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Quantum theory, EPR experiments and locality
Volume 133, number 9
PHYSICS LETTERS A
5 December 1988
QUANTUM THEORY, EPR EXPERIMENTS AND LOCALITY M.A.B. WHITAKER and J.G. DENNISON Department of Physics, University of Ulster, Coleraine, Northern Ireland Received 30 April 1988; revised manuscript received 29 August 1988; accepted for publication 4 October 1988 Communicated by J.P. Vigier
Kraus has claimed that there is no evidence that the quantum predictions for experiments of EPR-type exhibit non-locality. We suggest he has not considered fully correlations between the observations on the two arms of the apparatus.
Since the pioneering work of Bell [ 1 ], many papers have appeared asserting that the quantum-mechanical predictions for certain experiments of the EPR-type [2] are inconsistent with attribution of some basic properties to the physical universe. Experiments of Aspect et al. [ 3 ] suggest that the quantum predictions are correct, though other workers [4,5 ] continue to search for loopholes in the analysis of these experiments. The common assumption of Bell-type arguments is of locality (Einstein locality, EPR locality, to be discussed later). In addition, many papers [1,6-8] use the idea of hidden variables (or realism). In most of these papers, hidden variables are assumed. Bell [9], though, argues strongly that neither EPR, nor his own argument [ 1 ], assumes realism (or, indeed, determinism). Rather they move from locality to the concept of deterministic hidden variables in preliminary arguments. Other workers [ 10-15 ] have sought to present arguments with the same result, but without any use of the concept of hidden variables. They analyse the resuits of a run of experiments, and claim to demonstrate that the demands of locality are in conflict with the quantum predictions. Foremost among those adopting this position has been Stapp [ 10 ], who has put forward arguments of novelty and power in this direction. As practically a lone voice, Kraus [ 16,17 ], while accepting [ 17, p. 477] what he terms the usual proofs of Belrs theorem (i.e. those assuming, or making use of, hidden variables), has claimed that the predicted 466
results of all experiments of EPR-type may be explained without assuming non-local influences. He acknowledges that his conclusions are in direct opposition to those of Stapp [ 10 ] and others [ 11-15 ]. The assumptions of Stapp have themselves been strongly questioned by Kraus himself [ 16,17 ], and others [18,19]. The argument centres around the question of counterfactual definiteness (CFD) - the idea that unperformed experiments have definite, though unknown, results. The questions to be asked are to what extent this concept may be justified, and its role, if any, in Stapp's analysis. Stapp [20] has given what amounts to a reply to this criticism and has subsequently returned to the discussion in a number of publications [ 21,22 ]. The question remains one of considerable subtlety. Thus, if one were able to accept Kraus' own contributions, it might appear that the work of Stapp could be put on one side, and one might feel able to conclude, with Kraus, that there is no conflict between quantum mechanics and locality (though it should be stressed that this does not take into account the argument of Bell [9 ] mentioned earlier). Thus scrutiny of Kraus' arguments and conclusions seems a matter of considerable urgency, and it is the subject of this Letter. Analysis is made a little more difficult by developments - in particular, changes in terminology between the two papers of Kraus. In rcf. [ 16 ], the terminology used is macroscopic locality;it is this quantity which Kraus claims is completely consistent with quantum predictions of EPR-type experi-
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ments. He defines macroscopic locality as the condition that macroscopic events in one region are not influenced by macroscopic events in a second region, spacelike separated from the first. Macroscopic events may be divided into two cate g o r i e s - manipulated (m-type) and resultant (rtype). The former are operations carried out by supposedly-free experimenters - setting devices, passing signals, opening slits, and so on. The latter are macroscopic events that take place out of the control of experimenters. In particular, they include observations. An experimenter may set up a given measurement, but cannot, of course, determine what result is obtained. The distinction between events of m- and r-type is not to be taken for granted. Indeed it is the subject of a controversy between Bell [23], who does assume the distinction, and Shimony et al. [ 24 ]. The latter suggest that experimenters should not necessarily be considered free. Their actions may be influenced by previous events, which may also have influenced the objects the experimenters are studying, and, indeed, other objects with quantum states correlated with these. In his reply, Bell [ 25 ] says that the distinction may not be sound metaphysics, but he considers it the standard assumption of good theoretical physics. In this Letter we assume a clear distinction between m- and r-type macroscopic events. We now discuss influences between the different types of events, considering first influences between an m-type event and an r-type event. Stapp [ 21 ] distinguishes between the terms "influence" and "signal". A signal is defined as a special type ofinfluenee that may be initiated by human choice, and which controls a response at another point. An m ~ r process has this character. An m-type event is indeed initiated by human choice, and the response is the rtype event. The signal may be of the most obvious type - transmission and receipt of a pulse of light or radio waves, for example. But any m ~ r influence, whether of a single-shot type, individual manipulations being related in a reproducible way to individual observations, or of a statistical nature, only appearing when an ensemble of events is analysed, may be used to transmit information, and thus has the character of a signal. Special relativity rules out influences (signals) between any m-type event, and an r-type event outside
5 December 1988
its light-cone. For an m--.r influence to exist, the rtype event must lie inside the light-cone of the m-type event, and, of course, by definition of the m-type event as the action of a free experimenter, the m-type event must precede the r-type in all frames. There have been many proofs [ 12,26,27 ] that the predicted results of EPR-type experiments agree with relativistic causality. No signal may be passed from an m-type event to an r-type event with the use of EPR-correlations. This is accepted by Kraus and Stapp. This question is reasonably straightforward to analyse. Because of the very definition of an m-type event as a free action of an experimenter at a particular time, there can be no c o m m o n past relevant to an m-type and an r-type event, which could of itself provide correlations between the events. Any such correlation between spacelike separated m-type and r-type events, therefore, indicates a breakdown of relativistic causality. The principle of macroscopic locality must demand more; there must be no effective interaction between two events of r-type with a spacelike separation. Let us consider influences of the type rl ~r2. Since rm is dependent on one or more m-type events, in itself an r~--,r2 influence makes r2 depend on those same m-type events. Globally, of course, any experiment has a structure m ~ r . But in a non-deterministic universe, neither r~ nor r2 will be completely determined by the various m-type events that influence them. There is thus a possibility for one to influence the other. This is just one aspect of the fact that study of r ~ r influences is far more difficult than that of m-~r influences. As well as m-type events, the common pasts of the entities participating in the two r-type events may themselves produce correlations. Consideration of whether all such correlations may be so explained is likely to be model-dependent. I f one could show that no model may explain the correlation, one would have shown that the principle of locality is not obeyed. Alternatively, if one were able to produce a model which can explain all correlations without inyoking interactions between spacelike separated rtype events, one could justifiably claim to have shown that macroscopic locality survives. In ref. [16 ], Kraus does not consider at all correlations between events of r-type. He considers only 467
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correlations between choice of field direction of Stern-Gerlach apparatus on arm (1) of an E P R Bohm apparatus, and the results of the other arm (2), that is, signals between an event of m-type and another of r-type. His argument is that, for macroscopic locality to be maintained, it must be possible for a given distribution of results on arm (2) to be found, independent of the setting on arm ( 1 ) (and conversely, the existence of such a possibility confirms that macroscopic locality is, in fact, maintained). This may easily be shown to be the case; Kraus himself describes the analogous analysis in ref. [ 17] as exceedingly simple, and the conclusions as apparently self-evident. His conclusions then agree with the general proofs [ 12,26,27] that relativistic causality is not threatened. They say nothing, though, about macroscopic locality as we have discussed it, following unambiguously, we would claim, Kraus' definition. It should be mentioned that Kraus himself [16, p. 75] suggests that macroscopic locality is indeed identical to relativistic causality. Even if one felt that this could be correct (and, as we have just stated, we do not), he would surely then be incorrect in maintaining any disagreement with Stapp and others [ 11,15 ], whose position is certainly not to deny relativistic causality. Macroscopic locality, as we have defined it, is distinct from Einstein or EPR locality. A model of a physical event is EPR-Iocal if it assumes no influence between two spacelike separated events, macroscopic or microscopic. For any physical event for which macroscopically local models are available, one will trivially be able to find models which are macroscopically local but not EPR-local. The more important question, though, is whether local models are available for a given physical event. The criterion for availability of a maeroscopically local models is identical to that for an EPR-local model. We now turn to Kraus' second paper [ 17 ]. Here he adopts the term causality, but appears to use the word in the same way as macroscopic locality in ref. [ 16 ]. The argument of ref. [ 17 ] is rather more general than that of ref. [ 16] but is identical in principle. Again we cOnsider it fails to establish its point, as it does not consider correlations between events of r-type. The authors of refs. [1,7-15] do consider such correlations to investigate the possibility of r--,r in468
5 December 1988
fluences. In the context of EPR-type experiments, this implies analysis of correlations between the observations on the two arms of the apparatus. Naturally the results of these authors will gain a degree of acceptance in proportion to the adequecy of their assumptions. We add a few remarks on ref. [17]. Kraus comments [ 17, p. 462 ] that it would appear conspiratorial for statistical averages of results to fail to show superluminal connections present in individual resuits. In fact it appears very natural if one commences from the relations NI+ = N l _ =N2+ =N2_ = N / 2 (in an obvious notation). That is all that is required to give statistical independence (as discussed by Kraus). The correlations we discuss are implicit in
N++ =N__ = N o t = N - N _ + = N - N + _ , with a not in general equal to 1/2. There seems no conspiracy involved. We now turn to Kraus' concluding remarks [ 17, p. 478 ]. Many of the points Kraus includes mirror some of ours made earlier here, but the conclusions he draws from them are dramatically different. He recognises the observed correlations in EPR-type experiments as a result of a common past. Significantly, though, he uses the strange terminology of a common past of measurements. It seems difficult to say how a measurement as such may have a past. What may have pasts are the entities being measured, and a common past may be expressed in terms of a coupled state-function. If one considers a coupled statefunction for the original E P R - B o h m experiment (with fields aligned), of the form ~ = ( 1 / ~ / 2 ) (a,+ a2_ - a l _ a 2 + ) , it does indeed express the common past of the two particles - they result from the decay of the S = 0 state of the composite particle. But this feature, of course, gives no information about the results of the relevant measurement on either particle. Discussion of the results of measurements in terms of common past for this particular type of experiment, seems to push one firmly in the direction of hidden variables. This follows, of course, Bell [ 1 ], but such a move would presumably be strongly resisted by Kraus, a fact which
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may explain his attribution o f the c o m m o n past to the measurements. Kraus also discusses the perfect anti-correlation o f the results o f this particular experiment using the language o f causality. The fact that all components a- (o'1 + er2) o f the total spin along arbitrary direction a must be zero, is termed a causal description o f the correlations. It is certainly a description, but it seems much more difficult to think o f it as a cause, particularly when our comments about c o m m o n pasts are taken into account. The word "cause" is, o f course, particularly subtle o f definition. One might possibly be prepared to say that, in as much as the zero sum o f components implies the appropriate correlation, it is a cause o f it. We believe it is m u c h clearer just to regard the zero sum o f components as a re-statement o f what requires to be explained. (Explicitly, how can the sum o f two components be guaranteed to be zero at a measurement, if one elects not to go down the hidden variable path, so that neither is defined before the measurement, and yet no ineraction between the measurements o f each component is allowed?) Kraus admits that q u a n t u m theory provides no explanation o f the correlations. One should not, in fact, expect it to. Rather it describes what happens, and the real question is whether what it describes necessarily involves non-local influences. Since Kraus does not investigate this problem, his conclusions would seem to be o f little relevance. Rather one must get involved with the other papers cited, with their assumptions o f maybe differing degrees o f acceptability. We should mention that the question o f locality may perhaps be circumvented by the procedure o f Bohr [28 ] in his reply to the original E P R argument. In q u a n t u m physics, as distinct from classical physics, he maintains, one must include all relevant features o f measured object and measuring device in a unified description. In particular, one cannot analyse an EPR-type situation into two electrons (or photons), and discuss interactions between them in response to external experimental manipulations. Such an approach vitiates the analysis o f EPR, Bell and their followers. The approach o f Bohr has, o f course, been much debated, but it appears that it could, in principle, formally restore Kraus' result, by making non-dis-
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cussable what Kraus does not discuss. It must be said, however, that Kraus does not take this path. He readily discusses EPR-type pairs o f particles in precisely these terms, and discusses explicitly the possibility or otherwise o f interactions between them. This appears to be in complete contrast to the Bohr approach. To conclude, we do not feel that Kraus' arguments establish the local nature o f the q u a n t u m predictions o f EPR-type experiments. It must be stressed that this does not, o f course, necessarily render correct the arguments o f refs. [10-15 ], which claim to demonstrate non-locality without the use o f hidden variables. It suggests that the subtle points in these proofs are deserving o f further attention. The possibility o f obtaining a p r o o f o f non-locality without use o f hidden variables still appears very open. We would like to thank Professor Stapp for sending us copies o f papers prior to publication.
References [ 1] J.S. Bell, Physics 1 (1964) 195. [ 2 ] A. Einstein, N. Rosen and B. Podolsky,Phys. Rev. 47 ( 1935) 777. [ 3 ] A. Aspect, P. Grangier and G. Roger, Phys. Rev. Lett. 49 (1982) 91; A. Aspect, J. Dalibard and G. Roger, Phys. Rev. Lett. 49 (1982) 1804. [4] T.W. Marshall, Phys. Lett. A 100 (1984) 225. [5] S. Caser, Phys. Lett. A 102 (1984) 152. [6 ] J.F. Clauser, M.A. Home, A. Shimony and R.A. Holt, Phys. Rev. Lett. 26 (1969) 880. [7] E.P. Wigner, Am. J. Phys. 38 (1970) 1005. [8] A. Peres and W.H. Zurek, Am. J. Phys. 50 (1982) 807. [9] J.S. Bell, J. Phys. (Paris) 42, Coll. C2 ( 1981 ) 41. [10] H.P. Stapp, Phys. Rev. D 3 (1971) 1303; Found. Phys. 7 (1977) 313; 9 (1979) 1; 10 (1980) 767; Nuovo Cimento 40 (1977) 191;Am. J. Phys. 53 (1985) 306. [ 11 ] P.H. Eberhard, Nuovo Cimento B 38 (1977) 75. [ 12 ] P.H. Eberhard, Nuovo Cimento B 46 (1978) 392. [ 13] A. Peres, Am. J. Phys. 46 (1978) 746; S.J. Feingold and A. Peres, J. Phys. A 13 (1980) 3187. [ 14] T.M. Corwin, Am. J. Phys. 52 (1984) 371. [ 15 ] C.W. Rietdijk, in: Open questions in quantum physics, eds. G. Tarozzi and A. van der Merwe (Reidel, Dordreeht, 1984) p. 129. [ 16 ] K. Kraus, in: Open questions in quantum physics, eds. G. Tarozzi and A. van der Merwe (Reidel, Dordrecht, 1984) p. 75. 469
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[ 17] K. Kraus, in: Symposium on the foundation of modern physics, eds. P. Lahti and P. Mittelstaedt (World Scientific, Singapore, 1985) p. 461. [ 18] B. d'Espagnat, Phys. Rep. 110 (1984) 201. [ 19 ] H. Neumann, in: Symposium on the foundations of modem physics, eds. P. Lahti and P. Mittelstaedt (World Scientific, Singapore, 1985) p. 497. [20 ] H.P. Stapp, in: Symposium on the foundations of modem physics, eds. P. Lahti and P. Mittelstaedt (World Scientific, Singapore, 1985) p. 637. [21 ] H.P. Stapp, in: Quantum mechanics versus local realism the Einstein, Podolsky and Rosen paradox, ed. F. Selleri (Plenum, New York, 1988). [22]H.P. Stapp, Found. Phys. 18 (1988) 427, 833, in: Microphysical reality and quantum formalism, eds. A. van der Merwe, F. Selleri and G. Tarozzi Reidel, Dordrecht,
470
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1988 ); in: Philosophical consequences of quantum theory, eds. J. Cushing and E. McMullin (Univ. of Notre Dame Press, 1989); Nonlocat character of the Rastall model (Lawrence Berkeley Laboratory Report LBL-25436, 1988). [23] J.S. Bell, Epistomological Lett. (March, 1976). [24 ] A. Shimony, M.A. Home and J.F. Clauser, Epistomological Lett. (October, 1976). [ 25 ] J.S. Bell, Epistomological Lett. (February, 1987 ). [26] G.C. Ghirardi, A. Rimini and T. Weber, Lett. Nuovo Cimento 27 (1980) 263. [27] D.N. Page, Phys. Lett. A 91 (1982) 57. [28] N. Bohr, Phys. Rev. 48 (1935) 696.
PHYSICS LETTERS A
5 December 1988
QUANTUM THEORY, EPR EXPERIMENTS AND LOCALITY M.A.B. WHITAKER and J.G. DENNISON Department of Physics, University of Ulster, Coleraine, Northern Ireland Received 30 April 1988; revised manuscript received 29 August 1988; accepted for publication 4 October 1988 Communicated by J.P. Vigier
Kraus has claimed that there is no evidence that the quantum predictions for experiments of EPR-type exhibit non-locality. We suggest he has not considered fully correlations between the observations on the two arms of the apparatus.
Since the pioneering work of Bell [ 1 ], many papers have appeared asserting that the quantum-mechanical predictions for certain experiments of the EPR-type [2] are inconsistent with attribution of some basic properties to the physical universe. Experiments of Aspect et al. [ 3 ] suggest that the quantum predictions are correct, though other workers [4,5 ] continue to search for loopholes in the analysis of these experiments. The common assumption of Bell-type arguments is of locality (Einstein locality, EPR locality, to be discussed later). In addition, many papers [1,6-8] use the idea of hidden variables (or realism). In most of these papers, hidden variables are assumed. Bell [9], though, argues strongly that neither EPR, nor his own argument [ 1 ], assumes realism (or, indeed, determinism). Rather they move from locality to the concept of deterministic hidden variables in preliminary arguments. Other workers [ 10-15 ] have sought to present arguments with the same result, but without any use of the concept of hidden variables. They analyse the resuits of a run of experiments, and claim to demonstrate that the demands of locality are in conflict with the quantum predictions. Foremost among those adopting this position has been Stapp [ 10 ], who has put forward arguments of novelty and power in this direction. As practically a lone voice, Kraus [ 16,17 ], while accepting [ 17, p. 477] what he terms the usual proofs of Belrs theorem (i.e. those assuming, or making use of, hidden variables), has claimed that the predicted 466
results of all experiments of EPR-type may be explained without assuming non-local influences. He acknowledges that his conclusions are in direct opposition to those of Stapp [ 10 ] and others [ 11-15 ]. The assumptions of Stapp have themselves been strongly questioned by Kraus himself [ 16,17 ], and others [18,19]. The argument centres around the question of counterfactual definiteness (CFD) - the idea that unperformed experiments have definite, though unknown, results. The questions to be asked are to what extent this concept may be justified, and its role, if any, in Stapp's analysis. Stapp [20] has given what amounts to a reply to this criticism and has subsequently returned to the discussion in a number of publications [ 21,22 ]. The question remains one of considerable subtlety. Thus, if one were able to accept Kraus' own contributions, it might appear that the work of Stapp could be put on one side, and one might feel able to conclude, with Kraus, that there is no conflict between quantum mechanics and locality (though it should be stressed that this does not take into account the argument of Bell [9 ] mentioned earlier). Thus scrutiny of Kraus' arguments and conclusions seems a matter of considerable urgency, and it is the subject of this Letter. Analysis is made a little more difficult by developments - in particular, changes in terminology between the two papers of Kraus. In rcf. [ 16 ], the terminology used is macroscopic locality;it is this quantity which Kraus claims is completely consistent with quantum predictions of EPR-type experi-
0375-9601/88/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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ments. He defines macroscopic locality as the condition that macroscopic events in one region are not influenced by macroscopic events in a second region, spacelike separated from the first. Macroscopic events may be divided into two cate g o r i e s - manipulated (m-type) and resultant (rtype). The former are operations carried out by supposedly-free experimenters - setting devices, passing signals, opening slits, and so on. The latter are macroscopic events that take place out of the control of experimenters. In particular, they include observations. An experimenter may set up a given measurement, but cannot, of course, determine what result is obtained. The distinction between events of m- and r-type is not to be taken for granted. Indeed it is the subject of a controversy between Bell [23], who does assume the distinction, and Shimony et al. [ 24 ]. The latter suggest that experimenters should not necessarily be considered free. Their actions may be influenced by previous events, which may also have influenced the objects the experimenters are studying, and, indeed, other objects with quantum states correlated with these. In his reply, Bell [ 25 ] says that the distinction may not be sound metaphysics, but he considers it the standard assumption of good theoretical physics. In this Letter we assume a clear distinction between m- and r-type macroscopic events. We now discuss influences between the different types of events, considering first influences between an m-type event and an r-type event. Stapp [ 21 ] distinguishes between the terms "influence" and "signal". A signal is defined as a special type ofinfluenee that may be initiated by human choice, and which controls a response at another point. An m ~ r process has this character. An m-type event is indeed initiated by human choice, and the response is the rtype event. The signal may be of the most obvious type - transmission and receipt of a pulse of light or radio waves, for example. But any m ~ r influence, whether of a single-shot type, individual manipulations being related in a reproducible way to individual observations, or of a statistical nature, only appearing when an ensemble of events is analysed, may be used to transmit information, and thus has the character of a signal. Special relativity rules out influences (signals) between any m-type event, and an r-type event outside
5 December 1988
its light-cone. For an m--.r influence to exist, the rtype event must lie inside the light-cone of the m-type event, and, of course, by definition of the m-type event as the action of a free experimenter, the m-type event must precede the r-type in all frames. There have been many proofs [ 12,26,27 ] that the predicted results of EPR-type experiments agree with relativistic causality. No signal may be passed from an m-type event to an r-type event with the use of EPR-correlations. This is accepted by Kraus and Stapp. This question is reasonably straightforward to analyse. Because of the very definition of an m-type event as a free action of an experimenter at a particular time, there can be no c o m m o n past relevant to an m-type and an r-type event, which could of itself provide correlations between the events. Any such correlation between spacelike separated m-type and r-type events, therefore, indicates a breakdown of relativistic causality. The principle of macroscopic locality must demand more; there must be no effective interaction between two events of r-type with a spacelike separation. Let us consider influences of the type rl ~r2. Since rm is dependent on one or more m-type events, in itself an r~--,r2 influence makes r2 depend on those same m-type events. Globally, of course, any experiment has a structure m ~ r . But in a non-deterministic universe, neither r~ nor r2 will be completely determined by the various m-type events that influence them. There is thus a possibility for one to influence the other. This is just one aspect of the fact that study of r ~ r influences is far more difficult than that of m-~r influences. As well as m-type events, the common pasts of the entities participating in the two r-type events may themselves produce correlations. Consideration of whether all such correlations may be so explained is likely to be model-dependent. I f one could show that no model may explain the correlation, one would have shown that the principle of locality is not obeyed. Alternatively, if one were able to produce a model which can explain all correlations without inyoking interactions between spacelike separated rtype events, one could justifiably claim to have shown that macroscopic locality survives. In ref. [16 ], Kraus does not consider at all correlations between events of r-type. He considers only 467
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correlations between choice of field direction of Stern-Gerlach apparatus on arm (1) of an E P R Bohm apparatus, and the results of the other arm (2), that is, signals between an event of m-type and another of r-type. His argument is that, for macroscopic locality to be maintained, it must be possible for a given distribution of results on arm (2) to be found, independent of the setting on arm ( 1 ) (and conversely, the existence of such a possibility confirms that macroscopic locality is, in fact, maintained). This may easily be shown to be the case; Kraus himself describes the analogous analysis in ref. [ 17] as exceedingly simple, and the conclusions as apparently self-evident. His conclusions then agree with the general proofs [ 12,26,27] that relativistic causality is not threatened. They say nothing, though, about macroscopic locality as we have discussed it, following unambiguously, we would claim, Kraus' definition. It should be mentioned that Kraus himself [16, p. 75] suggests that macroscopic locality is indeed identical to relativistic causality. Even if one felt that this could be correct (and, as we have just stated, we do not), he would surely then be incorrect in maintaining any disagreement with Stapp and others [ 11,15 ], whose position is certainly not to deny relativistic causality. Macroscopic locality, as we have defined it, is distinct from Einstein or EPR locality. A model of a physical event is EPR-Iocal if it assumes no influence between two spacelike separated events, macroscopic or microscopic. For any physical event for which macroscopically local models are available, one will trivially be able to find models which are macroscopically local but not EPR-local. The more important question, though, is whether local models are available for a given physical event. The criterion for availability of a maeroscopically local models is identical to that for an EPR-local model. We now turn to Kraus' second paper [ 17 ]. Here he adopts the term causality, but appears to use the word in the same way as macroscopic locality in ref. [ 16 ]. The argument of ref. [ 17 ] is rather more general than that of ref. [ 16] but is identical in principle. Again we cOnsider it fails to establish its point, as it does not consider correlations between events of r-type. The authors of refs. [1,7-15] do consider such correlations to investigate the possibility of r--,r in468
5 December 1988
fluences. In the context of EPR-type experiments, this implies analysis of correlations between the observations on the two arms of the apparatus. Naturally the results of these authors will gain a degree of acceptance in proportion to the adequecy of their assumptions. We add a few remarks on ref. [17]. Kraus comments [ 17, p. 462 ] that it would appear conspiratorial for statistical averages of results to fail to show superluminal connections present in individual resuits. In fact it appears very natural if one commences from the relations NI+ = N l _ =N2+ =N2_ = N / 2 (in an obvious notation). That is all that is required to give statistical independence (as discussed by Kraus). The correlations we discuss are implicit in
N++ =N__ = N o t = N - N _ + = N - N + _ , with a not in general equal to 1/2. There seems no conspiracy involved. We now turn to Kraus' concluding remarks [ 17, p. 478 ]. Many of the points Kraus includes mirror some of ours made earlier here, but the conclusions he draws from them are dramatically different. He recognises the observed correlations in EPR-type experiments as a result of a common past. Significantly, though, he uses the strange terminology of a common past of measurements. It seems difficult to say how a measurement as such may have a past. What may have pasts are the entities being measured, and a common past may be expressed in terms of a coupled state-function. If one considers a coupled statefunction for the original E P R - B o h m experiment (with fields aligned), of the form ~ = ( 1 / ~ / 2 ) (a,+ a2_ - a l _ a 2 + ) , it does indeed express the common past of the two particles - they result from the decay of the S = 0 state of the composite particle. But this feature, of course, gives no information about the results of the relevant measurement on either particle. Discussion of the results of measurements in terms of common past for this particular type of experiment, seems to push one firmly in the direction of hidden variables. This follows, of course, Bell [ 1 ], but such a move would presumably be strongly resisted by Kraus, a fact which
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may explain his attribution o f the c o m m o n past to the measurements. Kraus also discusses the perfect anti-correlation o f the results o f this particular experiment using the language o f causality. The fact that all components a- (o'1 + er2) o f the total spin along arbitrary direction a must be zero, is termed a causal description o f the correlations. It is certainly a description, but it seems much more difficult to think o f it as a cause, particularly when our comments about c o m m o n pasts are taken into account. The word "cause" is, o f course, particularly subtle o f definition. One might possibly be prepared to say that, in as much as the zero sum o f components implies the appropriate correlation, it is a cause o f it. We believe it is m u c h clearer just to regard the zero sum o f components as a re-statement o f what requires to be explained. (Explicitly, how can the sum o f two components be guaranteed to be zero at a measurement, if one elects not to go down the hidden variable path, so that neither is defined before the measurement, and yet no ineraction between the measurements o f each component is allowed?) Kraus admits that q u a n t u m theory provides no explanation o f the correlations. One should not, in fact, expect it to. Rather it describes what happens, and the real question is whether what it describes necessarily involves non-local influences. Since Kraus does not investigate this problem, his conclusions would seem to be o f little relevance. Rather one must get involved with the other papers cited, with their assumptions o f maybe differing degrees o f acceptability. We should mention that the question o f locality may perhaps be circumvented by the procedure o f Bohr [28 ] in his reply to the original E P R argument. In q u a n t u m physics, as distinct from classical physics, he maintains, one must include all relevant features o f measured object and measuring device in a unified description. In particular, one cannot analyse an EPR-type situation into two electrons (or photons), and discuss interactions between them in response to external experimental manipulations. Such an approach vitiates the analysis o f EPR, Bell and their followers. The approach o f Bohr has, o f course, been much debated, but it appears that it could, in principle, formally restore Kraus' result, by making non-dis-
5 December 1988
cussable what Kraus does not discuss. It must be said, however, that Kraus does not take this path. He readily discusses EPR-type pairs o f particles in precisely these terms, and discusses explicitly the possibility or otherwise o f interactions between them. This appears to be in complete contrast to the Bohr approach. To conclude, we do not feel that Kraus' arguments establish the local nature o f the q u a n t u m predictions o f EPR-type experiments. It must be stressed that this does not, o f course, necessarily render correct the arguments o f refs. [10-15 ], which claim to demonstrate non-locality without the use o f hidden variables. It suggests that the subtle points in these proofs are deserving o f further attention. The possibility o f obtaining a p r o o f o f non-locality without use o f hidden variables still appears very open. We would like to thank Professor Stapp for sending us copies o f papers prior to publication.
References [ 1] J.S. Bell, Physics 1 (1964) 195. [ 2 ] A. Einstein, N. Rosen and B. Podolsky,Phys. Rev. 47 ( 1935) 777. [ 3 ] A. Aspect, P. Grangier and G. Roger, Phys. Rev. Lett. 49 (1982) 91; A. Aspect, J. Dalibard and G. Roger, Phys. Rev. Lett. 49 (1982) 1804. [4] T.W. Marshall, Phys. Lett. A 100 (1984) 225. [5] S. Caser, Phys. Lett. A 102 (1984) 152. [6 ] J.F. Clauser, M.A. Home, A. Shimony and R.A. Holt, Phys. Rev. Lett. 26 (1969) 880. [7] E.P. Wigner, Am. J. Phys. 38 (1970) 1005. [8] A. Peres and W.H. Zurek, Am. J. Phys. 50 (1982) 807. [9] J.S. Bell, J. Phys. (Paris) 42, Coll. C2 ( 1981 ) 41. [10] H.P. Stapp, Phys. Rev. D 3 (1971) 1303; Found. Phys. 7 (1977) 313; 9 (1979) 1; 10 (1980) 767; Nuovo Cimento 40 (1977) 191;Am. J. Phys. 53 (1985) 306. [ 11 ] P.H. Eberhard, Nuovo Cimento B 38 (1977) 75. [ 12 ] P.H. Eberhard, Nuovo Cimento B 46 (1978) 392. [ 13] A. Peres, Am. J. Phys. 46 (1978) 746; S.J. Feingold and A. Peres, J. Phys. A 13 (1980) 3187. [ 14] T.M. Corwin, Am. J. Phys. 52 (1984) 371. [ 15 ] C.W. Rietdijk, in: Open questions in quantum physics, eds. G. Tarozzi and A. van der Merwe (Reidel, Dordreeht, 1984) p. 129. [ 16 ] K. Kraus, in: Open questions in quantum physics, eds. G. Tarozzi and A. van der Merwe (Reidel, Dordrecht, 1984) p. 75. 469
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[ 17] K. Kraus, in: Symposium on the foundation of modern physics, eds. P. Lahti and P. Mittelstaedt (World Scientific, Singapore, 1985) p. 461. [ 18] B. d'Espagnat, Phys. Rep. 110 (1984) 201. [ 19 ] H. Neumann, in: Symposium on the foundations of modem physics, eds. P. Lahti and P. Mittelstaedt (World Scientific, Singapore, 1985) p. 497. [20 ] H.P. Stapp, in: Symposium on the foundations of modem physics, eds. P. Lahti and P. Mittelstaedt (World Scientific, Singapore, 1985) p. 637. [21 ] H.P. Stapp, in: Quantum mechanics versus local realism the Einstein, Podolsky and Rosen paradox, ed. F. Selleri (Plenum, New York, 1988). [22]H.P. Stapp, Found. Phys. 18 (1988) 427, 833, in: Microphysical reality and quantum formalism, eds. A. van der Merwe, F. Selleri and G. Tarozzi Reidel, Dordrecht,
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1988 ); in: Philosophical consequences of quantum theory, eds. J. Cushing and E. McMullin (Univ. of Notre Dame Press, 1989); Nonlocat character of the Rastall model (Lawrence Berkeley Laboratory Report LBL-25436, 1988). [23] J.S. Bell, Epistomological Lett. (March, 1976). [24 ] A. Shimony, M.A. Home and J.F. Clauser, Epistomological Lett. (October, 1976). [ 25 ] J.S. Bell, Epistomological Lett. (February, 1987 ). [26] G.C. Ghirardi, A. Rimini and T. Weber, Lett. Nuovo Cimento 27 (1980) 263. [27] D.N. Page, Phys. Lett. A 91 (1982) 57. [28] N. Bohr, Phys. Rev. 48 (1935) 696.