The Degrees of Symmetry functions

TL;DR

This paper introduces a continuous symmetry measure function that varies with reference position and time, providing a new way to analyze how external influences affect system symmetry and conservation laws.

Contribution

It generalizes symmetry as a continuous function dependent on reference points, enabling analysis of symmetry evolution over time in closed systems.

Findings

Symmetry functions can indicate external influences on systems.

Time evolution of symmetry functions reflects external agent effects.

Framework applicable to various closed systems.

Abstract

We propose a generalization of the concept of symmetry as a continuous function of the reference center or line location. We suggest that this concept can be applied to many closed systems and exploring its time evolution. When the function changes along time it is an indication that external factors are acting on the system.The change in the symmetry function along time can be thought as a current in the symmetry degree and its time behavior a measure of the effect of the external agent. Keywords: Symmetry, conservation laws, degree of parity.