A BACKGROUND ESSAY
JAMES T. GUSHING

(Partial support for this work was provided by the National Science Foundation under Grants No. SES-8606472 and No. SES-8705469. I thank
especially Don Howard, Ernan McMullin, and Abner Shimony for comments on an earlier draft of this essay.)

The purpose of the papers in this volume is to discuss the hard questions and hard choices that recent quantum physics has
presented for philosophy in general, not just for the philosophy of science. The authors examine what has been established, what
options are still available, and what revisions, radical or otherwise, may be necessary in our philosophical views. Since the volume
is intended for philosophers in general, and not just for experts in the foundational problems in quantum theory, the papers are not
thick with technical details. A central development to which all of these papers are in some way related is Bell's theorem. There is
an enormous literature on the technical aspects of Bell's theorem and on the foundational problems of quantum mechanics (see,
for example, Ballentine 1987). My task here is to provide some introductory material that will help the reader new to this subject
to understand the subsequent papers. Let me be explicit in stating that the tale which follows is not always chronologically faithful
to the historical record nor is it in all details a literal transcription from the original papers cited. By way of orientation, I begin
with a general and somewhat loose overview of the subject and then proceed to define terms and concepts more precisely.

1. A little history
While it is true that interest in the interpretative problems of quantum mechanics received major impetus from the
seminal paper of John Bell (1964) on the Einstein-Podolsky-Rosen (EPR) paradox, there was life in the field before Bell-and before
EPR too (see, for example, Wheeler and Zurek 1983). As early as 1913, before Bohr's paper of that year on the semiclassical model
of the hydrogen atom had appeared in print, Rutherford pointed out a problem for causality in Bohr's model. Bohr had postulated
that the frequency v of light emitted by an electron in its transition from an initial energy level E,n to a final level E,, (figure 1) is
given by

Em - E = hv

To Rutherford, it appeared as though the electron would have to know to what energy level it was going before it could
decide what frequency it should emit (Hoyer 1981, 112). By 1917, Einstein wanted to know how, in Bohr's model, the photon
decided in what direction it should move off (figure 2). Schr6dinger attempted a largely classical interpretation of his own
equation, but Max Born (1926) proposed a consistent statistical interpretation of quantum mechanics. Determinism, in the sense
of our being able to predict the unique outcome of a measurement on an event-by-event basis, was gone from the formalism,
although Einstein and Schr6dinger struggled (Przibram 1967) against what became codified as the "Copenhagen" interpretation of
quantum mechanics. True, the majority of physicists (if they chose to think about the issue at all) believed that atomic events
could not, even in principle, be predicted on an event-by-event basis. Still, one could (and some notables did) question the
completeness of quantum mechanics, asking whether there might not exist a successor theory which could, in principle, make such
event-byevent predictions. In fact, von Neumann ([1932] 1955, 313-328) offered a "proof" that such "hiddenvariables" theories
could not exist. Much later, Bell (1966) did address the question of the relevance of that "proof."

In 1935, Einstein, Podolsky and Rosen (EPR) published a paper in which they questioned the completeness of quantum
mechanics. That is, they asked whether one could be certain, on physical grounds, that more could be specified (or known) about a
system than could be predicted with certainty by the formalism of quantum mechanics. By means of a specific thought experiment,
they argued that the incompleteness of quantum mechanics was entailed by the formalism of quantum mechanics itself, along with
entirely plausible assumptions excluding action at a distance ( "locality") and about the reality (or definiteness) of a physical
quantity independent of our choice to observe it. Their argument has been lucidly discussed by Shimony (1978). We do not
consider the original EPR thought experiment here. For pedagogical purposes, there is a simpler one due to Bohm (1951). The EPR
paper did not offer any alternative theory to quantum mechanics, nor did it mention hidden variables. Nevertheless, the additional
parameters that would be necessary to give a complete specification of the state of a system have subsequently come to be referred
to as "hidden variables" and any theory encompassing such parameters as a "hidden-variables theory."
.

2. Bell's theorem
Prior to Bell's 1964 paper, the question of whether or not there could exist a deterministic hiddenvariables theory with no
instantaneous action at a distance seemed incapable of resolution. Of course, no one had succeeded in writing down an empirically
adequate example of one. But, that did not prove that one could not exist. After all, if a student fails to solve a difficult homework
problem, the reason could be that he or she lacks the wit to do it or, indeed, it could be a problem with no solution. In the absence
of a successful deterministic, local, hidden-variables theory, discussion of the possibility of such a theory could appear to be little
more than idle argument appropriate only for a free Saturday afternoon or for cocktail parties. Bell's paper changed that in a
dramatic fashion. The strength of a theorem is inversely proportional to the strength of the assumptions it makes. That is, if you
assume a lot and prove a little, no one is particularly impressed. But if you (apparently) assume practically nothing and obtain a
remarkable result, that is impressive.

In effect, Bell (1964) argued that determinate (i.e., predetermined prior to the measurement) projections for the spins of
the electrons and locality are incompatible with the (spin) correlations predicted by quantum mechanics.
.
In fact, the actual experiment (in a real laboratory with real equipment) is much more difficult to do than my rather glib
characterization in figure 3 might lead one to expect. A detailed discussion of the experimental situation can be found in the
comprehensive review article by Clauser and Shimony (1978) and in Redhead (1987b). There also exists a general, less technical
review by Shimony (1988). Such experiments have been earned out, some of the latest and most convincing being those by
Aspect, Grangier, Dalibard, and Roger (1981, 1982) in Paris. The empirical results are representable, well within the limits of
experimental error, by the simple distributions.
.
The logical skeleton of the argument is that the assumptions of locality and determinism, plus the actual experimentally observed
distributions of the real world, have produced the contradiction of Eq. (7). Although one can, in principle, attempt to undermine
the empirical leg of the triad upon which this argument rests (cf. Clauser and Shimony 1978), each successive experiment
forecloses more such possible loopholes and makes such a line of attack ever less plausible. So, the arrow of modus tollens appears
more reasonably directed at the assumptions of locality and/or determinism. We have purposely not gone into the details of the
argument by which Bell passed from Eq. (3) to the (Bell) inequality of Eq. (4) because we want to focus on the logical structure of
the argument. In the appendix to this essay, the reader can find a simple proof of a contradiction like Eq. (7). So, Bell's remarkable
result, or theorem, is that no deterministic, local hiddenvariables theory can account for the empirical result of the experiment. It
is worth emphasizing that these types of correlations are a pervasive feature of the quantum world. They are not peculiar to the
Bohm-EPR class of experiments alone. However, the Bohm-EPR configuration is in a sense the "simplest" one yet known which
exhibits these "mysterious" quantum correlations.
.
Let me stress two points here. First, Bell never wrote down a single local, deterministic theory. Rather, he proved, without ever
having to consider any dynamical details, that no such theory can in principle exist. The entire class was killed at a stroke-a classic
"no-go" theorem. Second, Bell's theorem really depends in no way upon quantum mechanics. It refutes a whole category of
(essentially) classical theories without ever mentioning quantum mechanics. And it turns out that the experimental results not
only refute the class of local, deterministic theories but also agree with the predictions of quantum mechanics. (That is, a
straightforward application of the rules of quantum mechanics does lead to the results of Eqs. [5].) Abner Shimony (1984b, 35) has
appropriately given the name "experimental metaphysics" to this type of definitive empirical resolution of what appears to be a
metaphysical question.

3. Some distinctions
In my presentation thus far, I have been rather cavalier in oversimplifying the issues and in conflating terms that must be carefully
distinguished. So I now turn to the purpose of the subsequent papers in this volume and to some of the work that the authors have
done in recent years. Today, when one looks back at Bell's original paper and at some of the early responses to it, one is struck by
at least two facts. First, the paper contains a modicum of mathematical formalism. Depending upon one's level of mathematical
sophistication, the proof may not be immediately transparent and one can wonder whether something has gone awry in those pages
and symbols. After all, the result is so remarkable: it forces us to face indeterminism and/or nonlocality in principle. Could the
proof be flawed? As often happens with great discoveries, proofs are subsequently fashioned which make the important result seem
almost self-evident. Bell's theorem was no exception. Eventually, there were picture proofs and nonmathematical discussions
(d'Espagnat 1979; Mermin 1981a, 1985) of Bell's result and of the quantum-mechanical riddles it makes us face. While such
discussions are nontechnical, they can remain rather long and involved. The reader's eyes may glaze over before the end. However,
if one is willing to pay the price of a little algebra-really, only about six lines of arithmetic-one can immediately go from Bell-type
premises and a requirement of empirical adequacy to a contradiction like 1 > 2 (Stapp 1971, 1979; Redhead 1987a). The
mathematics is so simple and brief you are certain no error has been made. You think you understand it all! (The details of such a
proof are given in an appendix to this paper.)
    So then, first, the formalities or manipulations in the proofs were greatly simplified. But then, the second, and in many
ways more difficult, phase began-unpacking the assumptions and the meanings of the terms used in these proofs and coming to
some understanding of just what the implications are. This is a job that philosophers are particularly well equipped to do. The
terms `reality', `determinism', and `causality' cannot be used interchangeably and one must be especially careful to distinguish
between locality and reparability. Perhaps a few sketchy definitions will help for a start:

reality - existence of an objective, observer-independent world (often closely related to determinate values)
determinism - sufficient information at to allows prediction of a specific result at a later time t
causality - a specific preceding event (or "cause") for every effect - a concept familiar from prequantum, classical theories
locality - no influence transmitted faster than light
separability - spatially separated systems always have independently definable properties and existence (and these
properties exhaust the description of any system made up of these subsystems).
    Arthur Fine (1984a, 1984b) and Don Howard (1985, 1987) have provided a useful perspective for several of these issues by their
careful and enlightening historical reconstructions of Einstein's views on locality and reparability, bringing out essential differences
here between Einstein and Bohr. Henry Folse (1985), Don Howard (1986), and Dugald Murdoch (1987) have done similar work in
reconstructing Bohr's philosophy of science. Furthermore, as we indicated previously in Eq. (3), a crucial mathematical step in the
usual proof of Bell's theorem is the factorization of a certain expression for joint probabilities. A long debate has arisen as to the
physical warrant for this step. This factorizability (or "Bell" locality or statistical independence) is not implied by the first signal
principle of relativity ( "Einstein" locality). Michael Redhead (1983) and Linda Wessels (1985) have analyzed in detail the assump
loin the present context, the term `determinism' is usually predicated of a theory, as in a deterministic theory. In quantum field
theory, `causality' is used in a sense rather different from (but related to) the classical cause-effect one. (See Gushing, 1986, for a
fuller discussion of the meaning of the term `causality' in modem theoretical physics.) The reader should be warned that the terms
`locality' and `reparability' are the most problematic as far as universally-agreed-upon definitions are concerned. The ones I give
here alert the reader to a distinction between these terms. However, each author below must be checked carefully for his or her
own precise use of these terms. It is also true historically that the evolution of an explicit distinction between those two terms was
a long time in coming. (See Howard [1985] and Folse [this volume] for careful discussions of this issue.) Furthermore, we
distinguish among different types of locality and nonlocality. Finally, d'Espagnat (1984) treats the issues of reality and of
separability carefully and at great length.
....
    Another insightful observation about the meaning of the Bell inequality was made by Fine (1982b). He argued that Bell
inequalities of the type in Eq. (4) above are the necessary and sufficient conditions for the existence of a deterministic
hidden-variables model which will produce the joint distributions for the Bohm (EPR) experiment of figure 3. But the existence of
such a complete set of state variables A is equivalent to a common-cause explanation (in the common past of the parts of the
system to be observed) for these distributions or experimental outcomes. Knowing that there is such an empirically applicable test
for the possibility of a common-cause explanation will prove important for the discussions which follow in subsequent papers in
this volume.

4. Philosophical implications
We can now ask just what the implications of all of this are for our view of the physical world. Thus far we have pointed out
certain restrictions on allowable world views (or representations of reality) that are demanded by quantitative relations (the Bell
inequalities) containing only empirically measurable distributions of experimental results. In a sense, the tone has been negative
since we have stressed what type of theories or explanations are not possible. Must we, for example, abandon belief in an
observer-independent reality? Or, as David Mermin has put it, "Is the moon there when nobody looks?" We have shown what
cannot work rather than exploring some theory or explanatory framework that is successful in reproducing the results of experiment.
    Of course, we do have an empirically adequate theoretical framework within which to organize the observational datanamely,
quantum mechanics. However, this enormously empirically successful theory has difficult interpretative problems associated with it.
Henry Stapp (1979, 14) makes a point similar to Mermin's when he characterizes our immediate reaction to a literal acceptance of
some of the more extreme interpretations of quantum mechanics:

One objection to this view is that it seems excessively anthropocentric, at least if consciousness is reserved for human beings
and higher creatures. Before the appearance of such creatures the world would be synthesizing endless superposed
possibilities, with nothing actual or real, waiting for the first conscious creature to occur among the possibilities. Then a
gigantic collapse would occur. Similarly, the Martian landscape would be nothing but superimposed possibilities until
Mariner landed and some observer in Houston viewed his TV screen. Then suddenly the rocks and boulders would all snap
into their observed places. This view seems to assign a role to such observers that is out of proportion to their place in the
world they create.
That is, our most successful theory of processes at the microlevel, namely quantum mechanics, poses serious problems for scientific
realism (which requires roughly and at a minimum that our scientific theories are to be taken as giving us literally true descriptions
of the world).
    Bas van Fraassen (1982a; this volume) has argued that the experimental violation of the Bell inequality tells against
scientific realism. That is, if scientific realism does not work at the microlevel, then it cannot be generally valid. In a provocative
article, Asher Peres (1985) has posed yet another quantum paradox "as a challenge to those physicists who claim that they are
realists" (p. 201). His conclusion at the end of that article (p. 205) is that "Any attempt to inject realism in physical theory is bound
to lead to inconsistencies. "(At the 1986 Quantum Measurement Theory Conference (Greenberger 1986) in New York City, I
mentioned to Peres that his position appeared to be an instrumentalist one. He replied with no apparent discomfort that others had
told him that before. For a physicist's statement on an instrumentalist interpretation of quantum mechanics, see Peres (1988).)

    At the other end of the spectrum from van Fraassen (1980) or Peres on views of scientific realism, we find Ernan McMullin
(1984) who points to the great success structural theories have enjoyed in several sciences (such as chemistry, astrophysics, geology,
and genetics) in taking a starkly realistic view of the entities contained in those theories. It is in regard to the interpretation of the
ontologies underlying mechanical theories (whether classical or quantum) that problems most often arise (McMullin 1989).
McMullin recommends treating these theories as a special class and considers as inappropriate the demand for a realistic
interpretation of force or field that would be unproblematic for molecule or gene or galaxy. He is willing to put aside for the present
certain difficult questions of a realistic interpretation for mechanics (that is, classical mechanics, quantum mechanics, quantum field
theory-all of what would seem to many to be the foundations of physics): "Because of its many special features, mechanics is quite
unsuitable as a paradigm of science generally, though philosophers are wont to overlook this" (1984, 10). Rather than being the
paradigm of natural science, much of physics becomes, at least in the context of this issue, an anomaly. It appears that McMullin
restricts consideration to cases that satisfy, in some broad sense, Newton's Rule III of Reasoning in Philosophy in Book III of the
Principia (Newton [1726] 1934):14 "The qualities of bodies, which admit neither intensification nor remission of degrees, and which
are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies
whatsoever. " This rule is often taken as saying that we may extrapolate general features of the macroworld to the microworld. To
some, McMullin's circumscription of mechanics may be too costly a move to make on behalf of scientific realism. Somewhere
between van Fraassen and McMullin, we find Heisenberg (1958, 185) with his suggestion that we must admit a new class of physical
entity into our theories: potentia (Shimony 1978, 1986; Stapp 1979, 1985a). Bell (1984) has made a similar suggestion in speaking
of the "beables" of quantum field theory.
    One of the most interesting philosophical questions, perhaps, concerns the relations among empirical adequacy,
explanation, and understanding for quantum phenomena. Are explanation and understanding really possible when a detailed causal
explanation is in principle impossible? In Bas van Fraassen's (1985) terms, are the EPR correlations a mystery? Paul Teller has
suggested that relational properties of physical objects may not simply supervene wholly upon nonrelational properties of localizable
individuals, but that a type of "relational holism" is essential in which the objects have inherent relations among themselves. He
claims that this is "a holism we can understand" (Teller 1986, 73). But is it? A central issue is whether or not we can truly
understand such descriptions of our world. These problems are forced upon us, of course, when we take the present formulation of
quantum mechanics as exactly correct, needing no modification.

    In the same vein, we can even ask whether all the desiderata, which we may want in a theory that accords with the
phenomena of the real world, can be mutually compatible. Peres and Zurek (1982) set up a triad (figure 5) involving the three
"wishes" of determinism, verifiability, and universality and argue that no theory can, even in principle, satisfy simultaneously all
three demands. (By "verifiability" here they mean the freedom of choice of an observer or experimenter to fix a given setting on, or
orientation of, a measuring device to test the predictions of a theory.) We can have at best just any two of the three. In the end,
quantum mechanics may be the best theory it is possible to have.
    We might question the value of discussing the implications that essentially nonrelativistic quantum mechanics (say, the
usual Schrodinger equation) has for such issues, since the more complete (and problematic) theory in use today is relativistic
quantum field theory. I have argued elsewhere in some detail (Gushing 1988) that the root of quantum paradoxes is the superposition
principle and that remains in any quantum theory. Michael Redhead and PaulTeller (cf. Brown and Harre 1988) do believe that
quantum field theory introduces new philosophical problems which must now be faced. These would, of course, be in addition to,
and not solutions of, the interpretative difficulties already presented here.
This introductory essay may at least establish a prima facie case for the relevance of quantum mechanics to general philosophical
issues related to epistemology and ontology. There are serious problems here, not simply questions of mathematical formalism.
Hence, the rationale for this volume. Several years ago John Bell (1975, 98) made an observation about the understanding of our
world which quantum theory gives us:

The continuing dispute about quantum measurement theory is not between people who disagree on the results of simple
mathematical manipulations. Nor is it between people with different ideas about the actual practicality of measuring
arbitrarily complicated observables. It is between people who view with different degrees of concern or complacency the
following fact: so long as the wave packet reduction is an essential component, and so long as we do not know exactly when
and how it takes over from the Schrodinger equation, we do not have an exact and unambiguous formulation of our most
fundamental physical theory.
In our search for a new understanding, we face the challenge characterized by Costa De Beauregard (1983, 515-516) in this way:
 
Hard paradoxes . . . are resolved only by producing a new and adequate paradigm, in Kuhn's words. In physics, this implies
the production of a new mathematical recipe (e.g., Copernicus's heliocentrism, or Newton's inversesquare law) and tailoring
an explanatory discourse exactly fitting the mathematics (e.g., Einstein's interpretation of the Lorentz-Poincare formulas; or
still better, Minkowski's).
This sort of "explanation" is usually felt (and often for a long time) as itself paradoxical. Newton's action at a distance,
Einstein's "reciprocal" interpretation of the Lorentz contraction, have very often been deemed "hardly explanations at all."
What occurs in the "paradox and paradigm" peripateia (or, in Kuhn's words, in a "scientific revolution") is a victory of
formalism over modelism. In the EPR case we do have, since many years, the formalism. We are at home with it for
performing calculations, but not yet for viewing our world, and our relation to it.
The papers in this volume are attempts to fashion an explanatory discourse with a view to producing an understandable
view of our world. The ultimate goal is to construct a framework that is empirically adequate, that explains the outcomes of our
observations, and that finally produces in us a sense of understanding how the world can be the way it is. These are three linked but
distinct goals. It remains an open question whether all of these are simultaneously attainable.