Stochastic Quantum Trajectories without a Wave Function

TL;DR

This paper explores extending Bohmian quantum mechanics to include spin without relying on wave functions, proposing a stochastic trajectory approach that incorporates spin as a discrete variable.

Contribution

It introduces a wave function-free formulation of quantum trajectories with spin, building on Bell's pilot wave theory and extending Bohmian mechanics.

Findings

Wave function-free stochastic trajectories for spin are formulated.

The approach generalizes Bohmian mechanics to particles with spin.

A consistent model for spin in trajectory-based quantum mechanics is developed.

Abstract

After summarizing three versions of trajectory-based quantum mechanics, it is argued that only the original formulation due to Bohm, which uses the Schr\"odinger wave function to guide the particles, can be readily extended to particles with spin. To extend the two wave function-free formulations, it is argued that necessarily particle trajectories not only determine location, but also spin. Since spin values are discrete, it is natural to revert to a variation of Bohm's pilot wave formulation due originally to Bell. It is shown that within this formulation with stochastic quantum trajectories, a wave function free formulation can be obtained.