One day Mr Tompkins was going home, feeling very tired after the long day's work in the bank, which was doing a land office business. He was passing a pub and decided to drop in for a glass of ale. One glass followed the other, and soon Mr Tompkins began to feel rather dizzy. In the back of the pub was a billiard room filled with men in shirt sleeves playing billiards on the central table. He vaguely remembered being here before, when one of his fellow clerks took him along to teach him billiards. He approached the table and started to watch the game. Something very queer about it! A player put a ball on the table and hit it with the cue. Watching the rolling ball, Mr Tompkins noticed to his great surprise that the ball began to ‘spread out’. This was the only expression he could find for the strange behaviour of the ball which, moving across the green field, seemed to become more and more washed out, losing its sharp contours. It looked as if not one ball was rolling across the table but a great number of balls, all partially penetrating into each other. Mr Tompkins had often observed analogous phenomena before, but today he had not taken a single drop of whisky and he could not understand why it was happening now. ‘Well,’ he thought, ‘let us see how this gruel of a ball is going to hit another one.’

Next morning Mr Tompkins was dozing in bed, when he became aware of somebody's presence in the room. Looking round, he discovered that his old friend the professor was sitting in the armchair, absorbed in the study of a map spread on his knee.

‘Are you coming along?’ asked the professor, lifting his head.

‘ Coming where?’ said Mr Tompkins, still wondering how the professor had got into his room.

‘To see the elephants, of course, and the rest of the animals of the quantum jungle. The owner of the billiard room we visited recently told me his secret about the place where the ivory for his billiard-balls came from. You see this region which I've marked with red pencil on the map? It seems that everything within it is subject to quantum laws with a very large quantum constant. The natives think that all this part of the country is populated by devils, and I am afraid it will hardly be possible for us to find a guide. But if you want to come along, you had better hurry up. The boat is sailing in an hour's time and we still have to pick up Sir Richard on our way.’

‘Who is Sir Richard?’ asked Mr Tompkins.

‘ Haven't you ever heard about him?’ The professor was evidently surprised. ‘He is a famous tiger-hunter, and decided to go with us, when I promised him some interesting shooting.’

PROSPECTIVE

The concern of this paper will be different from that of most studies of quantum gravity. There will be no discussion of the problem of quantizing the gravitational field equations, hence nothing about the modifications which quantization requires of space-time structure at distances of the order of the Planck length (∼ 10−33 cm). The emphasis will be rather upon the implications of quantum mechanics for certain general properties of events and processes which occur in the theatre of space-time, specifically with non-locality and nonlinearity.

Quantum mechanics is undoubtedly a non-local theory when it treats correlated spatially separated systems. When one examines closely the character of this non-locality, however, one does not find reasons for modifying the causal structure of space-time as described by special or general relativity theory, but rather reasons for refining the concept of an event. The occurrence of definite outcomes of measurements implies that there are processes in nature governed by nonlinear laws. Nonlinearity is very peculiar from the standpoint of quantum mechanics, since it is contrary to the linearity of the time-dependent Schrödinger equation, which is commonly assumed to govern the dynamics of any isolated physical system. Hence it is necessary to inquire whether a rational treatment of the occurrence of outcomes is possible without some modifications of current quantum mechanics. Whatever decision is reached on this question, however, it does not appear to bear directly on space-time structure, but rather on the general character of processes.

This is the first of two papers showing that the quantum problem of measurement remains unsolved even when the initial state of the apparatus is described by a statistical operator and when the results of measurement have a small probability of being erroneous. A realistic treatment of the measurement of observables of microscopic objects (e.g., the position or the spin of an electron) by means of observables of macroscopic apparatus (e.g., the position of a spot on a photographic plate) requires the consideration of errors. The first paper considers measurement procedures of the following type: An initial eigenstate of the object observable leads to a final statistical operator of the object plus apparatus which describes a mixture of “approximate” eigenstates of the apparatus observable. It is proved that each of a large class of initial states leads to a final statistical operator which does not describe any mixture containing even one “approximate” eigenstate of the apparatus observable.

INTRODUCTION

Several writers have tried to solve the quantum-mechanical problem of measurement through one or both of the following proposals: (a) describthe initial state of the measuring apparatus by a projection onto a subspace of the associated Hilbert space or by a statistical operator, thus taking into account the practical impossibility of knowing the exact quantum state of a macroscopic object; (b) recognizing that there may be some physical inaccuracy, such as a small error in the position of a pointer needle, in the final registration of the outcome of the measurement by the apparatus.

Many of the pioneers of quantum mechanics – notably Planck, Einstein, Bohr, de Broglie, Heisenberg, Schrodinger, Born, Jordan, Landé, Wigner, and London – were seriously concerned with philosophical problems. In each case one can ask a question of psychological and historical interest: was it a philosophical penchant which drew the investigator towards a kind of physics research which is linked to philosophy, or was it rather that the conceptual difficulties of fundamental physics pulled him willynilly into the labyrinth of philosophy? I shall not undertake to discuss this question, but shall cite an opinion of Peter Bergmann, which I find congenial: he learned from Einstein that “the theoretical physicist is … a philosopher in workingman's clothes” ([1], q. v.).

The problems with which I am preoccupied concern the philosophical implications of quantum mechanics – either epistemological, bearing on the extent, validity, and character of human knowledge; or metaphysical, bearing on the character of reality. Although quantum mechanics is not a system of philosophy, one can wonder whether it is susceptible to coherent incorporation in a philosophical system. I propose to examine the thought of three masters of quantum mechanics – Bohr, Heisenberg, and Schrödinger – not with a critical or historical intention, but in hope of finding some enlightenment concerning the problems posed by contemporary physics. I can say in advance that enlightenment will continue to elude us; nevertheless, the ideas of Bohr, Heisenberg and Schrödinger are rich and evocative for new studies.

The Structure of Scientific Revolutions and Kuhn's afterthoughts (1970a, 1974) have been subjected to so much penetrating criticism that any further examination might be supposed redundant. There are, however, two epistemological theses in his work which have not, in my opinion, received adequate analysis. They are not essentially dependent upon considerations of Gestalt switches, theory-ladenness of observation, incommensurability, or the ambiguity of the word ‘paradigm’, which have received much critical attention.

The first thesis is that the progress of science ought not be construed as the approach to a fixed goal which is the truth about nature.

Kuhn maintained this thesis in his replies to critics and even strengthened it somewhat: “If I am right, then ‘truth’ may, like ‘proof’, be a term with only intra-theoretic applications” (1970a, p. 266). The second thesis is that the procedures of scientific investigation can be shown to be rational, and the appropriate sense of “rationality” can be explicated, only by drawing upon the substantive achievements of science.

Dr. Bell's paper, “The Theory of Local Beables”, performs a valuable service in clarifying two fundamental concepts: namely, locality and physical reality. His clarification leads him to a fundamental and highly reasonable assumption, expressed in equation (2) of Sect. 2. He then attempts in Sect. 4 to prove inequality (16) as a consequence of his equation (2). Unfortunately, we believe that his proof is not correct. A counter-example shows that (16) does not follow from (2) alone. Our objections are not given in a spirit of skepticism, since (16) does follow from other reasonable assumptions of locality and physical reality. These assumptions were discussed in an earlier paper and will be reconsidered in this letter.

To illustrate the falsity of his claim we consider the following local beable situation. A person concocts a set of correlation experiment data. The data consist of four columns of numbers, indexed by event number j. Two of the columns contain the apparatus parameter settings, aj and bj, while the other two columns contain the experimental results, Aj and Bj. These data have been so contrived as to exhibit the correlation specified by quantum mechanics. The person sends the result columns (Aj and Bj) to an apparatus manufacturer; he sends the apparatus parameter settings to the secretaries of two physicists who will perform a correlation experiment using apparatus supplied by the manufacturer. The manufacturer preprograms the apparatus simply to display in sequence the results Aj (Bj) independently of what parameter setting is employed by physicist 1 (2).

Criticisms are presented against Eger's challenge to the demarcation between the natural sciences and ethics. Arguments are given both against his endorsement of the “new” philosophy of science and against his rejection of the fact-value dichotomy. However, his educational recommendations are reinforced rather than weakened by these criticisms.

Martin Eger's essay is extraordinarily rich in penetrating philosophical comments and in educational good sense. Nevertheless, I believe that there are serious errors in his fundamental philosophical theses, and much of this commentary will be devoted to exhibiting them. I shall then try to show that for the most part his educational recommendations are reinforced rather than weakened by my theoretical criticisms.

“NEW” AND “OLD” PHILOSOPHY OF SCIENCE

Eger challenges the demarcation of the natural sciences from the study of morals by questioning that they are different cognitively. The demarcation was clear and strict, he says, as long as an old, essentially positivist conception of the natural sciences was maintained and as long as the factvalue dichotomy was accepted. The “new philosophy of science,” however, has profoundly criticized the old conception, and in spite of some reservations Eger on the whole assents to these criticisms.

THE MOTIVATION FOR MODIFYING QUANTUM DYNAMICS

A cluster of problems – the “quantum mechanical measurement problem,” the “problem of the reduction of the wave packet,” the “problem of the actualization of potentialities,” and the “Schrödinger cat problem” – is raised by standard quantum dynamics when certain assumptions are made about the interpretation of the quantum mechanical formalism. Investigators who are unwilling to abandon these assumptions will be motivated to propose modifications of the quantum formalism. Among these, many (including Professor Ghirardi and Professor Pearle) have felt that the most promising locus of modification is quantum dynamics, and they have suggested stochastic modifications of the standard deterministic and linear evolution of the quantum state (PSA 1990, A. Fine, M. Forbes, and L. Wessels (eds.), East Lansing, Michigan: Philosophy of Science Association, 1991). Others who have followed this avenue of investigation are F. Károlyházy, A. Frenkel, and B. Lukács (Károlyházy et al. 1982), N. Gisin (1984, 1989), A. Rimini and T. Weber (in Ghirardi et al. 1986), L. Diósi (1988, 1989), and J. S. Bell (1987, pp. 201–12). At a workshop at Amherst College in June 1990 Bell remarked that the stochastic modification of quantum dynamics is the most important new idea in the field of foundations of quantum mechanics during his professional lifetime. My own attitude is somewhat cautious and exploratory.

INTRODUCTION

My epistemological position can be described as naturalistic, or, with obvious latitude, as Copernican. It recognizes that a human being is a minute part of a universe which existed long before his birth and will survive long after his death; it considers human experience to be the result of complex interactions of human sensory apparatus with entities having careers independent of their being perceived; and it acknowledges the probability that the fundamental principles governing the natural order will seem extremely strange from the standpoint of ordinary human conceptions. In order to proclaim oneself a Copernican at the present stage in history, one admittedly does not have to be radical and nonconformist. Copernicanism is part of the generally accepted scientific world view, and it has been the doctrine of a number of philosophical schools, such as the American naturalists, the eighteenth-century materialists, the Lockean empiricists, and (anachronistically) the Greek atomists. Nevertheless, this familiar point of view is worthy of restatement, partly because it provides a perspective which can prevent narrowness in the technical investigations of philosophy of science and partly because its implications have by no means been exhaustively explored.

From the Copernican point of view it is natural to see two grand philosophical problems, which may be described by borrowing the vivid phrases of Heraclitus.

The purpose of this lecture is to give a self-contained demonstration of a version of Bell's theorem and a discussion of the significance of the theorem and the experiments which it inspired. The lecture should be comprehensible to people who have had no previous acquaintance with the literature on Bell's theorem, but I hope that explicitness about premisses and consequences will make it useful even to those who are familiar with the literature.

All versions of Bell's theorem are variations, and usually generalizations, of the pioneering paper of J. S. Bell of 1964, entitled “On the Einstein–Podolsky–Rosen Paradox.” All of them consider an ensemble of pairs of particles prepared in a uniform manner, so that statistical correlations may be expected between outcomes of tests performed on the particles of each pair. If each pair in the ensemble is characterized by the same quantum state φ, then the quantum mechanical predictions for correlations of the outcomes can in principle be calculated when the tests are specified. On the other hand, if it is assumed that the statistical behavior of the pairs is governed by a theory which satisfies certain independence conditions (always similar to the Parameter and Outcome Independence conditions stated below, though the exact details vary from version to version of Bell's theorem), then it is possible to derive a restriction upon the statistical correlations of the outcomes of tests upon the two particles.

ASPECTS OF THE DEBATE

The debate between Niels Bohr and Albert Einstein concerning the interpretation of quantum mechanics extended from the fifth Solvay Conference in 1927 until the end of Einstein's life. The most dramatic exchange occurred in 1935, when Einstein, in collaboration with B. Podolsky and N. Rosen, published a paper in Physical Review entitled “Can quantum-mechanical description of physical reality be considered complete?”, concluding with a negative answer, and Bohr replied in the same journal, with a paper of the same title but giving a positive answer. Their arguments were restated, in some respects with greater clarity, in the Library of Living Philosophers volume on Einstein in 1949. The disagreements between Bohr and Einstein concerned not only the physical question expressed in the common title of their papers, but also philosophical questions about physical reality and human knowledge.

Much light was thrown upon the Bohr–Einstein debate by the theorem of J. S. Bell (1964) and the experiments which it inspired. Bell showed that any physical theory which applies to a pair of spatially separated systems (as considered in the thought experiment of Einstein, Podolsky, and Rosen) and satisfies a certain locality condition will, in certain circumstances, disagree statistically with quantum mechanics. Consequently, the supplementation of the quantum mechanical description envisaged by Einstein and his collaborators (usually referred to as a “hidden variables theory”) must either violate the locality condition or clash with quantum mechanical predictions.

PHILOSOPHICAL PERSPECTIVE

The literature of natural science freely employs locutions that prima facie refer to entities – for example, to atoms, the electromagnetic field, a galaxy, black holes, a DNA molecule, a neuron. Scientists speak of properties and states of these entities, of the temporal development of their states, of their interactions with other entities, and of their detection by suitable instruments. Contemporary philosophers of science have intensively discussed metaphysical questions about the ontological status of these putative entities, epistemological questions about cognitive claims regarding them, and semantical questions about the reference of scientific terms and the truth of scientific statements. Although much of the argumentation on these questions is analytically subtle, it is typically not carried out in the context of a broad philosophical world view. This feature of current philosophy of science may be regarded as a virtue by those who are generally suspicious of systems of philosophy, but I dissent.

The purpose of this paper is to discuss various aspects of the problem of realism, especially the ontological status of putative scientific entities, in a broader and I hope more systematic way than usual. I propose to relate the problem of realism to a program which is familiar in systematic philosophies of the past: to understand the knowing subject as an entity in nature and to assess claims to knowledge in the light of this understanding.

INTRODUCTION

One of the virtues which Whitehead claims for his philosophy of organism is that it provides a conceptual framework for quantum theory (SMW chapter 8, PR 121–2 and 145). The theory which he has in mind is the ‘old’ quantum theory, consisting of the hypotheses of Planck (1901) and of Einstein (1905) that electromagnetic energy is emitted and absorbed in quanta, together with Bohr's model of the atom (1913) in which discontinuous transitions were supposed to occur between discrete electronic orbits. The philosophy of organism was presented in a preliminary form in the Lowell Lectures of 1925 (published in the same year as SMW) and in its most systematic form in the Gifford Lectures of 1927–28 (published as PR in 1929). It was during the years 1924–28 that de Broglie, Schrödinger, Heisenberg, Born, Jordan, Bohr, Dirac, and others developed the ‘new’ quantum theory, which was more systematic than the old, much more successful in its predictions, and more revolutionary in its departures from classical physics. Whitehead never refers to the new quantum theory, and it would be unreasonable to expect that even so imaginative a philosopher and scientist could have anticipated it except in the most general terms. Nevertheless, it is important in evaluating the philosophy of organism to determine how well its physical implications agree with quantum theory and with contemporary microphysical theory in general. To do this is the primary purpose of the present essay.

The study of hidden-variable interpretations of quantum mechanics was transformed by two papers of Bell. In his 1966 paper in Reviews of Modern Physics [1] he analysed the argument of von Neumann [2] and the more powerful arguments of Jauch and Piron [3] and of Gleason [4], all leading to similar conclusions about the nonassignability of simultaneous values to all the observables of a nontrivial quantum system; and he showed that these arguments do not exclude what may be called “contextualistic” hidden-variable theories, in which the value of an observable O is allowed to depend not only upon the hidden state λ, but also upon the set C of compatible observables measured along with O. In Bell's 1964 paper in Physics [5] (written later than the other, in spite of the earlier publication date) he gave a new kind of argument against a hidden-variable interpretation of quantum mechanics, by showing that no hidden-variables theory which satisfies a certain condition of locality can agree with all the statistical predictions of quantum mechanics.

The main purpose of this lecture is to discuss an experiment, designed by Clauser, Horne, Holt and myself [6], which is based on Bell's proof of the incompatibility of quantum mechanics and local hidden-variable theories. Before doing this, however, I wish to make several comments.