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Physics Today

John Bell, relativistic causality, and the arrow of time

Nathan Argaman

Published Mar 1, 2016• 0 citations
Publisher

Abstract

Reinhold Bertlmann’s reminiscences of John Bell (Physics Today, July 2015, page 40) are a pleasure to read and faithfully summarize the generally accepted wisdom on the topic. However, the article ends at a seemingly insurmountable theoretical impasse: the conclusions of Bell’s 1980 review describing the apparent incompatibility of quantum correlations with Lorentz invariance. It would perhaps be preferable to conclude on a more optimistic note, by emphasizing the tacit underlying assumption—the causal arrow of time. After all, the quantum correlations are incompatible not with Lorentz invariance per se but with relativistic causality, a time-asymmetric notion. The culprit, apparently, is in the manner that time asymmetry is introduced into the context of a microscopic theory.Bell himself fully acknowledged the relevance of causality in his 1990 review of the topic,11. J. S. Bell, in Between Science and Technology: Proceedings of the International Conference Between Science and Technology, Eindhoven University of Technology, The Netherlands, 29–30 June, 1989, A. Sarlemijn, P. Kroes, eds., North-Holland, 1990), p. 97. though he remained unwilling to consider the alternative of retrocausation. He clarified that the “locality” of local realism is merely shorthand for “local causality.” In his concluding paragraph he wrote, “The more closely one looks at the fundamental laws of physics the less one sees of the laws of thermodynamics. The increase of entropy emerges only for large complicated systems, in an approximation depending on ‘largeness’ and ‘complexity.’ Could it be that causal structure emerges only in something like a ‘thermodynamic’ approximation, where the notions ‘measurement’ and ‘external field’ become legitimate approximations?” That is the question Bell left us with.Is there hope for a more palatable theoretical description?11. J. S. Bell, in Between Science and Technology: Proceedings of the International Conference Between Science and Technology, Eindhoven University of Technology, The Netherlands, 29–30 June, 1989, A. Sarlemijn, P. Kroes, eds., North-Holland, 1990), p. 97. Bell’s theorem tells us that it would require either abandoning local causality or abandoning the causal arrow of time altogether, perhaps replacing it with a weaker temporal arrow, an arrow of information or entropy. At the level of a simplistic toy model, an explicit retrocausal (but otherwise local) formulation can reproduce Bell-type correlations.22. N. Argaman, Am. J. Phys. 78, 1007 (2010). https://doi.org/10.1119/1.3456564 The challenge remains to formulate a general retrocausal and spacetime-local description of quantum phenomena. Such a reformulation of quantum theory, if achieved, is likely to have important ramifications, perhaps comparable to those following from Feynman’s development of path integrals.REFERENCESSection:ChooseTop of pageREFERENCES <<1. J. S. Bell, in Between Science and Technology: Proceedings of the International Conference Between Science and Technology, Eindhoven University of Technology, The Netherlands, 29–30 June, 1989, A. Sarlemijn, P. Kroes, eds., North-Holland, 1990), p. 97. Google ScholarCrossref2. N. Argaman, Am. J. Phys. 78, 1007 (2010). https://doi.org/10.1119/1.3456564, Google ScholarCrossref, ISI© 2016 American Institute of Physics.

DOI
10.1063/pt.3.3094

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John Bell, relativistic causality, and the arrow of time

Reinhold A. Bertlmann

► Bertlmann replies: In analyzing Bell’s theorem, Nathan Argaman emphasizes the tacitly assumed time asymmetry, which becomes the “culprit” in the context of a microscopic theory. John Bell certainly was aware of retrocausal formulations, where the causal arrow of time was abandoned, but he did not consider them as alternatives to local hidden-variable theories. The reason was simply that Bell, like Albert Einstein, did not accept the possibility that an effect might happen before the cause.Sticking to his “no signals faster than light” idea, Bell demonstrated that ordinary quantum mechanics is not locally causal. We have to accept that nonlocal structure of quantum mechanics, which is experienced in nature.In Argaman’s retrocausal model, the propagation of information from the apparatus backward in time to the source is allowed, and thus no instantaneous action at a distance is needed. Therefore, Argaman may conclude that Einstein’s spooky action occurs in the past rather than at a distance.Since the variables, carrying information that has propagated into the past, must not be accessible on a macroscopic level, doesn’t Argaman’s retrocausal model just shift the problem from “nonlocality” to the arrow of time? Nevertheless, it is an interesting interpretation of an experiment like Einstein-Podolsky-Rosen and Bell.© 2016 American Institute of Physics.

Physics Today•Mar 1, 2016•0 citations

A Lenient Causal Arrow of Time?

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One of the basic assumptions underlying Bell's theorem is the causal arrow of time, having to do with temporal order rather than spatial separation. Nonetheless, the physical assumptions regarding causality are seldom studied in this context, and often even go unmentioned, in stark contrast with the many different possible locality conditions which have been studied and elaborated upon. In the present work, some retrocausal toy-models which reproduce the predictions of quantum mechanics for Bell-type correlations are reviewed. It is pointed out that a certain toy-model which is ostensibly superdeterministic-based on denying the free-variable status of some of quantum mechanics' input parameters-actually contains within it a complete retrocausal toy-model. Occam's razor thus indicates that the superdeterministic point of view is superfluous. A challenge is to generalize the retrocausal toy-models to a full theory-a reformulation of quantum mechanics-in which the standard causal arrow of time would be replaced by a more lenient one: an arrow of time applicable only to macroscopically-available information. In discussing such a reformulation, one finds that many of the perplexing features of quantum mechanics could arise naturally, especially in the context of stochastic theories.

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Einstein held that the formalism of quantum mechanics involves “spooky actions at a distance.” In the 1960s, Bell amplified this by showing that the predictions of quantum mechanics disagree with the results of any locally causal description. It should be appreciated that accepting nonlocal descriptions while retaining causality leads to a clash with relativity. Furthermore, the causal arrow of time by definition contradicts time-reversal symmetry. For these reasons, Wheeler and Feynman, Costa de Beauregard, Cramer, Price, and others have advocated abandoning microscopic causality. In this paper, a simplistic but concrete example of this line of thought is presented, in the form of a retro-causal toy model that is stochastic and provides an appealing description of the quantum correlations discussed by Bell. It is concluded that Einstein’s “spooky actions” may occur “in the past” rather than “at a distance,” resolving the tension between quantum mechanics and relativity and opening unexplored possibilities for future reformulations of quantum mechanics.

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Readers offer their own magic moments with John Bell

N. Bykovetz

I greatly enjoyed reading Reinhold Bertlmann’s article “Magic moments with John Bell.” Sprinkled with levity, it discussed Bell’s life, work, and outstanding insights and achievements in the foundations of quantum mechanics (QM). In my view, the reading should also make one acutely aware that scientists, despite our expectations of them, are sometimes still prone to the same failings that beset the rest of humanity.Bertlmann outlines very nicely Bell’s theorem and inequalities and the consequences of their violation; that work led to the subsequent startling experimental results on “entangled” quantum mechanical states, which, Bertlmann writes, showed “that nature contains a nonlocality in its structure.” Nonlocality, in Bell’s conception of it, is clearly a violation of special relativity (SR), so we have a problem. The startling thing for me is that Bell actually does appear to solve the problem, at least in principle, but at the same time he seems afraid to say so and, in fact, distances himself from the proposed solution.The essence of his ambivalence is conveyed in the following paragraph, quoted by Bertlmann:It may be that we have to admit that causal influences do go faster than light. The role of Lorentz invariance in the completed theory would then be very problematic. An “ether” would be the cheapest solution. But the unobservability of this ether would be disturbing. So would be the impossibility of “messages” faster than light.Clearly, faster-than-light propagation is not possible in SR. But it is permissible in the approximately 100-year-old ether-based Lorentzian theory of relativity (LR), developed by Joseph Larmor, Hendrik Lorentz, Henri Poincaré, and others. Bell was explicitly cognizant of LR and discussed it in his book Speakable and Unspeakable in Quantum Mechanics (2nd edition, Cambridge University Press, 2004). It is well known that LR and SR are totally congruent in their kinematics and dynamics, for speeds equal to or less than c. All predictions are identical. However—though one cannot find this in any standard textbooks—the LR ether theory differs from SR by allowing, without contradiction, speeds greater than c.Historically, Einstein’s SR gained ascendancy, and LR was relegated to the scrap heap of history for many reasons, but I think predominantly for the following. SR was viewed as being far more elegant and simple to develop—from the perspective of theory formation—because it followed deductively from Einstein’s two simple axioms. On the other hand, LR theory was developed from a realism perspective, where waves were thought to need a medium to wave in (the luminiferous ether).Considering that Bell was clearly aware of LR and was entertaining the idea, albeit reluctantly, of “causal influences [going] faster than light”—that is, being consonant with LR—I find it difficult to understand his expressions in the quote above about cheap solutions and disturbing features. It seems to be part of human psychology that once a set of ideas or a theory is accepted as valid for a long enough time by a community of people, as has been the case for SR, it gets transformed into belief, psychologically not unlike religious belief. Once that happens, those who would question the established dogma are treated as if the questioning was ill-intentioned, if not downright sacrilegious.© 2015 American Institute of Physics.

Physics Today•Nov 30, 2015•0 citations

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It may well be that a relativistic version of the theory, while Lorentz invariant and local at the observational level, may be necessarily non-local and with a preferred frame (or aether) at the fundamental level. – John Bell [1] Introduction Bell's theorem establishes a contradiction between locality (and a few other assumptions) and certain predictions of quantum mechanics [2]. There have been two main issues surrounding the deep implications of this celebrated theorem. The first issue is basic, and it concerns whether the theorem really establishes that nonlocality is a necessary feature of any empirically viable theory and hence a feature of nature itself. One aspect of the issue concerns exactly what the underlying assumptions of Bell's theorem are. For example, some argue that these assumptions include the assumption of counterfactual definiteness [3–5], while others disagree [6–8]. The other aspect of the issue concerns which assumption should be dropped due to the resulting contradiction. Some believe that standard quantum mechanics may avoid nonlocality by denying counterfactual definiteness [3–5]. The second issue is much deeper, and it concerns how to make sense of the strange nonlocality when assuming that Bell's theorem establishes that our world is nonlocal. In particular, it has yet to be determined whether such quantum nonlocality is compatible with the theory of relativity, e.g., whether the nonlocality requires the existence of a preferred Lorentz frame [7, 9, 10]. It seems that “there is a preferred frame of reference, and in this preferred frame of reference things do go faster than light … Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant” [11]. But it also seems possible that the existence of a preferred Lorentz frame is an illusion, since it cannot be detected according to standard quantum mechanics. A more subtle issue is whether quantum nonlocality permits superluminal signaling. It is widely thought that the answers to these questions will lead to a deeper understanding of Bell's theorem and quantum nonlocality. In this paper, we will present a new analysis of quantum nonlocality and its apparent incompatibility with relativity.

Cambridge University Press eBooks•Aug 31, 2016•1 citation

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Gerard ’t Hooft

It is brought forward that viable theories of the physical world that have no variable at all that can play the role of time, do not exist; some notion of time is one of the very first ingredients a candidate theory should possess. Almost by definition, time has an arrow. In contrast, time reversibility, or even the possibility to run the equations of motion backwards in time, is not at all a primary requirement. This means that the direction of the arrow of time may well be uniquely defined in the theory, even locally. It is explained that a rigorous definition of time, as well as a formulation of the causality and locality concepts, can only be given when one has a model for the physical phenomena described. The only viable causality condition is one that is symmetric under time reversal. We explain these statements in terms of the author’s favoured deterministic cellular automaton interpretation of quantum mechanics, also to be referred to as 'vector space analysis', and expand on these ideas. It is also summarised how our more rigorous causality condition affects Bell’s theorems. What distinguishes quantum systems from classical ones is our fundamental inability to control the microscopic details of the initial state when phenomena are studied in the light of some theoretical model.

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Reinhold Bertlmann’s reminiscences of John Bell (Physics Today, July 2015, page 40) are a pleasure to read and faithfully summarize the generally accepted wisdom on the topic. However, the article ends at a seemingly insurmountable theoretical impasse: the conclusions of Bell’s 1980 review describing the apparent incompatibility of quantum correlations with Lorentz invariance. It would perhaps be preferable to conclude on a more optimistic note, by emphasizing the tacit underlying assumption—the causal arrow of time. After all, the quantum correlations are incompatible not with Lorentz invariance per se but with relativistic causality, a time-asymmetric notion. The culprit, apparently, is in the manner that time asymmetry is introduced into the context of a microscopic theory.Bell himself fully acknowledged the relevance of causality in his 1990 review of the topic,11. J. S. Bell, in Between Science and Technology: Proceedings of the International Conference Between Science and Technology, Eindhoven University of Technology, The Netherlands, 29–30 June, 1989, A. Sarlemijn, P. Kroes, eds., North-Holland, 1990), p. 97. though he remained unwilling to consider the alternative of retrocausation. He clarified that the “locality” of local realism is merely shorthand for “local causality.” In his concluding paragraph he wrote, “The more closely one looks at the fundamental laws of physics the less one sees of the laws of thermodynamics. The increase of entropy emerges only for large complicated systems, in an approximation depending on ‘largeness’ and ‘complexity.’ Could it be that causal structure emerges only in something like a ‘thermodynamic’ approximation, where the notions ‘measurement’ and ‘external field’ become legitimate approximations?” That is the question Bell left us with.Is there hope for a more palatable theoretical description?11. J. S. Bell, in Between Science and Technology: Proceedings of the International Conference Between Science and Technology, Eindhoven University of Technology, The Netherlands, 29–30 June, 1989, A. Sarlemijn, P. Kroes, eds., North-Holland, 1990), p. 97. Bell’s theorem tells us that it would require either abandoning local causality or abandoning the causal arrow of time altogether, perhaps replacing it with a weaker temporal arrow, an arrow of information or entropy. At the level of a simplistic toy model, an explicit retrocausal (but otherwise local) formulation can reproduce Bell-type correlations.22. N. Argaman, Am. J. Phys. 78, 1007 (2010). https://doi.org/10.1119/1.3456564 The challenge remains to formulate a general retrocausal and spacetime-local description of quantum phenomena. Such a reformulation of quantum theory, if achieved, is likely to have important ramifications, perhaps comparable to those following from Feynman’s development of path integrals.REFERENCESSection:ChooseTop of pageREFERENCES <<1. J. S. Bell, in Between Science and Technology: Proceedings of the International Conference Between Science and Technology, Eindhoven University of Technology, The Netherlands, 29–30 June, 1989, A. Sarlemijn, P. Kroes, eds., North-Holland, 1990), p. 97. Google ScholarCrossref2. N. Argaman, Am. J. Phys. 78, 1007 (2010). https://doi.org/10.1119/1.3456564, Google ScholarCrossref, ISI© 2016 American Institute of Physics.
► Bertlmann replies: In analyzing Bell’s theorem, Nathan Argaman emphasizes the tacitly assumed time asymmetry, which becomes the “culprit” in the context of a microscopic theory. John Bell certainly was aware of retrocausal formulations, where the causal arrow of time was abandoned, but he did not consider them as alternatives to local hidden-variable theories. The reason was simply that Bell, like Albert Einstein, did not accept the possibility that an effect might happen before the cause.Sticking to his “no signals faster than light” idea, Bell demonstrated that ordinary quantum mechanics is not locally causal. We have to accept that nonlocal structure of quantum mechanics, which is experienced in nature.In Argaman’s retrocausal model, the propagation of information from the apparatus backward in time to the source is allowed, and thus no instantaneous action at a distance is needed. Therefore, Argaman may conclude that Einstein’s spooky action occurs in the past rather than at a distance.Since the variables, carrying information that has propagated into the past, must not be accessible on a macroscopic level, doesn’t Argaman’s retrocausal model just shift the problem from “nonlocality” to the arrow of time? Nevertheless, it is an interesting interpretation of an experiment like Einstein-Podolsky-Rosen and Bell.© 2016 American Institute of Physics.
One of the basic assumptions underlying Bell's theorem is the causal arrow of time, having to do with temporal order rather than spatial separation. Nonetheless, the physical assumptions regarding causality are seldom studied in this context, and often even go unmentioned, in stark contrast with the many different possible locality conditions which have been studied and elaborated upon. In the present work, some retrocausal toy-models which reproduce the predictions of quantum mechanics for Bell-type correlations are reviewed. It is pointed out that a certain toy-model which is ostensibly superdeterministic-based on denying the free-variable status of some of quantum mechanics' input parameters-actually contains within it a complete retrocausal toy-model. Occam's razor thus indicates that the superdeterministic point of view is superfluous. A challenge is to generalize the retrocausal toy-models to a full theory-a reformulation of quantum mechanics-in which the standard causal arrow of time would be replaced by a more lenient one: an arrow of time applicable only to macroscopically-available information. In discussing such a reformulation, one finds that many of the perplexing features of quantum mechanics could arise naturally, especially in the context of stochastic theories.
Einstein held that the formalism of quantum mechanics involves “spooky actions at a distance.” In the 1960s, Bell amplified this by showing that the predictions of quantum mechanics disagree with the results of any locally causal description. It should be appreciated that accepting nonlocal descriptions while retaining causality leads to a clash with relativity. Furthermore, the causal arrow of time by definition contradicts time-reversal symmetry. For these reasons, Wheeler and Feynman, Costa de Beauregard, Cramer, Price, and others have advocated abandoning microscopic causality. In this paper, a simplistic but concrete example of this line of thought is presented, in the form of a retro-causal toy model that is stochastic and provides an appealing description of the quantum correlations discussed by Bell. It is concluded that Einstein’s “spooky actions” may occur “in the past” rather than “at a distance,” resolving the tension between quantum mechanics and relativity and opening unexplored possibilities for future reformulations of quantum mechanics.
I greatly enjoyed reading Reinhold Bertlmann’s article “Magic moments with John Bell.” Sprinkled with levity, it discussed Bell’s life, work, and outstanding insights and achievements in the foundations of quantum mechanics (QM). In my view, the reading should also make one acutely aware that scientists, despite our expectations of them, are sometimes still prone to the same failings that beset the rest of humanity.Bertlmann outlines very nicely Bell’s theorem and inequalities and the consequences of their violation; that work led to the subsequent startling experimental results on “entangled” quantum mechanical states, which, Bertlmann writes, showed “that nature contains a nonlocality in its structure.” Nonlocality, in Bell’s conception of it, is clearly a violation of special relativity (SR), so we have a problem. The startling thing for me is that Bell actually does appear to solve the problem, at least in principle, but at the same time he seems afraid to say so and, in fact, distances himself from the proposed solution.The essence of his ambivalence is conveyed in the following paragraph, quoted by Bertlmann:It may be that we have to admit that causal influences do go faster than light. The role of Lorentz invariance in the completed theory would then be very problematic. An “ether” would be the cheapest solution. But the unobservability of this ether would be disturbing. So would be the impossibility of “messages” faster than light.Clearly, faster-than-light propagation is not possible in SR. But it is permissible in the approximately 100-year-old ether-based Lorentzian theory of relativity (LR), developed by Joseph Larmor, Hendrik Lorentz, Henri Poincaré, and others. Bell was explicitly cognizant of LR and discussed it in his book Speakable and Unspeakable in Quantum Mechanics (2nd edition, Cambridge University Press, 2004). It is well known that LR and SR are totally congruent in their kinematics and dynamics, for speeds equal to or less than c. All predictions are identical. However—though one cannot find this in any standard textbooks—the LR ether theory differs from SR by allowing, without contradiction, speeds greater than c.Historically, Einstein’s SR gained ascendancy, and LR was relegated to the scrap heap of history for many reasons, but I think predominantly for the following. SR was viewed as being far more elegant and simple to develop—from the perspective of theory formation—because it followed deductively from Einstein’s two simple axioms. On the other hand, LR theory was developed from a realism perspective, where waves were thought to need a medium to wave in (the luminiferous ether).Considering that Bell was clearly aware of LR and was entertaining the idea, albeit reluctantly, of “causal influences [going] faster than light”—that is, being consonant with LR—I find it difficult to understand his expressions in the quote above about cheap solutions and disturbing features. It seems to be part of human psychology that once a set of ideas or a theory is accepted as valid for a long enough time by a community of people, as has been the case for SR, it gets transformed into belief, psychologically not unlike religious belief. Once that happens, those who would question the established dogma are treated as if the questioning was ill-intentioned, if not downright sacrilegious.© 2015 American Institute of Physics.
It may well be that a relativistic version of the theory, while Lorentz invariant and local at the observational level, may be necessarily non-local and with a preferred frame (or aether) at the fundamental level. – John Bell [1] Introduction Bell's theorem establishes a contradiction between locality (and a few other assumptions) and certain predictions of quantum mechanics [2]. There have been two main issues surrounding the deep implications of this celebrated theorem. The first issue is basic, and it concerns whether the theorem really establishes that nonlocality is a necessary feature of any empirically viable theory and hence a feature of nature itself. One aspect of the issue concerns exactly what the underlying assumptions of Bell's theorem are. For example, some argue that these assumptions include the assumption of counterfactual definiteness [3–5], while others disagree [6–8]. The other aspect of the issue concerns which assumption should be dropped due to the resulting contradiction. Some believe that standard quantum mechanics may avoid nonlocality by denying counterfactual definiteness [3–5]. The second issue is much deeper, and it concerns how to make sense of the strange nonlocality when assuming that Bell's theorem establishes that our world is nonlocal. In particular, it has yet to be determined whether such quantum nonlocality is compatible with the theory of relativity, e.g., whether the nonlocality requires the existence of a preferred Lorentz frame [7, 9, 10]. It seems that “there is a preferred frame of reference, and in this preferred frame of reference things do go faster than light … Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant” [11]. But it also seems possible that the existence of a preferred Lorentz frame is an illusion, since it cannot be detected according to standard quantum mechanics. A more subtle issue is whether quantum nonlocality permits superluminal signaling. It is widely thought that the answers to these questions will lead to a deeper understanding of Bell's theorem and quantum nonlocality. In this paper, we will present a new analysis of quantum nonlocality and its apparent incompatibility with relativity.
It is brought forward that viable theories of the physical world that have no variable at all that can play the role of time, do not exist; some notion of time is one of the very first ingredients a candidate theory should possess. Almost by definition, time has an arrow. In contrast, time reversibility, or even the possibility to run the equations of motion backwards in time, is not at all a primary requirement. This means that the direction of the arrow of time may well be uniquely defined in the theory, even locally. It is explained that a rigorous definition of time, as well as a formulation of the causality and locality concepts, can only be given when one has a model for the physical phenomena described. The only viable causality condition is one that is symmetric under time reversal. We explain these statements in terms of the author’s favoured deterministic cellular automaton interpretation of quantum mechanics, also to be referred to as 'vector space analysis', and expand on these ideas. It is also summarised how our more rigorous causality condition affects Bell’s theorems. What distinguishes quantum systems from classical ones is our fundamental inability to control the microscopic details of the initial state when phenomena are studied in the light of some theoretical model.