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arXiv:1010.5049

Determinism and Quantum Mechanics with time Bell inequalities

Ramón Lapiedra, Perez, A.

Published Oct 25, 2010• 0 citations
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Abstract

We propose a definition of determinism for a physical system that includes, besides the measurement device, the surrounding environment. This enlarged system is assumed to follow a predefined trajectory starting from some (unknown) initial conditions that play the role of hidden variables for the experiment. These assumptions, which are different from realism, allow us to derive a type of time Bell inequalities, which are violated by Quantum Mechanics. In order to illustrate this violation, we discuss the particular case of measurements on a spin 1/2 particle.

DOI
10.48550/arxiv.1010.5049

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We propose a definition of determinism for a physical system that includes, besides the measurement device, the surrounding environment. This enlarged system is assumed to follow a predefined trajectory starting from some (unknown) initial conditions that play the role of hidden variables for the experiment. These assumptions, which are different from realism, allow us to derive a type of time Bell inequalities, which are violated by Quantum Mechanics. In order to illustrate this violation, we discuss the particular case of measurements on a spin 1/2 particle.
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.
We propose a definition of determinism for a physical system that includes, besides the measured system, the measurement device and the surrounding environment. This enlarged system is assumed to follow a predefined trajectory starting from some (unknown) initial conditions that play the role of hidden variables for the experiment. These assumptions, which are different from realism, allow us to derive some Leggett-Garg inequalities, which are violated by Quantum Mechanics in the particular case of consecutive measurements on individual photon polarizations.
Bell inequality is violated in quantum mechanics and in experiments. Bell's theorem, on the other hand, concludes that quantum physics or nature is hence nonlocal. Bell's derivation of such a theorem comes in two versions, BT1 in which he started with determinism assumption in his 1964 original paper, and BT2 in his 1976 paper where he started with a "local causality" condition (LC). In this paper we show that (LC) does not follow from the physical concept of local causality except in the determinism limit. A local hidden variable model for the singlet pair is given that yields the correct quantum predictions for pair correlations. We also show determinism flagrantly violates quantum predictions. Thus Bell's theorem has no scope of applicability on possible hidden variable theory for quantum mechanics.
Locality and realism are two main assumptions in deriving Bell's inequalities. Though the experimentally demonstrated violations of Bell's inequalities rule out local realism, it is, however, not clear what role each of the two assumptions solely plays in the observed violations. Here we show that two testable inequalities for the statistical predictions of two-qubit systems can be derived by assuming either locality or realism. It turns out that quantum mechanics respects a nonlocal classical realism, and it is locality that is incompatible with experimental observations and quantum mechanics.
Abstract Quantum states in superposition cannot be observed, suggesting that they merely embody information on possible measurement results. Yet, we think of them as describing physical systems that evolve in time according to given mathematical equations. Furthermore, evolution takes place in physical space-time, and local causality is imposed on space-time by Special Relativity (a sequence of cause and effect that constitutes a fundamental principle by which we think about and do scientific work). It is therefore strange that there is non–locality and violation of causality embedded in Quantum Mechanics. We try to give here a first step to see whether a deterministic and local interpretation is possible. We will show that Bell’s inequality is not conclusive about the non–local nature of Quantum Mechanics, in that there exists an interpretation of reality (which we put forward) which is local and in which Bell’s inequality cannot be derived. Assuming determinism and locality a new Bell-like inequality is derived, which is always satisfied by Quantum Mechanics and which allows for local hidden variables [1].
By implicitly assuming that all possible Bell-measurements occur simultaneously, all proofs of Bell's Theorem violate Heisenberg's Uncertainty Principle. This assumption is made in the original form of Bell's inequality, in Wigner's probability inequalities, and in the ``nonlocality without inequalities'' arguments. The introduction of time into derivations of these variants of Bell's theorem results in extra terms related to the time order of the measurements used in constructing correlation coefficients. Since the same locality assumptions are made in the Heisenberg-compliant derivations of this paper, only time-independent classical local hidden variable theories are forbidden by violations of the original Bell inequalities; time-dependent quantum local hidden variable theories can satisfy this new bound and agree with experiment. We further point out that factorizable wavefunctions have been used to describe some EPR experiments and can be used to describe others. These will generate local de Broglie-Bohm trajectories in the description of the data. This second, independent, line of argument also shows that violation of Bell's inequality is only evidence that Heisenberg's Uncertainty Principle cannot be ignored.