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L [BRA R Y
Michigan State
University

 
 

This is to certify that the
thesis entitled

Quantum Theory and the Independent
Existence of Physical Objects

presented by

Clyde H. Evans

has been accepted towards fulfillment
of the requirements for

_ih_._D_.__degree in Physics 8c Philosophy

Major professor E

Date—Maw

0—7639

 

 

 

ABSTRACT

QUANTUM THEORY AND THE INDEPENDENT
EXISTENCE OF PHYSICAL OBJECTS

BY

Clyde H. Evans

We note that quantum theory has reopened consider-
ation of a philosophical problem of long standing: the
question of the independent existence of physical objects.
In particular, the problem we consider is whether the

properties of physical objects can be considered inde-

 

pendent and objective, as Opposed to being subjective

and dependent (upon other factors distinct from the object
itself). We examine the results of different theories of
physics as they might pertain to our problem. We find

that classical physics gives an account of physical objects
as being completely objective and independent. With rela-
tivity theory we find a collapse of this ideal of complete
independence and objectivity; but not a total collapse.

In quantum theory we find a further collapse of this ideal,
but in a different way from that in either classical or
relativistic physics. This leads to the central conclusion

of the thesis: the existence of microscopic subjectivism.

Clyde H. Evans

This is the claim that on the microscopic level, physical

objects do not possess their properties in an independent

 

manner. In some states in which the micro objects can
exist (viz, the states of superposition) the object has a
given property but has no determinate or definite "value"
for this proPerty, unless it interacts with another object.
Until such an interaction, the property is undefined and
indeterminate: it has no value at all. We consider
various possible responses to the claim of microscopic
subjectivism. The one that seems most "desirable" is
that which accepts the subjectivism on the micro level,
but rejects it on the macro level. We examine these
proposals in detail. We find that none are completely

satisfactory. We conclude that, as of yet, no complete

 

understanding is apparent of how to incorporate this new
"fact" of microscopic subjectivism into our overall world
view. We note finally that this inclusion in physical
theory of a subjectivism at a fundamental level repre-

sents a radical departure from previous scientific thought.

 

QUANTUM THEORY AND THE INDEPENDENT

EXISTENCE OF PHYSICAL OBJECTS

By'

a ‘J

Clyde Hg Evans

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Departments of Physics and Philosophy

1971

My 3&5

DEDICATION
This work is dedicated to Anita, and to

to all those who will hopefully benefit from

my training, education, and experiences.

ii

ACKNOWLEDGMENTS

I wish to thank Richard Schlegel who has been
generous with his time and assistance, gracious in his
criticisms, stimulating in his collaborations, and un-
failing in his encouragement and support. I thank him
most of all for his friendship. I wish also to thank

Richard Hall for cheerful and valuable assistance.

iii

TABLE OF CONTENTS

Part Page
I. INTRODUCTION . . . . . . . . . . . 1
II. THE EVIDENCE OF PHYSICS . . . . . . . 16
Classical Physics. . . . . . . . . l7
Relativistic Physics. . . . . . . . 21
Quantum Physics . . . . . . . . . 30
Basic Ideas of Quantum Theory . . . . 3O

Situation in QT Does Qualify as Being
"Subjective" . . . . . . . . . 33

Difference Between Classical and

Quantum Physics . . . . . . . . 36

Probability as Entrance of Subjectivism
Into QT: Arguments for Non-Classical

Probability . . . . . . . . . 39
Experiment As Entrance of Subjectivis
IntO QT c o o o o o o o o o o 54

III. CONSEQUENCES OF MICROSCOPIC SUBJECTIVISM:
POSSIBLE RESPONSES TO CLAIM OF MICROSCOPIC

SUBJECTIVISM . . . . . . . . . . . 73
A. Deny Microscopic Subjectivism . . . 78
B. Accept Microsc0pic Subjectivism,

Reject Macrosc0pic Subjectivism . . 88
C. Accept Microsc0pic Subjectivism,

Accept Macroscopic Subjectivism . . 88
D. Subjective/Objective Distinction

Is Useless . . . . . . . . . 92
Alternatives Under B. . . . . . . . 97

Difficulties Associated with Reducation
of Wave Function. . . . . . . . 102
Particular Alternatives . . . . . . 112

iv

 

Part Page

IV. CONCLUSION . . . . . . . . . . . 138
POSTSCRIPT: PHYSICS AND METAPHYSICS . . . . 154
BIBLIOGRAPHY . . . . . . . . . . . . 168
APPENDIX. . . . . . . . . . . . . . 172

 

PART I

INTRODUCTION

Quantum theory (hereafter QT) has brought to the
fore--in a scintillating way——an old philosophical problem
of long standing: the problem of the nature of the exist- }'
ence of physical objects. This problem has many different
aspects and can be formulated in quite different ways: Do
physical objects really exist at all, or are they just
"constructions" out of our experience? Do objects persist
while not being observed? Which characteristics of an
object are intrinsic to it, and which are "contributed"
by an observer? Do all the properties of an object have
the same status?

The question with which we shall be concerned is
the question of the independence of the various properties
or attributes of physical objects. We will seek to dis-
cover to what extent the properties of physical objects
can be considered independent and objective, where this
is meant in the following sense: if the exact nature of
a property that an object in fact has, can be specified

without appeal to anything distinct from the object itself,

then this property will be considered to be character-
istic of the object independently of anything else; it is
considered objective since its complete specification is
not subject to any conditions other than those pertaining
to the object itself. If it is not possible to provide
such a specification for a given property, then this
property will be considered as not being completely deter—
mined solely by the given object alone; for specification
of this property will require reference to something else
other than the object. To the extent that specification
of the property is subject to these “outside" factors, it
is considered a subjective property.

It will be our wish here to study this question in
light of whatever we can learn from physics. We hope to
determine, in particular, in light of what we learn from
physics, if any of the prominent historical solutions to
the problem, must be reconsidered. We will attempt to
form the best possible (present) understanding, consistent
with present-day physics, of the independent/non-independent
status of the properties of physical objects, and consider
what epistemological or ontological consequences follow
from such an understanding.

With such a complex problem it is not surprising
that any such inquiry as this is beset with many diffi-
culties, obstacles, and sub-problems. It will, of course,

be impossible here to do more than indicate the appearance

of each of these aspects (of our overall problem). By the
same token, we shall be obliged to assume a solution to
some of these sub-problems, or presume a resolution of some
difficulties--ignoring the (sometime formidable) objections
associated with the adopted position. This procedure is
acceptable for two reasons. The first is methodological:
in the overall discussion, some problems appear earlier,
others later. The problem of primary importance to us is
one of the later ones. Thus, if we did not finally accept
a given solution to a question (just so that debate on
that issue could be closed) our inquiry would never get
off the ground; and we could never proceed beyond consider-
ation of the most preliminary questions. The second reason
is pragmatic: the position which we shall adopt is one
which is widespread, and for that reason will provide us
with a base for profitable and useful discussion. (During
our discussion I will not assume the responsibility of
indicating, at each critical point, all the possible and
actual divergent points of view-~except when deemed helpful
for the continuation of our discussion. I will presume
that the reader will recognize these points and permit me
(with the justification given above) to "gloss over" some
very controversial points.)

Let us take a brief look at how this issue—~of the
independence of the properties of physical objects--has

become such an important philosophical problem; and let us

try to formulate more clearly the exact nature of the
problem.

I suppose that belief in an external world, popu—
lated by different objects, is one of the most "reasonable"
beliefs imaginable. But justification of this belief
proves to be disconcertingly difficult. Some have taken
the tack of modern science: ignore the question of the
"reality" of the physical world, simply take our experience
of the physical world as giygp, assume that it is an object
worthy of study, and then get on with the task of trying
to find out as much as we can about it. Others have simply
accepted the existence of objects "out of hand" as it were.

But the existence of physical objects has not always
been accepted so unquestioningly. It has been argued that
though we can never find justification, it is inevitable
that we should believe in the existence of bodies inde—
pendent of our minds. David Hume says in the chapter
entitled 'Skepticism with Regard to the Senses' (Treatise,

I, iv, 2): "We may well ask, What causes induce us to

 

believe in the existence of body? but 'tis vain to ask,

 

Whether there be body or not?" And further: "'Tis im—

 

possible upon any system to defend either our understand-
ing or senses."

Still in this century, philosophers continue to be
concerned about the existence of entities. Carnap [l5]

draws a sharp distinction between questions which arise

 

 

' ---=w

within a given system of concepts, or framework of ideas,
and questions which are sometimes raised 22232 that frame-
work or system. Questions of the first sort belong to the
field of some science or of everyday life, and are answered
by the methods appropriate to those fields. Questions of
the latter sort have traditionally appeared in metaphysics
in the misleading form of questions about the reality or
existence of some general class of entities corresponding-
to the fundamental ideas of the system of concepts in
question. Thus philosophers have asked whether there really
existed such things as numbers, whether space-time points
were real, etc. But such questions can be significantly
understood only as raising the practical issue of whether
or not to employ and use the given conceptual scheme or
framework of ideas. To answer affirmatively is, accord—
ing to Carnap, simply to adopt such a framework for

use.

This question-~the justification of the existence of
external objects--is by no means settled. But it is cer—
tainly true that not only is the existence of external
objects (bodies) accepted by most--including philosophers,
scientists, and men-in-the-street. It is also true that
throughout most of the history of philosophy this belief
has been almost exclusively dominant. This was certainly

so for the Greeks.

As a matter of fact, the early Greek philosophers
devoted their attention almost exclusively to cosmology,
the inquiry into what makes the physical world tick and
why it is the way it is. Leaving aside the question of
the relation between the objects of our awareness and the

"ultimate constituents, we know that the early Greeks
surely believed in the existence of objects external to
themselves. Not only did the Greeks accept the existence
of external objects in their philosophy but gradually they
also developed a distinction which was to prove of im-
portance of the first rank: the distinction between an
object and its qualities (properties).

It is clear from the writings of the Presocratic
philosophers that they did ESE have the concept of a
quality. That is, they just did not think in terms of
qualities at all. They certainly had no single wppd for
quality; but also their general discussion shows that they
did not possess the concept either. Where wg should talk
of qualities they tended to talk of things. The tra—
ditional opposites, for example——qualities like heat and
cold—-were always thought of as things.

In the development of Plato‘s philosophy some sensi-
tivity to the necessity of distinguishing between qualities
and things begins to emerge. In the earlier formulation
of the Theory of Forms, the Forms correspond to qualities

and yet are thought of as, in some sense, things. In the

 

Theatetus (182a), however, Socrates is made to introduce,
with apologies, the wpgd for quality (n010'1n§)——a word
literally meaning "what—sort-of—ness," which was con-
structed out of the word meaning "what sort of" (wdloc)
which was already in use. Nevertheless, the dialogues

show that Plato never became completely acclimated to the
necessity of making a rigorous distinction in his thought
between things and qualities. He could not fully appreciate

what it was to think of something as a quality, as distinct

 

from a thing.

Aristotle laid the philosophical foundations of the
distinction in his doctrine of categories. Philosophical
categories are classes, genera, or types supposed to mark
necessary divisions within our conceptual scheme, divisions
that we must recognize if we are to make literal sense in
our discourse about the world. To say that two entities
belong to different categories is to say that they have
literally nothing in common, that we cannot apply the same
descriptive terms to both unless we speak metaphorically
or equivocally. Aristotle first used the word "category"
in a short treatise called Categories. He held that every
uncombined expression signifies (denotes, refers to) one
or more things falling in at least one of the following
ten classes: substance, quantity, quality, place, time,
posture, state, action, and passion. By "uncombined
expression" Aristotle meant an expression considered apart

from its combination with other expressions in a sentence.

A

(We might note that Aristotle intended this account to
apply only to those expressions which we now call "de—
scriptive" and "non-logical.") Two considerations are
essential to Aristotle's theory of categories: that
substances be properly distinguished from accidents and
essential predication from accidental predication. The
first is the one of most interest to us, and the accident
of most interest to us is that of quality.

According, now, to Aristotle's account, the earlier
Greek philosophers failed to make a distinction between
the category substance (i.e., the object) and the category
quality. Actually, it turns out that in some of his
philosophical discussion, Aristotle shows that he was not
completely at home with the distinction either. A dis-
tinction of this significance is not easily come by, and
the struggle to understand it apparently is long and hard.

But sooner or later, the distinction between an
object and its qualities (of which, in general, there are
several) does become entrenched. At this point immedi-
ately (logically, if not historically) another problem

raises its head: do all of the qualities (properties)

 

have equal status? And here "status" can have any of

 

several different meanings: do all the qualities have
the same status logically, physically, psychologically,
causally, epistemologically, ontologically, etc.? For

instance, are any of the qualities of an object "more real"

than any others? There is a second question that appears
at this point which is also quite important: is this
question (viz, about the status of the various qualities)
a question for philosophy or a question for physics? We
will see that this question arises more than once during
our inquiry. We will postpone consideration of it until
later.

Let us consider the first question, i.e., whether
all the qualities of an object have equal status (in any
of the several senses of status). One answer that has
been given (and a historically prominent one) is NO. The
qualities are not all on the same footing. There are pri—
mary qualities and there are secondary qualities. So, in
addition to the distinction between an object and its
qualities, we have the further distinction between those
qualities that are primary and those that are merely
secondary. This distinction dates back in principle to
Democritus, who said that sweet and bitter, warm and
cold, and color, exist only by convention (véuw), and
in truth there exists only the atoms and the void (EEEE'
mgppe Egg Vorsokratiker, H. Diels and W. Kranz). The dis—
tinction was revised by Galileo and accepted by Descartes,
Newton, and others (among them Robert Boyle and signifi—
cantly, John Locke).

With regard to the motivation for re-introducing
this distinction (around the seventeenth century), I be—

lieve that the motivation for this was more methodological

10

than metaphysical. That is, the distinction was propounded
not so much because of what was realized or understood
regarding the "intrinsic nature" of objects. Rather, it
was prOpounded because of the requirements of the new—found
methodological tool of the scientists of the day, viz,
mathematics. It was the case that, given the science of
the day, gems qualities of objects were susceptible to
mathematical handling and others were not. It was the

case furthermore, that, given the science of that time,

all observed phenomena could be satisfactorily explained
by taking into account jpgp the first set of qualities
(viz, the ones susceptible to mathematical manipulation).
Thus, it was believed that these qualities were of pp;-
mggy importance for our understanding of the phenomena and
consequently for the intrinsic nature of the phenomena

(and objects) themselves.

We will discuss the particular solution of the
seventeenth century thinkers (of the problem of the status
of the qualities of objects) a bit more in detail later.
Here I wish only to point out that though the motivation
for re-introducing the distinction can be called into
question, and though the motivating reasons are clearly

not all philos0phical, this does not, in itself, preclude

 

 

the possibility of just such a philosophical distinction.
In philosophy, the connection between argument and truth

(in an elementary and intuitive sense) is a tenuous one.

v--_ f

11

A position might be a true one, even though the argument
in support of it is itself a bad argument. Thus, even
though the methodological (i.e., mathematical) motivating
reasons might be called into question, the position which
these reasons are designed to support (viz, the primary/
secondary distinction) should be judged on its own merits.
In other words, though this particular line of argument
might not be convincing or adequate, there may indeed be
another line of argument which is.

And pgimg fagig there does seem to be ample evidence
for believing in a distinction between the several proper—
ties of an object. We are all familiar with the case of
a piece of clothing, say a necktie, that appears to be one
color when looked at in the showcase, but appears to be of
a noticeably different shade (of the same color) when
looked at in the natural light outside the shop. It is
also a common experience to find the same object appear
to be of different colors when viewed under different
kinds of light. Hence, the color of the object seems
clearly to be a property that is relative to the observer
or the conditions of observation and is not inherent in
the object itself. On the other hand, regardless of the
kind of light present, or any other of the usual kinds
of changes in the conditions of observation, the mass
(or weight) of the object remains the same. Thus, there
does seem to be grounds for a distinction between some of

the properties.

 

 

12

It is important to note that we can always recognize
both a physical and a psychological correlate for each of
our sensations. Thus, with respect to a coin there is the
experienced_(seen) shape and size, and there is the physical
shape and size that can be measured. There is the physical
shape of the coin (round), which can be measured with a
compass, and the physical size, which can be measured with
a ruler; and there is the sensible or experienced shape
(round if seen from a perpendicular, elliptical if seen
from other angles) and the sensible or experienced size
(smaller if one recedes from the object).

In all this there is no distinction between primary
and secondary qualities: both sets of qualities, we might
say, have both their primary (physical) and secondary
(experienced) aspects. This distinction between the
physical and the experienced aspects was not always
realized by philosophers. (This is especially true of
some of the arguments advanced by Locke.) But when this
distinction is kept in mind, many of the traditional argu—
ments fall apart. Instead of a distinction between pri—
mary qualities (for example, mass) and secondary qualities
(for example, color), we end up with a distinction between
physical qualities and sensible qualities (which extends
throughout most of the range of 2933 the Lockean primary

and secondary qualities).

 

13

To say this much is indeed helpful and is certainly
progress. But the problem is not thereby removed. It is
natural at this point to regard (for example) the physical

shape as a quality of the object and the experienced shape

 

as characteristic of our sense experiences. Now it is
also true that there will always be some variation in the
properties of an object—-as perceived by an observer-—
because of the varying conditions under which the per—
ception is made. The following question now arises (and

this is the real question): can the Lockean distinction

still be maintained in essence, even though the terminology

has changed? That is, can we maintain a picture in which
there is a sharp dichotomy between those properties of an
object which are susceptible to variation due to varying
conditions of observation (sensible qualities), and those
properties which (on the other hand) are not susceptible
(physical qualities)? Can we retain the distinction be—
tween those properties which are relative (i.e., relative
to an observer) and those properties which are intrinsic
to the object and completely independent from any other
object, most especially, an observer?

Hence we see that the basic issue in our inquiry
poses itself in several different ways. There are at
least three different ways of formulating the problem

that will be helpful for what follows:

14

a. Are there some properties of an object that
never change?

b. Are there some properties of an object in terms
of which all the remaining properties can be
specified? That is, are there a certain set
of predicates such that taking these predicates
as primitive, all other predicates can be
defined?

c. Is it possible to give a completely objective
account of all the objects (and phenomena) of
which we are aware; or must any such account

inevitably include an irreducible element of

subjectivism?

In formulation (c) I wish "subjectivism" to be under—
stood in the following specific sense (which is perhaps
slightly different from the meaning it frequently has):
an explanatory account of the nature of objects would be
considered objective if we could account for the existence
and the characteristics (of these objects) solely by
appeal to the objects under question, without in any way
needing to consider any object distinct from the given
ones; that is, if we could show that they were completely
independent—-in all their essential features——of all other
objects. However, if this is not possible, if we find
that some characteristics are subject to conditions deter-

mined by other objects, then our account, to that extent,

 

15

is subjective. (Two comments are in order. First, when
I speak of accounting for the existence of objects, I do
not mean this in the sense of saying "where they came
from." I mean this only in the sense of explaining why
the objects exist in a certain state, or in a certain
manner. Secondly, I am of course aware that one object
can interact with another. In this case there is no
question of providing an explanatory account which does
not take into consideration "other objects." I am asking,
rather, whether in those cases when there is no such
interaction, i.e., when the object is isolated, is such
an independent account possible. In short, I am asking
whether we can maintain this concept of an isolated body.)
In the next part we will examine whatever physics
can tell us regarding the basic question of our inquiry,

as formulated in the three questions above.

PART II

THE EVIDENCE OF PHYSICS

According to the third formulation above of our
central issue, our question has come down to this: can
we give an account of objects and phenomena (the constitu-
ents of the physical universe) which is free of any element
of dependence upon other objects or phenomena? Can we give
an account of "external" objects in which they are not only
"external" but also "independent"—-independent of both:
(1) other objects, and (2) us as observers? (Since we as
observers are also objects, the desired distinction is
clearly the element of consciousness which enters with
observers. Historically, only the second of these points
has been of great concern. But we shall see that the
first is of at least equal importance. This point will
receive detailed attention below.)

To seek answers to our questions we shall now appeal
to the different accounts of nature provided us by physics.
But first, it would be helpful to examine in a bit more

detail what we have in mind when we speak of subjectivism.

l6

17

(As noted above, there are two ways in which the inde—
pendence of physical objects can be eliminated: (l) by

the need to take into account other objects; and (2) by

the need to take into account other objects with conscious—
ness, namely, human observers. The second has received

the most attention historically. So let us, for the time
being, treat the problem just with regard to the second
issue. We will, soon enough, find sufficient reason to

consider also the first.)

Classical Physics

 

In what follows we will take subjectivism to mean
the claim that the properties of external objects are not
completely independent of any observer or any knower.
This is the claim that in any discussion of external
objects or their properties it is essential to include
the observer; for the presence of and action of the ob—
server is a crucial determinate of the properties of
external objects. (We take the existence of these
objects as given.) A moderate subjectivism would make
the following claim: the action of the observer——or the
interaction between observer and object—~in some way or
other has an effect upon the properties of the object.

A more extreme subjectivism might claim that the object
Egg no properties whatever independently of the inter-

action between observer and object.

18

Those thinkers that would be labelled subjectivist
according to the above criteria claim subjectivism only

with reSpect to the prpperties of objects, not to the

 

existence of these objects. There have been those who
wished to maintain this sort of subjectivism also with
regard to the existence of the objects. There are diffi-
culties facing both groups, but the subjectivist (accord-
ing to our criteria) might have, at the beginning, to face
some additional ones: (1) if all the properties of the
object are included under the "subjective" classification,
‘what sense does it make to speak of an independently
existing object with no properties? (2) But if, on the
other hand, only gpmg of the prOperties are subjective,
then how do we decide which are subjective and which are
not?

The subjectivism we are considering here is not the
trivial claim that prOperties are subjective because we
always require an observer to observe them. This is
always the case and is granted. The subjectivism meant
here asks the question: "is observation simply the
ascertaining of properties of objects that the latter
possess whether they are observed or not, or is it an
interaction that yields information only about the result
of the interaction?" And subjectivism decides in favor
of the latter. It denies that the properties exist

independently in the object whether they are observed

19

or not; and it asserts that it is only in the act of
observation that the properties exist, or come into
existence; are created.

The position adopted by the seventeenth century
thinkers (and subsequently, the position underlying all
of classical physics) was to specify certain properties
of an object such as mass, motion, shape (the exact
nature of the list varied from person to person) as
objective and primary, and to specify all others as
subjective and secondary (e.g., taste, smell, color,
etc.). These latter properties were only secondarily

properties of the objects. They were primarily relational

 

properties between the object and the observer. If we
take away the relation, we take away the property. Thus
Galileo asks if there were no human beings around could
the feather still cause a tickling sensation? But the
most important element of this solution (of classical
physics) was the claim that all the subjective, secondary
properties could be ”explained" in terms of the objective,
primary properties. Hence, even though sweetness is a
secondary prOperty, the sweetness of the water can be
explained in terms of the relative number, the configu-
ration, and the relative motion of the water molecules
and the sugar molecules. So even though the sweetness
could only be tasted by an observer, the situation which

accounted for (which caused) the sweetness--viz, the

 

20

molecular configuration and motion——could be explained
and accounted for by appealing only to objective, primary
properties (i.e., mass and motion). Hence even though
there are properties that could only exist in an experi—
encer, i.e., an observer, the scientific account of the
external objects, the properties of those objects, and the
interaction between the objects and the observer were all
completely given in terms of the objective, primary
properties of those external objects and their elementary
constituents. In short, classical physics said that: (1)
there were two kinds of properties, objective properties
and relational properties; and (2) the relational proper—
ties could be explained in terms of the objective proper-
ties. So the account of the world provided by classical
physics was at root objective, with no subjective element
entering at any essential point.

We note that with regard to all three formulations
of our basic question classical physics must be regarded
as in no way subjective, but completely objective. For:
(a) there are certain properties of an object that do not
change (viz, the primary properties, e.g., mass); (b)
there are certain basic properties in terms of which all
others can be specified (e.g., mass and motion); and (c)
classical physics provides an account which is completely

objective and independent.

21

This account of the world provided a picture in
which certain "primary" properties were possessed "by the
object" or existed "in the object"; in the fullest sense,
these were properties "of the object." They were deter-
mined completely and solely by the nature of the object
itself, and were in no way connected with anything distinct
from the object itself. Thus we have a picture in which
objects have a completely objective and independent
existence. They are capable of existing independently
(much like the old concept of substance) and evolving
independently in time. When there is an interaction be-
tween a given object and some other object, we can, of
course, no longer consider the object as evolving inde—
pendently. But even here, we can account for the new
time evolution of the object-—and this, by appeal solely
to those basic properties of the object which are them—
selves immutable and "objective." Hence in a very strong

sense, this account of classical physics is an objective

 

one o

Relativistic Physics
From this point on (i.e., from the culmination of
classical physics), the total and absolute objectivity of
classical science becomes successively eroded away. Each
of the two major advances in physical theory since the
appearance of classical Newtonian mechanics (viz, rela—

tivity theory and QT) has been accompanied by a loosening

22

of this "objective" picture painted by science. With
both of these developments we find an increase in the

number of properties that are construed to be relational,

 

and a corresponding decrease in the number of properties
which retain their objective, independent status. Let us
consider first relativity theory.

Since the time of Galileo the concept of relativity,
in its broadest sense, has always been present in physics.
Loosely speaking, this concept can be expressed simply as
a question: do the laws of nature, and hence the physical
situations described by them, always appear to be the same
to different observers, even though the state of motion of
the observers is not identical?

In classical physics, the state of any mechanical
system at some time t0 can be specified by constructing a
set of coordinate axes and giving the coordinates and
momenta of the various parts of the system at that time.
If we know the forces acting between the various parts,
Newton's laws make it possible to calculate the state of
the system at any future time t in terms of its state at
to. It is often desirable that during or after such a
calculation we specify the state of the system in terms
of a new set of coordinate axes, which is moving relative
to the first set. A two-fold question then arises: how
do we transform our description of the system from the

old to the new coordinates, and what happens to the

 

 

23

equations which govern the behavior of the system when we
make the transformation? The set of equations that
describes the relations between the two sets of coordinates

are known by the name of the Galilean transformation

x = x' + ut'

y=y'
z = z'
t=t'

In these equations it has been assumed that the coordinate
axes in S and S' (the two coordinate systems) are parallel,
that their origins coincide, and that the motion takes
place in the x-direction; u is the velocity of the primed
coordinate system 8', relative to the unprimed one S.

Thus the principle of relativity takes the following
form in classical mechanics: if S is an inertial system
of reference, and S' a system of reference that moves with
a constant velocity relative to S, then the laws of
mechanics must have the same form in S and 8', provided
x, y, z, t, and x', y', z', t', are connected by a Galilean
transformation. In short, we say that the laws of New-
tonian mechanics are invariant under Galilean transfor-
mations. Of course, the next question is whether the rest
of the physical laws are also invariant under this trans-

formation (in addition to those of classical mechanics).

24

If so, this would mean that even experiments that do not
rely exclusively on the laws of mechanics should also fail
in telling the observer whether he is at rest or in uni—
form motion, using the connections given by the equations
above between the primed and unprimed coordinates. It is
precisely this problem--which puzzled scientists for nearly
twenty years--that is solved by the next development of
the concept of relativity: Einstein's special theory of
relativity.

Einstein discerned the three assumptions underlying
the Galilean principle of relativity and the different
roles the constancy of light velocity plays in each. The
three assumptions are the following: (1) there are
inertial systems in which the laws of physics are identi-
cal; (2) if one system is inertial, any system of refer-
ence that moves with a constant velocity relative to the
first one is also inertial; (3) the transcription of
space and time data from one inertial system to another
has to be done according to the Galilean transformation
as given above. The first two assumptions assert that
the relative configurations of bodies determine the
physical occurrences (not the configurations and motions
relative to some external frame of reference). This
emphasis on the relative configurations of bodies will
turn out to be of importance later. The third assumption

indicates how observers must translate the results they

25

have obtained in one inertial frame to get the results
observed in any other inertial frame. Experiments indi—
cate that the first two assumptions should be valid
regardless of what assumptions are made about the velocity
of light. But with respect to the third, it is known that
the Galilean transformations tacitly assume that the time
of occurrence of an event is the same in all inertial
frames. The question arises whether or not this assumption
is reasonable if the velocity of propagation of signals
(light signals) is not infinite. Einstein showed that
this is not a valid assumption. Rejection of this
assumption left Einstein in this position: we can say
that the constancy of the velocity of light in different
frames (which has iron-clad experimental support), and

the existence of equivalent frames, are logically com—
patible if we modify the transcription rules of space and
time data from one inertial system to another. This means
we must find another set of transformations to replace the
Galilean set--a set such that the velocity of light should
be the same for both frames of reference. These are

called the Lorentz transformations

I
x = (X + ut')Y

y'1 = /1 — 82
y=y'
z = z'
— E
x'u B _ c

26

Any physical description which satisfies these conditions
is called Lorentz invariant.

Naturally, we will expect that some interesting
consequences arise from the fact that we no longer have
an absolute time, the same in all frames of reference.

It turns out that the spatial distance between points will
change as we change systems of reference. The duration of
a process will change as we change reference frames (with
a corresponding change in frequency and wavelength). Also,
the mass will change as we change reference frames.

It will be recalled that earlier in our discussion
we noted that even though the distinction, as originally
formulated by Locke, between primary and secondary quali-
ties could not be maintained, we saw that the essence of
the distinction could still be preserved by distinguishing

the experienced quality from the physical quality (i.e.,

 

the measured quality). It was by appeal to this physical
property——i.e., a measured quantity—~that one could still
plead the case for objective, independent properties which
were characteristic of the object and in no sense re—
lational. Thus, even though a rod might appear smaller

as we move away from it (experienced size), the length of
the rod as measured by a ruler (physical size) would have
the same value regardless of our position. Clearly,
length was a property of the object. So also with mass.

And the time of duration was a property of the process or

27

phenomenon. These prOperties were objective and inde—
pendent.

But this is precisely the verdict that is reversed
by the theory of relativity. It has been seen that the
mass of an object will change as we change our frame of
reference (i.e., change our state of motion). Hence we
can no longer think of the mass simply as characteristic

of an object. Rather it is now a relational property

 

between the object and the observer (as represented by

a given frame of reference). Hence, the mass of an object
has ceased being an objective, independent characteristic
and now must share the ignominy of all the other proper-
ties which it had helped to relegate to the depths of
non-independent, subjective existence. And also with
spatial distance and time duration. Whereas, before, we
clearly had three instances of objective properties, after
relativity theory these properties are now also seen to be
subjective.

It is undeniable, now, that relativity has put a
crack in the edifice of objectivity erected by classical
science. But it is valuable to ask the following question:
did relativity completely demolish the structure or did
it leave some elements of objectivity intact?

Just from what we have seen already it is under-
standable how the prevailing metaphysical interpretation
of physics had become so intrenched as to be almost

instinctive. This interpretation asserted that physical

28

experience can be regarded as an effect on our senses of
an objectively existing external world having certain
definite and ascertainable properties. Modern science
originated, however, in the determination to ignore the
metaphysical question and to accept experience as an
object of study, whether or not it was "real." But it
comes as no surprise that, in fact, through force of
habit, the metaphysical question yes implicitly answered,
and the phenomena studied by physics accepted as £22l.With
not as much as a batting of the eye.

It was the great lesson of relativity to teach us
that this kind of metaphysical picture was no longer
feasible. It had to be modified. And a better picture
was devised. In the old picture the world consisted of
pieces of matter, measured essentially by their mass,
moving about, without thereby becoming changed, in an
infinite extension called Space and an independent
extension called time. According to the revised picture,
space and time are no longer independent but merge into
a single continuum, space-time. This merger was made
possible by the fact that, according to the definitions
adopted for the time relations of separated events, a
certain combination of space and time separations of
events (the space-time "interval") is independent of the
state of motion which we choose to assign to any one of the
bodies concerned. Thus we can suppose that this combi—

nation of our measurements measures some absolute property

29

of events, just as we previously thought that the measure-
ment of length indicated some absolute property of a body.

It is still true, however, that the masses of bodies
change with motion. But going farther in the same
direction, the general theory of relativity succeeds in
prescribing a combination of space, time, and mass measure-
ments that is independent of motion altogether, and so-—
for the time being at any rate--can pose as an aspect of
an external world of which physical measurements provide
a quantitative description.

Thus with regard to our three formulations we find
that the theory of relativity has wrought some substantial
changes. With regard to (b) we can still say that there
are certain basic properties in terms of which all others
can be specified; and to this extent we still have objec-
tivity. But with regard to (a) we find that many of the
important properties that were considered objective in
classical physics are now subjective in relativity theory,
e.g., mass, length. There are other properties that are
just as objective in relativity theory as they were in
classical physics (e.g., electric charge which is Lorentz
invariant). So according to formulation (a) we find that
spme subjectivism has sneaked in. And we find the same
with regard to formulation (0), for now some of the pr0per-
ties must be specified relative to other things (inertial
reference frames) distinct from the object, and are, accord—

ing to this formulation, now subjective. But again as in

30

(a) there are still some properties that remain objective
even according to formulation (c).

Hence, though we see that in both the special and the
general theory we begin a process of relativization of the
properties of objects, it is by no means the case that
these theories leave our physical experience completely
devoid of any objective foothold at all. What we have is
a partial relaxation of the claims of objectivity in the
external world. We will see now that though quantum theory
goes even further with this process of relativization, it
too results in only a partial and not a complete rejection
of the idea of independently existing objects. But the
subjectivism that is introduced by QT goes much deeper than
anything we have seen till now, and cuts across all three

of our earlier formulations.

Quantum Physics

 

Basic Ideas of Quantum Theory.--Now is there anything

 

in QT that resembles the subjectivism we have been discuss-
ing? Let us consider the principle of superposition in QT.
This principle is so central to QT that Dirac [19], in his
definitive treatise, could derive most of QT from just this
principle. The principle states that if we have a solution
*1 to the Schroedinger equation, and another solution $2,
then there exists still another solution to the equation

given by

w = awl + bwz with Ia

Or in other words, if, for a given physical system, we
have a definite, physically observable state represented
by $1 and another state represented by wz, then there is
another definite state, physically observable and distinct

from either $1 or wz, represented by
w = awl + bwz.

What about the prOperties of the physical system in
these various states? With respect to a given property
(observable) QT says that the system can assume only cer-
tain specified values for the values of that observable.
Not all values are permissible. The values of the observa-

ble are quantized. (We assume discrete, non-degenerate

 

spectra.) To each of the possible values of the observable
there is a corresponding state of the system, represented
by a state function wi. To each of these states wi there
is associated a number ai called the eigenvalue for that
state. Thus whenever the system is in the state wi' the
value of the observable will be given by ai. Also, upon
repeated measurements of the observable, either on the
same system or identically prepared systems, the value ai
is repeatedly obtained.

Suppose now that our system has a state W1 with

eigenvalue a1, and also a state $2 with eigenvalue a2.

32

Then according to the superposition principle there is

also a state w = awl + bwz. It is found that upon measure-
ment we obtain (for the system in the state W) the value

1 sometimes, and obtain the value a2 sometimes. (The

relative proportions are determined by the numbers a and

a

b.) The order of occurrence of a1 and a2

random; and in any given observation we are totally in-

is completely

capable of saying which of the two values we will obtain.
Also, no other values besides al and a2 occur.

So the situation in QT is the following (with respect
to a given property or observable): there are some states,
pure states, to which the theory attributes definite and
well-defined values of the observable in question. And
upon measurement, in these states, those values invariably
obtain. But according to the superposition principle,
there are also superposition states such that: (l) the
theory attributes no definite value of the observable;
and (2) measurement of the observable yields different
values on different trials. Thus, before the measurement,
our description of the physical system (the object)-—i.e.,
what the theory tells us about the system--contains (and
is capable of containing) no reference whatsoever to the
value of the observable. All the theory can tell us is
that there are a certain group of values, one of which
will emerge upon measurement. It cannot tell us which

one will emerge. And most importantly, the theory cannot

33

associate any particular one of the values with the state
before a measurement is performed. Hence, as far as the
theory is concerned, before the measurement the system is
in a definite state with respect to the observable in
question; but has no definite value for the given observa-
ble. But a definite value does always emerge upon measure-
ment. So if we ask the question: "before measurement,
before any interaction with an observer, what is Ehe_value

of a given observable?," the theory can give no value. The

 

theory can give the probability of a given value emerging

upon measurement. But as to what the value is right now,

 

before a measurement, the theory is powerless to say.
Afpep the measurement, we can point to one definite value
as being the value of the system.

To conclude this introduction I wish to do two
things: (1) show how this situation in QT qualifies to
be called subjectivism; and (2) show why this subjectivism
is different from and more far-reaching than anything

allowed in classical physics.

\ Situation in QT Does Qualify as Being "Subjective".--
From our preceding discussion of subjectivism an adequate
statement of the subjectivist point of View might be the
following: the properties of external objects have no
status independent of an observer. Further, the proper—
ties of an object either only become definite (moderate

subjectivism) or only come into existence at all (extreme

34

subjectivism) in the interaction between the observer and
the object. Is this the way QT works? I wish to answer
yes! In QT the interaction we are concerned with is the
interaction designed to give us knowledge or information
about a system, i.e., a measurement. We have seen that
there are certain states (viz, the superposed states)

such that certain properties indeed have no status inde-
pendent of the observer (who forces the interaction). For
with a superposition the very possibility of assigning a

value to the observable requires the interposition of an

 

interaction.

 

But what about the system before a measurement? Is
this not a definite, perfectly well-defined state already
--even by our own superposition principle? And does not
a definite, perfectly well-defined state have definite,
perfectly well-defined properties? Yes and no! Suppose
the property we are considering is spin. Then our answer
is yes: a superposition is a definite, perfectly well-
defined state. It is crucial to realize this. And this
state will exhibit physically properties that none of the
"single" eigenstates (which constitute the superposition)
will exhibit alone. But we must also answer pp: it does
app have definite, perfectly well-defined pr0perties in
this state. So even though this is a definite (and
distinct) spin state, the state does not have a definite

value of the spin associated with it. This is simply a

 

35

peculiarity of QT: there are some states where a given

property has no value at all.

 

But at this point one might be inclined to ask: but
if this is a definite spin state, as you say, what are we
to say about the spin of this definite spin state before
we make a measurement? Two obvious answers come to mind:
(1) The state has no spin at all before the measurement.
Clearly, this leaves you open to the charge of subjectivism
of the most extreme kind. (2) The state is "somehow"
simultaneously in all the spin states, but then becomes
completely in one of the Spin states upon measurement. And
even this move still is subject to the charge of moderate
subjectivism. I know of no interpretation with respect to
the superposition principle that can completely avoid the
charge of subjectivism. So in answer to the question "what

are we to say about the spin before measurement?, one
might well be inclined to reply "nothing." But if we are
incapable of saying anything before a measurement, and yet
are capable of saying something EEEEE a measurement; and
if furthermore, this incapacity is theory-imposed, then I
see no way to avoid the claim that the theory contains

subjective elements--subjective because we are prevented,

in theory, from ascribing any value to the property unless

 

and until there is an interaction between the object

described and the observer who is describing.

36

Difference Between Classical and Quantum Physics.--

 

But one might ask "is the situation in QT really any
different from the situation in classical physics?" Does
not classical physics also require a measurement before

we can ascribe a given property to a given system? The
answer is emphatically no! In classical phase space the
orbit or path, indicating the evolution or development of

a system, isua continuous line; and through a given point
only one line passes. The continuity of the path assures
the continuity of the evolution of the system, preventing
any discontinuous jumps or changes. A given point is fixed
byia complete Specification of a pair of generalized canoni-
cally conjugate variables at that point. And these in

turn completely specify the state of a system described

 

by those variables. Thus since only one line passes
through any given point, this means that whenever a system
is in a state described by the specified values of the
variables at that point in phase space, the time develop-
ment of that system is completely determined (i.e., there
is only one path to follow). Thus if we know the state
at any given time, we can always specify what its state
will be at any given time in the future, or in the past.
(If a system passes through a given point in phase Space,
then it has a uniquely determined future and a uniquely
determined past.) Thus for any system in any state, if

we know a previously completely defined state, we can

37

always give another completely defined state at any
desired time. This is also possible in QT. But in
classical physics a completely defined state means in—
cluding the values for all observables. Thus in classi—
cal physics, according to the theories, a system always
has a definite value for each observable--and this inde—

pendently of whether a measurement is undertaken to reveal

 

that value or not. The value can be given by the theory.

 

And since in classical physics the disturbing effect of
a measurement can be omitted in theoretical discussions,
not only does the property of the system exist inde-
pendently of the observer, but is also stable and fixed
in the face of an interaction with the observer. Clearly,
this is radically different from the situation in QT.
Finally, I would like to make one last distinction
to emphasize the difference between classical physics and
quantum physics. In scholastic philosophy a distinction
was made between what were called determinables and
determinates. The modern revival of these terms was due
to the Cambridge philosopher and logician, W. E. Johnson.
In his Lpgig (1921) he states: "I propose to call such
terms as colour and shape determinables in relation to
such terms as red or circular which will be called depep—
minates" [32]. It is easily seen that in classical physics
the properties ascribable to physical systems are both

determinable and determinate. Whereas in quantum physics

 

38

the properties are at most only determinable. For, using
our example above, we cannot say that the system has a
particular value for the spin; we can only say that it

is in a Spin state. But there is another difficulty.
Suppose we consider the relation between determinable and
determinates to be one of class to members. That is,
suppose the determinable is a class whose members are the
determinates (e.g., the determinable shape is a class
which has as members triangular, rectangular, elliptical,
etc.). Thus to say of a property that it is determinable
is to say that though we cannot specify which particular
determinate is applicable, we do know that one of them

is applicable. But this is not possible in QT. Eugene
Wigner [57] has shown that it is inconsistent with the
laws of QT to assume that for a superposed state, we can,
without contradiction, treat the state as though it were
"really" in one of its constituent states. That is, for
a superposed state, we cannot ascribe any one of the
particular states to the system--even though the particular
states we have in mind exhaust 311 the possibilities. But
then what sense is there in the claim that the property

is determinable? Admittedly, though it is not possible
to say of a superposed state that it has a particular
spin, it ii possible to say that the state has spin
properties; it is in a state of spin. This is undeniable.

But I do think that we must admit the strangeness of the

39

situation which allows us to say of a system that it has
a certain property, and at the same time forbids us saying
that it has a particular value for that property--even
though unknown.

This is the situation of QT: I believe I have
Shown that here is a situation: (1) that is pegf-classi-
cal physics contained nothing of the sort; and (2) that is
contrary to our everyday common sense notions regarding
external objects. (And of course, this is the View culti-

vated by classical physics also.) There is a substantial

 

and irreducible element of subjectivism in our description

 

of external physical objects--as described by present QT.

Probability as Entrance of Subjectivism Into QT:

 

Arguments for Non-Classical Probability.--It is generally

 

thought that subjectivism enters QT at two points: proba-
bility and experiment. I wish to argue that subjectivism
does enter QT through both experiment and probability. I
will also examine the exact nature of the probabilities
used in QT, in order to determine if these are ordinary
classical probabilities or whether they are, in some sense,
unusual non-classical kinds of probability.

It is, of course, well known that probability was
not first used with QT. Probability was used and already
fully developed in classical physics. But in pre—quantum
physics we could always make a clear distinction between

those areas which did and those which did not involve

40

probabilities. Classical mechanics, electromagnetism, and
thermodynamics would belong to the second group; kinetic
theory, statistical mechanics would belong to the first
group. The last statement should be regarded as an ip
principle statement. For it must be admitted that because
we have experimental error, because we never have abso-
lutely precise data, and because we sometimes do not have
complete information, probability makes an intrusion into
even classical mechanics. But it is precisely the intro-
duction of probabilities which enlarges the range of appli—
cation of, say, classical mechanics in important ways,
adapting the laws of that subject to the limitations of
human powers of observation and of reasoning. But it is
important to remember that the probabilities of classical
physics are always manipulable, or reducible (using the
terminology of Henry Margenau) [40]. That is, they can
always be reduced to certainties on the addition of more
evidence or information. Thus, if we knew all the initial
conditions for a given throw of a die, we could (assuming
all the calculations could be done) reduce the probability
of a four appearing from one-sixth (for a fair die) to
either one or zero. In other words, the inability to
Specify the outcome of a given experiment was due pp; to
any characteristics or properties of the experimental
system itself. Rather, this inability was seen to derive

from the human limitations in completely specifying the

41

experimental situation to which our laws are to be applied.
And the last element of the story is simply that this in—

ability was in principle removable; it was only a practical

 

 

blemish on the face of classical physics; it was a matter
of "refinement." And finally, we could always approach
the completely specified state as closely as we wished.
Thus the lack of specificity which comes with probability
could be dismissed as only a practical matter. It was
characteristic of our knowledge, not of the "objects"

known; and it could, in principle, be eliminated. Hence,

 

we could still maintain a picture of objects or events as
well-defined existents with well-defined prOperties. It
was just our knowledge of them that was fuzzy, and we
could make it as clear as we wished.

However, QT always involves probabilities--even in

principle! (See Quantum Mechanics, Albert Messiah [44].)

 

 

The probabilities arise in QT not merely when we attempt
to get information about a system and we run into the
human limitations mentioned above. Those probabilities
are certainly present; but there are others also. And
these probabilities are involved in the very definition
of the properties to be observed. Furthermore, these
probabilities are ppp reducible by the appearance of more
information. Even with the maximum information allowed

these probabilities remain.

 

42

But now (as is easily seen), the lack of specificity
which comes with probabilities cannot be dismissed as a
mere aggravation that can in principle be eliminated. Nor
can we any longer attribute this lack of specificity
solely to our knowledge of physical phenomena and restrict

it there (so that our picture of the phenomena themselves

 

in no way becomes tainted with this fuzziness). Since our
very description of physical phenomena includes——irreducibly
——this lack of Specificity, it would certainly appear--at
least on first g1ance—-that this lack of specificity must
extend over to the phenomena themselves. If this 12 the
case, this conclusion has very important consequences of
a metaphysical or ontological nature: metaphysical be-
cause there would be placed very strong limits on the
nature of the phenomena (and objects) themselves. Hence
it is important to understand both the presence of proba-
bilities in QT and the nature of those probabilities.

It has been argued (by Feynman [22], Suppes [54],
for instance) that even though the probabilities in QT
are irreducible and are "here to stay," these proba-
bilities are somehow different from the probabilities
used in classical physics. I believe that even granting
this, the force of the above epistemological observations
is not lessened. But it is of value to examine this
claim, if for no other reason than to help us delineate

those aspects in which QT is both a physical and a

43

logical development frpm_classical mechanics (rather than
being everywhere divided by a sharp, radical, and irrecon-
cilable schism).

A. I would like to present first the argument of an
emminent physicist, Richard P. Feynman [22]. At the
Second Berkeley Symposium on Mathematical Statistics and
Probability Feynman delivered a paper in which he stated:
"The new theory asserts that there are experiments for
which the exact outcome is fundamentally unpredictable,
and that in these cases one has to be satisfied with com—
puting probabilities of various outcomes. But far more
fundamental was the discovery that in nature the laws of
combining probabilities were app those of the classical
probability theory of Laplace." In that paper Feynaman
never explicitly states in exactly what way the "combining"
of probabilities changed from the "classical" means. But
his intention seems clear and I shall attempt to recon-
struct what I take to be his argument.

Consider a double slit experiment performed with
electrons. If the electrons are allowed to pass through
slit A (with slit B closed), we will obtain a probability
distribution Pl for the arrival of the electrons on the
screen. If the electrons are allowed to pass through
slit B (with slit A closed), we will obtain a probability
distribution P for the arrival of the electrons at the

2

screen. If the electrons are allowed to pass through with

44

2922 slits A 229 B open, we will obtain a probability
distribution P12 for the arrival of the electrons at the
screen. Now it is an experimental fact that P12 ¢ Pl + P2.
This is as far as Feynman goes explicitly, so I must fill
in what I take to be the rest of his argument.

We can write down the axioms of classical proba—
bility theory quite easily. Following Kolmogorov [34]

we have:

If X is a non-empty set,

and f is a o-algebra of subsets of X,

then P is a probability measure on f such that

(l) P(X) = 1

(2) 0 : P(A) : l for any A in f

(3) P(AUB) = P(A) + P(B), if A and B are mutually
disjoint sets. (AUB) is just the union of the two

sets A and B.

Now when Feynman refers to the "combining" of probabilities,
I presume that he has in mind combining probabilities
according to axiom 3. Thus if we have two "events" A and

B, which are mutually exclusive, then the probability of
either event A pp event B is given by P(AUB) = P(A) + P(B).
Now if P(AUB) # P(A) + P(B) then we most certainly have a
case of failure of the combinatorial laws of classical
probability. But is that what Feynman had in mind? The

probability statement written by Feynman was P12 fl Pl + P2.

 

45

If we are to read Feynman as claiming that his equation
implies a breakdown of classical probability we must
interpret the equation in something like the following
way: "The electron can arrive at the screen by passing
through slit A, yielding probability Pl; pr the electron
can arrive at the screen by passing through slit B, yield-
ing probability P2. The electron certainly cannot pass
through both slits A and B at one and the same time.

(This also makes the two possibilities mutually exclusive.)
Thus the probability of the electron passing through either
slit A or through slit B should be the probability of

(AUB) which is just P(A) + P(B)."

Now it is well known that speaking of elementary
particles like the electron as having a particulate nature
is a "loose" way of speaking and can be very misleading
in some experimental situations. Indeed, the kernel of
Bohr's complementarity principle is that ifi we insist on
speaking of the elementary constituents of atoms as
"particles" and/or "waves," then we cannot use one picture
to the exclusion of the other. We must use them both.

And failure to do so quite simply lands us in conflict
with empirical facts.

Now Feynman is as aware as anyone that the kind of
talk used above about the electron is incautious talk.

And consequently he does not use it. A phraseology

closer to what Feynman would probably say (had he filled

 

46

in his argument) is the following: "The electron can
arrive at the screen with only slit A open. The electron
can arrive at the screen with only slit B open. The
electron can arrive at the screen with BEER slits A and B
open." But now there is a non-negligible difference
between the two formulations. Whereas in the first formu-
lation, the third possibility (viz, that the electron goes
through ppph_slits A and B at one and the same time) was
declared clearly ridiculous, this is not the case now.
For the third alternative under the second formulation is
a viable one (viz, that the electron arrives at the screen
with both slits A and B open). So now we have three
alternatives, instead of just two. But the precise state-
ment of axiom 3 is P(UiAi) = §P(Ai). This means that the
probability of any event which is the union of other
mutually exclusive events is the sum of the probabilities
of each of the constituent events taken separately. But
the sum is taken over as many different alternatives as
there exist. Thus in our more precise statement of the
double slit experiment (and hence more accurate and more
adequate) there are three distinct alternatives, and the
formalism of classical probability theory should give us
three terms in the summation, not two.

In short, the fallacy in the above argument for
non-classical probability is the assumption that the

Situations represented by P1 and P2 are mutually exclusive

47

229 exhaustive. They are pp; exhaustive. There £3 a
third possibility and the presence of that third possi—
bility is indicated by the "interference" term. The
presence of the third term (the interference term) also
shows that the formalism of classical probability BEE
correctly accounted for all the alternatives and accord-
ingly has a term in the summation for each alternative.
[It is obviously true that the three alternatives are
both: (1) exhaustive, and (2) mutually exclusive. (1)
There are only four logical possibilities: A open, B
open; A open, B closed; A closed, B open; A closed, B
closed. We have utilized the first three cases. The last
case is ruled out physically since then pp electrons would
arrive at the screen and we would have no experiment at
all. (2) It is likewise clear that with A open and B
closed, we cannot have at the same time either A open and
B open or A closed and B open.]

We can see from the above just how dangerous "loose"
and "incautious" ways of speaking can be. It deprived us
of one of our alternatives. But we have seen that when
we speak in more precise language, it is not the case that
classical probability fails. For if adequate account is
taken of ill the possible alternatives the classical
formalism will adequately describe the phenomena. So even
if we attribute to Feynman the precise version of the
experiment, I can still find no grounds for accepting his

conclusion that QT requires a non-classical probability.

 

48

Let me mention briefly another argument for non-
classical probability, which will be seen to be just a
generalization of Feynman's argument, and hence guilty of
the same error. It will be worthwhile to see the case
stated in its full generality. Suppose A is an observable
with eigenfunctions ¢1’¢2'¢3 ... . Let B be an observable
that does not commute with A. (We will assume discrete,

non-degenerate spectra.) Now the average value <B> of B

in the state ¢ = Zai¢i is given by <B> = ElaiI2<Bi> + I

i i
where <B> = (oi,B¢i) is the average value of B in state ¢i
and I = .Z a.a*(¢i,B¢j). The interference terms are

. . l j
17‘:
represented by I. Non—classical probability might be

claimed here on the basis of the following erroneous
argument. The events Ei' where 'Ei' = 'the system is in
the state ¢i', are mutually exclusive and exhaustive, with
probabilities Iailz. If the classical formalism of

probability applied we would have

<B> Z (probability of Ei)(average value of B in Ei)

<B>

2
Elail <Bi>

This differs, however, from the previous--and quantum

 

theoretically correct--formula precisely by the inter-
ference terms I. Thus, the argument runs, the probability
employed by QT must be non-classical. Here again the

error involved is the assumption that the Ei are jointly

49

exhaustive. The error is based on a failure to understand
the implication of superposition. As was stated earlier,
the superposed state is a physically distinct state. Thus
not only may the system be in some state ¢i' but it may
also be in any of the infinitely many superpositions of oi.
And in the case at issue the system 15 in just such a V
superposition, namely ¢. (This example is due to Fine
[23].)

B. The only other persuasive argument for non-
classical probability in QT that I know of was given by
Suppes [54]. This argument is also the one which strikes
deepest into the heart of the theory of probability itself.
Suppes has himself stated his case so succinctly that I
will merely repeat it here:

Premise 1: In physical or empirical contexts in-

 

volving the application of probability theory as a
mathematical discipline, the functional or working
logic of importance is the logic of the events or
propositions to which probability is assigned, not
the logic of qualitative or intuitive statements
to be made about the mathematically formulated
theory. (In the classical applications of proba-
bility theory, this logic of events is a Boolean

algebra . . . usually . . . a o-algebra.)

50

 

Premise 2: The algebra of events should satisfy
the requirement that a probability is assigned to

every event or element of the algebra.

Premise 3: In the case of quantum mechanics proba-
bilities may be assigned to events such as position
in a certain region or momentum within certain
limits, but the probability of the conjunction of

two such events does not necessarily exist.

Conclusion: The functional or working logic of

quantum mechanics is not classical.

Suppes supplies arguments in support of each of his
premises. For these I refer the reader to his article.
I will only quote one passage regarding premise 3. Suppes
writes: "We conclude that in general the joint distri-
bution of two random variables like position and momentum
does not exist in quantum mechanics and, consequently, we
cannot talk about the conjunction of two events defined
in terms of these two random variables." In Short, Suppes
argues as follows: in classical probability theory we
can assign probability to any two events and also the
conjunction of those two events. In QT, in general, it
is not possible to assign a probability to a conjunction
of two events (even though we can assign a probability to
each separately). And how do we know that in QT this is

generally not possible? By the fact that in QT,

51

generally, there does not exist a joint distribution of
two random variables.

Arthur Fine answers Suppes--and I think adequately--
by going directly to the imputed reason why in QT we cannot
assign a probability to a conjunction, viz, the non-
existence of joint distributions for random variables.

Fine shows that the quantities in QT are app random vari-
able, but rather what he calls statistical variables.

(This distinction was first explicitly made by Menger
[43].) The basic distinction between the two is the
following: (1) gryep a classical probability space <X,f,P>
we can always define a real-valued function f, called a
random variable, on X such that f-1(B)ef for every Borel
set B. (2) A statistical variable refers to a quantity
whose set of values X is such that for some f and some P

we can construct <X,f,P> such that <x,f,P> is a classical

 

probability space. So, in a real sense, the difference
amounts to this: which comes first? the classical proba-
bility space on which you define the variable (i.e., random
variable), or the variable (i.e., statistical variable)
about which you construct a classical probability space.
The benefit gained from making this distinction is
seen in the following: a joint distribution for two random
variables always exist, whereas, a joint distribution for
two statistical variables may or may not exist. The non-

existence of joint distributions for statistical variables

l Liliulllllllllul

52

is neither surprising nor disturbing. [As to the claim
that the quantities of QT are not random variables, all
we need do is look at any textbook on QT. It is easily
seen that no one has ever pretended that the quantities
were functions on the events of some pre-established
classical probability space. What QT does in fact, is to
take a given quantity and assign to each set of its values
the probability that the quantity takes a value from that
set. (See the spectral theorem for hermitian operators.)
Thus the actual procedure in QT is to treat each quantity
just as it comes, but to incorporate the set of values

of the quantity into a classical probability space.]

Hence the non-existence of joint distributions for
the quantities of QT shows not that the probability used
is non-classical, but rather that the quantities referred
to cannot be random variables. And if we examine the way
QT does in fact handle its quantities and associated
probabilities, we see that the quantities of QT are not
random variables but rather statistical variables.

Fine has shown that given a non—empty set of
questions (or propositions) Q and a non—empty set of
states S, each state 588 is a real—valued function from Q
into the interval [0,1]. That is, for each state 5, each
question q induces a probability measure P: which is a
classical probability. A different question, say p--for

the same state s—-induces a different classical probability

53

measure PE. It is important to stress that both of these
are classical probability measures. Now, given the state
s if we try to ask both questions q and p at the same

time, we would have a function given by P: q' This would
I

be the joint distribution of p and q in the state 5. But
8
Prq

conditions for the existence of P: q are just the same as
I

P does not in general exist. (It turns out that the

the well-known conditions of compatibility of propositions
or commutativity of operators.) When P; q exists, it too
I

is a classical probability measure. What this means is

that the two component probability measures P: and P: can

S
ppq‘

But since we have seen that in general this is not possible

be combined into one "joint" probability measure P

in QT, it follows that in general it is not possible to
form one "over-arching" probability measure which will

apply to all states and all qpestions. But in spite of

 

 

this, the probability used in QT for each state and for
each question remains as classical as ever. (It is as

though Suppes wants to take one element from a given

 

probability Space P:--whose underlying structure is indeed
a Boolean algebra--and another element from a different
probability Space P:--whose underlying structure is also
a Boolean algebra--and then demand that these elements so
chosen form themselves a Boolean algebra. We have seen
that this demand is not met in the general case. But we

have also seen that this condition is not required in

54

order to have a classical probability measure for each
probability that we do in fact use.)

In a loose sense, Fine's answer to the question
whether QT uses a non-classical probability is yes and no.
On a grand scale no, because it is not always possible to
form a "comprehensive" probability measure. But on the
small scale, in each individual case in which probabilities
are actually used, yes. But the impossibility of forming
a joint distribution (and hence the impossibility of form-
ing a "comprehensive" probability measure) is an odd fea-
ture of QT that neither arises from nor leads to the

incursion of any sort of non—classical probability in

 

the theory. In his article, Fine provides a model for
a classical probabilistic framework that is both adequate
for the formulation of QT, and faithful to its appli-
cations.

Thus, I believe the sting has been dissipated from
Suppes' objection. And again we have not found sufficient
grounds for claiming that QT employs a non-classical

probability.

Experiment As Entrance of Subjectivism Into QT.--Is

 

experiment an avenue by which subjectivism can enter QT?
The answer is certainly yes! For it is precisely because
of the nature of experimental results that we have the
irreducible, irremovable probabilities in QT. And we

have seen that the presence of these probabilities does

55

involve, to some extent or other, a renunciation of the
"objective" character of physical systems and physical
phenomena. But I must point out that in my initial pre-
sentation of the case for subjectivism, I made no mention
at all of the many controversies which have raged over
just these issues. It is abundantly clear that the
problem of subjectivism is somehow connected with the
so-called problem of measurement. And the many different
points of view with respect to that problem are well-
known. But I wish to claim that the case for microscopic
subjectivism (i.e., subjectivism, restricted, for the
present, to the level of microscopic particles and events)
can be made without having first a complete and satis—
factory solution to the problem of measurement. Hence,

to this extent these two problems can be treated separately
(i.e., the problem of measurement and the problem of
microscopic subjectivism). Thus, it is possible to make
the case for subjectivism without actively considering all
the difficulties associated with the problem of measure-
ment itself. To Show this as clearly as possible, I have
tried to show the bare skeleton of the argument in the
form of four premises and a conclusion. I will first
state the premises and the conclusion, then I will give
reasons for accepting each premise. I hope, by this, to
Show that: (l) the conclusion of microscopic subjectivism

is an unavoidable one; and (2) this conclusion can be

56

reached without getting ourselves embroiled in the hotly

debated questions concerning the problem of measurement.
For the sake of Simplicity let us consider a physical

system which can assume one of two values for a given

observable (property). Let the property be the spin of

the system. Hence any fermion (spin one-half system) will

do. We know that the system can exist in a state $1 with

its spin being C1; or it can exist in a state $2 with spin

 

:2. But according to the superposition principle the
system can also exist in a state w = awl + bwz (as we have

seen earlier). Now the argument goes as follows:

1. w = awl + bwz This is a possible state of
the system, and furthermore,

it is a spin state.

 

2. But to the system in state w (before measure-
ment) we cannot attribute either C1 or C2.

3. Thus, to the system in state w (before measure—
ment) we can attribute no spin whatever.

4. But whenever we observe the system, the system

always has a spin assoc1ated With it (:1 or C2).

 

Conclusion: Thus, :1 (or :2) comes to be associ-
ated with the system only in the act

of observation.

57

Premise l: (A) w 13 a state. For support of this claim

 

we can, quite simply, make appeal to the principle of
superposition. This principle demands that the super—
position exist and that this be a possible state of the
system. As to the question "Is this state not only
possible but also actual?," we can appeal to the host of
interference phenomena which reguire the superposition
principle for their satisfactory explanation. There is,
thus, both theoretical and experimental support for this
claim.

(B) u is a spin state. For support of this
claim we notice that: (i) u can be expanded in a complete,
orthonormal set of states (here just $1 and wz), which are
themselves spin states; (ii) m can be adequately described
in terms of the Pauli spin matrices just as are $1 and $2;
(iii) w exhibits all the characteristics properties of spin
states, e.g., coupling with magnetic fields.

(C) u is a physically different state from

 

either Y1 or wz; and w has properties that neither of the

states 11 or $2 has. (See Wigner [57].)

Premise 2: Wigner has Shown (in the same article mentioned

 

above) the inconsistency between decomposing w into W1 or
$2 (and thus attributing C1 or :2 respectively) and the
superposition principle. Thus, to avoid contradiction,
we are forbidden to say that our system is, on some

occasions, actually in state wl possessing spin Cl and on

58

some occasions actually in state $2 with spin :2. (Or
using an ensemble of many systems: we are forbidden to
say that some of the systems are actually in state $1 with
spin :1, and some of the systems are actually in state $2
with spin C2.) If this w is to be the state function
satisfying the Schroedinger equation, then it must ppp_be
decomposed, in any way, into the constituents $1 or $2.
But whereas $1 and $2 both have a definite value of spin
associated with the state, w has pp definite value of
spin associated with it. Hence, if we are forbidden to
associate with our system either W1 or $2, then we are
also forbidden to associate with the system in state w

either :1 or :2.

Premise 3: If we cannot attribute to the state w either

 

C1 or :2, then there is no spin at all that we can attrib-
ute to the state w. (And this is equivalent to saying
that a system in state w has no spin whatever associated
with it.) This is because Cl and :2 are the only two

spin values which we could conceivably attribute to the
state m. For these are the only two values of spin for

which QT provides any warrant at all for associating with

the state w in any way. Consider two cases: (1) if an

 

observation is made; (2) if an observation is not made.
(1) The only values that are ever obtained for the spin
are :1 and :2. This is in agreement with: (a) the

postulates of QT, and (b) experimental fact. (2) If an

 

 

59

observation is not made, we know that we cannot attribute
a definite value of spin to the system. But QT does allow
us to associate with each possible value of the spin a
certain probability of occurrence upon observation. And
even here the only spin values ever mentioned with re-
spect to the state w are Cl and :2. It is as though we
have the following logical statement

<w>(clw v czw v A:Clw v Nw)

C2

that is, for every system in the state w, either we can
attribute to it :1, or we can attribute :2, or we can
attribute apy other spin besides C1 and :2, or we can
attribute no spin at all to the system. (This is cer—
tainly in agreement with orthodox QT, for by definition
a complete set of eigenfunctions is exhaustive of the
state function for which it is an expansion. To use other
words, the eigen-vectors which form the complete set span
every subSpace of the Hilbert space associated with the
system. To be sure, the complete set here consists of
just *1 and $2, but the number of members in the complete
set is of no importance. But this does mean that either
you are in the subspace spanned by ml or the subspace
spanned by $2. There are no other subspaces.)

It is worthwhile to point out that we have here a

 

state with a given determinable property, but to which

60

we can attribute £233 of the particular determinate proper-
ties—-even though the determinate properties we have in
mind do exhaust all the possibilities for the previously
ascribed determinable property. This is like saying we
have in a plane a line and a point off the line, and we
know that the point has some location or other (determi-
nable property). But we know the point is not above the
line and we know that the point is not below the line.

And this clearly exhausts all the possibilities.

Premise 4: As indicated above this is simply: (l) in

 

agreement with the postulates of QT; but more importantly,
(2) a matter of experimental fact. Hence, our Situation
is now this: if we do not observe the system in state w,
we have a system with a determinable prOperty (is a spin
state) but without a determinate property (no definite
value of Spin). But if we do observe, we have a system
with both a determinable and a determinate property (is

a spin state apg has a definite value of spin associated

with it).

Conclusion: Hence, if before observation the system had

 

a determinable property but no determinate property, and
as soon as we like after observation the system had both
a determinable property and a determinate property, then
the determinate property (:1 or :2) came to be associated

with the system only in the act of observation.

 

61

At this point an objection might be raised: alright,
even if we admit that before observation the system had
no definite spin, and after observation it did have
definite spin, your point is not made (i.e., that the
determinate property came to be associated with the system

only in the act of measurement). For you have failed to

 

realize that you are talking about two different states:
before the observation, when there was no definite spin,
the state of the system was u; but after the observation,
when there was definite Spin, the state is no longer w, Ehe_

state has changed. And there is nothing unusual about

 

having two different Situations (with different impli-
cations regarding the spin) when the system is in two
different states.

I would like to make two replies to this objection.
(1) Clearly, here is a point where we find ourselves
facing one of the questions traditionally associated with
the problem of measurement, viz, the projection postulate.
Roughly put, this is the claim that a change of a certain
sort occurs in the state of a physical system when an
observation is made on the system. In particular, if
u = Eaiwi before observation, then after observation the
systém is no longer represented by u, but rather by one
of the wi‘ That is, the state has changed from w to wi'

Clearly, the force of the above objection rests on the

validity of the projection postulate (in some formulation

62

or other). Some have argued against the projection
postulate [40]. But we can make our reply without taking
sides on the projection postulate issue.

(2) Regardless of the outcome of the projection
postulate debate, the objection can be avoided. Even if
we grant the projection postulate and admit that we are
dealing with two different states, it is still true that

we are talking about the same physical system! And we

 

have shown above that the system had no definite spin
before the observation, but had a definite spin after

the observation. I would end my replies to the objection
with the following observation: (even admitting that
there are two different states) though there may be nothing
unusual about having two different values for the spin
when the system is in two different states, there is cer-
tainly something unusual about having "two different EEEET
ations“ for the spin when the system is in two different
states, if the "situation" in one of the states entails

a definite yalpe for the spin, and the "situation" for

the other state has no value at all associated with it!

 

I would like to conclude this section with some
remarks on an article by Joseph Sneed [52] in which he
criticizes an empirical argument advanced by Von Neumann
for the projection postulate. Though his objective in
that paper was much different from mine here, some of

his observations are pertinent. The point I wish to

63

establish, by this consideration of Sneed's work, is that
the import of the conclusions we draw here are of an

ontological rather than an epistemological nature. I wish

 

to make the point that, if we take our theory seriously,
if we attribute any empirical import to our theory, then
we must allow that when the theory makes an assertion this
is a reflection of what is "going on" in nature. Hence

I wish to claim that the limitations we discover in our
inquiry are not merely limitations on our ability to know
about phenomena; rather they are limitations upon the very
nature of the phenomena themselves.

Sneed gives an account of an experiment (collision
of an x-ray with an electron) which Von Neumann mentions.
The idea is that by observing the paths of the recoil
particles (by use of counter detectors), we can determine
the central line of the collision (i.e., the line along
which the vector sum of momenta of all particles lies).
Von Neumann considers the detection of the two recoil

particles as two different measurements, M1 and M2, of

 

the same observable, R (the central line). Then, accord-
ing to Sneed, Von Neumann's argument goes something like
this:

1. Prior to making a measurement of R we are justi-
fied in making only statistical statements, i.e.,
probability statements about the value of R that
will be obtained when any measurement of R is made.

2. After M1 occurs, yielding the value r for R, but
before M2 occurs, we are justified in making the
statement that the value of R which will be ob-
tained when M2 occurs will be r.

64

3. Therefore, the state of the physical system, on
which M1 and M2 are made, changed when M1 occurred,
from a state in which we are justified in making
only statistical statements about the value of R
which will be obtained from any measurement of R,
to a state in which we are justified in making a
statement that some one particular value of R
will be obtained from any measurement of R.

Sneed denies the soundness of the argument and states
that

the only thing that is described as changing when M1
occurs is the membership of the set of statements one
is justified in making about the result of M2. Indeed,
that this change does not follow from (1) and (2) un-
less one adds the addition premise:

A. If (i) one is justified in making only sta-
tistical statements about the result of any
measurement of R on physical system P then
it is not the case that (ii) one is justified
in making a statement that a certain result
will be obtained from a particular measurement
of R on P.

It seems quite natural to regard A as being true by
virtue of the meaning of "statistical statements," and
consequently to regard it as an implicit assumption of
Von Neumann's argument. However, in order to conclude
that the state of a physical system changed, something
in addition to A is needed. The following additional
premise would be sufficient to allow this conclusion
to be drawn:

B. The state of a physical system P when (i) is
true of P is different from the state of P
when (ii) is true of P.

Sneed then considers how to justify B given A. He suggests
that B may follow deductively from A given some statement
like:
C. The state of a physical system is identical
with the set of statements one is justified
in making about the results of measurements
made on P.

Sneed then concludes:

One might ordinarily say that the state of a physical
system (at a given time) is, or is described by, the

65

set of all true statements about the system (at this
time). We would not normally identify the state of
a physical system only as the statements we were
justified in making about it. Clearly, the set of
statements one is justified in making about a system
might change even though the set of statements which
are true about the system did not change.

Sneed has drawn a distinction between "the set of
statements one is justified in making about a system" and
"the set of statements which are true about a system."
This is a distinction which, in general, would find
sympathetic listeners. But if made without extreme care,
it is a distinction which I think to be quite insidious.
The difficulty I have in mind can be illustrated by simply
asking the following question: how do we determine the
membership in the set of statements which are true about
a system? That is, how do we know which statements are
true as Opposed to those statements which we are merely
justified in making? An example will help. We are told
that a coin is flipped. Nothing more. We are surely
p22 justified in saying (about the coin) that it landed
heads up (or tails up). We are justified in saying only
that the probability of heads up is a certain number p
and the probability of tails up is a certain number
q = l - p. So we have the set of statements which we are
justified in making about the coin (our system), viz, the
two probability statements. Now, what is the set of
statements which are true about the system? (We are,

of course, restricting our inquiry to just the heads-or-

tails status of the coin, not its temperature or color or

66

shape, etc.) That set of statements consists of exactly
ppe statement: either heads up pr tails up. We just
happen not to know which one right now. (It is true, of
course, that there are an infinite number of other state-
ments, all "physically" equivalent to these two, that could
be included in the set of true statements (e.g., the
statement 'either heads or tails'), but this does not
change the conclusion reached below.) But a quick look,

an observation, will take care of that. Suppose we look
and we find heads. Well if the coin is heads now it is
certainly true that it was heads before we looked. For,
since nothing is happening to the coin besides our looking
at it, it must have been heads before we looked or how

else would we have seen heads when we did look? Thus,

here is a clear case of a difference between the set of
statements we are justified in making and the set of state-
ments which are true about a system. Or so the argument
goes.

But in order to conclude that the coin was heads
before we looked, it was necessary to infer the truth of a
statement at an earlier time from the truth of a "corres-
ponding" statement at a later time. That is, we con—
cluded that the coin was heads before we looked, from the
fact that the coin was heads after we looked. But as we
have seen already in too much detail, this kind of

"retroductive inference" is precisely what is forbidden

67

in QT: e.g., from the observation of spin :1 for a system,
we certainly gap_ppp conclude that the spin of the system
was Cl before the observation. Hence it is seen that this
proposed method of determining which statements about a
system are true, as opposed to those statements which we
are merely justified in making will simply not draw the
distinction for which it was intended. But this proposed
method was nothing more than observation, plain and simple.
And appeal to any other method besides observation can
easily lead us out of the realm of science and into meta-
physics of the worst kind.

I would like to maintain that the distinction drawn
by Sneed is an indefensible one. The idea that there are
statements which are true about a system over and above
(or independently of) those statements we are justified
in making is an unexamined carry-over from the time of
classical physics. In classical physics we had a picture
of a uniquely determined world developing quite inde-
pendently of our knowledge or ignorance of its progress.
Classical physics was at once the result, the corrobo-
ration and the determiner of our intuitive feelings about
the way the world "really" is. Hence, we could always
maintain our idea of what was true about a system as
opposed to what we were merely justified in saying. What
was true was the actual state of the independently develop-

ing physical world; what we were justified in saying

68

depended on the extent of the knowledge we had about the
independent development (and remember, we could always
make that knowledge approach as closely as we pleased to
the actual state of the world).

But I wish to argue that this distinction requires
re—examination in QT just as does the notion of a "state"
require re-examination in QT. Certainly, observation
would be the likely candidate for telling what is true
(and then hopefully, what gag true) about a system. But
when that fails, we must make appeal to other critiera.
Now this does not mean that any other criteria will auto-
matically be unfit. But they should be carefully scruti—
nized. For in the absence of any empirical grounding of
such criteria, even a "reasonable-sounding" criteria can
turn out to be mis-directed and can lead us along a
fruitless path. This danger is especially present in QT.
For here we are in a strange land, where our intuitions
about what sounds like a reasonable extra-empirical
criterion were formed in another place and time, viz, in
classical physics. And we should be naturally suspicious
in a strange land that our previous biases mighp not re—
tain their validity (if indeed, they ever really had any
to begin with). The historical development of QT strik-
ingly confirms us in this suspicion.

(The Einstein—Podolsky-Rosen paradox [20] is such

a beautiful paradox because the initial, extra-empirical

69

criterion imposed by Einstein, Podolsky, and Rosen is

such a "reasonable" one. And one to which we are all
surely sympathetic. But this was a criterion born out

of classical physics and out of a mind "raised" on classi-
cal physics and a classical—physics View of the world (his
theory of relativity notwithstanding). But what is
reasonable in classical physics might not be reasonable

at all in quantum physics. And this, in essence, was
Bohr's answer [11] to Einstein, Podolsky, and Rosen.)

Am I trying to say that all there is of the physical
world is what we know of it? What I am trying to say is
that if what we claim to have are empirical theories,
theories about the world, then we must regard them as such.
And we must regard their pronouncements as having some
significance and relevance for the world they are supposed
to describe. I realize that the questions which are at
issue here are difficult and complex ones, and do not
admit of simplistic answers. But I also think that if
we are to allow any descriptive content to our theories
at all, then we must also allow that content to be
descriptive of the world to which the theory applies. I
do not wish to imply that we must accept a theory lock-
stock-and-barrel, like it or not. I do believe that some
"extra-theoretical" considerations are appropriate and
even necessary. I only wish to maintain that i: a con—

flict arises between the two, we should be strongly

70

inclined to reject the "extra—theoretical" considerations--
especially when those considerations can be clearly seen

to arise out of a theoretical framework different (and in
some aspects, alien) to the one under discussion. And I
certainly believe that the notion of what is true about a
system falls into this category.

Returning to Sneed, we see that an analysis of his
premise C shows us that it is indeed true, i.e., that the
state of a physical system is described by the set of
statements one is justified in making about the results of
measurements made on the system P. To use borrowed termi-
nology of Henry Margenau [40] and Josef Jauch [29]: a
state is the result of a series of physical manipulations
on the system which constitute the preparation of the
state. Two states are identical if the relevant conditions
in the preparation of the state are identical. And what
does a state tell us? We have seen that it is a funda—
mental fact of QT that identical states do not yield
identical results for the truth or falsehood of a propo-
sition. Thus, a measurement of proposition a may some—
times give the value 1 (true) or 0 (false). But if we
know the state (the relevant conditions in preparation),
we can form a probability measure and can determine the
probability of any proposition a. And since a proposition
is just a yes-no experiment, this means we can give the

probability of any experimental outcome, i.e., any

71

measurement made on the system P. So the state determines
what statements we are justified in making about the re—
sults of measurements made on P.

Thus, since we no longer have this store of "true"
statements, the best we can do is the set of statements
we are justified in making. N93, the change (admitted by
Sneed) in the set of statements we are justified in making
is an important one. For the set of statements we are
justified in making is just what the theory tells us, and
what the theory tells us is--for all purposes—-what the
world is like. Thus, if what the theory tells us changes,
what it is that is described by the theory, i.e., the
world itself, also changes. Then all of Sneed's remarks
are seen to be in good agreement with my position. Indeed,
Sneed (later in his paper) proposes "to give up the view
that a particular physical system must possess a unique
value (in the usual sense of numerical value) for every
observerable associated with it." This statement of
Sneed's becomes even more pointed when we realize that in
some cases the physical system not only possesses no
unigue value, but indeed possesses no value at all!

But let us notice that even if we are willing to
admit the demonstrated subjectivism for electrons, protons,
etc., we have no inclination whatever to ascribe this same
subjectivism to the coin we mentioned above. And this is

true whether we are acting as philosophers, scientists,

72

or men-in—the-street. In spite of what QT obliges us to
say about micro-systems, we still do believe that the coin
was definitely heads before we looked at it. But if we
believe the micro level to be that which "makes-up" the
macro level, what happens to the subjectivism as we move
from electrons to coins? Is the subjectivism in fact
still present? Do we have any basis for believing that

it is not? In particular, are there any physical reasons
--i.e., reasons that can be provided by QT itself--for
rejecting this subjectivism on the macro level? It is

to these questions that we must now turn.

PART III

CONSEQUENCES OF MICROSCOPIC SUBJECTIVISM:
POSSIBLE RESPONSES TO CLAIM OF

MICROSCOPIC SUBJECTIVISM

Given the results of Part II it is fitting to ask
what consequences flow from these conclusions? Just how
serious is this subjectivism? How do we incorporate this
new-found subjectivism into our world picture--as given by
science? What adjustments or modifications are required
in the way we think of the physical world in view of this
subjectivism? Even if one is forced to admit the sub—
jectivism we have discussed, there certainly seems to be
nothing of the sort in our everyday experience. Can we
account for both of these "facts" at the same time? In
short, how do we respond to this claim of irreducible
subjectivism in physical nature?

In what follows I shall, on numerous occasions,
refer to the distinction between microscopic and macro-
scopic. By microscopic I mean that realm (of events,
phenomena, interaction, systems, etc.) which is specifi—

cally governed by the laws of QT. By macroscopic I mean

73

74

that realm in which the laws of QT are generally not re-
quired for the explanation of phenomena, and the laws of
classical physics are for the most part adequate. Gener-
ally speaking, the microscopic realm is associated with
small size, say, atomic and sub—atomic size; and the
macroscopic realm is associated with large scale bodies
(i.e., large relative to the microscopic bodies). This
includes the familiar world of tables, chairs, billiard
balls, etc. But the essential difference to keep in mind
is that the microscopic is associated with specifically
quantum effects and behavior; whereas the macroscopic is
devoid of these effects.

For the most part, the macroscopic bodies we will
discuss will be macroscopic measuring devices. That is,
we will be specifically interested in those bodies, of
macroscopic size, which obey the laws of classical
mechanics and in addition whose states can serve as the
final states of a device designed to give us information
about a measured (observed) system. Hence, though it is
possible to observe specifically quantum behavior with
"large" bodies——in, say, the Josephson effect, properties
of superconducting bodies, the emission of light-—these
will not be macroscopic systems suitable for use as a
measuring device (in which we must have macroscopically

distinguishable final states).

75

There are several responses one can make in face of
the claim of irreducible subjectivism on the migrg level,
ranging all the way from saying it is an accursed lie to
saying this subjectivism extends throughout the entire
universe. A. One could simply gepy the subjectivism even
on the micro level. Here, there would be no question of
incorporating the results into our overall physical pic-
ture. Rather, the energy expended here will be to the
effect of showing how we can avoid such a result to begin
with. B. One could accept the subjectivism on the micro
level, but wish to reject it on the macro level, so that
we could still maintain a more or less realistic View with
regard to the events of our daily experience. It would be
incumbent upon holders of this View to show exactly how
we can maintain this dualistic position: subjectivism on
the micro level and realism (objectivism) on the macro
level. This problem becomes especially significant if one
wishes to hold that in some way or other, the macroscopic
is composed of, made-up of, constituted by, the micro—
scopic. These proponents must tell us exactly how we
can account physically for this dualism. They must deter-
mine if QT can explain this Situation adequately. They
must determine if QT can tell us what happens--if anything
-—as we go from the micro level to the macro level to
account for the "disappearance" of the subjectivism.

There may be philosophical problems associated with

76

holding such a dualistic view, but this is also a problem
for physics, in the sense that this View must be compatible
with present physical theory. If there are philosophical
considerations which make this position unacceptable, then
they must be weighed. But also, physics must tell us if
this position is even scientifically acceptable. We will
concentrate here on the physical issue.

9. A further reSponse to the claim of microscopic
subjectivism would be to accept not only the subjectivism
on the micro level, but to accept it on the macro level as
well. Here we will wish to distinguish between those who
wish the subjectivism to apply to only inanimate (i.e.,
without consciousness) macro bodies, and those who wish
the subjectivism to apply also to conscious observers.

Q. A very interesting possibility would be to respond in
somewhat the following way: this label of so-called
"subjectivism" is worthless because, as a matter of fact,
the distinction between the "subjective" and the "objective"
is a meaningless one. We have no way to distinguish one
from the other, and thus any attempted distinction is
futile. We will see in detail what this proposal entails
below.

It is clear that of all the different kinds of re-
sponses just outlined, that type under group B is the
least reactionary (most middle of the road)--in the sense

that this response would require the least amount of

77

adjustment of our overall world picture (while allowing

us to accept the conclusion of microscopic subjectivism).
For this View would allow us to wholeheartedly accept the
conclusion of the new physics (in its proper realm of
application, viz, with respect to microscopic phenomena),
while at the same time permitting us to preserve, intact
(at the macroscopic level), that world picture which has
served us so well for so long, viz, that associated with
classical physics. Hence, we would be able to weave into
our total picture, the new threads required by the new
micro physics, without completely destroying the overall
pattern in scientific thinking predominant from the seven—
teenth century. This would seem to be the most desirable
avenue to take, not only for the sake of preserving tra-
dition, but also since we have no way of knowing what the
"correct" explanation will be, the (pragmatically) easiest
and therefore (pragmatically) wisest thing to do is to make
the change that disturbs the total explanatory system
least. (I am aware of course of the important instances
when the best explanation was also the most radical. How-
ever, the great majority of our explanatory attempts are
clearly app of this kind. These radical revisions are

the "revolutions" that are, almost by definition, few and
far between. In other words, I intend this to be an "all—
other-things—being-equal" statement.) At any rate, there

is much (understandable) sentiment for this kind of

78

solution. So I shall give only a brief discussion of the
proposals in groups A, C, and D: and treat those under B

in greater detail.

A. Deny Microscgpic Subjectivism
I wish to consider in this section the views of those
authors who respond to the claim of irreducible subjectivism
by denying it. Those writers do not attempt to discover
what consequences follow from the conclusion of microscopic
subjectivism; they simply deny the conclusion and reject
the subjectivism altogether.

Hidden variable theories. The first kind of proposal

 

I wish to consider are the so-called hidden-variable
theories. By this I have in mind any attempt to remove
the novel features of QT (i.e., the subjectivism) by re—
placing the statistical QT on the micro level with a
deterministic theory on, say, a sub-micro level. Or, to
put it less crudely, this is an attempt to introduce
hidden variables in order to characterize a phase space
of microstates on which real-valued functions can be
defined to represent the physical properties of micro
objects in the manner of classical mechanics, so that the
peculiar statistical relations of QT are simply explained
by the incompleteness of the theory. Then when the vari—
ables associated with these "hidden states" are taken
into account, we obtain a completely deterministic account

of observed phenomena——the indeterministic nature of the

 

79

account in orthodox QT being explained by the fact that
we simply had an incomplete specification of all relevant
data.

The first thing we must note is that a great deal of
'confusion exists regarding hidden variable theories. For
example, contrary to popular opinion, the "hidden variable
program" as stated above is manifestly app what was
attempted by Bohm [6] and his collaborators. But at the
same time, this kind of program has been the object of
many discussions and proofs and has been the raison d’étre
for much ridiculing of Bohm. Hence, I shall wish to be
especially clear about what we have in mind as we discuss
hidden variable theories below.

Though it is true that Bohm does not advocate the
simple minded kind of theory outlined above, many proofs
have been directed to this kind of proposal. It is
worthwhile to examine the import of those proofs. The
first thing that comes to mind in any discussion of hidden
variables is the now—famous proof of Von Neumann. But,
as is certainly well known by now, the proof of Von Neumann
--to the effect that hidden variables are impossible—-does
not prove all that it claimed to. We will consider,
rather, the work of Kochen and Specker [33]. It can be
shown that the Von Neumann proof is a weaker version of
the same problem as re—formulated by Kochen and Specker:

i.e., the Von Neumann proof does not rule out a large

 

80

class of hidden variable extensions of QT that are ruled
out by the theorem of Kochen and Specker. Hence a study
of the work of Kochen and Specker will give us our strong—
est conclusions.

Kochen and Specker identify the physical parameters
of QT with the hermitian Hilbert space operators. Now, a
hidden variable extension of QT, as usually understood,
involves the interpretation of the hermitian operators in
Hilbert space as representing the physical attributes of
objects. The problem--for the hidden variable theorists--
is then to embed the QT into a more fundamental theory, so
that these attributes are represented by real-valued
functions on a phase Space of hidden states, in such a
way that it becomes possible to give a statistical
mechanical derivation of the statistical theorems of QT
in the classical manner. Kochen and Specker show that

this kind of embedding is impossible.

 

However, if the physical parameters of QT, as repre-
sented by hermitian Hilbert Space operators, are not
interpreted as referring to attributes or properties of
"quantum objects," then there is no motivation at all for
developing a hidden variable theory (of the type discussed
here). Kochen and Specker point out that the hidden vari-
able problem without a certain condition which they derive
is trivial: it is always mathematically possible to

introduce a phase space, and to associate real-valued

 

81

functions on the phase space with the physical parameters
of a statistical theory, in such a way that the statistical
theorems are recovered. The special condition of Kochen
and Specker imposes a structure on the set of physical
parameters suggested by their interpretation as physical
attributes of objects. However, it is just this interpre-
tation which is incompatible with the representation of
physical parameters by hermitian Hilbert space operators.
Hence, any proposal which maintains this interpretation

is seen to be indefensible.

However, if one rejects this interpretation——of the
physical parameters of QT as physical attributes of
objects--then we have quite a different story. This is
done by Bohm. We will examine shortly his rather un-
expected results.

In addition to the results of Kochen and Specker,
some recent work by J. S. Bell [3,4] places some very
stringent restrictions on any hidden variable theory
(including the type we have been discussing). QT pre—
dicts the probabilities of the various possible results
of a measurement, not the individual results themselves.
Bell asks if a more complete theory is possible: is it
possible to have a theory that agrees with the pre-
dictions of QT but predicts the individual results,

instead of merely their probabilities?

82

Bell considers the Einstein—Podolsky-Rosen Paradox.
(Actually, he considers a variation of the original problem
as formulated by Einstein, Podolsky, and Rosen. He con-
siders the measurement of the spin of two particles which
have interacted, by allowing each particle to be deflected
through a Stern-Gerlach apparatus.) He shows that it is
easy to make a hidden variable model that will work if
the result of the measurement on particle one is allowed

to depend also on the direction of the other magnet (of

 

the other Stern-Gerlach apparatus). However, if Einstein's
hypothesis of the independence of separated non-interacting
systems is accepted then Bell demonstrates that no such
hidden variable model can agree with all the predictions
of QT (to within variations of, say, 5%). Thus, Bell con-
cludes: "In a theory in which parameters are added to QT
to determine the results of individual measurements, with—
out changing the statistical predictions, there must be a
mechanism whereby the setting of one measuring device can
influence the reading of another instrument, however remote.
Moreover, the signal involved must propagate instan—
taneously, so that such a theory could not be Lorentz
invariant." (For a more detailed discussion of Bell's
theorem, see appendix.)

Besides being a very stringent restriction on hidden
variable theories, this conclusion is significant because

it essentially echoes the conclusion of Bohm—-who started

83

out explicitly adopting the hidden variable approach. In
both Bell and Bohm we find a relaxation of the traditional
concept of the independence of physical objects.

In a now classic paper, Moyal [45] investigated the
possibility of reproducing the quantum statistics from
joint probability distributions for position and momentum,
i.e., of relating the statistical states of QT to a proba-
bility over a classical phase space. Moyal showed that
the phase Space probability distribution associated with 4
a certain statistical state is not fixed but varies with
the relevant physical parameters, i.e., the probability
distributions may be said to be "relative to the measure-
ment context."

Bohm, too, explicitly pointed out this aspect in
his original 1951 "hidden variable" theory. In a section
on Von Neumann's proof, he wrote [6]:

His conclusions are subject, however, to the criticism
that in his proof he has implicitly restricted himself
to an excessively narrow class of hidden parameters and
in this way has excluded from consideration precisely
those types of hidden parameters which have been pro—
posed in this paper. . . . For example, if we consider
two non-commuting observables, p and q, then Von
Neumann shows that it would be inconsistent with the
usual rules of calculating quantum-mechanical proba-
bilities to assume that there were in the observed
system a set of hidden parameters which Simultaneously
determined the results of measurement of position and
momentum 'observables.‘ With this conclusion we are
in a reement. However, in our suggested new interpre—
tation of the theory, the so—called 'observables' are
. . . not properties belonging to the observed system
alone, but instead potentialities whose precise
development depends just as much on the observing
apparatus as on the observed system. . . . Thus, the
statistical distribution of 'hidden' parameters to be

 

r— '1

84

used in calculating averages in a momentum measurement
is different from the distribution to be used in calcu—
lating averages in a position measurement. Von
Neumann's proof . . . that no single distribution of
hidden parameters could be consistent with the results
of QT is therefore irrelevant here, since in our inter-
pretation of the measurements of the type that can now
be carried out, the distribution of hidden parameters
varies in accordance with the different mutually ex-
clusive experimental arrangements of matter that must
be used in making different kinds of measurements. In
this point, we are in agreement with Bohr, who repeat-
edly stresses the fundamental role of the measuring
apparatus as an inseparable part of the observed
system. [Italics added.]

 

Hence, even on Bohm's proposal we find that we do
not recover a picture in which we have the deterministic
development in time of independently existing entities.

We find, rather, that we must entertain a picture in which
objects no longer "possess" properties or attributes in
the sense of these properties being characteristic solely
of the object, and independent of any other object. There
is now an "inter-dependence" among objects; a loss of that
independence and complete "isolatability" that an indi-
vidual object was once believed to have. And since this
is precisely the conclusion to which we are driven by our
acceptance of microscopic subjectivism, it is seen that
Bohm's analysis is in satisfactory agreement with ours.

Purely statistical interpretation. We considered

 

above the attempt to deny the basic claim of irreducible
subjectivism by trying to replace the statistical laws of
QT by deterministic laws on a sub-quantum level. And

even though that was not the exact intent of some of the

85

actually proposed hidden variable models (e.g., those of
Bohm), we considered some of the restrictions that would
have to be met by any theory of this type. We will now
consider an attempt of a different sort to avoid the con-
clusion of an irreducible subjectivism in the micro world.
I now refer to the school of thought that advocates

a purely statistical interpretation of QT [2]. The central

 

issue is this: these writers maintain that QT is a theory
about ensembles of systems, and not about single systems.
In particular, they assert that a quantum state (pure or
otherwise) represents an ensemble of similarly prepared
systems. A quantum state, according to this View, does
293 provide a complete description of an individual system.
But how do we then interpret the lack of specificity associ-
ated with a quantum state? They reply that this lack of
specificity is pep to be associated with the properties

of a given individual system. Rather, each single system
has well-defined properties at each instant; and this lack
of specificity refers to the lack of complete uniformity
among the observable properties of the different indi-
vidual systems in the ensemble (to which the state
function, by assumption, refers). That is, the statisti—
cal interpretation considers that physical systems which
have been subject to the same state preparation will be
similar in some properties, but not in all of them. And

this difference among the different individual systems is

86

the proper meaning of the "indeterminateness“ of the state.
Indeed, according to this View, the physical implication
of the uncertainty principle is that no state preparation
procedure is possible which would yield an ensemble of
systems identical in all of their observable properties.

Many arguments, pro and con, have been given on
this point, and the controversy has raged Since the time
of the Einstein, Podolsky, Rosen paradox. I do not wish
to recount all these arguments giving their merits and
demerits. Instead I will present a simple recent experi-
mental result which I think tells decisively against the
statistical interpretation.

Recently Mandel and Pfleegor [39] performed an
experiment that is essentially just the double slit
experiment. For the light sources they used two single—
mode lasers, attenuated sufficiently so that generally
only one photon was in the apparatus at any one time.

To understand the experiment, it is crucial to remember
that instead of a single light source, Mandel and Pfleegor
used a double source; and furthermore, the two lasers were
operated independently of each other. The two beams were
superimposed on one another as a result of a small angle
of difference in the direction of propagation.

Now essentially what happened was just this: even
with the assurance of only one photon in the apparatus

(for this see the experimental data), Mandel and Pfleegor

87

found clear evidence of interference. Furthermore, when
one of the lasers was turned off, all such evidence dis—
appeared. They concluded that their experiment supports
the well—known statement of Dirac: " . . . each photon
interferes only with itself. Interference between differ-
ent photons never occurs" [19].

How can we account for such a strange phenomenon?
In the traditional double-slit analysis we can appeal to
the interference of the wave fronts coming from the two
slits. But here that does not seem possible since the
experiment was intentionally designed to insure that the
photon was from a single laser. But the resolving point
here is that an uncertainty principle analysis shows that
it is not possible to tell from ghrgh laser the photon
came. Considering the photon as a particle and making
an appropriate analysis in terms of position and momentum,
it can be shown that if we identify the source as laser
one or two, we will destroy the conditions required for
the interference patterns (conditions from physical optics).
But if the particle analysis is objectionable, Mandel and
Pfleegor show that their results follows, in accordance
with the usual principles of QT, from a superposition of
the wave functions for electromagnetic fields from the
two lasers. Thus, either because of the uncertainty
principle or the superposition principle we are forbidden

to know from which laser the photon was emitted. And

88

finally, it seems patently clear that in this experiment
dealing with single systems, we have striking proof of
the validity of QT not only statistically, but even for
individual systems, thus laying to rest any contentions
of restricting QT to merely ensembles.

B. Accept Microscopic Subjectivism, Reject
Macroscopic SubjectiviSm

 

 

The kinds of solutions offered under group B seem to
be the most "desirable," in that they would allow us to
accept the new "fact" of microscopic subjectivism, but also
allow us to reject this subjectivism on the macroscopic
level——i.e., the level of familiar everyday experiences.
For this reason we will postpone consideration of these
proposals, and consider them in detail later.

C. Accept Microscopic Subjectivism, Accepp
Macroscopic Subjectivism

 

 

There are also those who, having accepted the sub-
jectivism on the micro level, go on to entertain the possi—
bility of subjectivism also on the macro level. I will
distinguish, within this position, between those who wish
to restrict the subjectivism to just inanimate (i.e., un-
conscious) macroscopic bodies, and those who wish to
include also conscious observers. (Jauch clearly places
himself in the first group, but does so rather subtlely.

We will see more of his position later.) We will consider
here first the work of Von Neumann [55] and then the work

of Wigner [58].

89

Von Neumann argues that if we observe an object
system I by use of an apparatus, system II, we will obtain
the same results by use of an apparatus system III, to
observe the combined system I + II. (This means in par-
ticular, that if the object system I was in a super-
position, then the combined system I + II + III will also
be in a superposition.) Likewise, a system IV, when used
to observe combined system I + II + III, will again give
the same results. (And again, the combined system of
I + II + III + IV will be in a superposition.) This series
can be continued on indefinitely, argues Von Neumann. In
particular, the procedure can be carried on until the
combined system is large enough to include the experi—
menter himself (in the sense that the combined system now
includes the sensory apparatus of the scientist performing
the observation). But,argues Von Neumann, the combined
system cannot be extended to include the consciousness of
the observer. We are perfectly free to draw the line
between "object" and "apparatus" anywhere we wish all the
way from the initial microscopic system to the physical
body of the observer-—we will obtain the same results.

But with the consciousness of the observer we have the
final demarcation line. We can, if we wish, continue to
think of a superposition for the combined system of
object plus apparatus all the way up to the consciousness

of the observer. But here the superposition is invariably

90

reduced. Hence Von Neumann excludes the superposition
(and thus the subjectivism) from the conscious states of
the observer. But he does clearly allow the subjectivism
to exist on the macroscopic (inanimate) level. That is,
Von Neumann "takes QT seriously" and applies it to all
(inanimate) systems whatever.

In a more recent article, Wigner has also "taken QT

seriously,’ and entertained the question of the subjectiv-
ism extending to the consciousness of the observer. But
Wigner is concerned with a serious difficulty facing any

such account. Let the wave function of the observed

1

s + u: where w: and w: represent mutually

system S be us = w
exclusive situations. Consider a device that measures
accurately which alternative is realized upon a given
measurement. The superposition principle then ensures

that us 8 wm must develop into a superposition of wave

functions for the two alternatives:
1 2 l l 2 2
(ws+ws)®wm—+vs®wm+wsewm

where wm represents the wave function of the measuring
device before the measurement; W; and w; represent the
wave functions of the measuring device corresponding to
the device having registered the occurrence of the respec-
tive alternatives. Now if we go further and include the

observer in the quantum mechanical system, then we have

91
Mimi)ewmewofiwiewiewi+wjavg-13¢:

where w: and w: correspond to the observer's having ob—
served alternative one or two respectively.

But we recall now that the alternatives one and two
are mutually exclusive. Yet our theory gives a result
that requires BEER mutually exclusive possibilities to
exist in nature--until such time as the superposition is
reduced by a measurement. Thus, if we have Wigner's
friend observe the result of a yes—no experiment, QT
tells us that for the compound system including the state
of the observer, we must have a superposition of yes and
no states. Hence, until Wigner asks his friend for the
result of the experiment which was observed--thus per-
forming the measurement--his friend must be in a state
which includes both the yes and the no outcomes of the
experiment. It thus appears that until he is asked,
Wigner's friend does not know himself which alternative
did in fact occur.

If we substitute for Wigner's friend some simple
physical apparatus, such as an atom which may or may not
be excited as a result of the yes—no experiment, then
" . . . there is no doubt that [mi 8 W; 8 w: + w: 8 w; 8 $2]
describes the properties of the joint system correctly, the
assumption that the wave function is either [¢: 8 w; 8 o:

OR w: 8 W; 8 mg] does not" [58], because there is a

92

difference in observable effects between these two possi-
bilities. Wigner concludes that a being with consciousness
must have a different role in QT than an inanimate measur-
ing device. Also, he feels that this argument is entirely
cogent as long as we accept the tenets of orthodox QT in
all their consequences. He suggests that there is a vio—
lation of physical laws where consciousness plays a role.
(In this particular case, perhaps there is a breakdown in
the linearity of the equations of motion.)

D. Subjective/Objective Distinction

Is Useless

The adherents [18,21,561 of this View do not wish to
tamper substantially with the conclusions of Part I. They
accept the existence of the superposition on the micro—
scopic level (which is hardly surprising), and they admit
that some ontological consequences will follow. But they
interpret the meaning of the superposition in a different
way. Crudely put, these authors replace the "indeterminate—
ness" of the state with the "indeterminate—ness" of reality
itself, or with the "indeterminate—ness" of the universe
as a whole.

Wholesale application of the principle of super-
position to all objects or systems seems to drive one to
the conclusion that several mutually exclusive possi—
bilities all somehow exist in nature at the same time.

These authors accept this conclusion at face value and

93

then go on (understandably) to Show how our idea of "nature"
must accordingly be modified. First, each component state
of the superposition represents reality, i.e., a possible
world. And since there never is any such thing as a re—
duction of this superposition (they say), each component
is realized. That is, there is a raal world existing for
each of the components, and there are as many different
real worlds as there are components. Thus the fall physi—
cal world would contain a superposition of a myriad of
interconnected physical worlds of the kind we know. An
individual observer would personally be aware of only one
response of a macroscopic measuring device, but a full
account of reality would include all the other possible
responses on an equal footing, though perhaps with unequal
"weights." Thus human observers would be aware of only
individual branches of the full reality of the world.

Now though these authors will readily admit that this
proposal is counter—intuitive, they maintain that it would
not involve any conflict with experience. For the mutually
exclusive possibilities would be essentially non—interfer-
ing, e.g., the memories of individual observers could not
contain cross references to the non-interacting branches
of the wave function associated with the various "incom-
patible" possibilities. Thus no individual would be aware
of more than one branch of the full objective reality.
(Hence, the different "worlds" are in perfect peaceful

co-existence.)

94

It is now clear why these authors can be described
as advocating the abolition of the subjective/objective
distinction. For if the "objective" is thought of as
somehow existing independently of any particular indi-
vidual, and the "subjective" is thought of in some way as
a particular aspect of objective reality as—apprehended-
by a given individual, then it is seen why, under this
proposal, this dichotomy is not very enlightening. For

according, to this view, the world of the individual

 

observer (i.e., the subjective) and the world of the
"super-reality" (i.e., the objective) are separated by a
gap that is—-in principle-—never to close. The world of
the individual observer is, for him, the entire whole;
this world contains all there is for him to know and all
he ever could know-~even under the most ideal conditions.
This world, though it may be called subjective, is as
objective a world as he will ever know. And indeed he
will never know another. Hence his world has all the
characteristics usually associated with an "objective"
world. And to call this world "subjective" and not
"objective" surely seems misguided. [It is true that
this world——of the individual observer-—is not objective
in the usual sense of "being the same" for everybody.
Different observers will, in general, live in different
worlds. But there is no way of knowing this, since our

equations can contain no terms of cross reference between

i
l
1
l

95

the different "branches" of the wave function (i.e., be—
tween the different worlds). To a given observer, all
other observers live in hla world; and vice versa. Hence
Leibniz's dictum "the best of all possible worlds" takes
on a new significance. This is indeed the best of all
possible worlds. But why? Because it is the only world
(game) available to us (in town).]

Stapp [53] has pointed out that the usual interpre-
tation of QT does not unequivocally rule out this possi—
bility. Rather, it effectively circumvents the question
by representing the responses of the measuring devices by
specificaations that link the responses of the measuring
devices to the experiences of the scientists that use the
theory. This means that QT would then be a theory that
describes what happens on a particular branch. Then the
question of whether there are other branches of some
"super-reality" becomes irrelevant.

It seems to me, further, that perhaps we have here
an equivocation on the word "actual" or real." These
authors promise to reveal to us a new insight regarding

what "actually' is or exists. But what we find is that
we are presented with an enlargement of our original
picture, and that the property of being actual is ascribed
not to the same level as it was in the original picture
(and this level is still present), but rather to a "higher"

level. In truth, all we have done is to shift the level

to which "actual" is ascribed, but in such a way, I claim,

5.1....1; .

96

that we do great violence to the original meaning of the
word. For according to this proposal, what is actual is
the "super-reality"; and thus we are left in the position
that what is "actual" cannot, in principle, ever be experi—
enced by anyone.

In one sense, what is "actual" is what is actual to
a given individual. That is, according to ordinary lin-
guistic usage, we effectively identify actuality with the
aspect of things that are relevant to our own personal
experience. At the same time, there is a sense of "actual"
which seems to refer to that which exists independently
of any particular individual, and over and above any par—
ticular assessments of it. But if, in principle, it is
impossible to know or to experience or to establish the

existence of this "super-reality,‘ then it seems grossly
inappropriate to ascribe "actuality" to it. (This seems
comparable to another situation: when trying to show that
we sometimes suffer illusions, and we sometimes experience
dreams, and, and that the dreams sometimes seem just as

raal as "reality,' some thinkers have gone to the extreme
of then asking if we cannot infallibly distinguish dreams
from reality, how do we know that everything is not a
dream. This is only superficially plausible, for it can
be seen that the word "dream" is now being used in a
sense different from what it originally was: "dream" was

originally used to distinguish two kinds of states; but

now there is only one kind of state, and "dream" has been

“.ii..vL

97

mis-appropriated to refer to this state—-mis-appropriated
because the meaning of "dream" has now changed drastically
from what we expected it to mean from its previous usage.
That is, if there is now only one kind of state, why use
"dream" to describe it? we already have a perfectly good
word which has just that meaning: waking-state.)

At any rate, one lesson is certainly clear: we
must be very careful in our use of words in these matters;
for ordinary linguistic usage is tied to our common sense
ideas about the world. And here, it is precisely these
ideas that are being called into question.

Besides all the above objections (if I may be
facetious), Occam--at the sight of this proposal——must be
turning over on his razor. But to be serious again (pity),
though this proposal cannot be logically disproven, its
import is so intuitively unappealing that, in the words
of Stapp [53]: "It is doubtful that any theoretical con-
struct could be secure enough to warrant acceptance at

this price." The price is certainly too great for me.

Alternatives Under B

 

Let us now examine what possible solutions are
available to us if we accept the subjectivism on the level
of microscopic phenomena, but wish to reject or deny it on
the macroscopic level. Before we look at actual alter— J

natives, a few general comments will be helpful.

by... ,. . n

98

Removal of subjectivism related to reduction of wave
function. According to current terminology the following
equation is unfortunately used to represent two radically

different states
w = awl + bwz

In the first case, this could be the equation for a para
state. Here, we have a given state w expressed as an
expansion in a set of other states, W1 and $2. With re-
spect to that observable for which $1 and W2 are the eigen-
states, the state w is in an "indeterminate" state, as we
have seen earlier. The system (represented by w) is not
in the state W1 and it is not in the state $2. However,
upon measurement one always obtains (for the value of this
observable) either the eigenvalue associated with $1 or
the eigenvalue associated with $2. In short, w is a
superposition--with all the properties we discussed above.
But the same equation could also be used to repre—
sent a state called a mixture. The characteristics of
this state can be expressed differently depending on the
experimental context, but the meaning is the same. (a)
To say of a single system that it is in a mixture given
by our equation, means that the state of the system, w,
is definitely either W1 pr $2. The system is in one
state, and one state only. Our inability to say which

is only a matter of ignorance. And all this is true

-—-Aa.__<

99

whether or not a measurement is performed to ascertain

the state. If a measurement is performed, the probability
of finding the system in $1 is l and the probability of
finding the system in $2 is 0; or vice versa. (b) If we
have a single system re-prepared in the same state w many
times, then we can state the meaning of the mixture by
saying that the system is again definitely in either

state $1 or state $2, and has the corresponding eigen—
value for the value of the observable (again, whether or
not a measurement is performed); but now we can say further:
after some preparations the system will be in $1 and after
some preparations the system will be in $2. This is just
an ensemble of many systems in time. Sometimes the state
is wl’ sometimes $2. (c) There is a third way of thinking
of a mixture. If we have many identical systems, identi—
cally prepared, and present at the same time, then we have
an ensemble of many systems in space. Now, each separate
system is definitely either in $1 or $2; a given fraction
are in $1 and a given fraction are in $2. The important
thing to notice--and this is what is common to all three
situations——is that when we have a mixture there is not
the same "indeterminate" character of the state, as with

a superposition. The state is definite and fixed; but
more importantly the values of all observables are also l
definite and fixed. And most importantly, there are not
the "interference effects" in a mixture that we find with

a pure state.

100

Now, according to a widespread interpretation (which
dates back to Von Neumann)[55] there are two ways in which
the quantum state of a system can change (using the

notation of statistical density operators to represent

the state):
(1) w + w' = 2<¢n,W¢n)Pn
n
1 i
— gHt gHt
(2) W + W = e We

t

The second case is just the continuous time evolution as
prescribed by the Schroedinger equation. The first case
is the discontinuous abrupt change brought about by the
performance of a measurement on the system. Clearly
process (1) results in a mixture. Thus, if we have a
system initially in a superposition and perform a measure-
ment on the system, we will end up with our system in a
mixture, Viz, W'; the system will be in one of the distinct
states on. In other words, the measurement "forces" the
system from the state in which it is a superposition of
the states on to one of the particular states oi. This

process has been called the reduction of the wave function

 

(or reduction of the wave packet, referring to the Special
case of a particle), since the wave (state) function of
the system is "reduced" from a superposition of states to

a single state.

101

The reader will notice that this process is of great
importance for our inquiry: quite Simply, we have found
the subjectivism to accompany the superposition, and we
found the subjectivism to be absent in the mixture. And
so if reduction of the state function always results in
the transition of a superposition to a mixture, then per-
.haps this is just the process by which the subjectivism
is removed or eliminated. In short, the answer to the
question "exactly hay is the subjectivism eliminated?"
might be found by examining the reduction of the state

function. Then one could claim that the subjectivism is

always removed because superpositions (which are the source

of the subjectivism to begin with) are invariably reduced
to mixtures. And since any event or phenomenon of a
macroscopic nature (subject to the indicated restrictions
regarding macroscopically distinguishable final states)
will have involved interactions (with the microscopic
system) amounting to measurements, we could finally claim
that though there is the subjectivism on the microscopic
level, this subjectivism is systematically excluded from
the realm of macroscopic phenomena--and the mechanism of
exclusion is just the reduction of the state function.
Hence a lot of effort has been exPended by the
iPeople in this group, trying to understand the reduction
Of the wave function, how it comes about; does it really

accomplish what we wish, or if there are other ways to

102

accomplish the same end? Before we look at some of those
attempts let us discuss in general terms, the basic idea
of a reduction of the state function. For though there
does indeed seem to be a connection between the reduction
and the removal of subjectivism; and (on the given inter—
pretation of measurement) though the necessity of such a
reduction seems to be clear, we will see that the very
idea of a reduction is not without its inherent diffi—

culties—-some of which appear to be insuperable.

Difficulties Associated with Reduction of Wave

 

Function.-—Arthur Komar [35] has shown that the following

three assumptions are inconsistent:

(a) The initial state of the apparatus can be repre-
sented by means of some well-defined wave
function III;j>

(b) When the apparatus interacts via the Schroedinger
equation with the system I, assumed to be
initially in the state II;i>, it "grinds" or
"forces" the system into an eigenstate of the
operator N,II;n(i,j)>, where the eigenvalue
n(i,j) is some unique function of the arbitrarily
chosen initial states of the system and the

apparatus, i and j, respectively.

v

(c The apparatus should be a measuring device for

the quantity N in the sense that if the system I

Nah-....I- _. 1

103

is initially in an eigenstate of N then, inde-
pendent of the initial state of the apparatus,
the apparatus will leave the state of the system

unaltered.

In conformity with assumption (a) Komar assumes that the
initial uncorrelated state of the combined system of the
object being measured and measuring apparatus can be repre—

sented by the state vector
|I+II;i,j> E |I;i> III;j> (8)

where II;i> and III;j> represent the initial states of the
system and apparatus respectively. The systems I and II
are now brought into interaction and due to this inter-

action the combined system evolves to a final state
II+II;f> = SII+II;i,j> (9)

where the only property of the Schroedinger equation we
require is that it is linear.

If we are considering an apparatus which is to
measure the property N of system I it will be convenient
to expand |I+II;f> in terms of a complete set of eigen—
states II;n> of the operator N. Thus

|I+II;f> = z |I+II;n,k> <I+II;n,kIS[I+II;i,j> (10)
n,

himng . _

104
where
|I+II;n,k> E II;n> lII;n,k> (11)

The states of the apparatus lII;n,k> are denoted by two
letters to indicate that there are many states of the
apparatus which correspond to a given reading of the
instrument.

From assumption (b), which is the hypothesis of the
reduction of the wave function, we conclude that there

exists a unigue n(i,j) such that, for some k
<I+II;n(i,j),kIS|I+II;i,j> s o (12)
and for all k
<I+II;n',k|SII+II;i,j> = 0 n' ¢ n(i,j) (13)

Assumption (c), the statement that system II is a measuring

device, requires that for each j there is some k such that
<I+II;n,k|SII+II;n,j> s o (14)
and that for all j and k
<I+II;n',k|s|I+II;n,j> = 0 n' s n (15)

Let us now consider the particular initial state of

system I:

lI;i> = dII;nl> + BII;n2> d,B expansion coefficients

105

where dB(n2 — n1) # 0 and II;nl> and II;n2> are under-
stood to be eigenstates of the operator N which apparatus
II is purportedly measuring. From eq. (8) we can con-

clude that for all n

<I+II;n,k|s|I+II;i,j> = d<I+II;n,k|S|I+II;nl,j>

(17)
+ B<I+II;n,k|s|I+II;n2,j>

If we set n equal to I11 in eq. (17) we have as a conse—

quence of eqs. (14) and (15) that for some k

<I+II;nl,k|S|I+II;i,j> = d<I+II;nl,k[SII+II;nl,j> a 0 (18)

Thus, from eqs. (12) and (13) we must conclude that for

this particular choice of i and j
n(i,j) = nl

However, if in eq. (17) we set n = n2, we get, for the

same choice of i and j,
n(i,j) = n2

We have thus contradicted assumption (b), viz, the unique-
ness of n(i,j). Hence we have shown that assumptions (a),
(b), and (c) are mutually contradictory.

Assumption (a) is just the position that physical
systems--including macroscopic systems—-are correctly

represented by wave functions. Assumption (0) is just a

106

statement of the essential property a system must have if
it is to be adequate for performing measurements in QT.
Yet, if we accept (a) and (c) we find we cannot also
accept (b). Assumption (b) is just a statement of the
intuitive idea that if we could follow in detail the
quantum mechanical interaction between the system being
measured and the measuring device, we would understand
the precise result of the experiment. Alternatively, (b)
is just the hypothesis of the reduction of the wave
function. We have seen that we cannot accept (b) [assum-
ing we accept (a) and (c)]. Thus it would appear that if
reduction of the wave function is understood in terms of
assumption (b), then the idea of a reduction of the wave
function cannot be fitted into the formal structure of QT.
And this conclusion is purely general, dependent in no
way on the particular mechanism assumed for the reduction.
Whereas Komar has shown formally that the reduction
of the wave function cannot be explained within the frame—
work of conventional QT, Peres and Rosen [46] argue that
as a matter of fact it is not even necessary to consider
such a reduction. Peres and Rosen follow Von Neumann in
allowing that interactions can be constructed such that,
if the initial state of the object system S is o = ch¢n,
and if the initial state of the instrument is To, then
the Schroedinger equation for the compound system leads

to

107

icn¢nwo ———+ icndnwn (l)

where the Tn are orthogonal to each other. The process
(1) is called by Von Neumann a "measurement"; but this
definition agrees with the usual meaning of the word
"measurement" only if the states Tn are macroscopically
distinguishable (e.g., different positions of a pointer
on a scale). It is the second expression in eq. (1) that
has caused all the trouble in this aspect of our inter—
pretation of QT. It is valuable to ask ourselves why this
is so. Put simply chonTn is very disturbing. Why is it
n

disturbing? Well, it is not always disturbing, it is

only so in case: (1) the expression ch¢nTn represents

a superposition; and (2) the Tn repregent macroscopic
states, which furthermore, are macroscopically distin—
guishable. And this is disturbing because now we
apparently have a state in which, for instance, our
pointer occupies no one of the positions on the scale
corresponding to paa of the states Tn. Rather the pointer
is in a superposition of the Tn. This is counter-
intuitive, paradoxical, and surely disturbing.

Before we consider ways out of the cul-de-sac, let
us, for just a moment, remove the restriction of the
instrument as being a macroscopic device. Let the instru-
ment be microscopic. Now let us ask what is it about QT

that inclines us to think of chonTn as a superposition
n

108

and not as a mixture? (We again assume that the initial
state of the system is a superposition.) The answer is
the Schroedinger equation and Eugene Wigner. In the proof
referred to earlier, Wigner has shown that the time—evolved
state from a pure state must also be a pure state and not
a mixture. Hence if we begin with a superposition and the
process is describable by the Schroedinger equation, then
we must end up with a pure state also. Therefore our
expectation that chdnTn is a superposition has nothing

to do with the magroscopic nature of the instrument. Let
us then, again confine our attention to those cases in
which the instrument la macroscopic. We will also assume
that condition (2) above (i.e., the conditions for being
disturbing to our sensibilities) is satisfied, viz, that
the Tn are macroscopically distinguishable. It would thus
appear that the only path remaining open to us is to deny
condition (1), i.e., to deny that choan is in fact a
superposition. This is what Peresnand Rosen do.

Peres and Rosen argue that the formalism of QT cannot
speak for itself; it must be interpreted. An uninterpreted
calculus is of no value to us, we must have rules of
correspondence also. The appearance of ch¢nTn does not,
by itself, tell us whether it representsna superposition
or a mixture. Something else, besides the pure formalism,

must be brought to bear. Peres and Rosen argue as follows:

109

. . . in orthodox QT we are compelled to interpret

¢ = 2cn¢n as a superposition of states, and not as a
mixture, because interference effects between the
various components ¢n can be demonstrated experi—
mentally. We now intend to Show that if we are deal—
ing with macroscopically distinguishable states Tn of
a particle of sufficiently large mass, it is ex eri-
mentally impossible to get them to interfere With one
another. It follows that, in this case, we are not
compelled to interpret the right-hand side of (l)
[chonwn] as a superposition and can therefore inter-
pret it as a mixture while maintaining agreement with
experiment.

Peres and Rosen consider a mental experiment in
which they have a macroscopic body of size a, density p and
mass m ~ pa3, passing through a screen in which there are
two slits a distance b apart (b > a) and impinging on
another screen, a distance L away. If this experiment is

repeated many times interference fringes will be expected

on the second screen, a distance d s %% apart, where
l = g is the de Broglie wavelength. Thus L z 2% > 3&9
. mv .
and Since p = 2 : mv it follows that the dur—
(1 —V—>1/2
2
L mad 4d
ation of each experiment is T = G > —h— ~ 2%T_° Now we

assume that T < 108 years (estimated total lifetime of
the universe). Also, in order to have observable fringes,
d cannot be smaller than 10_8 cm, the interatomic dis-
tance in solid bodies. We then obtain, with Q ~ 1 35%
(this is a universal constant: a few nucleons per 23bic

Bohr orbit),

a < 1 cm , m < 1 gm (2)

110

Macroscopic objects which do not satisfy eq. (2) cannot
display interference effects in our experiment. Or
alternatively, for any bodies larger or heavier than this,
the time required for the experiment would be greater than
the total lifetime of the universe!

However, to complete the proof if must be shown
that the same holds for a macroscopic system coupled to
a microscopic one. To do this Peres and Rosen Show that
the process represented by eq. (1), which was obtained
from the Schroedinger equation, is irreversible. They
argue that in order to reverse the arrow in eq. (1) in
such a way that the left-hand side will again be inter-
pretable as a superposition, we need a mechanism which
brings back the macroscopic body from its possible final

positions with the correct phase. This implies, in the

 

WKB approximation, that we need an accurate control of
the phase factor exp(ifpdq/h) for the whole process.
This means that roughly we must have pdq < h where p is
the mean momentum of the macroscopic body and dq is the
uncertainty in its papal path q (i.e., the limit of re-
producibility of the experimental setup).

Again the total duration of the experiment will be
T ~ %? > E9389. For a macroscopic setup we cannot achieve

8 cm (the interatomic dis-

anything better than dq ~ 10—
tance) and we obtain, with, e.g., m = 1 gm and q = 1 cm,
that the experiment must again last longer than the total

lifetime of the universe.

111

I would like to note, in passing, that logically
there was one more alternative open to Peres and Rosen:
instead of denying either: (1) that the state is a super-
position, or (2) that the Tn are macroscopically distin-
guishable, Peres and Rosen might simply reply that there
is nothing strange or disturbing at all about the initial
analysis of the situation. That is, instead of denying
either half of the paradox, they could simply say that the
conclusion of the supposed paradox actually is not para—
doxical at all. Logically speaking, this is just as much
a viable alternative as either of the others.

It is not surprising that this alternative (of simply
saying there is nothing paradoxical about having a super—
position of macroscopically distinguishable states) has
not been one of the most frequently chosen. For the very
thing that makes this situation disturbing (to most) is
also what makes it exceedingly difficult to understand in
what conceivable way this situation could be construed
such that it is no longer disturbing. I would think that
the proposal of Everett, ap_al. considered above would
qualify as alternatives of this kind. This kind of pro-
posal seems akin to the "resolution" given by Carl Hempel
to the paradoxes of confirmation in which he does not
"disprove" either half of the paradox; rather he "shows"
why the "paradox" should actually app sound paradoxical
at all. Of the two, the "resolution" of Hempel seems much

the more reasonable to me.

112

Particular Alternatives.--Let us recall that all the

 

solutions proposed in this section are such that: (l) we
accept the subjectivism on the microscopic level, and (2)
we reject the subjectivism on the macroscopic level. The
adherents of this position claim that though the subjectiv—
ism is undeniably present in the microscopic realm, it
"somehow" gets eliminated as we "move up to" the macro—
scopic level. To help us distinguish the possible alter-
natives (and the proposals actually made), let us separate
the solutions according to what extent the subjectivism

can be restricted to just the original object system, and
to what extent the (physical) "surroundings" are also in—
volved with this subjectivism. A crude way of stating this
is to say we will separate the solutions according to yhara
the reduction of the wave function takes place (i.e., how
far from the original system does the reduction take place).

1. Indivisibility of the quantum. For all the

 

following proposals, we will always assume the situation
of interest is that of an atomic system (object) initially
in a state of superposition, and then interacting with
another system (apparatus) for the sake of making a
measurement. And we recall that we associate the sub—
jectivism with the presence of the superposition. Now,
this first proposal claims that the subjectivism gets no
farther than the first interaction, i.e., that the super—

position is reduced right at the first interaction. The

113

argument here is that in any interaction whatever--
whether or not it is a measurement--there is always the
exchange of a single quantum between the two systems, e.g.,
a quantum of energy, a quantum of angular momentum, etc.
And this proposal accepts as a basic postulate the indi-
visibility of the quantum, where that is here interpreted
to mean that a given quantum is always associated with a
given value for the quantity of the property exchanged.

A quantum cannot be associated with several different
values for the observable. Hence, a quantum is "whole"
and cannot be "divided" among different values.

Now consider the case when one of the interacting
systems is in a superposition. This is a state which has
associated with it several different values of the ob-
servable in question. (It is the desire to measure this
given observable that determines "what kind of" quantum
is exchanged.) But the exchanged quantum cannot likewise
be associated with several different values. Hence, upon
interaction, the exchanged quantum is associated with paly
gag of the states constituting the superposition. On
different repetitions of the interaction, the quantum
exchanged is associated with the value of the observable
corresponding to the different constituent states of the
superposition, with the respective probabilities of the
different values being given according to the usual rules.

A concrete example: we have an electron in a superposition

114

of spin up and spin down states. Now the quantum ex-
changed in any subsequent interaction with the electron
cannot be partially a quantum of angular momentum "up,"
and partially a quantum of angular momentum "down."
Hence, the actual exchanged quantum is a quantum associ-
ated either with spin up pp spin down.

It is seen that the "indivisibility of the quantum"
makes it impossible to retain the "indeterminate-ness"
of the initial state. It forces a decision to be made
between the constituent states of the superposition. Thus,
as regards any "physics" of the situation after this first
interaction, we are dealing with a mixture and no longer
with the initial superposition.

This account claims to accomplish two things: (a)
it allows us to accept the subjectivism on the micro level,
while at the same time allowing us to prevent its occur—
rence at the macro level, and (b) it appya us exactly what
mechanism accounts for this prevention, viz, the indi—
visibility of the quantum.

As far as I know, the only person who has ever
maintained a position of this sort is Niels Bohr [9,10].
Bohr's writings (on this and other aspects of the problem)
are very incisive and deserve, I feel, more attention than
they currently receive. But I also think there are cer-
tain difficulties and weaknesses with Bohr's solution.

Bohr's proposal has an initial attraction because we seem

115

to have learned something very basic and profound about
the way nature, on its elementary levels, can and cannot
interact with itself. But by the same token, to say this
much and no more really leaves the question unanswered.
For if we can find nothing more to say about the "indi-
visibility of the quantum" besides the fact that it is
there, then we have merely replaced one question with
another--without any substantial gain in the process. It
might be replied that if we can solve the subjectivism/
objectivism problem by appeal to the problem of the ex-
change of the quantum (which we would have regardless),
then we have made progress: we have reduced two problems
to one. But this does not seem to be the case. For the
problem of the exchange of the quantum is just the problem
of how systems interact. And it is precisely here, in the
nature of the interaction between systems, that we seek
the solution to the subjectivism/objectivism problem.
Hence, we have not solved one problem by reducing it to
another; we have merely replaced one formulation of the
problem with another formulation of the same problem.
However, the most serious objection to this proposal
seems to be the following: if it is correct then it is
never possible in an interaction to preserve a super—
position; the coherence among the component states of the
superposition is invariably destroyed. This would mean--

for either the second system in the interaction or for

116

the combined system--that the subsequent physical behavior
would be the same whether the first system was a super—
position or a mixture. And since we can only obtain in-
formation about a system from its effects on other systems
--through interactions--this proposal would apparently
make it impossible for us to ever detect the difference
between a superposition and a mixture. And this is
patently untrue.

In particular, this proposal seems to rule out any
interactions of the type
To chon = ch¢nTO ———» chonwn

n n n

This interaction is just a simple consequence of the
Schroedinger equation. Bohr (or a supporter) might reply
that it is alright that this proposal does conflict with
the Schroedinger equation in this way. For we have known
ever since Von Neumann that there are interactions which
do not obey the Schroedinger equation, viz, measurements.
So the conflict between our proposal and the Schroedinger
equation is neither new nor surprising, they might say.
But the difficulty with this reply is that the "indi-
visibility" proposal is not restricted to just measure—
ments; it applies to all interactions. And unless we
are given some criteria for distinguishing those inter-
actions which are measurements, our criticism of the

proposal must remain.

 

117

2. Jauch [30] claims that the measurement problem
is a pseudo-problem. He accepts the subjectivism on the
micro level. As to whether the subjectivism is also
present at the macro level, his answer is a unique one.
But he claims to have shown the problem to be a pseudo-
problem because he can, with just a straightforward appli-
cation of his formalism, reconcile, on the one hand, the
invariable appearance of a mixture upon measurement, with
the theoretical prediction (according to the equations of
motion) of a pure state, on the other hand.

Jauch considers the traditional View that the state

of a system can change in two radically different ways:

W + W'

z<¢n,w¢n>Pn (1)
n

i i
- —Ht -Ht
W+W =U(t) WU+(t) =e h Web (2)

where W represents a density operator for the state in

question; Pn is just a projector onto the state ¢n. The

first process represents the change that comes about as a

result of a measurement on the system, always resulting

in a mixture. The second process is the change wrought

Simply by the unmolested time evolution of the system;

this change obviously satisfying the Schroeding equation.
Jauch wishes to consider the observation of a

quantum mechanical system S by a measuring device M = m + A.

The measuring device can be decomposed, for the purpose of

118

analysis, into a microsc0pic part m in which all the
specifically quantum mechanical effects take place, and
into a second part A, which merely serves to provide

amplification of the quantal effects in m to the level of

 

macrosc0pic events so that they might be observed by an
experimenter. Then the problem of measurement reduces
to the following: if we apply the equations of motion
(i.e., eq. 2) to the combined system of object (S) and
measuring device, we expect a pure state; but if a measure-
ment has truly been performed we expect (from eq. 1) a
mixture. How can these both be?

Jauch says there are two cases to consider: (1) we
apply the equations of motion to the combined system of
S + m; (2) the combined system is S + M. To understand
the treatment of the union of two quantum mechanical
systems Jauch appeals to work done essentially by Von
Neumann [55]. Let the density operator for the object
system S be WI; for the measuring device WII. Each of
these operators is given in the respective Hilbert space
of the two systems. Finally, let W be the density operator
of the combined syStem; this operator is given in the
space which is the tensor product space of the two com—
ponent spaces.

Jauch shows that if both WI and WII represent pure
states, then W will also represent a pure state. But the

reverse question is, of course, the one of interest, viz,

119

if W represents a pure state, what can we say about WI

II?

and W Jauch shows that the necessary and sufficient

condition for WI

and WII to be pure states, given that W
is a pure state, is that T = ¢ 8 u, where ¢ is the state
vector in the combined space, and o and w are the state
vectors respectively in the component spaces I and II.
In general, if W is pure, WI and WII will be mixtures.
Let us consider first the combined system S + m
and thus apply the theory to the object system S and the
microscopic part m of the apparatus. Let @io E ¢i 8 $0
where we have assumed system I to have a two-dimensional
state vector space; also ¢+ and ¢_ are two orthogonal
vectors in this Space and are eigenstates of the quantity
to be measured. If the states above represent pure
initial state vectors before I and II interact, then the

joint system is also in a pure state after the interaction

and given by

The state vectors of system 11 define a three-dimensional
space. It contains a state wo Which describes a "state
of readiness" of the measuring device and two more states,
denoted by 0+ and w_. Here w+ is the final state of
system II after it has measured system I in the initial

state ¢+; likewise w_ is associated with state ¢_.

120

We now consider the general initial state of the

form

<I>=OL<I> +0L<I> (14)

where d+ are two arbitrary constants subject to the normal-

. I C U 2 O C .
ization condition Ia + la I = 1. Since U is a linear

+

Operator, we must have for the final state after the

measurement in this case

0 = U00 = d+¢+ O ¢+ + d_¢_ 8 w_

This is the state of system I+II after the measurement.
It is pure, as it must be since the initial state was pure.
But Jauch now asks why does this state furnish us
with a measurement of the alternatives ¢+,¢_? The reason
is that, when reduced to the measuring system II, the
state is a mixture, therefore each individual system
realizes one of the events of the mixture and these events
can, by virtue of the amplifying device A, be made data

for an observer. That is, even though the combined system

 

is in a pure state (W is pure), we do not "consult" the
combined system (for our information); rather we consult
one of the component systems, m (through the intervention
of A, of course), and this component system is in a mix—
ture. Thus, it is the mixture that is presented to us.

Hence, the relevant part of the state 6 for us is its

121

reduction to the system II. Jauch has rules for Obtaining

the reduced density operator, and he Obtains

w = (a [2 |2 P (15)

+ P+ + I“—

2 2

Q+ + |d_| Q (16)

WII = Id_|
where he introduces the projection operators Pi'Q: with
one-dimensional ranges containing Oi,wi reSpectively.

Thus Jauch concludes: "This result shows clearly
the reason for the occurrence of process (1) under the
influence of a measurement. It is here merely a mathe-
matical consequence of the reduction of a pure state (14)
to one of its component subspaces." Hence, Jauch seems
to have reconciled the prediction of a pure state with
the appearance of a mixture—~and all this without appeal
to any specific "measurement" process; everything here
is obedient to the Schroedinger equation.

But suppose we apply the theory to the combined
system S + M. Now, we have combined the measuring device
M with the system S to form a larger (classical), system
S + M which is now simultaneously a system and a measuring
device. In this case there is no question Of reducing
the state (14) to one of the component systems. There is
therefore no possibility of changing the state into a
statistical mixture in this manner. Yet, we believe that
considered as a measuring device, S + M will record a

mixture.

122

Jauch introduces the projection operators H+ = P+ O Q+
and H_ = P_ O Q_. QT, in accordance with process (2), tells
us that the final state of S + M considered as the system
is the pure state (14). However, process (1) applied to
S + M considered as the measuring device tells us that this
final state Should be W = Id+I2H+ + |d_I2H_. Now what do

we make of these two separate states? Jauch claims that

these two states are in the same equivalence class. By

 

that Jauch means that two states W1 and W2

with respect to a given set of observables P if

are equivalent

TrAW = TrAW

l 2 for all ASP

Thus physically, this means that the two states W1 and W2
cannot be distinguished by any measurement whatsoever with
observables from the set F.

Jauch's claim is thus to the effect that the pure
state (14) and the mixture (17) are equivalent states, and
thus cannot be distinguished by any measurement from the
same set of observables that contain the projectors H+
and H_. Hence in case we have 8 + M as the combined system
there never is a reduction of any kind--not of the com-
bined state vector (which is pure), nor of the density
operator to a component subSpace. But one might now be
inclined to ask: granted that the two states "look alike"

as far as measurements are concerned, which state do we

really have present? If Jauch wishes to preserve his

123

solution Of the first case (i.e., S + m) and again avoid
appeal to process (1) then he must surely opt for state
(14). And this he does: Jauch writes:

A final question: does this result mean that the two
states (14) and (17) can under all circumstances, never
be distinguished by a measurement? It does not mean
this. It means, this can never be accomplished with
measurement from the Abelian set P which contains the
two projections H+ and H_. In order to distinguish
them it is necessary to have at one's disposal an
observable which is not in this set. An observation
of such a quantity will no doubt reveal that it la
indeed (14) which is the final state after the inter-
action, in agreement with the Schroedinger equatiOn.

[Italics added.]
It is crucial, in Jauch's argument, that we take

into account the classical nature of the measuring device

 

S + M. For this classical nature assures us that the set
of observables of the system forms an Abelian set. And it
is this which enables us to place the states of the system
into equivalence classes. Thus, a classical (i.e., macro-
scopic) device is definitely necessary for this analysis.
It would thus appear that Jauch has shown that even grant-
ing the subjectivism on the micro level, the special
characteristics of systems on the macro level make it
impossible for the subjectivism to be present there--and
this was shown by a straightforward application of Jauch's
formalism. But this conclusion would be mistaken. First,
it will be noticed that we can always perform the quantum
analysis on the system S + m. In that case, the "measure—
ment," the "reduction," the elimination of the subjectivism

takes place purely with reference to m, which is by

 

124

definition the micrOSCOpic part of the apparatus. The
amplification by A, bringing to bear the macroscopic part
of the apparatus, might not take place for some time after
the original interaction between S and m (as has been
pointed out by Jauch himself). Hence, the elimination of
the subjectivism has occurred much earlier than the macro-
scopic part of the apparatus ever enters the picture.
'Furthermore, Jauch himself says that the true state
of the system (when we use S + M) is the pure state (14).
This certainly means that Jauch would expect—-even on the
macroscopic level--the manifestation of a pure state, and

hence, the presence of the subjectivism if we could find

 

a suitable observable. It is Jauch's position that there

 

is indeed subjectivism on the macro level, but as a matter

 

of fact, we cannot detect it as long as we measure obser-
vables in the same set with the projections H+ and H_.
Unfortunately, Jauch gives us no hint at all of what kind
of observable is required to break the equivalence be—
tween the two states (14) and (17). In other words, we
actually do have subjectivism on the macro level, but for
all practical purposes, it never shows its face.

Jauch has given us an account which completely
avoids process (1) and obeys the Schroedinger equation.
It would thus seem that the measurement problem has been
solved. But I do not think this is the case. For in—

stance, the reader will notice that (with system S + m)

125

after the interaction not only is m in a mixture, but so
is S (and we recall that S was initially in a pure state).

So looking at Jauch's analysis physically we have a system

 

S in a pure state, then after interaction with m, it is
in a mixture. It is true that this can be accounted for
with Jauch's formalism, but actually all that Jauch has
given us is a new mathematical formalism to account for

the same physical process as was accounted for under the

 

usual interpretation of QT, viz, upon interaction a system
in a pure state is "forced" into a mixture. There is in-
deed value in the new formalism, but it has added no more
to our physical understanding than we already had. In
particular, this formalism has contributed one thing of
great importance. It shows that the reduction from the
pure state to the mixture (thought of in the usual sense)

is not dependent upon interaction with a macroscopic

 

system. This reduction occurs even when the second system
is microscopic. The reader will notice the similarity
here to the previous proposal of the "indivisibility of
the quantum." And to the extent that Jauch's proposal is
similar, it is subject to the same comments as above.
Another attempt at accounting for the removal of

subjectivism by appeal to the specifically macroscopic

 

nature of the apparatus is that due to D. I. Blokhintsev
[5]. Blokhintsev wishes to measure the linear momentum

of a micro particle by letting it collide with a sphere

126

of macroscopic proportions. The Sphere is resting at the

top of an inverted potential well as Shown below.

y um)

 

If
C)

 

Figure l

The well is narrow enough so that a slight "push" in
either direction will tumble the sphere from the well.
The well is high enough so that we get an irreversible
reaction, i.e., once the Sphere has fallen from the tOp
of the well, it can never get back to the tOp.
Blokhintsev's procedure is then the following: he
writes a wave function for the particle as a superposition
of plane waves of plus and minus momenta. He writes a
wave function for the sphere as a Gaussian wave distri—1
bution centered about the potential. He then writes a
combined wave function for the compound system. Blokhint-
sev then assumes a Simple coupling between the two systems
representing the energy of interaction. He then writes a
Hamiltonian for the total system, puts this into the
time-dependent Schroedinger equation and seeks a solution
for the wave function of the compound system after the

interaction. To find the wave functions Blokhintsev uses

127

first-order perturbation theory. Once he obtains these
wave functions he uses them to form the density matrix
for the compound system. This matrix has numerous terms;
in particular, most of them are cross-terms representing
interference states.

But at this point Blokhintsev takes the crucial step
for his solution: he takes the asymptotic solution of the
density matrix at t+00 and when the sphere is far away from
the center of the potential well. With this, all terms
drop out of the expression for the density matrix but two:
that term which gives a probability of 1 that the sphere
will be found to the left of the well (when the coordinate
of the sphere Q+-W); and that term which gives a proba-
bility of 1 that the sphere will be found to the right of
the well (when the coordinate of the sphere Q++w). Hence
by a simple application of the laws of QT, Blokhintsev
has shown how we can go from an initial state of super-
position (for the combined system) to a mixture. And
this was done by invoking the macroscopic nature of the
measuring instrument. For it is the macroscopic nature
of this particular apparatus that results in the irre—
versible reaction, and thus justifies the use of the
asymptotic solutions.

What Blokhintsev has done I believe to be valuable,
but its chief weakness I feel, is its lack of generality.

It is certainly a "contrived" situation we have with the

128

sphere perched precariously on top of the potential well.
But it is true, of course, that we do wish our measuring
devices to be in metastable states before a measurement.
However, this example seems quite limited in its appli-
cability and it seems to have none of the "general"
characteristics of more general kinds of measurement
situations. Furthermore, this approach is subject to
the same objections as are all those which place the
"reduction" in the macrOSCOpic behavior of the measuring
device. That is, the macroscopic part of the apparatus
might not be utilized for some time after the original
interaction between the object system and the apparatus;
and we do not expect that the pure state persists through—
out this indefinite time. For instance, we certainly feel
that a photographic plate will perform a measurement--and
hence a reduction--of the result of a single photon
through a double Slit experiment. Yet, the arrival of
the photon could very likely be recorded by a single
silver halide complex. And it might be days before the
film is developed. But surely the measurement has been
performed as soon as the photon strikes the plate; and
we believe that the superposition does not persist for
the weeks or months until the (macroscopic) process of
developing occurs.

3. In the solution of Daneri, Loinger, and

Prosperi [16,17], the measuring apparatus is schematized

129

as a macroscopic system which possesses, besides the
energy, at least one other macroscopic constant of the
motion. The value of this constant characterizes an in-
variant manifold ("channel"). In each manifold certain
ergodicity conditions hold and there exists an equilibrium
macro-state towards which the system evolves spontaneously.
The apparatus is assumed to be initially in the equilibrium
state belonging to a given channel and the interaction with
the observed system determines a transition of the appa-
ratus towards a state belonging to another channel, which
depends on the initial state of the observed system. Then
the apparatus evolves towards a new equilibrium state.
Following the notation of Daneri, Loinger, and

Prosperi and using statistical operators, we have:

case 1: W = PI PII before measurement
0 [¢k] [9 1 interaction
O
W' = P right after inter-
[¢k®k] action
wt = U(t) P U+(t) after long time
l¢k¢k1
I II
case 2: WO = P P before measurement
[¢k] [9 1 interaction
0
W' = PI right after inter-
[¢k9k] action
Wt = PI PII Nk after long time

[U(t)¢k] ckek

130

I II

case 3: WO = P P before measurement
[:Cr¢r] [do] interaction
W' = P right after inter—
[ZCr¢r¢r] action
r
Wt = ZICrI2 PI PII Nr after long time
r [U(t)¢r] Crer

W represents a statistical operator. P[ 1 denotes the
projection Operator onto the manifold [ ], i.e., P[¢]
denotes the statistical Operator P representing a pure
ensemble of systems each in the same quantum mechanical
state represented by the Hilbert space vector w. Nk is
just a normalization factor. U(t) is the time evolution
operator exp(-%Ht).

The three cases are distinguished as follows: in
case 1 (initially) the object (system I) is in the state
ok; the apparatus (system II) is in the state To. Each
system is represented by a Hilbert space vector in its
respective space. Right after the interaction the com-
posite system is represented by a vector in the product
space. After a long time the interaction has ceased, the
two systems evolve independently, but yet remain corre-
lated such that we can still represent the state of the
combined system by a projection in the composite (tensor

product) space of the two systems. In this case system II

is considered to be a non-macroscopic system.

131

In case 2 everything is the same except now system
II is a macrOSCOpic device. Now, according to Daneri,
Loinger, and Prosperi, the time evolution of the macro-
scopic apparatus is known: this is just the ergodic be-
havior of the macroscopic apparatus. Thus a sufficiently
long time after the interaction, the two systems will have
evolved independently, and the apparatus will be in the
equilibrium cell of channel k (where this channel is
determined by the initial state of the object).

In case 3, the apparatus is again macroscopic, but
now the object is in a superposition of different states
¢r. Right after the interaction the projection is onto
a manifold determined by a superposition of vectors.
After a long time, the apparatus is in a plaaa_equilibrium
state; the object is in the corresponding time-evolved
state; and all this with statistical weight ICrIZ.

System I is, in all three cases, microscopic.

Daneri, Loinger, and Prosperi explicitly write down
only the equations for case 3. The equations for case 2
are implicit in their writings. They do not consider
case 1 at all. It is valuable to consider case 1 because
it highlights the fact that for Daneri, Loinger, and

PrOSperi, "measurement" is a macrOSCOpic phenomenon; and

 

if we restrict system II to being a microscopic system,
"measurement" will never result. The reason for this

is clear: it is only in virtue of the fact that we have

 

 

132

macroscopic devices that we can appeal to the ergodic

 

evolution for the removal of the interference terms present
in W' of case 3. The ergodic development of system II is
dependent upon the fact that it is macrOSCOpic. Hence, a
microscopic device would not be subject to the ergodic
develOpment, and thus would not result in the destruction
of the interference as required.

Unfortunately, the program of Daneri, Loinger, and
Prosperi does not accomplish all that it claims. Note, in

case 3, that the transition from W' to W is not given by

t
the continuous time evolution equation for density (sta-

tistical) operators, viz,

+
Wt = U(t) WO U (t)

Rather, W is simply written down to correspond to what

t
"we know" we will obtain upon a measurement. This in
itself is not surprising, for the recognition of two
distinct modes of change of state (as represented by the
density operator) goes back to Von Neumann in 1935. But
what is objectionable--or rather, regrettable—-about
Daneri, Loinger, and PrOSperi, is that they give us no
more understanding of the connection between the two than
did Von Neumann. It is precisely the transition from W'
to Wt that we wish to understand. And this is precisely

what Daneri, Loinger, and Prosperi cannot tell us. As

pointed out by Bub [12], the ergodic theory of Daneri,

133

Loinger, and Prosperi gives us the develOpment of the
macroscopic apparatus only in that case when the apparatus
is initially in a given channel. Their theory has no
mechanisms by which we can understand the development
of the apparatus if it initially is in a superposition
of different channels. It is only after the apparatus
can be assigned to a single particular channel that the
ergodic theory is applicable. But at this point the
troublesome aspect of the whole measurement problem has
been "passed." How to account for the fact that we go
from a superposition of states to one particular state
is precisely the measurement problem. Daneri, Loinger,
and Prosperi have shed no new light on this question.
Why is the Daneri, Loinger, and Prosperi theory

unsuccessful in this? Daneri, Loinger, and PrOSperi have

shown that
S
' kv S
- 2 kv
M Elm .,U(t)§2 .)| :__25
i=1 kvi kuj sk vek
Skv
*
IM i:1(akvi . U(t)Qkuj) (kai , U<t>Qkufi) I <<
S
£<<6 :0 (ua‘u')

Sk vek

134

Here, M is just the operation of time averaging, Q are

kvi
the eigenvectors characteristic of a given channel and
given cells, 5k is the number of dimensions of the kth
channel and Skv the number of dimensions of the vth cell.
Thus they can argue that if the initial state of the appa-

ratus is given by

2
v (o) = z w .n . where z |w .| = 1
k . k k . k
“3 u: u: u] u]
then the norm of the projection of Tk(t) = U(t)Tk(o) onto
the cell Ck (time—averaged) is just e 6 . That is,
v vek

after sufficiently long time state vector of apparatus is

(approximately) certainly in Cke .
k
On the other hand, if the initial state of the appa-

 

ratus is a superposition from different channels, we have

2
T(o) = z w .n . |
. k k

kn] u: u:

z.|w . = 1
. k
kuj uJ

Now, the norm of the projection of T(t) = U(t)T(o) onto

cell C (time-averaged) is z p ,6 , where
k vek.

I2. Note that pk, # l, but 2

k'v

pk' = 2IIW
uj . .
Following the notation of Daneri, Loinger, and Prosperi,

kuuj k' pk' = l.

skv
we let ukv(t) = Z [(9

, u(t)To)|2, then we have in the
i=1

kvi

first instance and the second instance respectively

135

M ukv(t) z (SVek (908)

M ukv (t) 2‘ pkévek (909)

The difficulty facing Daneri, Loinger, and Prosperi is a
satisfactory interpretation of eq. (9.9). Daneri, Loinger,
and Prosperi interpret ukv(t) as "the probability of find-

ing the system in the macrostate C at the time t." This

kv
appears uncontroversial. Indeed it seems to be just the
Born interpretation of probabilities. But this is not the

case! The Born interpretation identifies the norm of a

projection of vector

 

 

Skv 2 ‘where PC is a pro-
. _ jection operator onto
norm[PCk wk(t)] — ifl kai’wk(t) the manifold repre-
v — sented by C

-kv

with the "probability of being found in that state" only

on the condition that a measurement is performed, i.e.l

 

an interaction. And this condition cannot be satisfied in

 

the Daneri, Loinger, and Prosperi model. For the proba-
bility in question is supposed to be the probability of
the apparatus being found in a given macrostate. But
during this time no interaction of any kind takes place.
The interaction with the object has long since ceased,
and the apparatus is evolving as a free, closed system.

This interpretation of Daneri, Loinger, and PrOSperi

136

results from a licentious use of the Born interpretation.
In addition, in their interpretation of eq. (9.9) Daneri,
Loinger, and Prosperi say the equation shows that the
apparatus is in the macrostate Ck with probability pk.
This also is mistaken. What Daneri, Loinger, and Prosperi
showed was that the vector T(t) has non-zero projections
(viz, pk) on a given set of manifolds. But it does not
follow that the vector T(t) then has a probability pk to
be in the kth manifold.

These Objections have the effect of vitiating
Daneri, Loinger, and Prosperi's interpretation of eq.
(9.9). Thus Daneri, Loinger, and PrOSperi are left with—
out a satisfactory account of the transition from the
superposition to one of the states of the superposition.
Hence their account is of no value in accounting for the
removal Of the subjectivism which accompanies the super-
position. When the apparatus is in a given channel, their
account is both valuable and correct. But when the appa-
ratus is initially in a superposition of states from
different channels, then the theory of Daneri, Loinger,
and Prosperi does not help us to understand the evolution
of the system to one of the constituent states (of the
superposition). And hence the theory of Daneri, Loinger,
and Prosperi is of no help in solving the problem of
measurement, nor is it of any help in understanding the
"removal" of subjectivism by appeal to a macrOSCOpic

interaction.

137

The following diagram should help the reader to
visualize the objection to the theory of Daneri, Loinger,

and Prosperi.

 

 

 

interaction
DLP(???) DLP \j ___)_t
r]
t . . + . .t .
superPOSition one equilibrium
from channel cell of one
different channel
channels

Figure 2

The theory of Daneri, Loinger, and Prosperi is clearly
applicable after the apparatus is in one channel. But the
theory is not applicable before that point. Hence Daneri,
Loinger, and Prosperi can give no account of "how" the
apparatus gets to be in one channel.

(I might note in passing that it is clear that
Daneri, Loinger, and PrOSperi renounce the validity of
the Schroedinger equation in their pr0posal. For the
objection can be raised that if we start with a pure
state, eq. (9.9) and if its evolution is governed by the
Schroedinger equation, then Wigner's proof shows that we
must end up with a pure state, and not with a mixture as
do Daneri, Loinger, and Prosperi. Daneri, Loinger, and
Prosperi have attempted to answer this Objection, but, it

seems to me, in a very unsatisfactory manner.)

PART IV

CONCLUSION

I think it would be very valuable, as I begin this
concluding section, to state exactly what I wish to affirm
and what I wish to deny. This investigation has certainly
been a study of "physical reality." But I do not wish here
to deny or even question the reality of physical nature.
Rather, what I wish to question in this study are certain
aspects of physical nature. In particular, I wish to

question traditional beliefs about the independence of the

 

existence of individual physical systems; I wish to ask if
we can think of individual physical systems as having an

objective existence, in the sense that they exist and have

 

their prOperties independently of other physical systems.

But, it is just these aspects or features of physical

 

nature that I wish to question, not the reality of physi-
cal nature. Let me indicate two considerations that Show
not only that we gap, but also that we ppap, accept the
micro cosmos as raal.

First, a consideration directly from the principle

of superposition. We have seen that it is the existence

138

139

of superpositions that leads us to question the inde—
pendence of individual physical systems. But the limi-
tations placed upon physical nature by QT do not go so far
as to deny reality to the phenomena under question. I
mentioned, during the discussion of relativistic physics,
that though relativity theory eliminated some of the marks
of independence of a physical system, it by no means re-
moved them all: the relativization was a partial one, not
a complete one. I also stated that this is likewise the
case in QT: in QT we have a further relativization (of
the independence of physical systems), but again it is a
partial one.

In QT we find that for a system which is in a super-
position Of states we are no longer able to think of the
system as possessing all its prOperties completely inde-
pendently from other systems. We find that for a complete
Specification of a given property, reference must be made

to other physical systems. (By complete specification, I

 

mean being able to say not only that the system has the
given prOperty, but also that it has a definite yalpa for
that property. And of course, the glyap property is that
for which the component states of the superposition are

eigenstates.) Hence, the independent characterization of

 

a particular physical system is restricted to this extent.
But it is a simple tenet of QT that, for a given

system, even if it la_in a superposition with respect to

140

a specified observable, it can, at the same time, be in an

 

eigenstate with respect to another observable. For example,
if a given micro-particle is in a superposition of x-spin,
then it can be in an eigenstate of y-Spin. Hence, though
the first observable requires reference to another distinct
physical system for its complete specification, the second
observable suffers no such limitations. This second Obser-
vable can be identified and assigned a definite value by
appeal solely to our Object system. Thus, with reSpect to
phla observable we can still Speak of a system as possess-
‘lag a property, and of the prOperty being characteristic
of the system as opposed to being merely a relational
property between the system and something else.

Thus while papa of the prOperties of a physical
system must be considered subjective and relational, others

--at the same time--are just as Objective and independent

 

as ever. SO what we have is neither a complete or absolute
subjectivism nor a complete or absolute objectivism (i.e.,
absence of subjectivism). We do not have the claim that a
micro physical system--in every respect—-has a subjective,
relational, and "dependent" existence. Rather at any

given time, same of the properties of the system do not
have an independent existence. But this "lack Of inde-

pendence" does not permeate the system. There are other

 

properties, at the same time, that maintain their inde—

pendent status. And since it was this lack of independence

141

which prompted us to question the objective existence of
some of the prOperties, then the independence of the other
prOperties compels us to attribute to them an objective
existence--and thereby, an objective existence (i.e.,
reality) to the system as a whole which possesses these
independent properties.

We notice finally, that under different circum-
stances different observables will be the "independent"
ones. Thus, no one set of observables are forever rele-
gated to being "dependent." The roles of "independent"
and "dependent" can be interchanged at will. For instance,
if a given system is in an eigenstate of y-spin ("inde-
pendent" y-spin), it will be in a superposition of x-spin
("dependent" x-spin). But this situation can be completely
reversed simply by allowing the system to pass through a
Stern-Gerlach device which has its magnetic field oriented
in the x-direction. Then the system will be in an eigen-
state of x-Spin ("independent" x-spin) and in a super—
position of y-spin ("dependent" y-spin).

We also notice that there are some observables that
seem not to participate in this drama at all, and are
always found to be "independent." I am speaking of those
observables for which no superposition has ever been found,
e.g., electric charge. This is a clear violation of the
superposition principle, and understandably, this proves

to be a suspension of the primary conclusions of this

142

thesis. The reader will note that the existence of these
states which violate the superposition principle (i.e.,
those states associated with different values of electric
charge, states which fall under the so-called EEEEEI

selection rules) gives even stronger evidence of the

 

objective, independent existence of the physical system
itself, since we have here a property of the system that
is always independent.

The second consideration which leads us to attribute
a real existence to micro physical systems comes from rela-
tivistic QT. We have considered the results of classical
physics, relativistic physics, and quantum physics. We
have not, until now, mentioned relativistic quantum physics.
But it is essential to do so, primarily because non-
relativistic QT is basically a limited and incomplete
theory. This is due to the fact that non-relativistic QT
is incapable of accounting for the following fundamental
aspects of the physical universe: (1) The merger of space
and time into a single four-dimensional continuum effected
by the special theory of relativity as we have seen. (2)
The spatio-temporal pervasiveness Of the basic physical
quantities requiring a field—theoretic approach to physical
nature. (3) The discovery of the sub-universe of elemen-
tary particles including the unexpected variety of their
masses, life-spans, and their numerous quantal character-
istics such as spin and strangeness, in addition to their

susceptibility to creation and annihilation. In

143

contrast to non-relativistic QT, several contemporary
relativistic field theories are able to account, more or
less satisfactorily, for these three aspects of the physi-
cal world. In particular, these can be accounted for by
quantum electrodynamics, which is the only theory which

we shall consider.

First of all, the essential elements of QT are also
present in quantum electrodynamics. Thus, several field
quantities, e.g., the electric and magnetic field
strengths, are not measurable simultaneously because they
are represented, in the new theory, by non-commuting
hermitian Operators. But what can quantum electrodynamics
tell us about the reality of micro physical systems? What
quantum electrodynamics tells us is basically this: from

quantum electrodynamics we can stress the existential

 

import of the fact of the countabilipy of various types

 

of elementary particles possessing various momenta,
charges, spins, etc. This is a way of establishing the
existence of physical entities that was used by Poincare
in another context. Poincare argued that molecules are
real since the number of molecules in a particular region
can often be reliably determined:‘ he felt that it would
be impossible to count non-existent or unreal things.

If this type of argument is accepted, then we can apply
the same kind of reasoning in quantum electrodynamics to
Feynman's rules concerning the matrix elements related

to various processes at the quantum level.

144

We find that the physical reality of electrons,
positrons, and photons (these are the three types of
elementary particles and their interactions with electro-
magnetic fields that form the subject matter of quantum
electrodynamics), including the reality Of the momenta,
energies, and polarizations ascribable to them, can be
supported by an argument exactly duplicating Poincaré's
argument in favor of molecular reality. We can argue that
electrons, positrons, and photons possessing specifiable
momenta, energies, and polarizations must exist since they
can be counted. The possibility of determining the numbers
of any of these particles assumed to possess any Specifi-
able momentum, energy, and polarization properties is made
apparent by the well—established Feynman rules concerning
the matrix elements (i.e., the amplitudes Of transition
probabilities) for any process involving the three types
of micro systems and their associated fields. According
to Feynman, any matrix element of this type corresponding
to a particular system S of elementary particles and their
reSpective fields involves several physically significant
numbers: (1) The number of electron-lines external with
regard to S which imply a specified momentum and polari-
zation. (2) The number of external photon-lines with a
specified energy, polarization, and possibly with a
specified external electromagnetic field. Further, (3)

the number of internal lines of the three types of

145

particles involved in every matrix element, in addition
to (4) the number of closed electron lOOps with an even
number of electron-lines.

It is also true that from within quantum electro-
dynamics we could stress the existential import of the
empirically verifiable occupation numbers. And the other
facts and laws concerning elementary particles contribute
to the establishment of an Objective, independent, physi-
cal world in many other ways. But I think the point has
been made. It is simply a logical triviality that ele-
mentary particles could not be created or destroyed if
there were no elementary particles at all. It is equally
obvious that no classification of elementary particles
paaag on their rest mass, or Charge, or Spin, or strange-
ness or any other attribute could have been validly
established if there were no set of elementary particles
to classify. The growing list of discoveries concerning
elementary particles and presupposing their physical
reality is as impressive as any physical discovery ever
was.

Therefore (at the risk of being accused of beating a

dead horse), it is not the physical reality_of physical

 

systems that I wish to question here, but only the question

of the objective, independent existence of the properties

 

 

of those systems. Having just given a defense of the

reality Of physical systems, and before we attend to our

146

final conclusions, let me give——from a new direction--a
defense of the claim of the "lack of independence" Of the
prOperties of micro physical systems. This argument comes
from a consideration of the so-called uncertainty principle
(or alternatively, the indeterminacy principle). Dis—
cussion of this principle has perhaps been conspicuously
absent from our investigation, for this principle is
rightly considered as one of the central tenets of QT.

We will show that the indeterminacy principle involves

us in the same kind of severe limitations as does the
superposition principle when it comes to ascribing proper-
ties to microphysical systems.

We will consider what can be conveniently called the
"strong indeterminacy principle." This theorem was proved
a few years after the discovery of Heisenberg's classical
and less comprehensive indeterminacy principle [38]. The
theorem can be stated as follows: let a, b, c, d be four
real numbers satisfying the inequalities b > a and d > c.
Let P(a,b) be the property possessed by any system S such
that S is within a sphere of radius b but outside a con-
centric Sphere Of radius a. Similarly, let M(c,d) denote
the property possessed by every system S such that the
modulus of the linear momentum of S exceeds 0 and is
smaller than d. Under these assumptions, the strong
indeterminacy principle asserts that the hermitian Oper—

ators on the Hilbert space associated with S and

 

 

 

147

correSponding to the prOperties P(a,b) and M(c,d), re-
spectively, do not commute with each other for any quad-
ruple of numbers satisfying the above inequalities.
According to the standard interpretation of QT, no system
S can have at the same time both properties P(a,b) and
'M(c,d) unless the numbers b and d are suitably restricted.
This means, however, that no matter how unsharply a
position and a corresponding momentum be defined, no
system can have either unless the outcome of a measure-
ment of either P(a,b) or M(c,d) performed on S entails,
in conjunction with other data and QT laws, that S has

the property measured. If none of these two properties

 

were measured on S then S would not have any P or M—

 

properties whatever. Thus we see, in a different context,

 

and using different words, the same severe limitations

whenever we attempt to Speak of the unobserved properties

 

of physical systems in the micro world.

Concluding remarks. We began our investigation with
the conviction that the kind of solutions proposed under
group B would be the most "desirable." That is, we felt
this kind of solution would require the least amount of
adjustment overall since it would allow us to accept the
subjectivism on the micro level (thus accepting the claims
of QT), and at the same time allow us to reject the sub-
jectivism on the macro level and thus retain an intuitive

macro realism (thus maintaining at least the approximate

148

validity of the metaphysical structure of classical physics
and common sense). Therefore we looked to these accounts
to tell us how we could have the subjectivism on the micro
level, but find that it had somehow been "dissipated" when
we come to the macro level. And, finally, we sought to
associate this "dissipation" of the subjectivism with the
reduction of the wave function. Let us recall what we

have discovered during our inquiry.

We found that the idea of a reduction of the wave
function, as usually understood, cannot be formally fitted
into the standard framework of QT (Komar). We were advised
that the question of a reduction actually need never arise:
a reduction is always a reduction of a superposition to a
mixture; it is not possible for the combined system (in-
cluding the macroscopic measuring apparatus) to ayar be in
a superposition to begin with--because if there were such
a superposition, detection of its interference effects
would require some wholly unreasonable conditions. Thus
for the combined system we always have a mixture (Peres
and Rosen). It is true that Peres and Rosen never tell

us how or why we get the mixture in the combined system

 

from the initial superposition of the Object system;

 

they only tell us that we know it must be a mixture. We

have found that it is consistent with QT to assume that

 

a reduction never occurs, but that there is some kind of

"localization of consciousness" (Everett, et al.). We

 

 

 

149

were told that formally, we could simultaneously account
for the presence of a superposition and also the fact that
it always appears as a mixture (Jauch). Unfortunately,

this prOposal gave us no greater physical understanding of

 

the problem than we had with the indivisibility argument

which makes appeal to an "irrational element" in nature

 

(Bohr). Further, we have found that specific attempts to
"locate" the reduction in the macrOSCOpic behavior of the
measuring device were less than satisfactory, both for
individual reasons peculiar to each account, and because
all such accounts suffer from the objection that some
times the macroscopic "amplification" of a measurement
result does not occur until much later after the inter-
action between the object system and the measuring instru-
ment (Blokhintsev, and Daneri, ap_al,).

Therefore we must conclude that, as of yet, no

 

satisfactory account of the reduction of the wave function,
as usually understood, has been given. To that extent we
have no complete understanding--in the direction originally
sought--Of how we can adOpt an overall view of physical
nature that is able to accommodate both the micrOSCOpic
subjectivism and the macrOSCOpic objectivism (lack or
absence of subjectivism). If one is still inclined to

hold onto the two "basic facts" of the situation--viz,

the existence of subjectivism on the micro level and its

absence on the macro level-~this is not necessarily cause

150

for despair. But of course, this is likewise no cause for
rejoicing.
What we sought was an account which begins with

microscopic subjectivism, and then explains, usinngT,

 

why this kind Of subjectivism is not present on the
macroscopic level; and this was to be achieved by showing
how the wave function is reduced. Though this has not
satisfactorily been accomplished--in complete generality—-
this does not mean that it cannot or will not be. It

does mean, however, that to the extent that this "expla-
nation" of reduction is required to complete the quantum
theoretical account of measurement, we still have with us
the exacerbating difficulties of interpretation that have
been with us from the beginning. (Let us hOpe that the
situation in QT is not of the same kind as prompted some—
one to say: "The poor we will always have with us.") In
particular for our investigation here, it means that to
this extent we have not been able simultaneously to
account for the subjectivism on the micro level and its
absence on the macro level. Hence our position would be
that of being obliged to accept the new-found subjectivism
on the microscopic level, but with the knowledge that
regrettably we do not yet have a full understanding of
how to incorporate this new "fact" into our overall

world-view.

 

 

151

But this Should not distract the reader's attention
from the truly significant result that we have obtained.
In micrOSCOpic subjectivism we have discovered an aspect
of physical nature that is surely remarkable. This is
an idea that is totally alien to the very spirit of scien—
tific thought which has prevailed essentially unchallenged
since the modern inception of science around the seven-
teenth century: this is the view that the physical world
can be described ultimately in terms of independently
existing individual parts with well-defined properties.
But viewing particles on the micro level as in some sense

the "ultimate constituents of matter,‘ we have found that
at the very heart of the physical world—-the independently
existing individual parts-~we cannot maintain this view.

There is an interconnection and interdependence between

 

 

these "ultimate constituents" that is nearly all-pervasive.

 

What is the nature of this interdependence? In the
absence of any definitive solution to the problem of the
reduction of the wave function, we cannot say categorically
that human consciousness will play no role in understanding
this process. But it certainly seems to be the case that
consciousness plays no essential part on the macroscopic
level. For we have a wealth of evidence supporting the
approximate validity of classical physics and thus support—
ing the assumption of an "observer-independent" physical
world embodied in this theory. However, on the micro-

scopic level we see clearly that the source of the

152

subjectivism found there is in no way connected with the
consciousness of any observer. We found that this
subjectivism (with respect to the properties of micro
objects) arises because of the need to take into account

other physical objectsL not other physical Objects with

 

 

consciousness. Consciousness has entered into our dis-
cussion in no essential way whatever. Thus we see that
with regard to the two ways of removing the independence
of an object (i.e., because of the need to take into
account: (1) other objects, (2) other conscious objects),
it is only the first that is in operation here. We have
found that micrOSCOpic objects have a dependent existence
alright, but it is an "interaction-dependence" not an
"Observer-dependence." We note that this runs counter to
a prominent philosophical tendency of considering only a
kind of "observer—dependence." To this extent our con-
clusion of micrOSCOpic subjectivism is substantially
different from many philOSOphical claims of subjectivism,
for we locate the origin of the subjectivism ppp_in the
presence of conscious Observers, but in the existence of
other physical objects.

It is well known that theories entailing some fea-
ture Of ultimate interconnection of this sort is not new
in philosophy. (Compare the coherence theory of truth
and the ontological position underlying it. See, for

example, the philosophy of F. H. Bradley.) But in

153

physics this idea is completely novel. Since the beginning
of modern science, physics has steadfastly refused to re-
linquish the straightforward ontological (and epistemo-
logical) realism that has served it so well and so long
(that is, until the advent of relativity theory and

quantum theory). It is indeed remarkable-—in light of

a long history of philosophical subjectivism, relativism,

and idealism--that physics now seems compelled to adopt

 

the View that at the very heart of the matter there is

this irreducible subjectivism. This clearly is a radical

 

shift in the very fabric of scientific thought. Investi—
gation of such a noteworthy result has unquestionably made

this inquiry worthwhile.

POSTSCRIPT:
PHYSICS AND METAPHYSICS

"A metaphysician,’ wrote James Clerk Maxwell, "is
nothing but a physicist disarmed of all his weapons,--a
disembodied Spirit trying to measure distances in terms
of his own cubit, to form a chronology in which intervals
of time are measured by the number of thoughts which they
include, and to evolve a standard pound out of his own
self-consciousness." [In a paper of 1873 on determinism

and contingency published posthumously in L. Campbell and

W. Garnett, The Life of James Clerk Maxwell (London, 1882),

 

p. 436.] Denunciation of metaphysics is, in fact, one of
the threads that has run unbroken through the history of
physics since its fantastic upsurge in the seventeenth
century. As a matter of fact, physics has not been the
only domain from which dispersions have been cast upon
Imetaphysics. Even within philoSOphy--in recent times,
especially--there have been those that have treated meta-
physics with distrust and even disdain.

It would not be surprising, one might argue, if we

discovered that physicists in fact had a jaundiced and

154

155

distorted View of what metaphysics really is. Hence we
would be prepared to treat their criticisms with perhaps
less seriousness than they would wish. But on the other
hand, similar criticisms by philOSOpherS plghp deserve
more careful attention. In particular, everyone knows
what a devastating critique Kant made of metaphysics. In
light of Kant's critique how could there be enough of
metaphysics "left standing" to warrant any further con-
sideration of it at this time? Let us try to discover

just what metaphysics la, or is supposed to be.

 

The name of the subject is the name given to a
treatise by Aristotle. He described the subject of his
treatise as the science of Being as such, a supremely
general study of existence or reality, distinct from any
of the special sciences and more fundamental than any of
them. Aristotle argued that there must be such a science;
since each of the special sciences, besides having its
own peculiar subject matter, made use in common with all
the others of certain quite general notions, such as
exist, same, like and unlike, unity and difference,
possible and impossible. Such common notions such as
these would provide the topics of the general science of
being. A more recent characterization of metaphysics is
provided by F. H. Bradley. He writes: "We may agree,
perhaps, to understand by metaphysics an attempt to know

reality as against mere appearance, or study of first

156

principles or ultimate truths, or again the effort to
comprehend the universe, not simply piecemeal or by frag—I
ments, but somehow as a whole."

One might be in complete sympathy with the program
as outlined by Aristotle and Bradley and still hold that,
as a matter of fact, the history of metaphysics shows us
that this discipline has gone from one state of disgrace—
ful shambles to another. Not only have metaphysicians
proposed some of the most peculiar systems of thought
imaginable, but different philosophers have proposed
radically different systems—-with these systems supposedly
"explaining" the same things. There seem to be as many
different metaphysical systems (many of which are quite
strange in their own right) as there are practicing meta-
physicians. There hardly ever seems to be any agreement
or any progress (one might continue). There just does not
seem to be enough in metaphysics which is generally agreed
upon, and which would make it stable enough, clear enough,
and well defined enough to warrant treating it as any-
thing like a mature and respectable discipline.

While these kinds of feelings might be considered
a bit extreme, they do point out something which is very
important, and which, to a great extent, accounts for the
kind of "multiplicity" of views mentioned above: many
important metaphysical arguments are not the sort of

arguments that can just be accepted as valid or rejected

157

as invalid by certain and generally agreed upon rules.
Their value or their faults are likely to lie much deeper,
in some central concept or idea which the metaphysician

is trying to articulate. And since, understandably, there
can be great variation in the central idea or concept
adopted by a philosopher, there will likewise be great
variation in the resultant conceptual systems—-which often
are simply mutually incompatible with each other.

Let us try to see in more detail exactly what it is
that metaphysics attempts to do. There are two ways in
which we can think Of metaphysics. It is only the first
that falls victim to Kant's criticisms. Kant argues that
we are inclined to think of the universe, its nature, and
its history as being in principle completely knowable. We
realize, of course, that our actual experience and knowl—
edge of it are inevitably partial and limited; no doubt we
do not think that we ourselves can sensibly aspire to know
everything about everything. But we still do, says Kant,
have the idea that what we do know is a fragment of some
ideal whole, that what we experience is a part of some
totality of things and events. In the same way, says
Kant, we have the ideal of some final and absolute expla-
nation. Here too, we are aware that our own explanations
of events are given merely in terms of further events,
which themselves stand in need of yet further explanation.

But as we extend our always limited power to explain, we

158

think of ourselves as making some approach to a goal,
getting nearer to the standpoint, which doubtless in fact
we shall never reach, from which everything could be
wholly explained without any remainder. The central idea

here is that of completeness. Our powers and our experi-

 

ence are always limited, but as we seek to extend our
knowledge and understanding, we are impelled to think of
ourselves as getting fractionally closer to the ideal

goal of complete knowledge, and complete understanding,

 

of the sum of all things.

Now Kant sees the metaphysician as a thinker Obsessed
by this ideal of completeness. He seeks the explanation
not of this or that, but of everything; he seeks to know
the nature, not of some things, but of all things. Be—
cause we know what it is to know something about something,
and to know more and more about more and more, the meta-
physician thinks that we must be able to say what it would
be like to know everything about everything.

It is this unrestricted use of "all" and "everything"
that is characteristic of the metaphysician. But this un—
bridled usage is precisely the real ground for the im-
possibility of this traditional kind of deductive.meta-
physical system: there can be no sense in the notion of

complete knowledge. By "extrapolating" his arguments all

 

the way to the top (as it were), the metaphysican has

extended the use of certain concepts beyond the domain

159

of their meaningful application, says Kant. Concepts that

we apply within the world cannot necessarily or even

normally be applied intelligibly to the world as a whole.
This kind of metaphysics, which we can call ppppf

logizipg, can never be justified. And the reason is quite

 

Simple. Any assertion of the existence of something, like
any assertion of the occurrence of something, can be denied
without logical absurdity. So the reasons for assertions
of existence or occurrence can never be purely conceptual
considerations. Hence we can never return to the kind

of metaphysics that begins with nothing but "first princi-
ples," and then proceeds to tell us what the world is like.
If we wish to know what there actually is, or what actually
goes on in the universe, then we must dig in the appropri—
ate parts of the universe itself.

However, there is another way in which we can think
of metaphysics which is not subject to the kind of criti-
cism levelled by Kant. To see this consider the following:
it is true that what most traditional metaphysicians had
in mind to do was to provide an ontology, a general pic-
ture of the world. But they would maintain that if an
ontology, an account of the actual structure of the uni—
verse, could be demonstratively established, important
consequences would ensue on the conceptual level. For
instance, if a materialist ontology, to the effect that

the universe is really a system of independently existing

160

material bodies influencing each other by impact, were

true, then it would follow that a certain conceptual

system, viz, that embodied in the language of classical
mechanics, was correct and that all others, however handy
for immediate practical purposes, were ultimately inadequate
and misleading.

Hence, we form a picture in which the real point of
constructing a metaphysical system is_the recommendation
of a particular conceptual framework, with the prime
aspiration of a metaphysician being that of conceptual
revision. Thus the enterprise of metaphysics emerges as,
above all, an attempt to re-order or to reorganize the set
of ideas with which we think about the world; assimilating
to one another some things which we customarily distin-
guish, distinguishing others which we normally assimilate;
promoting some ideas to key positions, downgrading or
dismissing others. It is supremely a kind of conceptual
revision which the metaphysician undertakes, a re—drawing
of the map of thought--or parts of it——on a new plan. And
the concepts which the metaphysician manipulates in this
revision, are always concepts like knowledge, existence,
identity, reality--which as Aristotle said, are common
to all the special and departmental studies.

Viewed in this manner, the metaphysician's purpose
is not simply to deduce a conclusion from the facts. It

is rather to Show that the account of those facts, when

umAn—eh on-

161

we reflect on them, has a hole in it, a hole which is
exactly filled by the metaphysician's special concept.
This concept may be one, like that of "an experience,"
which exists already in a rough form in our ordinary
language, and which the metaphysician takes up, dignifies
and refines into a principle of explanation. Alter-
natively, if he is a very thorough going metaphysician,
the concepts he uses in this way may be much more techni-
cal and remote from ordinary thinking, like Leibniz's

"monads" or Kant's "noumenal objects."

 

The metaphysician feels an inconsistency or diffi—
culty or incompleteness in what we naturally tend to think
about some features of our experience, or rather in what
seems to be presupposed by what we so think. In resolving
this, he will try to Show that some concept on which we
rely is secondary to, or presupposed by, some other con—
cept which he has introduced or extended from elsewhere.
This concept of his may have a special place in the answer
to the problem in question (like the empiricist's use of
"experience"), or he may use it widely elsewhere (like
Plato's Forms) to solve other problems. Hence, the meta-
physician's activity can be seen (and has been seen by
some) as primarily one of reallocation: the extension of
some favored concept to a primary place in the account

of things at the expense of more familiar concepts.

162

Thus, we must certainly conclude that deductive
metaphysics, viewed in the sense of providing an ontology
for the world, starting from "first principles," is no
longer a "feasible" activity for a philosopher. For under
this View what was commonly expected of a metaphysician
was that he should assert the existence or occurrence of
things unseen and give for these assertions purely philo—
sophical or conceptual reasons. If he was not an ontolog—
ist, he was not a metaphysician. But this view is no
longer a tenable one. And philosophy is the better for
it. If metaphysics is to be retained as a worthwhile
enterprise at all, then it must be in the sense of the
conceptual revision described above.

But by now the reader might feel that this is all
very nice and interesting about metaphysics, but what has
any of this to do with physics? Indeed, it might even be
felt that these are on exact opposite ends of the intel—
lectual spectrum. For (it might be felt) even the most
general and basic laws of physics would ultimately depend
for their acceptability upon the results of observation
and experiment in a way which is quite uncharacteristic
of the principles of a metaphysical system. The methods
of physics (and science in general), the tests for
acceptability of physical laws, remain quite different
from the methods of metaphysics and the test for accepta—

bility of metaphysical principles. Though this much seems

163

undeniable, the following is also true: even though the
most general laws or axioms of a unified science would not
count as metaphysics, it is true that many metaphysicians
have thought it at least a part of their task to lay, or
to lay bare, the foundations of science (e.g., Descartes
or Kant). They conceived of the relation as being between

metaphysical foundations and the scientific superstructure.

 

How are we to View the relation, if any, between

physics and metaphysics? Putting the question in a crude

 

way, we can quite bluntly ask: does physics aaaa meta-
physics? and does metaphysics paaa physics? The answer

to the second question is clear. We have seen that the
only kind of respectable metaphysics that is left is meta-
physics considered as a kind of conceptual reorganization;
wholesale ontologizing is gone forever. But clearly, the
activity of conceptual revision is also ontologizing of a
"milder" sort. For the revision Of conceptual frameworks
is recommended only because the new framework is regarded
as a more accurate reflection, or more adequate repre—
sentation of the way things really are. And the only
thing that can keep even this milder form of ontologizing
from becoming the vicious type is the assurance that this
ontologizing is not done solely by appeal to philosophical
and conceptual considerations. Rather there must be
proper regard for the contingent, empirical elements of

nature.

164

We noted earlier that if we wish to know about what
actually goes on in the universe, then we must quarry in
the appropriate parts of the universe itself. Thus to
keep our mild ontologizing from becoming vicious, we must
make our initial appeal not to ”first principles" but to
physics——since physics is precisely what tells us the
goings—on of the universe. Metaphysics of this kind--and
this is the only kind which remains defensible—-must be
done in light of physics. Philosophizing in this sense
is therefore a second—order enterprise which is done glyap
the results of the first—order studies, viz, physics. We
cannot, any longer, attempt to build a metaphysical system
from scratch, we can only build it "on top of" physics.
That is, we can erect a metaphysical structure only if it
has physics as its foundation.

But just as physics is so intimately connected with
metaphysics, I wish to argue, in conclusion, that meta—
physics is just as intimately connected with physics.

For physics seeks to give more than just a correlation
between facts. It seeks a deeper understanding of why
the facts are the way they are. It seeks, in other words,
to give a correlation between facts by appealing to "the
way the world is." And as physics progresses it attempts
to provide a more and more adequate understanding of "the
way the world is." Clearly now we can see that meta-

physical assertions arise out of the very depths of the

 

 

165

scientific enterprise. For not only does physics attempt
to tell us "the way the world is" (which is patently meta-
physical), but it seeks to do so in an ever more adequate
way. And a change to a more adequate view of nature will
very frequently make necessary a change in the ideas and
notions required to articulate this view of nature-—i.e.,
a conceptual revision. Physics, at its most fundamental
levels, la metaphysics.

Thus in a very meaningful sense, there was a kernel

of truth in the first part of Maxwell's statement. For

 

 

in many crucial ways both metaphysicians and physicists

are seeking the same treasure: understanding the "way the

 

world is" (as completely as possible). But instead of
saying "A metaphysician is nothing but a physicist dis—

armed of all his weapons,‘ we might more fairly, more
adequately, and certainly more ecumenically, express the
situation by saying "A physicist is a metaphysician armed
with all the weapons of modern science-—mathematics and
technology-—in all their awesome power."

And we have just seen in the body of this thesis, an
instance of precisely this kind of inter-dependence be—
tween physics and metaphysics. For we have arrived at a
conclusion regarding the ontological status of the ultimate
constituents of the physical universe (viz, the conclusion
Of microscopic subjectivism). This is most certainly the

kind of assertion sought after in traditional metaphysical

166

descriptions of the world. We note: (1) that this
assertion was arrived at by an investigation conducted
within physics. Hence we have a metaphysical claim aris—
ing out of a study of the fundamental aspects of physical
theory; and (2) since any acceptable philosophical theory
must not be in conflict with existing physical theory
(assuming, of course, that the philosophical theory is
about some aspect of the physical universe), any future
philosophizing of a metaphysical or ontological nature,
must be done in light of what we have discovered here
(from physics) about the ontological nature of the ulti—
mate constituents of the physical universe. Hence, we
see that any future metaphysics must be done in such a
way that it picks up where physics leaves off, in the
sense that it must paglp with whatever metaphysical con-
clusions are provided by physics and proceed from there.
In particular, any future metaphysical account of nature
must take into account the demonstrated interdependence
among the elementary constituents of the world.

Hence there is indeed a kind of study that is both
respectable and necessary for our understanding of the
physical universe. It may be thought of as a part of
physics, and we have seen that physics at its most funda—
mental levels, is indeed metaphysical in character. Or
it may be thought of as a part of philosophy. In that

case, we have seen that it is a second-order discipline

 

167

which requires physics as its
we see that the connection is
warrant consideration of both
a "complete" understanding of

world.

foundations. In either case,
certainly intimate enough to
aspects by anyone who seeks

the nature of the physical

BIBLIOGRAPHY

10.

11.

12.

13.

14.

U

U

U

2

DJ

BIBLIOGRAPHY

Albertson, American Journal of Physics, 29, 478
(1961).

E. Ballentine, Reviews of Modern Physics, 42(4),
358 (1970).

S. Bell, Reviews of Modern Physics, 38, 447 (1966).
5. Bell, Physics, 1(3), 195 (1964).

I. Blokhintsev, Soviet Uspekhi, 11(3), 320 (1968).
Bohm, Physical Review, 85, 180 (1952).

Bohm, physical Review, 85, 166 (1952); 87, 389
(1952); 89, 319, 458 (1953).

Bohm and J. Bub, Reviews of Modern Physics, 38,
453, 470 (1966).

Bohr, Atomic Theory and the Description of Nature
(Cambridge Univ. Press, New York, 1934).

 

Bohr, Atomic Theory and Human Knowledge (Inter-
science, New York, 1963).

 

Bohr, Physical Review, 48, 696 (1935).

Bub, "The Daneri—Loinger-Prosperi Quantum Theory
of Measurement" unpublished.

Bunge, ed., Quantum Theory and Reality (Springer,
Berlin, 1967).

A. Burtt, The Metaphysical Foundations of Modern

Ph sical Science (Routledge and Kegan-Paul, 2nd
edition, 1932).

168

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

E“

35

U1

V

CE

2}

2

169

Carnap, "Empiricism, Semantics, Ontology" (1950).

Daneri, A. Loinger, G. M. Prosperi, Nuclear Physics,
33, 297 (1962).

Daneri, A. Loinger, G. M. Prosperi, Nuovo Cimento,
44B, 119 (1966).

S. DeWitt, Physics Today, Sept., 1970.
A. M. Dirac, The Principles of Quantum Mechanics

(The Clarendon Press, Oxford, 4th edition, 1958),
p. 33.

 

Einstein, B. Podolsky, N. Rosen, Physical Review,
47, 777 (1935).

Everett, III, Reviews of Modern Physics, 29, 454
(1957).

P. Feynman, Proceedings of the Second Berkeley
Symposium on Mathematical Statistics and Proba—
bility, 533 (1951).

Fine, Philosophy of Science, 35, 101 (1968).

R. Hanson, The Concept of the Positron (Cambridge
Univ. Press, 1963).

 

Heisenberg, Physics and Philosophy (Harper and
Brothers, New York, 1958).

 

Heisenberg, The Physical Principles of Quantum
Theory (Univ. of Chicago Press, 1930).

 

J. Hirst, The Problems of Perception (Humanities
Press, New York, 1959).

 

Jammer, The Conceptual Development of Quantum
Mechanics (McGraw—Hill, New York, 1967).

 

Jauch, Foundations of Quantum Mechanics (Addison—
Wesley, Reading, Mass., 1968).

 

Jauch, Helvectica Physica Acta, 37, 293 (1964).

Jauch, E. P. Wigner, M. M. Yanase, Nuovo Cimento,
XLVIII, 144 (1967).

E. Johnson, Encyclopedia Of Philosophy, Vol. 2,
p. 357, "Determinables and Determinates."

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

U)

'11

:r:

II:

V

LI

170
Kochen and E. P. Specker, Journal of Mathematics
and Mechanics, 17, 59 (1967).
W. Kolmogorov, Foundations of the Theory of
Probabilit (Chelsea Publishing Co., New York,
2nd English edition, 1956).

Komar, Physical Review, 126, 365 (1962).

 

Koopman, Proceedings of the Symposium in Applied
Mathematics, VII, 97 (1957).

London and E. Bauer, La theorie de l'observation
en mechanique quantique (Actualities Industriells
et Scientifiques, Hermann, Paris, 1939).

 

 

Ludwig, Die Grundlagen Der Quantenmechanik
(Springer-Verlag, Berlin, 1954).

 

Mandel and R. L. Pfleegor, Physical Review, 159,
1084 (1967).

Margenau, Philosophy of Science, 30(1), 138
(1963).

Margenau and L. Cohen, in Quantum Theory and
Reality, ed. M. Bunge.

 

Mehlberg, in Quantum Theory and Reality, ed.
M. Bunge.

 

Menger, Proceedings of the Third Berkeley
Symposium on Mathematical Statistics and Proba—
bility, 2, 215 (1954).

Messiah, Quantum Mechanics (North Holland Publish—
ing Co., Amsterdam, 1964).

 

E. Moyal, Proceedings of the Cambridge Philosophi-
cal Society, 45, 99 (1949).

Peres and N. Rosen, Physical Review, 135, B1486
(1964).

Petersen, Quantum Physics and the Philosophical
Tradition (MIT Press, Cambridge, 1968).

 

Rosen, American Journal of Physics, 32, 597
(1964).

49.

50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

f“

:0

V

q

EC

171

Schlegel, Completeness in Science (Appleton-
Century—Crofts, New York, 1967).

 

Schlegel, Synthese, 21(1), 65 (1970).

Shimony, American Journal of Physics, 31, 755
(1963).

Sneed, Philosophy of Science, 33, 22 (1966).

P. Stapp, Physical Review D, 3(6), 1303 (1971).
Suppes, Philosophy of Science, 33, 14 (1966).
Von Neumann, Mathematical Foundations of Quantum

Mechanics (Princeton Univ. Press, Princeton,
19 5 .

 

A. Wheeler, Reviews of Modern Physics, 29, 454
(1957).

P. Wigner, American Journal of Physics, 31, 6
(1963).

P. Wigner, in The Scientist Speculates, ed. I. J.
Good (William Heineman, Ltd., London, 1961).

 

P. Wigner, American Journal of Physics, 38(8),
1005 (1970).

APPENDIX

 

 

 

APPENDIX

Bell's theorem states that no theory can: (a) give
contingent general predictions of the individual results
of measurements; (b) be compatible with the statistical
predictions of QT (to within, say, 5%); (c) satisfy "local
causes." I will explain what all this means. A prediction

of an individual result is, for example, the prediction of

 

whether an individual particle in a Stern-Gerlach device
will be deflected up or down. QT predicts the proba-
bilities of these two alternatives, but not, in general,
the individual result itself. The word general in con-
dition (a) specifies that the individual results of Stern—
Gerlach-type measurements are to be predicted by the
theory.

The axis of a Stern-Gerlach device can be rotated:
it can have different alternative possible settings. The

word contingent in condition (a) means that the theory

 

gives predictions for the various possible alternative
settings. It does not merely give predictions only for
the one unique setting that is actually chosen by the

experimenter.

172

173

Consider now an experiment in which two particles
are made to collide, with each of the scattered particles
going through one of two Stern-Gerlach devices, denoted
respectively by D1 and D2. Our three conditions are now
just: (a) if the experimenters had actually adjusted the
mechanical devices to give the alternative experimental
setup, then these alternative experiments would have had
certain definite results—-and these results are predictable
by the theory; (b) the equations of the theory, regarding
any correlations between the two devices, must hold (to
within 5%); (c) the requirement of local causes is that
the deflection of the particle going through the first
device should not depend appreciably on what is the
setting of the second device, and vice versa. The

setting of D can be made just before the arrival of

1
particle l and the setting of D2 can be made just before
the arrival of particle 2. In this case, any large de—
pendence of the results of a measurement made by Dl on
the orientation of D2 or any large dependence of the re—
sults of a measurement made by D2 on the orientation of
D1, would require a large and almost instantaneous effect
of a far-away cause.

These three assumptions all seem plausible. Yet
taken together they are incompatible and lead to a contra—
diction (see Wigner [59]; Stapp, Bell, Ballentine). The

immediate conclusion to be drawn from this theorem is that

174

the demands of causality, locality, and individuality
cannot be simultaneously maintained in the description
of nature (assuming we wish to have at least statistical
agreement with QT). Causality demands contingent pre-
dictions; locality demands local causes of localized
results; individuality demands the specification of indi-
vidual results, not merely their probabilities.

The contradiction posed by Bell's theorem is rather

disconcerting, for these three assumptions are such that

 

we would not want to give up any one of them. Assumption
(b) is obviously untouchable, there is simply too much
empirical support of the statistical predictions Of QT.
Assumption (a) is essentially just the requirement that
nature be fundamentally lawful, in the sense that the
individual results are specified by contingent rules.

And assumption (c) is just the condition that the world
be fundamentally separable into independent parts, on the
macroscopic level. For if a cause can have a large in—
stantaneous effect far away, then far apart macroscopic
Objects can no longer be considered separate and distinct

in the usual sense.

 

 

 

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