Deficiencies of Bohm Trajectories in View of Basic Quantum Principles

摘要

Quantum mechanics has been one of the most successful theories in physics, yet itsfoundation has remained a subject of discussion ever since it was incepted in the 1920s. Whilethe Copenhagen interpretation represents the main-stream view, recent years have witnessedrevived interest in the alternative deterministic, or pilot-wave, interpretation, pioneered byMadelung, de Broglie, and Bohm. It has been argued that these two interpretations are basicallyequivalent. In this article we show that this is not true. We exhibit the approximate nature ofparticle trajectories in Bohm’s quantum mechanics. They follow the streamlines of a superfluidin Madelung’s reformulation of the Schr¨ odinger wave function, around which the proper particletrajectories perform their quantum mechanical fluctuations that ensure Heisenberg’s uncertaintyrelation between position and momentum. These fluctuations explain the apparent discrepancyin the double-slit interference intensities between Bohmian mechanics and observations. Theyare also the reason for the non-existence of a possible radiation that would be emitted by anelectron if its physical trajectory were deflected by the Bohmian quantum potential.