Observer Equivariance and the Origin of Symmetry in Physics: A Condition for Shared Physical Law

Observer Equivariance as a Condition for Shared Physical Law develops a strict categorical model of a simple but far-reaching idea: physical law must be shareable across admissible changes of observer perspective.

The paper formalizes this idea using a split principal G-fibration in groupoids. The total category represents observer-dependent presentations, while the base category represents the publicly accessible structural content that remains stable under fiberwise changes of presentation. Within this normalized strict setting, the main theorem shows that every symmetry of the base lifts to a G-equivariant, cleavage-preserving autoequivalence upstairs, uniquely up to normalized fiber translation. This yields a short exact sequence that makes precise, in group-theoretic form, how shared law constrains observer-dependent presentation.

The aim of the paper is deliberately limited. It does not claim to provide a maximally general account of observer-dependence, nor a full reconstruction of relativistic or gauge-theoretic physics. Instead, it isolates a strict mathematical core: “shared physical law” is rendered as law definable on the base category, or equivalently as upstairs data admitting equivariant descent. In this sense, the article turns a philosophical intuition into a precise structural statement.

Worked examples include a normalized qubit model, a constrained Minkowski-style illustration, and a sketch of how local gauge situations would require a weaker stack-theoretic generalization. A final interpretive section situates the framework within a structurally realist orientation without allowing the philosophical discussion to outrun the proven mathematics.

This version is released as a working article on Zenodo. It is intended both as a standalone contribution on observer-equivariance and shared law, and as part of a broader research program on the relation between observer structure, objectivity, and the formal architecture of physical theory.