Time evolution with symmetric stochastic action

Abstract

Quantum dynamical time-evolution of bosonic fields is shown to be equivalent to a stochastic trajectory in space-time, corresponding to samples of a statistical mechanical steady-state in a higher dimensional quasi-time. This is proved using the Q-function of quantum theory with time-symmetric diffusion, that is equivalent to a forward-backward stochastic process in both the directions of time. The resulting probability distribution has a positive, time-symmetric action principle and path integral, whose solution corresponds to a classical field equilibrating in an additional dimension. Comparisons are made to stochastic quantization and other higher dimensional physics proposals. Five-dimensional space-time was originally introduced by Kaluza and Klein, and is now widely proposed in cosmology and particle physics. Time-symmetric action principles for quantum fields are also related to electrodynamical absorber theory, which is known to be capable of violating a Bell inequality. We give numerical methods and examples of solutions to the resulting stochastic partial differential equations in a higher time-dimension, giving agreement with exact solutions for soluble boson field quantum dynamics. This approach may lead to useful computational techniques for quantum field theory, as the action principle is real, as well as to ontological models of physical reality.