies
collapses. tamper with the state vector merely be- from one element of the superposition
In other words, what if we assert that cause we acquire new information as a to another, not only do both apparatuses
toformalismis all, that nothing else result of a measurement. within a given element observe the
is
needed? Can we get away with it? The obstacle to taking such a lofty value appropriate to that element, but
The answer is that we can. The proof view of things, of course, is that it also, by straightforward communication,
'f this assertion was first given in 1957 forces us to believe in the reality of they agree that the results of their ob-
»y Hugh Everett10 with the encourage- all the simultaneous worlds represented servations are identical. The splitting
ment of John Wheeler 11 and has been in the superposition described by equa- into branches is thus unobserved.
subsequently elaborated by R. Neil] tion 5, in each of which the measure-
Probability interpretation
Graham.12 It constitutes the third way ment has yielded a different outcome.
of We must still discuss the questions
getting out of the crisis posed by Nevertheless, this is precisely what
tlle EWG would have us believe. Accord- of the coefficients c,. in equations 6 and
catastrophe of infinite regression.
Everett, Wheeler and Graham ing to them the real universe is faithfully 7. EWG give no a priori interpretation
W postulate that the real world, represented by a state vector similar to to 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 given
state. Only for repetition on an ensemble of cats would live and dead cats be equally real.
-

an interpretation they introduce an ap- superposition is to be regarded as the

paratus that makes repeated measure- f(s;s1...sfr) = - £«„„ (19) real world. All are equally real, and
ments on an ensemble of identical sys- yet each is unaware of the others. •

tems in identical states. The initial Let us introduce the function These conclusions obviously admit of
state then has the form immediate extension to the world of
(20) cosmology. Its state vector is like a
(12) k
tree with an enormous number of .-
where where the iv's are any positive numbers branches. Each branch corresponds to
that add up to unity. This is the first a possible universe-as-we-actually-see-it.
for all i (13) of a hierarchy of functions that measure
and the successive measurements are the degree to which the sequence .s, . . . Maverick worlds

17 May 2024 07:00:09

described in terms of basis vectors •sv deviates from a random sequence The alert reader may now object that
with weights wa. Let us choose for the the above argument is circular, that in
\si)\st)...\AUAl...) (14) iv's the numbers defined in equation order to derive the physical probability
If the apparatus observes each system 11, and let us introduce an arbitrarily interpretation of quantum mechanics,
exactly once, in sequence, then the nth small positive number e. We shall call based on sequences of observations, we
measurement is represented by a unitary the sequence sx . . . ,sv "first random" if have introduced a nonphijsical prob-
transition of the form S(v, . . . Sjr) < c and "non-first-ran- ability concept, namely that of the
dom" otherwise. measure of a subspace in Hilbert space.
Suppose now we remove from the This concept is alien to experimental
superposition of equation 16 all those physics because it involves many ele-
\sl)\si)...\AuA,, 4n + gsm. ..) (15)
elements for which the apparatus mem- ments of the superposition at once, and
After N measurements the state vec- ory sequence is non-first-random. De- hence many simultaneous worlds, that •to aven
tor in equation 12 is changed to note the result by |* x e ) . This vector are supposed to be unaware of one an-
has the remarkable property that it dif- other.
fers negligibly from |*. v ) in the limit The problem that this objection raises
N —* co . More precisely, is like many that have arisen in the
(16)
Lim long history of probability theory. Actu-
where = 0
ally, EWG do not in the end exclude • : :

any element of the superposition. All « ID t|

for all t > 0 (21)
the worlds are there, even those in
. .\AX + gsuA» + .as?,. . .) A proof will be found in reference 13. which everything goes wrong and all
$(AuAz. . .) (17) A similar result is obtained if | ^ e ) the statistical laws break down. The N to n
i(.AltA». . .) = (Ai,A2. . . |<J>) (18) is redefined by excluding, in addition, situation is no different from that which
elements of the superposition whose we face in ordinary statistical mechanics.
Although every system is initially in memory sequences fail to meet any If the initial conditions were right, the
exactly the same state as every other, finite combination of the infinity of universe-as-we-see-it could be a place in filto
the apparatus does not generally record other requirements for a random se- which heat sometimes flows from cold
a sequence of identical values for the quence. The conventional probability bodies to hot. We can perhaps argue
system observable, even within a single interpretation of quantum mechanics that in those branches in which the uni-
element of the superposition of equation thus emerges from the formalism it- verse makes a habit of misbehaving in
16. Each memory sequence Si,s2, . . . self. .Nonrandom memory sequences in this way, life fails to evolve; so no intel-
Sy yields a certain distribution of pos- equation 16 are of measure zero in the ligent automata are around to be
sible values for the system observable, Hilbert space, in the limit as N goes to amazed by it.
and each distribution may be subjected infinity. Each automaton in the super- It is also possible that maverick
to a statistical analysis. The first and position sees the world obeying the worlds are simply absent from the grand
simplest part of such an analysis is the familiar statistical quantum laws. How- superposition. This could be the case if
calculation of the relative frequency ever, there exists no outside agency that ordinary three-space is compact and
function of the distribution: can designate which branch of the the universe is finite. The wave func-

34 PHYSICS TODAY / SEPTEMBER 1970

tfon of a tinite universe must itself con- the vector |*j) of equation 5. Each of interpretations may ultimately be made
tain only a finite number of branches. the latter systems is composed of one on grounds other than direct laboratory
It simply may not have enough fine of the original systems together with an experimentation. For example, in the
structure to accommodate maverick apparatus that has just measured the very early moments of the universe,
worlds. The extreme smallness of the observable s. In view of the packet during the cosmological "Big Bang,"
portion of Hilbert space that such orthogonality relations, given by equa- the universal wave function may have
worlds would have to occupy becomes tion 10, we shall find for the average possessed an overall coherence as yet
obvious when one compares the length of r in this case unimpaired by condensation into non-
of a Poincare cycle, for even a small interfering branches. Such initial co-
portion of the universe, to a typical herence may have testable implications
cosmological time scale. for cosmology.
Questions of practicality
Finally, the EWG interpretation of
The averages in equations 26 and 27 quantum mechanics has an important
The concept of a universal wave are generally not equal. In equation contribution to make to the philosophy
function leads to important questions 27, the measurement of s, which the of science. By showing that formalism
regarding the practical application of first apparatus has performed, has de- alone is sufficient to generate interpre-
the quantum-mechanical formalism. If stroyed the quantum interference effects tation, it has breathed new life into the
I am part of the universe, how does it that are still present in equation 26. old idea of a direct correspondence be-
happen that I am able, without running Thus the elements of the superposition tween formalism and reality. The
into inconsistencies, to include as much in equation 5 may be treated as if reality implied here is admittedly biz-
or as little as I like of the real world of they were members of a statistical en- arre. To anyone who is awestruck by
cosmology in my state vector? Why semble. the vastness of the presently known
should I be so fortunate as to be able, in This result is what allows us, in prac- universe, the view from where Everett,
practice, to avoid dealing with the state tice, to collapse the state vector after Wheeler and Graham sit is truly im-
vector of the universe? a measurement has occurred, and to pressive. Yet it is a completely causal
The answer to these questions is to be use the techniques of ordinary statistical view, which even Einstein might have
found in the statistical implications of mechanics, in which we change the accepted. At any rate, it has a better
sequences of measurements of the kind boundary conditions upon receipt of claim than most to be the natural end
that led us to the state vector of equa- new information. It is also what permits product of the interpretation program
tion 16. Consider one of the memory us to introduce systems having well begun by Heisenberg in 1925.
sequences in this state vector. This defined initial states, without at the
memory sequence defines an average same time introducing the apparatuses References
value for the system observable, given that prepared the systems in those states. 1. J. von Neumann, Mathematical Foun-
by In brief, it is what allows us to start dations of Quantum Mechanics, Prince-
at any point in any branch of the uni- ton University Press, Princeton (1955).

17 May 2024 07:00:09

versal state vector without worrying 2. H. Margenau, Phil. Sci. 4, 337 (1937);
s about previous or simultaneous PHYSICS TODAY 7, no. 10, 6 (1954).
If the sequence is random, as it is in- branches. 3. B. S. DeWitt, Dynamical Theory of
creasingly likely to be when N becomes We may, in principle, restore the in- Groups and Fields, Gordon and Breach,
New York (1965), pp. 16-29.
large, this average will differ only by terference effects of equation 26 by
an amount of order e from the average bringing the apparatus packets back 4. N. Bohr, L. Rosenfeld, Kgl. Danske
Videnskab. Selskab, Mat.-Fys. Medd.
together again. But then the correla- 12, no. 8 (1933).
(s) = £ «". (23) tions between system and apparatus are
5. E. P. Wigner, "Remarks on the Mind-
s destroyed, the apparatus memory is Body Question," in The Scientist
But the latter average may also be ex- wiped out and no measurement results. Speculates (I. J. Good, ed), William
pressed in the form If one attempts to maintain the correla- Heinemann Ltd, London (1961). Re-
tions by sneaking in a second apparatus printed in E. P. Wigner, Symmetries
(s) = (<p\s\>p) (24) to "have a look" before the packets are and Reflections, Indiana University
where |i//) is the initial state vector of brought back together, then the state Press, Bloomington (1967).
any one of the identical systems and vector of the second apparatus must be 6. D. Bohm, Phys. Rev. 85, 166 and 180
s is the operator of which the s's are the introduced, and the separation of its (1952); 87, 389 (1952); 89, 319 and
eigenvalues. In this form the basis packets will destroy the interference 458 (1953).
vectors \s) do not appear. Had we effects. 7. D. Bohm, J. Bub, Rev. Mod. Phys. 38,
chosen to introduce a different appara- 453 and 470 (1966).
tus, designed to measure some observ- Final assessment 8. A. Petersen, Quantum Physics and the
able r not equal to s, a sequence of re- Clearly the EWG view of quantum Philosophical Tradition, MIT Press,
mechanics leads to experimental pre- Cambridge (1968).
peated measurements would have
yielded in this case an average approxi- dictions identical with those of the 9. W. Heisenberg, "Quantum Theory and
Copenhagen view. This, of course, is Its Interpretation," in Niels Bohr (S.
mately equal to
Rozental, ed), North Holland, Wiley,
its major weakness. Like the original New York (1967).
{r) = <^|r|^) (25) Bohm theory6 it can never receive op- 10. H. Everett III, Rev. Mod. Phys. 29,
In terms of the basis vectors \s) this erational support in the laboratory. No 454 (1957).
average is given by experiment can reveal the existence of
11. J. A. Wheeler, Rev. Mod. Phys. 29,
the "other worlds" in a superposition 463 (1957).
(r) = V C*(S\T\S%> (26) like that in equations 5 and 6. How-
12. R. N. Graham, PhD thesis, University
s,s' ever, the EWG theory does have the of North Carolina (in preparation).
Now suppose that we first measure s pedagogical merit of bringing most of
13. B. S. DeWitt, "The Everett-Wheeler
and then perform a statistical analysis the fundamental issues of measurement Interpretation of Quantum Mechanics,"
°n r. We introduce a second apparatus theory clearly into the foreground, and in Battelle Rencontres, 1967 Lectures
that performs a sequence of observations hence of providing a useful framework in Mathematics and Physics (C. De-
On
a set of identical two-component for discussion. Witt, J. A. Wheeler, eds), W. A. Ben-
systems all in identical states given by Moreover a decision between the two jamin Inc., New York (1968). •

PHYSICS TODAY /SEPTEMBER 1970 35