Time-symmetric stochastic action in curved phase-space

Quantum field dynamics is equivalent to a forward-backward stochastic process in both time directions, and can be calculated from an equilibration in a fifth space-time dimension [1]. Stochastic time-symmetric action principles in a curved phase-space are central to these results. They can be used to compute a stochastic bridge, the probability for random paths between two states, with any positive or negative diffusion. Such bridges have other precision applications, in fields ranging from many-body quantum dynamics to cell biology, control theory and finance. Numerical methods and examples of solutions to the resulting stochastic partial differential equations in a higher time-dimension are obtained. These give agreement with exact solutions for bosonic quantum field dynamics, including entangled systems. This novel approach may lead to useful computational techniques, as the action principle is real. Of more fundamental significance is that it provides an ontological model of reality [2] in cosmological models, and allows an interpretation of objective measurement without wave-function collapse.

(1) P. D. Drummond, arXiv:1910.00001
(2) P. D. Drummond, M.D. Reid, arXiv:1909.01798