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NONLOCAL QUANTUM POTENTIAL INTERPRETATION OF RELATIVISTIC ACTIONS AT A DISTANCE IN MANY-BODY PROBLEMS

Marie Curie

Published Jan 1, 1985• 0 citations
OpenAlex

Abstract

Relativistic constraints on the behaviour of a system of N scalar particles correlated by causal many-body actions at a distance interactions are analysed in relativistic and quantum mechanics. It is shown I) that the many-body quantum potential associated to the stochastic interpretation of quantum mechanics yields perfectly causal actions at a distance 2) thar the cor­ responding set of distinguishable particle motions corresponds to Bose-Einstein statistics.

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Relativistic constraints on the behaviour of a system of N scalar particles correlated by causal many-body actions at a distance interactions are analysed in relativistic and quantum mechanics. It is shown I) that the many-body quantum potential associated to the stochastic interpretation of quantum mechanics yields perfectly causal actions at a distance 2) thar the cor­ responding set of distinguishable particle motions corresponds to Bose-Einstein statistics.
New relativistic mechanics of two-particle system is set forth, where the two constituent particles are interacting by an arbitrary (central) action-at-a-distance. The fundamental equations are presented in a form covariant under general transformation of parameters parametrizing the world lines of constituent particles. The theory represents the proper relativistic generalization of the usual Newtonian mechanics in the sense that it tends in the non-relativistic (and weak interaction) limit to the usual mechanics of two particles moving under a corresponding non-relativistic potential. For the analysis of theory it is convenient to choose a certain particular gauge (i.e., parametrization) fixed by two gauge relations. This brings the theory to a canonical formalism accompanied by two weak equations, and in this gauge quantization can be performed. The result verifies that the relativistic quantum mechanics for two particles interacting by an action-at-a-distance is just represented by a bilocal wave equation and a subsidiary condition, with the clarification of its correspondence-theoretical fundation and internal dynamics. As an example the case of Hooke-type force is illustrated, where the internal motions are elliptic oscillations in the center-of-mass frame. Its quantum theory just reproduces the original form of bilocal theory giving bound states lying on a straightly rising trajectory and on its daughter trajectories.
We show how the causal interpretation provides a physical basis for the Wigner phase-space formulation of quantum mechanics by analyzing the case of a relativistic spin-zero particle in an external electromagnetic field. The Wigner function can be interpreted as both a generalized transformation and a field which defines a quantum potential in phase space. We also propose a Lorentz-vector distribution function which always associates positive probability densities with the real motions of particles and antiparticles in phase space.
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.