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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

Action-at-a-distance and causality in the stochastic interpretation of quantum mechanics

Nicola Cufaro Petroni, Ph. Droz-Vincent, Jean Pierre Vigier

Published Jul 1, 1981• 36 citations
Publisher
DOI
10.1007/bf02776147

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We analyze the causal quantum behavior of two charged spinless particles having different masses interacting via an action-at-a-distance relativistic scalar Coulomb potential. Developing de Broglie's idea of splitting the potential energy between the particles, we show that the predictivity constraints of relativistic predictive mechanics established by Droz-Vincent and Sudarshan are satisfied. In this way we develop a relativistic theory of hydrogenlike atoms in the framework of the causal interpretation of quantum mechanics.
This paper implements in a simple but rigorous fashion a model of particle interaction involving all paths within a quantum system, both for configuration space and for spin. The model, which we call the space of all paths, leads to a locally explicable conceptual framework for quantum mechanics. Using it we present two counterexamples to Bell's theorem. Moreover, we show that the result places severe constraints on possible viable interpretations of quantum mechanics: Either an interpretation must in some form represent a quantum system in terms of all paths within the system or, alternatively, the interpretation must harbor "action at a distance." We take action-at-a-distance as a reductio ad absurdum argument for our framework for quantum foundations, since any mechanism in which causal effects can operate instantaneously across vast distances would be completely unknown and magical, a near absurdity.