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

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 present a numerical simulation of the double-slit experiment performed by Jnsson in 1961 with electrons. The method of Feynman path integrals allows to calculate the time dependent wave function. It shows that the interference phenomena appears only some centimeters after the slits. Moreover, the de Broglie-Bohm trajectories provide an explanation for the impact positions of the particles. Finally, we show how these trajectories converge to classical trajectories. Second, 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 to demonstrate the decoherence of the wave function and the three postulates of quantum measurement: quantization, the Born interpretation and wave function reduction. The spinor spatial extension also enables the introduction of the de Broglie-Bohm trajectories, which gives a very simple explanation of the particles' impact and of the measurement process. Third, we study the EPR-B experiment, 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. Finally, we suggest that a physical explanation of non-local influences is possible, compatible with Einstein's point of view on relativity.