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Physics Essays

An explanation of the quantum mechanics of particles

O. Chavoya-Aceves

Published Dec 11, 2015• 1 citation
Publisher

Abstract

The ontological status of the wave function as a purely mathemat- ical artifact is clari ed. Grounds are found to reject the de Broglie- Bohm formulation of the quantum mechanics of particles. The pre-sumption by Einstein-Podolsky-Rosen that quantum mechanics is not a complete theory is reinforced.
DOI
10.4006/0836-1398-28.4.417

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Based on a thought experiment the Einstein-Podolsky-Rosen paper’s authors concluded that in quantum mechanics the mathematical objects called wave functions fail to describe the physical reality and consequently quantum theory is incomplete. They left open the question of whether or not a complete description of the physical reality exists, but expressed their belief that such a complete theory is possible. In this paper I show that indeed a theory that gives a complete description of the physical reality exists.
We try to give a physical meaning to the wave function or quantum state of a system, apart from being a very efficient tool for predicting results of measurements on that system. In other words, we ask what does it mean for a system outside the laboratories to have a wave function? We first explain why two possible, and probably common, answers to that question do not really answer it. Then, we explain how the de Broglie – Bohm theory does give a satisfactory meaning to the quantum state outside the laboratories, while avoiding the problems faced by the other answers.
There are three possible interpretations of the wave function in the de Broglie-Bohm theory: taking the wave function as corresponding to a physical entity or a property of the Bohmian particles or a law. In this paper, we argue that the first interpretation is favored by an analysis of protective measurements. The de Broglie-Bohm theory is an alternative to standard quantum mechan-ics initially proposed by de Broglie (1928) and later developed by Bohm (1952). According to the theory, a complete description of a quantum system is provided by the configuration defined by the positions of its particles together with its wave function. The wave function follows the linear Schrödinger equation and never collapses. The motion of the particles, which are usually called Bohmian particles, follows the so-called guiding equation. Although the de Broglie-Bohm theory is mathematically equivalent to quantum mechanics, there is no clear consensus with regard to its physical interpretation. In particular, the interpre-
In many-particle quantum mechanics the wave function is irreducibly defined on configuration space. In the de Broglie–Bohm theory this fact is made explicit: both the wave function and the actual motion are naturally described as evolving in configuration space, while the familiar three-dimensional motions of particles arise only as projections of this higher-dimensional dynamics. In this paper we argue that configuration space should be regarded as the fundamental arena of quantum dynamics. On this view, the nonlocal correlations observed in ordinary three-dimensional space are not mysterious dynamical influences but direct consequences of local evolution in configuration space. This perspective is developed and illustrated through a detailed analysis of momentum measurement and which-way detection in the iconic two slit experiment, in the two-particle interferometry experiment of Horne–Shimony–Zeilinger and in the Einstein–Podolsky–Rosen experiment.