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Einstein’s Reply to Bell and Others? a Simple Constructive Classical Foundation for Quantum Theory

Gordon Watson

Published Aug 1, 2018• 0 citations
OpenAlex

Abstract

Having elsewhere refuted Bell’s theorem irrefutably with elementary mathematics, we here advance Einstein’s ideas similarly with a classical Lorentz-invariant theory, observationally-indistinguishable from quantum mechanics. Given that our elementary theory is straight-forward and non-mysterious, we provide an Einsteinian—a specifically local and truly realistic—advance toward understanding the classical nature of physical reality at the quantum level. We thus resolve Bell’s dilemma in Einstein’s favor: as Bell half-expected, he and his supporters were being rather silly.

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‘... all this action at a distance business will pass [like the ether]. If we're lucky it will be to some big new development like the theory of relativity. Maybe someone will just point out that we were being rather silly, with no big new development. But anyway, I believe the questions will be resolved,' after Bell (1990:9). ‘Nobody knows where the boundary between the classical and quantum domain is situated. More plausible to me is that we'll find that there is no boundary: the hidden-variable possibility,' after Bell (2004:28-29). Abstract: Studying Bell's work, using classical analysis and author-date referencing suited to undergraduate STEM students, we arrive at a new classical theory: local realistic quantum mechanics. Adjusting EPR to accord with Bohr's insight, and accepting Bell's principles (but not his false inferences), our method follows: (i) we allow Bell's pristine λ (and its pairwise twin μ) to be classical fair-coin vectors in 3-space; (ii) we complete the QM account of EPR correlations in a classical way; (iii) we deliver Bell's hope for a simple constructive model of EPRB; (iv) we justify EPR's belief that additional variables would bring locality and causality to QM's completion; (v) we refute key claims that such variables are impossible; (vi) we show that interactions between particles and polarizers are driven by the total angular momentum; (vii) we bypass Pauli's vector-of-matrices, but retain all the tools of the quantum trade. In short, under local realism: classically deriving the related results of quantum theory, we classically endorse Einstein's locally-causal Lorentz-invariant worldview.

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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
Having elsewhere refuted Bell’s theorem irrefutably with elementary mathematics, we here advance Einstein’s ideas similarly with a classical Lorentz-invariant theory, observationally-indistinguishable from quantum mechanics. Given that our elementary theory is straight-forward and non-mysterious, we provide an Einsteinian—a specifically local and truly realistic—advance toward understanding the classical nature of physical reality at the quantum level. We thus resolve Bell’s dilemma in Einstein’s favor: as Bell half-expected, he and his supporters were being rather silly.
Adjusting EPR (to accord with Bohr's insight), and accepting Bell's principles (but not his false inferences), we:— (i) complete the QM account of EPR correlations in a classical way; (ii) deliver Bell's hope for a simple constructive model of EPRB; (iii) justify EPR's belief that additional variables would bring locality and causality to QM's completion; (iv) refute key claims that such variables are impossible — including CHSH, Mermin's three-particle always-vs-never variant of GHZ, and this: in the context of Bell's theorem ‘it's a proven scientific fact that a violation of local realism has been demonstrated theoretically and experimentally,' (Annals of Physics Editors, 2016). In short: we refute Bell's theorem and endorse Einstein's locally-causal Lorentz-invariant worldview.
In our terms, this is Bell's 1964 theorem, ‘No local hidden-variable theory can reproduce exactly the quantum mechanical predictions.' Against this, and bound by what Bell takes to be Einstein's definition of locality, we refute Bell's theorem and reveal his error. We show that Einstein was right: the physical world is local; and we advance Einstein's quest to make quantum mechanics intelligible in a classical way. With respect to understanding, and taking mathematics to be the best logic, the author is as close as an email: eprb@me.com
Bell's theorem has been described as the most profound discovery of science; one of the few essential discoveries of 20th Century physics; indecipherable to non-mathematicians. However, taking elementary analysis to be an adequate logic here, we refute Bell's theorem, correct his inequality and identify his error. Further, we do this under the principle of true local realism, the union of true locality (or relativistic causality: no influence propagates superluminally) and true realism (or non-naive realism: some existents change interactively). We thus lay the foundation for a more complete physical theory: one in line with Einstein's ideas and Bell's hopes. Let's see.
‘... all this action at a distance business will pass [like the ether]. If we're lucky it will be to some big new development like the theory of relativity. Maybe someone will just point out that we were being rather silly, with no big new development. But anyway, I believe the questions will be resolved,' after Bell (1990:9). ‘Nobody knows where the boundary between the classical and quantum domain is situated. More plausible to me is that we'll find that there is no boundary: the hidden-variable possibility,' after Bell (2004:28-29). Abstract: Studying Bell's work, using classical analysis and author-date referencing suited to undergraduate STEM students, we arrive at a new classical theory: local realistic quantum mechanics. Adjusting EPR to accord with Bohr's insight, and accepting Bell's principles (but not his false inferences), our method follows: (i) we allow Bell's pristine λ (and its pairwise twin μ) to be classical fair-coin vectors in 3-space; (ii) we complete the QM account of EPR correlations in a classical way; (iii) we deliver Bell's hope for a simple constructive model of EPRB; (iv) we justify EPR's belief that additional variables would bring locality and causality to QM's completion; (v) we refute key claims that such variables are impossible; (vi) we show that interactions between particles and polarizers are driven by the total angular momentum; (vii) we bypass Pauli's vector-of-matrices, but retain all the tools of the quantum trade. In short, under local realism: classically deriving the related results of quantum theory, we classically endorse Einstein's locally-causal Lorentz-invariant worldview.
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.