On Entangled Multi-Particle Systems in Bohmian Theory

Abstract

AbstractArguments are presented to show that in the case of entangled sys-tems there are certain difficulties in implementing the usual Bohmianinterpretation of the wave function in a straightforward manner. Spe-cific examples are given. The three basic prescriptions of standard Bohmian quantum theory [1]are:(i) take the wave function ψto be a solution of the Schr¨odinger equation,(ii) impose the guidance condition p = mdx/dt= ∇Swhere Sis thephase of the wave function ψ= Rexp(iS/~), and(iii) choose the particle distribution P [t 0 ] at some arbitrary time t 0 (theinitial time) such that P [t 0 ] = |ψ| 2[t 0 ] = R 2[t 0 ] . This is known in the literatureas the ‘quantum equilibrium hypothesis’ (QEH). Given the prescriptions (i)through (iii), one can prove complete equivalence between this theory andstandard quantum mechanics by using the continuity equation for R 2 to showthat P [t] = R 2[t] for all subsequent times.While these prescriptions are self-consistent and work for single particleand factorizable many-particle systems, it turns out that non-factorizable1