Is symmetry identity?

TL;DR

This paper explores whether symmetry, as formalized by group theory, fundamentally represents identity in nature, examining the correspondence between physical entities and mathematical formalism to justify the effectiveness of mathematics in science.

Contribution

It provides a detailed analysis of the relationship between symmetry and identity, proposing that group theory encodes our experience of identification and exploring its potential to describe new entities.

Findings

Group theory closely matches physical entities and symmetry concepts.

Symmetry's effectiveness in science is justified by its design and correspondence.

Further validation suggests possible description of new entities via irreducible representations.

Abstract

Wigner found unreasonable the "effectiveness of mathematics in the natural sciences". But if the mathematics we use to describe nature is simply a coded expression of our experience then its effectiveness is quite reasonable. Its effectiveness is built into its design. We consider group theory, the logic of symmetry. We examine the premise that symmetry is identity; that group theory encodes our experience of identification. To decide whether group theory describes the world in such an elemental way we catalogue the detailed correspondence between elements of the physical world and elements of the formalism. Providing an unequivocal match between concept and mathematical statement completes the case. It makes effectiveness appear reasonable. The case that symmetry is identity is a strong one but it is not complete. The further validation required suggests that unexpected entities might be describable by the irreducible representations of group theory.