Chapter 28 Metaphysical Problems in the Foundations of Quantum Mechanics
Abner Shimony I propose to summarize a certain line of development in the foundations of quantum mechanics-partly theoretical and partly experimental-and to examine its philosophical implications. The major ideas of this line of development are fairly simple and can be conveyed without complicated calculations. In order to avoid arousing expectations which cannot be fulfilled, I wish to say in advance that the philosophical implications which will be drawn from analyzing the foundations of quantum mechanics are not unequivocal and unqualified. They take the form rather of a disiunction: there appear to be only two options left open by the results of experiments, and we cannot at the present time say which option is correct. I think we can confidently say that either option is momentous, metaphysically or epistemologically; we must recognize either that the intrinsic properties of the real world are very strange indeed, or that scientific theories say much less about the intrinsic properties of things than scientists have commonly assumed.
I. Data and Resulting Problems Let us begin our analysis by looking at some of the elementary formalism of quantum mechanics. It will be convenient to use the concept of the "state" of a physical system, even though it is a subtle concept that may have to be refined as a result of analysis. Roughly, a state of a physical system is a maximal specification of it-i.e., a specification of the contingencies of the system such that nothing more can be said of it that is not either redundant or contradictory. Quantum mechanics assumes that the set of possible states of a physical system obeys the superposition principle, which can roughly be explained as follows.' Suppose F is a dynamical variable of the system (often called an "observable") such as the position of the system along a certain axis. Let u, be a state of the system in which F has the value f, and let u, be a state in which F has the value f,, where f, and f, are unequal to each other. Then the superposition principle says that there are states of the system achieved by combining u, and u, (actually, infinitely many such states, by combining u, and u, in different ways), in which F has no definite value whatsoever. Thus, if u is one of these states, and F is taken to be position along the vertical axis, then a system in the state u does not have a definite position along the vertical axis. From the precise way in which u is obtained by combining u, and u, one can calculate the probability that F will be found to have the value f, and the probability that it will have the value f, in case F is measured. (The probability that it will be found to have a value other than f, or f, is 0.) It would not be correct, however, to construe this statement about probabilities as meaning that the Reprinted from International Philosophical Quarterly V111 (1978),pp. 2-17, by permission of the author and the publisher.
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value of F is definite but unknown and that the probabilities only refer to the observer's state of knowledge. Such an interpretation would conflict with the assertions that u is a state of the system, and that a state is a maximal specification of the system. Thus the superposition principle has the remarkable, and metaphysically significant, consequence that any dynamical variable which is non-trivial, in the sense that it can take on at least two distinct values, will have no definite value at all in some possible states of the system. The combination of the feature that a dynamical variable may have an indefinite value in a given state with the feature that the probabilities of various outcomes are well determined in case the dynamical variable is measured, led Heisenberg to assert that quantum mechanics gives potentiality a fundamental status in nature., To be sure, the quantum mechanical concept of potentiality is very different from the Aristotelian concept, but it seems appropriate to borrow Aristotle's terminology in order to characterize a situation of indefiniteness from which passage to a situation of definiteness can take place. Another remarkable consequence of quantum mechanics is obtained if we consider a composite system consisting of two simpler systems. Let u, and u, be states of component I in which F has distinct values f, and f,, and let v, and v2 be states of component II in which the dynamical variable G has distinct values g, and g,. One possible state of the composite system I I1 can be represented by u,v,, which signifies that component I is in state u, and component 11 is in state v,. (Representing the composite system in this way is not tantamount to denying that the two parts affect each other, for indeed each may exert forces on the other which modify their motions and their internal development. However, the effect of each on the other can be taken into account by considering the dynamical evolution of the composite system I II after it is prepared in the state u,v, at the initial time.) Similarly the composite system I I1 can be prepared in the state u2v2 which is to mean that I is in the state u2 and I1 is in the state v,. So far nothing has been said that conflicts either with common sense or with classical physics. Now, however, let us apply the superposition principle to the states u, v, and u,v,. There are many ways to combine u, v, with u2v2, but no matter how the combination is performed, provided that there is some contribution from both, the resulting state has a remarkable property which has been called "quantum nonseparability": it does not permit us to attribute to component I by itself a definite state and fo component II by itself a definite state.3 We thus have a quantum mechanical version of the meta-physical thesis of holism. The thesis is roughly that there are states of composite systems which cannot be fully expressed in terms of the states of the components. Traditionally, this is a thesis maintained by antireductionist biologists, who have asserted that even after one has completely specified every physical atom in an organism, there is something about the organism as a whole which has been omitted. Holism is still maintained by some biologists, but it appears that reductionism is the new orthodoxy, especially among molecular biologists. A very eloquent presentation of the reductionist position in biology is given by Jacques and it is interesting that a review of this book Monod, in his Chance and Nece~sify,~ was written by d'Espagnat under the title "Une lacune d'importance"5-the lacuna being the peculiar quantum mechanical version of holism that appears in the very formalism which Monod relies upon for giving a physical explanation of reproduction, teleonomy, and biological stability. It should be emphasized that the quantum mechanical version of holism is very unlike the traditional versions: it does not say that the state of the whole fails to be exhausted by a specification of the states of the parts but rather that the parts just are not in definite states. Even when this modification is recognized, however, it is ironical that tough-minded physicists have become the ad-
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vocates of a doctrine which historically was defended by tender-minded and romantic writers. But that is re cis el^ what the formalism of quantum mechanics requires, if we are forced to interpret it at face value. But must we interpret quantum mechanics at face value? Could it be that the apparent implications of indefiniteness of dynamical variables, of the ontological status of potentialities, and of quantum nonseparability all stem from an unwarranted assumption that the quantum mechanical state really is a maximal specification of the physical system? If the indefiniteness that is found in the quantum mechanical state is only an expression of the physicists' ignorance, rather than an intrinsic characteristic of the system, then the bizarre metaphysical implications of quantum mechanics would dissolve. There is indeed nothing paradoxical or strange about our state of knowledge being indefinite in certain respects, or consisting of probability evaluations, or about our knowledge of one component of a composite system being correlated with or contingent upon our knowledge of another component. (This last characteristic is exhibited trivially in classical physics when one deals with a conserved quantity which is partitioned in an unknown manner among several parts of a composite system.) Thus, an evident avenue of escape from the bizarre philosophical implications of quantum mechanics is to regard the quantum mechanical description of a physical system, that is, its quantum mechanical state, as being incomplete.
II. The EPR Argument There is a beautiful argument of Einstein, Podolsky, and Rosen (EPR) published in 1935, which purports to show that the incompleteness of the quantum mechanic description is not just a desideratum for the purpose of avoiding strange, or unintuitive, or nonclassical philosophical implications, but that it is actually required by the formalism of quantum mechanics i t ~ e l fMore . ~ precisely, their conclusion is required by the formalism of quantum mechanics together with two additional premises, which they regarded as entirely reasonable. I shall briefly summarize their argument, in a somewhat different form from the original presentation, partly in order to expedite the linkage to the later work of Bell and of experimentalists, and partly in order to make explicit the additional premises. Let us take the two-component system I 11, which was described only in very general terms so far, to be a pair of photons (which are the quanta of light). We shall make use of two quantum mechanical assertions concerning photons. The first is that if a photon is re pared in a state of linear ~olarizationalong a certain axis, then its state of polarization along any axis which is neither perpendicular nor parallel to the first is indefinite, and it has non-zero probability of passing and non-zero probability of not passing through an ideal analyzer oriented along the second axis. The second assertion is that a pair of photons can be prepared in a state \Y with the following characteristics: photon I is propagating in the positive direction along a certain axis, which we shall call the z-axis, and photon II is propagating in the negative direction along this axis. Neither photon I nor photon 11 is in a definite state of linear polarization, but their polarization properties are correlated, so that if photon I is found to have linear polarization along the x-axis or along the y-axis, then so also will photon 11. Here the x- and y-axes are any two axes which are ~erpendicularto each other and also to the z-axis. There are infinitely many choices of the x- and y-axes, since any pair of perpendicular directions in the plane perpendicular to the z-axis are suitable candidates, and we shall take x', y' and x", y" to be two distinct choices of these axes. It can be exhibits ' quantum nonseparability, but we shall not insist upon shown that the state '-I
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this fact at this point, since one of the motivations for conjecturing the incompleteness of quantum mechanics is to discover a deeper level of description at which nonseparability is eliminated. What cannot be eliminated, however, are the experimental predictions based upon Y, which must be correct if Y is a correct description on the quantum mechanical level. When Y correctly describes the photon pair, one can predict that if photon I passes through an ideal polarization analyzer oriented along the x' direction, then photon 2 will also pass through an ideal polarization analyzer oriented in that direction; and failure of the first photon to pass would imply failure of the second to pass. Similarly, photon I will pass through an ideal polarization analyzer oriented in the x" direction if and only if photon 2 will pass through an ideal analyzer oriented in that direction. The argument of EPR now proceeds in the following way. The experimenter can choose to observe the polarization of photon 1 relative either to the axis x'-y' or to x"-y". According to his choice, the polarization of the second photon would be well-determined relative either to the x'-y' or to the xu-y" axes, in view of the correlations implied by Y . In neither case is the second photon subjected to any disturbances-upon assumption that there is no action-at-a-distance. Consequently, each property of photon 2 which would be well-determined, if the experimenter measured the corresponding property of photon I, must in fact be well-determined no matter what observation the experimenter chooses to make upon photon I. It follows, therefore, that the polarization of photon 2 is well-determined relative to the x'-y'axes, to the xu-y" axes, and indeed to every set of axes perpendicular to the propagation direction. But this conclusion demonstrates the incompleteness of the quantum mechanical description, for the quantum mechanical state of a single photon can at most specify the polarization relative to a single pair of perpendicular axes and must leave polarization relative to any other set of axes indeterminate. Let us now recapitulate the premises of the argument of EPR. I. One premise is that it is possible to prepare two-photon systems so that Y correctly describes them (yields correct predictions). This premise needs no discussion, because it is implied by quantum mechanics and furthermore is quite strongly supported by experiment. 2. A second premise was already stated explicitly: that there is no action-at-adistance. If a certain action-at-a-distance does occur the conclusion of EPR does not follow. Specifically, one could imagine that when the two-photon state is represented by Y , then the polarization of photon 2 is well-determined in no direction at all; but as soon as the polarization of photon I is determined relative to some definite pair of axes x'-y' by virtue of confronting photon I with a polarization analyzer oriented along one of this pair of axes, then instantaneously photon 2 also acquires a definite polarization relative to x'-y'. EPR assume that no such instantaneous causal sequence occurs. 3. A third premise is implicit in the argument but has not been stated explicitly: it is a strong version of the famous EPR "reality criterion." Their criterion reads as follows: "If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity."' The reason for saying "strong version" is that there is an important ambiguous word in the criterion -the word "can." The word may be used broadly, so that it is true to say that we "can predict" the value of several quantities, which are such that the actual prediction of any one of them is incompatible with the actual prediction of another. In spite of this incompatibility, the word "can" is appropriate because the experimenter is free to make any choice among the quantities in question. O n the other hand, the word may be used narrowly, so that we "can predict" the value only of that quantity which will
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actually be measured, and it is false to say that we can predict the value of any quantity requiring an experimental arrangement incompatible with that which actually will be used. If "can" is used broadly, then we have a strong form of EPR's criterion; if it is used narrowly, then we have a weak form of the criterion. Unless the strong form of the EPR reality criterion is used, their conclusion does not follow. The weak form of the criterion would permit one to conclude only that the polarization of photon 2 is well determined relative to that set of axes which is picked out by the experimental arrangement actually used in examining photon I; then there would be no grounds for saying that the quantum mechanical description is incomplete. Whether the word "can" is used broadly or narrowly is not just a matter of semantical convention; an important issue of metaphysical commitment is involved. If a physical system is conceived to possess a set of intrinsic properties, independently of whether it is observed or not, then the broad sense is appropriate: since we could have been in a position to predict with certainty the value of a physical quantity, though actually we made a choice which prevented us from being in that position, we are entitled to say that there is an element of physical reality corresponding to the quantity, for what we choose to do is irrelevant to the intrinsic properties of the system. O n the other hand, if the set of properties which can be attributed to a system is relative to the experimental arrangement used for observing the system, then the narrow sense of "can" is obligatory. It should be evident, however, that from the realistic point of view of most working scientists the broad sense of "can" is unequivocally the appropriate one, and hence the strong version of EPR's criterion is correct. I hope that the rigor and beauty of the argument of EPR is apparent. If one does not recognize how good an argument it is-proceeding rigorously from premises which are thoroughly reasonable-then one does not experience an adequate intellectual shock when one finds out that the experimental evidence contradicts their conclusion. The shock should be as great as the one experienced by Frege when he read Russell's set theoretical paradox and said, "Alas, arithmetic totters!"
111. Testing for Hidden Variables
A number of attempts have been made (some of them antedating the argument of EPR) to construct descriptions of physical systems which are more complete than the quantum mechanical description.' The generic name for such descriptions is "hidden variables theories." I shall not try to summarize the complex history of these theories, but shall mention only the work of J. S. Bell and his followers, which threw the most light upon the argument of EPR. Bell showed that any hidden variables theory that satisfied a condition which he called "locality," which essentially asserted that there is no action-at-a-distance, must make statistical predictions which disagree with those made by quantum mechanic^.^ Suppose that the polarization analyzer for photon I can be oriented either along the x,' or the x," axes, and that the polarization analyzer for photon 2 can be oriented either along the x,' or the x," axes. Suppose a collection of photon pairs is prepared in a certain way, so that the statistical behavior of the collection is well determined. Let P,(x,') be the probability that photon I from one of these pairs will pass through the first polarization analyzer, if the analyzer is oriented in the direction x,', and let P,(x,") have a similar meaning. Likewise, let P2(x2')be the probability that photon 11 from one of these pairs will pass through the second analyzer, if it is oriented in the direction x,', and let P2(x2")be similarly defined. Let P(xI1,x,') be the probability that photons I and I1 will pass respectively through the
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first and second analyzers, if these are respectively oriented in the x,' and x,' directions, and let P(xll,x,"), P(xlU,x,") have similar meanings. An argument related to Bell's shows that if the collection of photon pairs is governed by any local hidden variables theory, l o then P(x,', x,') - P(x,', x,")
+ P(x,", x,') + P(x,", x,") - P1(xl") - P2(x2')1 0.
(I)
Now let us make a particular choice of the directions: All are to lie in the plane perpendicular to the direction of propagation of the photons, and x,' can be chosen arbitrarily, but x,', x,", and x," are to make angles respectively 2 2 9 , 45", and 6 7 9 relative to x,'. It can be shown that if the collection of photon pairs is prepared so that their quantum mechanical description is the state 'I'considered above, then the quantum mechanical values for the probabilities of photon passage through the analyzers are: P,(x,") - P,(x,')
=$
P(xll,x,') = P(xll', x,') = P(xlU,x,")
=
,427
P(xll,x,") = .074 Hence, according to quantum mechanics
in clear disagreement with the inequality (I)which governs all local hidden variables theories. This result is most remarkable, because of its great generality, for it shows that there is a discrepancy between quantum mechanics and all the hidden variables theories of the kind envisaged as physically reasonable by EPR. The existence of this discrepancy made it possible to design and carry out experiments which tested quantum mechanics against the entire family of local hidden-variables theories." What is the experimental evidence? Well, it is complex. At least seven experiments have been performed to test local hidden variables theories, and the results are not unanimous. Five favor quantum mechanics and two favor local hidden variables theories. This is not a question on which there should be majority rule, and it really is important to look carefully at the experiments and to try to assess the validity of each: the plausibility of assumptions made in each, the possibility of systematic errors, the possibility of random errors. I shall not try to do this, but shall only make three remarks. One is that the preponderance of opinion at a workshop on this question last year at Erice was that the most reliable experiments (those of Freedman and Clauser,12 Fry and Thompson,13 and Clauser14) were the ones favoring quantum mechanics. A second remark is that even if the score were not five to two in favor of quantum mechanics, but, say, three to four, I would have trusted the experiments favoring quantum mechanics, and this is not just because of conservatism in favor of a highly successful theory. My reason is that the quantum mechanics prediction is both highly correlated and very specific, while the local hidden variables prediction sets a limit on correlations and is relatively unspecific (only an inequality). If quantum mechanics is correct, it is easy to see how experimental errors could wash out high correlations and produce results in agreement with Inequality (I);but if some local hidden variables theory is correct, it would require a most improbable set of coincidences or conspiracies to produce the highly correlated and highly specific quantum mechanical predictions. A third remark is that some loopholes are left even by the experiments which favor quantum mechanics, which leave some hope for advocates of local hidden
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variable theories: especially, the experimental arrangements actually used in the experiments are such that Bell's locality assumption may not hold. Polarization analyzers are set in place for several minutes at a time, during which the hidden variables of one polarization analyzer could become aware of the orientation of the other analyzer and take appropriate action to allow an incoming photon to pass or not pass. Of course, this sounds like science fiction, but since we are aiming at results of great generality, it is desirable to exclude even such an implausible possibility, and indeed there is an experiment going on which is intended to block this loophole.
IV. Theoretical Implications: Option I For the rest of this article I shall take it that local hidden variables theories are excluded, so that one or the other of EPR's second and third premises must be false. I think it should be clear that this conclusion is momentous, as claimed at the beginning. If the second premise is false, then there is action-at-a-distance, contrary to the view of space-time structure which we have learned from special and general relativity theory, and contrary to an immense body of experimental evidence. If the third premise is false, then the strong version of the EPR reality criterion must be abandoned, which, as I tried to explain, is tantamount to abandoning the "realistic" view that a physical system is endowed with an intrinsic set of properties independent of what observations one intends to perfom upon it. We thus seem to be left with only two philosophical options, both of which are radical. I shall discuss the latter of these two options first-the abandonment of a realistic interpretation of quantum mechanics of physical systems-since it is the more familiar in the literature and indeed seems to have been the view of Niels Bohr, and with some variations, of various other advocates of the Copenhagen interpretation of quantum mechanics. Bohr's former assistant, Petersen, quotes Bohr as saying, "There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.'"' Petersen says elsewhere that the radical way in which Bohr broke with tradition was to abandon an ontological mode of thinking.16 I am not fully confident that this is the most accurate exegesis of Bohr's rather cryptic philosophical statements, but it does seem to me to be a way in which one can deny the strong version of EPR's reality criterion. It is possible, in my opinion, that we shall be forced to accept this non-ontological philosophy as a last resort, but for several reasons I find it very unappealing. (I) It is a very anthropocentric view of scientific knowledge, which does not accurately characterize the scientific enterprise. Obviously and trivially, there is no human scientific knowledge without human knowers, but this banal fact does not by itself imply that there is any feature of nature which is necessarily hidden from human beings because of human limitations, or that there is any uncorrectable distortion of our representations of things because of peculiarities of human faculties. The history of science has been in part a history of discoveries of corrections to anthropocentricism: of overcoming human limitations by inferring features of nature which are remote from direct perception from features which are directly perceivable, and of taking into account any correcting for peculiarities of our sensory and cognitive faculties. There is no evidence that the microphysics of the twentieth century has been a breakdown or a reversal of this history of corrections to anthropocentrism. It seems quite the contrary. The ingenious utilization by experimentalists of long causal chains has made it possible to measure spatial distances which are ten orders of magnitude or more
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smaller than can be discriminated visually. Nor does it seem that we are trapped by our innate intellectual equipment, for such feats as the entertainment of the conception of a superposition of states in which the position of a body is indefinite seems to me to indicate a remarkable elasticity of that equipment. (2) For the most part, those peculiarities of the quantum mechanial description of phenomena which can be cited against a "realistic" view of physical systems and in favor of a nonontological view do not seem to involve mutually incompatible experimental arrangements. Thus, Heisenberg's position-momentum uncertainty relation shows up in an expression for thermodynamic entropy in which there is no concern is with either a position or a momentum measurement. And quantum n~nseparabilit~ omnipresent in atomic, nuclear, and solid state physics in situations in which the experimentalists are not overtly measuring correlations. It is hard, therefore, to shake off the impression that these peculiarities of the quantum mechanical description are intrinsic characteristics of the things themselves and not just of our way of looking at or talking about the things. (3) Most important, I do not believe that a fully worked out and coherent formulation of a nonontological interpretation of quantum mechanics exists in the literature, in writings of Bohr or of any one else. We have a standard of comparison, for there is one great and quite fully worked out non-ontological philosophy which antedates quantum mechanics: namely, the transcendental philosophy of Kant. It is, of course, central to Kant's philosophy that we have no knowledge of things in themselves, but only knowledge of phenomena. But then Kant undertakes the obligation of explaining why our knowledge has the structure that it does have, if that structure cannot be attributed to the things-in-themselves: the structure is imposed by the knowing subject, the faculties of intuition supplying the forms of space and time and the faculty of understanding supplying the categories. I am completely unconvinced by Kant's explanation of the structure of our knowledge, but I do admire him for his sense of responsibility in undertaking to work out a detailed epistemology, instead of elliptically stating a program. What, according to Bohr, plays the role of Kant's transcendental self in establishing the structure of our physical knowledge? It seems not to be the knowing self since Bohr explicitly denies that he is any kind of idealist.17 If it is the character of experimental apparatus, then a nest of troublesome problems is opened: is the apparatus to be considered as "real" in an unequivocal sense, so that the position is not nonontological at all, but rather is a kind of ontological commitment to macrophysicalism? And is it not strange that the macrophysical apparatus has to be described in microscopic terms, and specifically quantum mechanically, in order to understand how it works-which would be a peculiar kind of macrophysicalism? In short, I am gladly willing to say that Bohr is a great phenomenologist of scientific research-that he has said some profound things about experimental arrangements-but I do not see that he has been able successfully to bypass the question of characterizing the intrinsic states of physical systems. V. Option I1
The other option is to admit at least one type of action-at-a-distance. The type that is called for can be seen by refemng to the argument of EPR. Suppose that we have a two-component system in a nonseparable quantum state, like the state Y/ of a 2photon system. The nonseparability is itself a metaphysically radical feature of the composite system, but it is not in contradiction with a "realistic" view of physical systems. It does, however, impose a peculiar understanding of realism. We are forced
! /\f
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to say that neither photon by itself can fully be considered to be a system, in the sense being in a definite state. Only the two-photon system is in a definite state, and like any system in a definite state it is such that certain dynamical variables have definite values whereas others have indefinite ones. But from a "realist" point of view, this peculiar web of actuality and potentialities constitutes the intrinsic character of the two-photon system. When photon I is confronted with a polarization analyzer oriented along the x-axis, then there is a transition from potentiality to a new actualitythe polarization of photon 1 relative to the x-axis becomes definite; and this transition implies that photon 2 also makes the same transition from potentiality to actuality, for it achieves a definite polarization with respect to the same axis. Since we are now construing the properties of physical systems realistically, the transitions in question are events, and they appear to be causally connected in spite of their space-like separation." Here, then, is an action-at-a-distance. But it is a very special action-ata-distance. It takes place only when one has a composite system exhibiting quantum nonseparability-which means that the potentialities of the components are interconnected-and when a transition from potentiality to actuality is induced in one of those components. One peculiarity of this situation is the following: there exists no dynamical variable (observable) of photon 2 which had one definite value prior to the experiment performed on photon I and a different value afterwards. The only changes which have occurred conceming photon 2 are from the indefiniteness of certain t ~very closely bound up with the dynamical variables to definiteness. This ~ e c u l i a r i is fact that there seems to be no way of utilizing quantum nonseparability and the kind of action-at-a-distance that we have just been discussing for the purpose of sending a message faster than light. Upon reflection, we may even question whether it was correct to characterize the transition from potentiality to actuality which occurred in photon 2 as an event, just because it fails to share one or more of the classical properties of events. If we understood better just what is involved in the quantum mechanical transition from potentiality to actuality, then we would be in a better position to assess the implications of the kind of nonlocality exhibited in nonseparable quantum systems. We should like to know what implications quantum n~nseparabilit~ has for the geometrical structure of space-time. If there is a genuine causal relation between two events with space-like separation, then our present conception of space-time structure must be changed, because in both special and general relativity theory such causal relations are excluded. Can we make any reasonable conjectures about the kind of change in the conception of space-time structure that would be required? Here is one possibility, suggested by Wheeler's idea of "wormholes," which crudely are topological modifications of space-time whereby two points are close to each other by one route and remote by another.19 (His motivation is entirely different from mine: it is to explain the occurrence of sources of lines of the electric field without postulating charge as a primitive physical entity. But there is no reason why we cannot use his idea for other purposes.) My conjecture is that when we have a system consisting of two apparently spatially separated but correlated components, the microstructure of spacetime exhibits a wormhole, and the two components are actually close to each other by one route (via the throat of the wormhole). Hence a causal connection between two events conceming the two components only apparently violates locality, because from a microscopic point of view the events do not have a space-like separation after all. Finally, we may suppose that in the rnaao-structure of space-time these wormholes cannot be capitalized upon to send messages between two points with apparent
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space-like separation. Wheeler's own reaction to this speculation was skeptical,20and I cannot but agree. Another possibility is to say that there can be a peaceful coexistence between the causal structure of relativistic space-time and the nonlocality exhibited in the EPR situation, just because different modalities of reality are involved in the two contexts. Classically, the structure of relativistic space-time governs causal relations between events, which are loci of actualities. Quantum mechanically, especially in quantum field theory, the structure of relativistic space-time governs causal relations between potentialities (technically, an observable A(x) constructed out of field operators at point x and an observable B(xl) constructed out of field operators are x', commute2' if x and x' are points with space-like separation). But the "events" in the EPR situation are hybrid entities-they are transitions from potentialities to actualities. Because of the hybrid character of these "events," they may be governed neither by the classical nor by the quantum mechanical versions of the relativistic restrictions upon causal relations. For this reason, there could be peaceful coexistence between relativistic spacetime structure and the nonlocality we have been discussing. This is indeed an answer, but is it a solution? It looks suspiciously like a way of avoiding the analysis of an extremely puzzling situation. Again, I would say that if we really understood what goes on in the transition from potentiality to actuality, we would be able to assess better whether or not we have a solution. I shall consider, finally, one very speculative line of thought on quantum mechanics. Several physicists have suggested that the transition from potentiality to actualitye.g., from a plane wave state in which position is indefinite to a state in which position is definite-is a real process which requires the intervention of mentality. J. M. BurgersZ2 and 0. Costa de BeauregardZ3 have boldly taken this position, and E. Wigner24 has quite cautiously considered it. I do not believe that this conjecture is correct, but I think that some considerations on mentality may make us open-minded towards the conjecture. The considerations I have in mind are these: First, mentality does prima facie seem to be a fact in nature, and not something outside of nature to which nature is presented; the facts of birth, death, sleeping, waking, anaesthesia, shock, inducement of sensations by direct stimulus of nerves, etc., all overwhelmingly support the thesis that mentality is a fact in nature. The second consideration is that the general framework of quantum mechanics seems to be tolerant of and perhaps even hospitable to mentality. The flickering and exploratory character of mentality might somehow be accommodated to the superposition principle, with its implications for the indefinite values of dynamical variables; the interplay between conscious and unconscious levels of mind seems to require a framework in which potentiality plays a crucial role; and the nonlocalization of mentality and its function in coordinating the organs and holistic of the body fit naturally into a framework which permits n~nseparabilit~ correlations. I do not mean to suggest that we have any clear theories about formulating psychology along quantum mechanical lines. I only want to convey the idea that the quantum mechanical framework has the kind of subtle structure which an adequate naturalistic theory of mentality requires. These considerations are enough to make us open-minded to the conjecture that the quantum transition from potentiality to actuality involves mentality, but this openmindedness ought to be balanced by a clear-minded critical attitude. In the spirit of critical open-mindedness, three of my students and I designed and performed a simple experiment to see whether mentality might be involved in a transition from potentiality to actuality.25 Gamma-rays from a sample of sodium-22 atoms were studied with an apparatus consisting of a scintillation detector, a series of amplifiers for amplifying
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pulses from the detector, and two scalers in separate rooms on each of which all detection events were registered. In the quantum theory of gamma emission a nucleus is regarded as being in a superposition of an "undecayed" and a "decayed" state, and the relative weights of these two states determine the probability of the decay. After an appropriate time interval the composite system consisting of source and apparatus is in a superposition of two states, one in which a detection of an emitted photon has occurred and one in which it has not. Now according to the speculative hypothesis under consideration, the transition of this superposed state to one in which there is a definite occurrence of a detection or a definite nonoccurrence of a detection takes place only when an observer looks at one of the scalers. Either of the two scalers can be used for this purpose, and if there are two observers A and B, one near each scaler, then presumably the first to look is responsible for the transition. Now suppose that A exercises an option to look or refrain from looking at his scaler, but if he does so, he does it before B looks. If A's looking actually changes the state of the physical system, then possibly B's experience will be different from what it would be if B were responsible for the transition. Now we examine whether A can send a message to B by choosing to look or not to look at his scaler. If A keeps a record of when he looks and when he refrains from looking on successive occasions, and B keeps a record of when he subjectively feels that he is responsible for the transition and when not, then a comparison of the two records should show whether A has communicated with B. It must be emphasized that this is not an ESP experiment. It is an experiment to test a certain type of psycho-physical interaction, and to see whether the action-at-a-distance considered previously could in fact be used to send a message. Without going into details, I report that the experimental result was negative. In 554 trials, exactly half of the decisions made by B about whether A looked were correct, and exactly half were incorrect. This is roughly the result we expected, though the fact that there was 0 deviation from the mean is almost too good. I do not want to claim too much for the decisiveness of our experiment. Two remarks will suffice. We did want to show that it is possible to be both open-minded to outre5 hypotheses and very tough-minded in testing them. And the fact that one is drawn into thinking about such speculative hypotheses should underline the bafflement which we feel at this stage in the history of quantum mechanics, in which each easy and commonsensical avenue of interpretation seems to have reached an impasse. I shall conclude with some wise advice from Hermann Weyl about the puzzling intellectual situation in which we find ourselves: "The example of quantum mechanics has once more demonstrated how the possibilities with which our imagination plays before a problem is ripe for solution are always far surpassed by reality."26 Notes The research for this paper was partly supported by the National Science Foundation. I. The superposition principle is discussed in all textbooks on quantum mechanics. A very good introductory discussion can be found in J. Andrade e Silva and G. Lochak, Quanta (New York: McGraw-Hill, 1969). A more advanced discussion of this principle and of most other topics in the foundations of quantum mechanics may be found in B. d'Espagnat, Conceptual Foundations of Quantum Mechanics, 2nd Ed. (Reading: Addison-Wesley, 1976). 2. W. Heisenberg, Physics and Philosophy (New York: Harper, 1958), p. 53. 3. E. Shrodinger, "Discussion of probability relations between separated systems," Proceedings of the Cambridge Philosophical Society, 31 (1935). 555-562. Also B. d'Espagnat, op. cit. 4. J. Monod, Chance and Necessity (New York: Knopf, 1971). 5. B. d'Espagnat, "Une lacune &importance,"Les Nouvelles Littiaires, May 16, 1977.
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6. A. Einstein, B. Podolsky, and N. Rosen, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" Physical Review, 47 (1935). 777-780. 7. Ibid., p. 777. 8. An excellent survey article is J. S. Bell, "On the Problem of Hidden Variables in Quantum Mechanics," Reviews of Modem Physics, 38 (1966). 447-452. 9. 1. S. Bell, "On the Einstein Podolsky Rosen Paradox," Physics, 1 (1964), 195-200. 10. R. A. Holt, Ph.D. Thesis, Harvard University, 1973 (unpublished); J. F. Clauser and M. A. Home," Experimental Consequences of Objective Local Theories," Physical Review, DIO (1974), 526-535. 11. J. F. Clauser, M. A. Home, A. Shimony, and R. A. Holt. "Proposed Experiment to Test Local Hidden-Variable Theories," Physical Review Letters, 23, (1969), 880-884. 12. S. J. Freedman and J. F. Clauser. "Experimental Test of Local Hidden-Variable Theories," Physical Review Letters, 28 (1972), 938-941. 13. E. S. Fry and R. C. Thompson, "Experimental Test of Local Hidden-Variable Theories," Physical Review Letters, 37 (1976). 465-468. 14. J. F. Clauser, "Experimental Investigation of a Polarization Correlation Anomaly," Physical Review Letters, 36 (1976), 1223-1226. 15. A. Petersen, "The Philosophy of Niels Bohr," Bulletin of the Atomic Scientists, 19, no. 7 (1963). 8-14. 16. A. Petersen, Quantum Physics and the Philosophical Tradition (Cambridge: MIT Press, 1968). 17. N. Bohr, Atomic Physics and Human Knowledge (New York: Science Editions, 1961), p. 11 and pp. 78-79. 18. Two events have space-like separation if it is impossible to send a signal from one to the other without exceeding the velocity of light. 19. J. A. Wheeler, Geometrodynamics (New York: Academic Press, 1962). 20. Private communication. 21. "Commutes" implies that their measurements d o not interfere with each other. 22. J. M. Burgers, "The Measuring Process in Quantum Theory," Reviews of Modem Physics, 35 (1963). 145-150, and Experience and Conceptual Activity (Cambridge: MIT Press, 1965). 23. 0 . Costa de Beauregard, "Time Symmetry and Interpretation of Quantum Mechanics," Foundations of Physics, 6 (1976), 539-59. 24. E. P. Wigner, "Remarks on the Mind-Body Question," in The Scientist Speculates, I. J . Good, ed. (London: Heinemann, 1962). reprinted in Symmetries and Repections (Bloomington: Indiana Univ. Press, 1967). 25. J. Hall, C. Kim, B. McElroy, and A. Shimony, "Wave-Packet Reduction as a Medium of Communication," Foundations of Physics, 7 (1977). 759-67. 26. H. Weyl, Philosophy of Mathematics and Natural Science (Princeton U. Press, 1949), p. 283.
