Stochastic Quantization of Electrodynamics and Linearized Gravity

TL;DR

This paper introduces a unified stochastic framework for electrodynamics and linearized gravity using a Poisson process that leads to wave equations, with probability emerging intrinsically from the process rather than as an external postulate.

Contribution

It presents a novel stochastic approach that derives electromagnetic and gravitational wave equations from a Poisson process, avoiding the need for external probability postulates.

Findings

Derivation of Dirac-like equations via analytic continuation.

Recovery of massless wave equations in the zero-mass limit.

Probability is intrinsic to the stochastic process, not externally imposed.

Abstract

We develop a unified stochastic framework in which a velocity- and helicity-reversing Poisson process gives rise to the Telegrapher's equation. Analytic continuation to the complex plane results in Dirac-like evolution equations for electromagnetic and linearized gravitational fields. A small but nonzero mass parameter is essential to enable helicity reversals. Yet, the correct massless wave equations are recovered as the physically relevant massless limit is approached smoothly, with the singular point excluded from the construction. Remarkably, probability does not enter as an external postulate as in the Born rule in standard quantum mechanics -- but is intrinsic to the stochastic process. This probabilistic structure becomes embedded in the wave fields through a natural rescaling by the Planck length.