Finite path integrals on stochastic branched structures

TL;DR

This paper introduces a finite, entropy-based path integral model on branched structures that unifies quantum interference and classical determinism, offering insights into wave function collapse.

Contribution

It proposes a novel finite path integral framework based on entropy, linking quantum and classical physics within a unified model.

Findings

Path integrals are finite and incorporate non-uniform path weights.

Wave function collapse may result from entropy maximization.

The model bridges quantum interference and classical determinism.

Abstract

In this paper, we present a statistical model of spacetime trajectories based on a finite collection of paths organized into a branched manifold. For each configuration of the branched manifold, we define a Shannon entropy. Given the variational nature of both the action in physics and the entropy in statistical mechanics, we explore the hypothesis that the classical action is proportional to this entropy. Under this assumption, we derive a Wick-rotated version of the path integral that remains finite and exhibits both quantum interference at the microscopic level and classical determinism at the macroscopic scale. In effect, this version of the path integral differs from the standard one because it assigns weights of non-uniform magnitude to different paths. The model suggests that wave function collapse can be interpreted as a consequence of entropy maximization. Although still idealized, this framework provides a possible route toward unifying quantum and classical descriptions within a common finite-entropy structure.