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arXiv:1807.00513 · Entropy

A Lenient Causal Arrow of Time?

Nathan Argaman

Published Apr 18, 2018• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.3390/e20040294

Related papers

John Bell, relativistic causality, and the arrow of time

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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.

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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.
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.
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.
This Comment argues that two assumptions, which are presented as basic assumptions of Bell's theorem in [J. Handsteiner et al., Phys. Rev. Lett. 118, 060401 (2017)] and elsewhere, in fact follow from more basic premises. Measurement independence follows from (i) the use of free variables and (ii) the causal arrow of time. Determinism follows from (i) local causality and (ii) perfect correlations (predicted by quantum mechanics). In particular, it is pointed out that the measurement-independence violating toy model of [M.J.W. Hall, Phys. Rev. Lett. 105, 250404 (2010)], is based on a retro-causal model. While this may be controversial, it should be possible to achieve concensus on the much simpler matter of what the basic assumptions of Bell's theorem are.
Bell's theorem rules out developing a locally causal theory to describe quantum phenomena. Many take this to imply that any model of quantum entanglement must employ variables (called beables by Bell) which follow nonlocal rules, even though signaling is local. The alternative is to adopt an all-at-once (block universe) approach, with beables which may depend on both past and future inputs, even though signaling is causal. Within this lenient-causality approach (a.k.a. retrocausal), simple cases of entanglement have been successfully described by locally mediated stochastic toy models, i.e.,~toy models which are local in a sense which generalizes Bell's local causality. Developing a widely applicable reformulation of quantum mechanics along these lines is a grand challenge. This work presents a general framework for such models and theories, and identifies the corresponding ontic and epistemic states. The epistemic state is closely analogous to the quantum state, yielding an explanation for the collapse of the wavefunction. In the case of the models of the framework, it is clear what the information is about. The expression for the empirically verifiable predictions of the models in terms of the ontic and epistemic states displays remarkable parallels to the Born rule. A toy-model example is discussed.
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.