# Spontaneous Symmetry Breaking Breaks Time-Reversal Symmetry

## TL;DR

This paper discusses how spontaneous symmetry breaking in physics, particularly in gauge theories with O(2) symmetry, explicitly leads to the breaking of time-reversal symmetry, impacting our understanding of the arrow of time.

## Contribution

It demonstrates that spontaneous symmetry breaking explicitly breaks time-reversal symmetry using a gauge theory model with O(2) symmetry.

## Key findings

- Spontaneous symmetry breaking can break time-reversal symmetry.
- The proof uses a time step function in the Lagrangian.
- Implications for the arrow of time are discussed.

## Abstract

The ideas related to the arrow of time are discussed briefly. I then focus on the prevalent physical mechanism in the evolution of the universe and developments in particle physics, spontaneous symmetry breaking, and show that it explicitly breaks time-reversal symmetry. For simplicity, I do this in a point mechanics gauge theory with symmetry group O(2). The proof of breakdown of time-reversal symmetry relies on the use of a time step function to express the Lagrangian valid for any time.