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arXiv:2312.11288 · AIP Advances

On removing the classical-quantum boundary

Khaled Mnaymneh

Published Oct 1, 2024• 0 citations
arXivHTMLPDF

Abstract

We argue that it is adherence to the axiom of counterfactual definiteness and not to that of locality and realism that results in Bell inequality violations. Furthermore, this axiom is not supported in classical mechanics because of deeper implications that arise from the principle of stationary action. This means that the Bell inequality fails classically, effectively removing the classical-quantum boundary–a conclusion prophesized by Bell himself. An implication here is that a local hidden variable theory, in the configuration space of classical mechanics, may not be ruled out. Basing our idea on Jacobi’s “initial variable” framework, we propose that a classical path of stationary action that recedes into the infinite past and stretches into an infinite future implies a reality that lacks counterfactual definiteness. We then corroborate this with recent experimental results, through which it could be understood that our world could be such a reality.

DOI
10.1063/5.0206221

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We argue that it is adherence to the axiom of counterfactual definiteness and not to that of locality and realism that results in Bell inequality violations. Furthermore, this axiom is not supported in classical mechanics because of deeper implications that arise from the principle of stationary action. This means that the Bell inequality fails classically, effectively removing the classical-quantum boundary–a conclusion prophesized by Bell himself. An implication here is that a local hidden variable theory, in the configuration space of classical mechanics, may not be ruled out. Basing our idea on Jacobi’s “initial variable” framework, we propose that a classical path of stationary action that recedes into the infinite past and stretches into an infinite future implies a reality that lacks counterfactual definiteness. We then corroborate this with recent experimental results, through which it could be understood that our world could be such a reality.
A recent experiment yielding results in agreement with quantum theory and violating Bell inequalities was interpreted [Nature 526 (29 Octobert 2015) p. 682 and p. 649] as ruling out any local realistic theory of nature. But quantum theory itself is both local and realistic when properly interpreted using a quantum Hilbert space rather than the classical hidden variables used to derive Bell inequalities. There is no spooky action at a distance in the real world we live in if it is governed by the laws of quantum mechanics.
We give a counter example to show that determinism as such is in contradiction to quantum mechanics. More precisely, we consider a simple quantum system and its environment, including the measurement device, and make the assumption that the time evolution of the global system, the quantum system plus this environment, is deterministic, i. e., the time evolution is given by a dynamical trajectory from some initial conditions. From this, we prove a type of Bell inequalities which are violated by quantum mechanics, reaching the conclusion that our quantum system evolves in a non deterministic way. In order to seize the interest of this conclusion, one must realize that it cannot be reached from the present experimental violation of Bell inequalities predicted by quantum mechanics, since this violation is compatible with non-local realism.
It is shown that when properly analyzed using principles consistent with the use of a Hilbert space to describe microscopic properties, quantum mechanics is a local theory: one system cannot influence another system with which it does not interact. Claims to the contrary based on quantum violations of Bell inequalities are shown to be incorrect. A specific example traces a violation of the CHSH Bell inequality in the case of a spin-3/2 particle to the noncommutation of certain quantum operators in a situation where (non)locality is not an issue. A consistent histories analysis of what quantum measurements measure, in terms of quantum properties, is used to identify the basic problem with derivations of Bell inequalities: the use of classical concepts (hidden variables) rather than a probabilistic structure appropriate to the quantum domain. A difficulty with the original Einstein-Podolsky-Rosen (EPR) argument for the incompleteness of quantum mechanics is the use of a counterfactual argument which is not valid if one assumes that Hilbert-space quantum mechanics is complete; locality is not an issue. The quantum correlations that violate Bell inequalities can be understood using local quantum common causes. Wavefunction collapse and Schr\odinger steering are calculational procedures, not physical processes. A general Principle of Einstein Locality rules out nonlocal influences between noninteracting quantum systems. Some suggestions are made for changes in terminology that could clarify discussions of quantum foundations and be less confusing to students.
Counterfactual definiteness must be used as at least one of the postulates or axioms that are necessary to derive Bell-type inequalities. It is considered by many to be a postulate that not only is commensurate with classical physics (as for example Einstein’s special relativity), but also separates and distinguishes classical physics from quantum mechanics. It is the purpose of this paper to show that Bell’s choice of mathematical functions and independent variables implicitly includes counterfactual definiteness. However, his particular choice of variables reduces the generality of his theory, as well as the physics of all Bell-type theories, so significantly that no meaningful comparison of these theories with actual Einstein-Podolsky-Rosen experiments can be made.
Most physicists agree that the Einstein–Podolsky–Rosen–Bell paradox exemplifies much of the strange behavior of quantum mechanics, but argument persists about what assumptions underlie the paradox. To clarify what the debate is about, we employ a simple and well-known thought experiment involving two correlated photons to help us focus on the logical assumptions needed to construct the EPR and Bell arguments. The view presented in this paper is that the minimal assumptions behind Bell’s inequality are locality and counterfactual definiteness but not scientific realism, determinism, or hidden variables as are often suggested. We further examine the resulting constraints on physical theory with an illustration from the many-worlds interpretation of quantum mechanics—an interpretation that we argue is deterministic, local, and realist but that nonetheless violates the Bell inequality.
Abstract Quantum mechanics predicts faster-than-light information transportation in order to satisfy quantum entanglement experimental results. Such a prediction violates the locality principle and Bell’s inequality. Quantum mechanisms also state that the world is intrinsically probabilistic. Such an idea was not welcome by many scientists including Einstein, Podolsky and Rosen. To resolve such a dilemma, the ”Many-world” theory was presented by Hugh Everett in 1975. Such a theory asserts that the universal wave function is real and that there is no wave function collapse. Also, it states that all possible outcomes of quantum measurements are physically realized in other parallel universes. Besides, in quantum mechanics, the observer effect defines a state transition of quantum objects. Such a phenomenon affirms that quantum objects behave differently depending on being observed or not. In this paper, we present few assumptions based on which we build a classical hidden-variable-based system that can violate Bell’s inequality. Therefore, adopting similar assumptions in explaining quantum entanglement could lead to a better explanation of quantum mechanics without violating the locality principle or adopting such weird assumptions. Hence, one can conclude that extending Quantum Mechanism by a set of similar hidden variables can resolve such a paradox and predict the quantum entanglement experimental results without violating the locality principle.