Two Types of Temporal Symmetry in the Laws of Nature

TL;DR

This paper investigates how assuming time symmetry and specific boundary conditions in deterministic laws with randomness can lead to two types of governing equations, explaining thermodynamic behavior and the arrow of time without assuming a preferred temporal direction.

Contribution

It introduces two forms of governing equations derived from time-symmetric boundary conditions, providing a novel mathematical framework for understanding temporal asymmetry in nature.

Findings

Derivation of symmetric and antisymmetric equations from time-symmetric assumptions

Explanation of thermodynamic characteristics and arrow of time without preferred direction

Mathematical structure of Markov bridges underpins temporal properties

Abstract

This work explores the implications of assuming time symmetry and applying bridge-type, time-symmetric temporal boundary conditions to deterministic laws of nature with random components. The analysis, drawing on the works of Kolmogorov and Anderson, leads to two forms of governing equations, referred to here as symmetric and antisymmetric. These equations account for the emergence of characteristics associated with conventional thermodynamics, the arrow of time, and a form of antecedent causality. The directional properties of time arise from the mathematical structure of Markov bridges, without requiring any postulates that impose a preferred direction of time.