Table of Contents
Physics Research International
Volume 2014 (2014), Article ID 605908, 16 pages
http://dx.doi.org/10.1155/2014/605908
Research Article

Measurement in the de Broglie-Bohm Interpretation: Double-Slit, Stern-Gerlach, and EPR-B

1University Paris Dauphine, Lamsade, 75 016 Paris, France
2École Nationale de l’Aviation Civile, 31000 Toulouse, France

Received 24 February 2014; Accepted 7 July 2014; Published 10 August 2014

Academic Editor: Anand Pathak

Copyright © 2014 Michel Gondran and Alexandre Gondran. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose a pedagogical presentation of measurement in the de Broglie-Bohm interpretation. In this heterodox interpretation, the position of a quantum particle exists and is piloted by the phase of the wave function. We show how this position explains determinism and realism in the three most important experiments of quantum measurement: double-slit, Stern-Gerlach, and EPR-B. First, we demonstrate the conditions in which the de Broglie-Bohm interpretation can be assumed to be valid through continuity with classical mechanics. Second, we present a numerical simulation of the double-slit experiment performed by Jönsson in 1961 with electrons. It demonstrates the continuity between classical mechanics and quantum mechanics. Third, we present an analytic expression of the wave function in the Stern-Gerlach experiment. This explicit solution requires the calculation of a Pauli spinor with a spatial extension. This solution enables us to demonstrate the decoherence of the wave function and the three postulates of quantum measurement. Finally, we study the Bohm version of the Einstein-Podolsky-Rosen experiment. Its theoretical resolution in space and time shows that a causal interpretation exists where each atom has a position and a spin.