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Quantum theory is incompatible with relativity: A new proof beyond Bell's theorem and a test of unitary quantum theories

Shan Gao

Published Jun 27, 2019• 5 citations
OpenAlex

Abstract

It has been debated whether quantum mechanics and special relativity are incompatible and whether there is a preferred Lorentz frame if they are incompatible. Bell's theorem is an important cornerstone, but it does not give us a definite positive answer due to the existence of supplementary assumptions or theoretical loopholes; there are unitary quantum theories which evade Bell's theorem and claim that they are compatible with special relativity. In this paper, I address the important issue of whether unitary quantum theories are compatible with special relativity. I propose a new Gedankenexperiment, a variant of the EPR-Bohm experiment with a superobserver who can undo a measurement. In this experiment, there is a stronger correlation (between the results of two spacelike separated measurements) than the correlation investigated in Bell's theorem. Based on an analysis of the correlations in different Lorentz frames, I prove that unitary single-world theories are incompatible with special relativity, and in order to avoid the incompatibility, there must exist a preferred Lorentz frame in these theories. Moreover, I argue that the incompatibility proof also applies to a proper version of the many-worlds interpretation of quantum mechanics. This closes the major theoretical loopholes of Bell's theorem, including relationalism, retrocausality, and superdeterminism. Finally, I argue that the stronger correlation found in the Gedankenexperiment cannot be explained by retrocausal processes or even the common causes in the past, but only be explained by nonlocal processes or actions at a distance. This provides a test of unitary quantum theories, as well as a further support for the new incompatibility proof beyond Bell's theorem.

Related papers

Some Thoughts on Quantum Nonlocality and Its Apparent Incompatibility with Relativity

Shan Gao

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

Unitary quantum theories are incompatible with special relativity

Shan Gao

It is shown that the combination of a unitary quantum theory and special relativity may lead to a contradiction when considering the statistics of certain measurement results in different Lorentz frames in a Gedankenexperiment. This result seems to imply that either unitary quantum theories are wrong or if a unitary quantum theory is right then there must exist a preferred Lorentz frame.

•Nov 6, 2018•2 citations

Beyond Bell?

Richard Healey

In a recent archive post Shan Gao has argued that quantum theory is incompatible with relativity. He calls this a new proof beyond Bell's theorem, arguing elsewhere that it closes the superdeterminism loophole in Bell's theorem. Such strong claims must be backed up by irrefutable arguments. My aim in this post to the workshop "Beyond Bell's theorem" is to refute Gao's "proof" and to show how quantum theory is compatible with relativity theory and so why Gao's "proof" does not take us beyond Bell's theorem.

•Nov 14, 2021•0 citations

Lorentzinvariance in modal interpretations

Rob Clifton

Abstract Although Bell’s theorem tells us that any interpretation of quantum mechanics must fail to satisfy Bell’s locality condition, the question of Lorentz­invariance is apparently left open by Bell’s theorem. In­ deed, it has been argued by many that nonlocality is compatible with Lorentz­invariance, given certain interpretations of the latter, or of the former. Some give a ‘weak’ interpretation of Lorentz­ invariance, compatible with a ‘strong’ violation of locality. For example, Bohm’s (1952) theory violates locality in a way that requires a preferred frame; but empirical Lorentz­invariance is preserved in the Bohm theory ­ there is no experiment that could determine the preferred frame. (See, for example, Valentini (199la,b), Bohm and Hiley (1993), and Cushing (1994).) On the other hand, ‘orthodox’ interpretations of special relativity maintain a notion of ‘fundamental

•Sep 23, 2009•0 citations

Bell's Theorem and the Theory of Relativity

Yutaka TANAKA

This paper starts with the observation that the combination of the so-calld EPR argument and Bell's theorem reveals one of the most paradoxical features of quantum reality, i.e. the no-separability of two contingent events. If we accept the conclusion of the revised EPR argument together with Bell's theorem, we are necessarily led to the denial of local causality which was presupposed by the original version of Einstein's criticism against quantum physics.. As the concept of local causality is a cornerstone of Einstein's theory of relativity, we next consider the problem of compatibility between the theory of relativity and quantum physics. Popper's proposal of going back to Lorentz's theory is examined and rejected because the quantum correlation of EPR is not to be interpreted as “an action at a distance” which we can control and use as the operational definition of absolute simultaneity. An inquiry into something like aether as hidden reality behind the theory of relativity is considered as retrogressive as the so-called hidden variable theory of quantum physics. Accepting the non-separability of local elements of reality as the undeniable fact, we discuss the possibility of a realistic interpretation of quantum physics which transcends scientific materialism and classical determinism. As an example of such projects, Stapp's theory is examined with respect to a Whiteheadean process philosophy which provides the meta-physical background for his realistic interpretation of quantum physics. Finally, we present another version of quantum meta-physics based on “the philosophy of organism” which is broad enough to include observer and observed, local causality and non-local correlation, space and time, and potentiality and actuality in the inseparable unity of physical reality.

Annals of the Japan Association for Philosophy of Science•Jan 1, 1992•0 citations

Closing the superdeterminism loophole in Bell's theorem

Shan Gao

It is well known that there is a freedom-of-choice loophole or superdeterminism loophole in Bell's theorem. Since no experiment can completely rule out the possibility of superdeterminism, it seems that a local hidden variable theory consistent with relativity can never be excluded. In this paper, we present a new analysis of local hidden variable theories. The key is to notice that a local hidden variable theory assumes the universality of the Schroedinger equation, and it permits that a measurement can be in principle undone in the sense that the wave function of the composite system after the measurement can be restored to the initial state. We propose a variant of the EPR-Bohm experiment with reset operactions that can undo measurements. We find that according to quantum mechanics, when Alice's measurement is undone after she obtained her result, the correlation between the results of Alice's and Bob's measurements depends on the time order of these measurements, which may be spacelike separated. Since a local hidden variable theory consistent with relativity requires that relativistically non-invariant relations such as the time order of spacelike separated events have no physical significance, this result means that a local hidden variable theory cannot explain the correlation and reproduce all predictions of quantum mechanics even when assuming superdeterminism. This closes the major superdeterminism loophole in Bell's theorem.

•Jul 9, 2019•0 citations
It has been debated whether quantum mechanics and special relativity are incompatible and whether there is a preferred Lorentz frame if they are incompatible. Bell's theorem is an important cornerstone, but it does not give us a definite positive answer due to the existence of supplementary assumptions or theoretical loopholes; there are unitary quantum theories which evade Bell's theorem and claim that they are compatible with special relativity. In this paper, I address the important issue of whether unitary quantum theories are compatible with special relativity. I propose a new Gedankenexperiment, a variant of the EPR-Bohm experiment with a superobserver who can undo a measurement. In this experiment, there is a stronger correlation (between the results of two spacelike separated measurements) than the correlation investigated in Bell's theorem. Based on an analysis of the correlations in different Lorentz frames, I prove that unitary single-world theories are incompatible with special relativity, and in order to avoid the incompatibility, there must exist a preferred Lorentz frame in these theories. Moreover, I argue that the incompatibility proof also applies to a proper version of the many-worlds interpretation of quantum mechanics. This closes the major theoretical loopholes of Bell's theorem, including relationalism, retrocausality, and superdeterminism. Finally, I argue that the stronger correlation found in the Gedankenexperiment cannot be explained by retrocausal processes or even the common causes in the past, but only be explained by nonlocal processes or actions at a distance. This provides a test of unitary quantum theories, as well as a further support for the new incompatibility proof beyond Bell's theorem.
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.
In a recent archive post Shan Gao has argued that quantum theory is incompatible with relativity. He calls this a new proof beyond Bell's theorem, arguing elsewhere that it closes the superdeterminism loophole in Bell's theorem. Such strong claims must be backed up by irrefutable arguments. My aim in this post to the workshop "Beyond Bell's theorem" is to refute Gao's "proof" and to show how quantum theory is compatible with relativity theory and so why Gao's "proof" does not take us beyond Bell's theorem.
Abstract Although Bell’s theorem tells us that any interpretation of quantum mechanics must fail to satisfy Bell’s locality condition, the question of Lorentz­invariance is apparently left open by Bell’s theorem. In­ deed, it has been argued by many that nonlocality is compatible with Lorentz­invariance, given certain interpretations of the latter, or of the former. Some give a ‘weak’ interpretation of Lorentz­ invariance, compatible with a ‘strong’ violation of locality. For example, Bohm’s (1952) theory violates locality in a way that requires a preferred frame; but empirical Lorentz­invariance is preserved in the Bohm theory ­ there is no experiment that could determine the preferred frame. (See, for example, Valentini (199la,b), Bohm and Hiley (1993), and Cushing (1994).) On the other hand, ‘orthodox’ interpretations of special relativity maintain a notion of ‘fundamental
This paper starts with the observation that the combination of the so-calld EPR argument and Bell's theorem reveals one of the most paradoxical features of quantum reality, i.e. the no-separability of two contingent events. If we accept the conclusion of the revised EPR argument together with Bell's theorem, we are necessarily led to the denial of local causality which was presupposed by the original version of Einstein's criticism against quantum physics.. As the concept of local causality is a cornerstone of Einstein's theory of relativity, we next consider the problem of compatibility between the theory of relativity and quantum physics. Popper's proposal of going back to Lorentz's theory is examined and rejected because the quantum correlation of EPR is not to be interpreted as “an action at a distance” which we can control and use as the operational definition of absolute simultaneity. An inquiry into something like aether as hidden reality behind the theory of relativity is considered as retrogressive as the so-called hidden variable theory of quantum physics. Accepting the non-separability of local elements of reality as the undeniable fact, we discuss the possibility of a realistic interpretation of quantum physics which transcends scientific materialism and classical determinism. As an example of such projects, Stapp's theory is examined with respect to a Whiteheadean process philosophy which provides the meta-physical background for his realistic interpretation of quantum physics. Finally, we present another version of quantum meta-physics based on “the philosophy of organism” which is broad enough to include observer and observed, local causality and non-local correlation, space and time, and potentiality and actuality in the inseparable unity of physical reality.
It is well known that there is a freedom-of-choice loophole or superdeterminism loophole in Bell's theorem. Since no experiment can completely rule out the possibility of superdeterminism, it seems that a local hidden variable theory consistent with relativity can never be excluded. In this paper, we present a new analysis of local hidden variable theories. The key is to notice that a local hidden variable theory assumes the universality of the Schroedinger equation, and it permits that a measurement can be in principle undone in the sense that the wave function of the composite system after the measurement can be restored to the initial state. We propose a variant of the EPR-Bohm experiment with reset operactions that can undo measurements. We find that according to quantum mechanics, when Alice's measurement is undone after she obtained her result, the correlation between the results of Alice's and Bob's measurements depends on the time order of these measurements, which may be spacelike separated. Since a local hidden variable theory consistent with relativity requires that relativistically non-invariant relations such as the time order of spacelike separated events have no physical significance, this result means that a local hidden variable theory cannot explain the correlation and reproduce all predictions of quantum mechanics even when assuming superdeterminism. This closes the major superdeterminism loophole in Bell's theorem.