A New Approach to Unification

TL;DR

This paper proposes a stochastic process-based framework for unifying fundamental interactions, deriving quantum features from classical randomness, and potentially offering a background-independent approach to quantum gravity and unification.

Contribution

It introduces a novel stochastic approach to unification, deriving quantum equations from classical processes and generalizing gauge fields without gauge symmetry.

Findings

Reproduces quantum field behavior at large scales

Regularizes infinities with a fundamental length scale

Provides a background-independent unification framework

Abstract

This paper presents a new perspective on unifying all fundamental interactions--gravitational, electromagnetic, weak and strong--based on stochastic processes rather than conventional quantum mechanics. Earlier work by Nelson, Kac and others have established that key quantum features such as the Schr\"{o}dinger and Dirac equations together with the Born rule can be derived from classical random processes involving finite speeds and probabilistic reversals. A fundamental length scale, inherent for dimensional consistency, regularizes the infinities that typically plague conventional field theories. The method can be used to quantize electrodynamics as well as linear gravity, using the Riemann-Silberstein vector and its generalization. To include fields beyond electromagnetism, the Riemann-Silberstein vector can be generalized to describe non-Abelian gauge fields without relying on gauge symmetry. These fields can be coupled to spin networks--geometric structures that discretize space--leading to a unified framework that includes both matter and geometrty. In the large-scale limit, the model reproduces familiar quantum field behaviour, while remaining finite and background-independent at the fundamental level. The emergence of equilibrium states resembling Wheeler-DeWill constraints in gravity adds further depth, suggesting a novel route to quantum gravity and unification grounded in physical stochasticity rather than quantization rules.