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Maximally Realistic Causal Quantum Mechanics

Roy, S M, Singh, V

Published Nov 19, 1998• 7 citations
OpenAlex

Abstract

We recently constructed a causal quantum mechanics in 2 dim. phase space which is more realistic than the de Broglie-Bohm mechanics as it reproduces not just the position but also the momentum probability density of ordinary quantum theory. Here we present an even more ambitious construction in 2n dim. phase space. We conjecture that the causal Hamiltonian quantum mechanics presented here is `maximally realistic'. The positive definite phase space density reproduces as marginals the correct quantum probability densities of $n+1$ different complete commuting sets of observables (e.g. $\\vec q$, $\\vec p$ and $n-1$ other sets). In general the particle velocities do not coincide with the de Broglie-Bohm velocities.

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PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association•Jan 1, 1994•20 citations
We recently constructed a causal quantum mechanics in 2 dim. phase space which is more realistic than the de Broglie-Bohm mechanics as it reproduces not just the position but also the momentum probability density of ordinary quantum theory. Here we present an even more ambitious construction in 2n dim. phase space. We conjecture that the causal Hamiltonian quantum mechanics presented here is `maximally realistic'. The positive definite phase space density reproduces as marginals the correct quantum probability densities of n+1n+1n+1 different complete commuting sets of observables (e.g. vecq\\vec qvecq, vecp\\vec pvecp and n−1n-1n−1 other sets). In general the particle velocities do not coincide with the de Broglie-Bohm velocities.
The De Broglie-Bohm (DeBB)\cite{DeBB} Causal Quantum Mechanics played a crucial role in Bell's discovery \cite{Bell1964} that quantum mechanics violates EPR local reality \cite{EPR1935}, and also in Bell's search for an exact quantum mechanics. The experiments of Aspect et al \cite{Aspect1981} confirm quantum correlations between plane polarizations of two photons and violation of Bell's inequalities by a factor $\sqrt 2 $. I prove that similar experiments with elliptic polarizers can also show quantum violations of Bell's inequality by the same factor. I summarize our construction of a maximally realistic causal quantum mechanics in n−n-n−dimensional configuration space \cite{Roy-Singh1995}. Phase space Bell inequalities and 'Marginal Theorems' \cite{Auberson2002} play a crucial role.
The non-relativistic quantum theory has been interpreted causally by de Broglie, David Bohm, and others, where a quantum entity is viewed as a particle with a definite position and momentum. This interpretation contrasts with the Copenhagen orthodox interpretation, which conveys uncertainty through the commutator relationship between position and momentum operators. This is further exacerbated by the de Broglie-Bohm interpretation, which uses no operators corresponding to these observables. We reconcile these opposing viewpoints by introducing mathematical nonlinear transforms in Bohmian mechanics for the momentum observable. While these nonlinear operator-like transforms cannot be easily represented as matrices in the Hilbert space, we show that they can be utilized in the de Broglie-Bohm interpretations of quantum theory.
Philosophers of science have not paid much attention to recent developments in quantum cosmology. This fact is surprising, since quantum cosmology is replete with conceptual issues involving (e.g.) the fundamental nature of time and space, the interpretation of quantum mechanics, and the ultimate meaning of probability. One notable exception, Quentin Smith, has recently examined the Hartle-Hawking (1983) proposal. Trying to make sense of the view, he resorts to an instrumentalist picture, which treats the proposal as merely a heuristic device for the algorithm responsible for predictions. While we do not examine Smith's account here, we would like to contrast it with the model presented in this note, in which a fully realistic interpretation of quantum cosmology is developed. Recently there has been a resurgence of interest in the de Broglie-Bohm causal interpretation of quantum mechanics.