The Reality Condition of Parity: Gyroscopes, Mirrors, and the Phase-Space Criterion for Symmetric Structures

Parity is traditionally understood as a spatial symmetry—an operation that inverts coordinates while leaving physical laws invariant. Its apparent violation in certain weak interactions has been interpreted as a fundamental breakdown of this symmetry. Here we propose a different interpretation: parity is not a transformation, but a condition of physical existence. Within a new theoretical framework, we define parity as a criterion that tests whether a mirror-reflected configuration can be realized as a stable physical state in phase space. Using the Wu experiment as a case study, we argue that the observed electron emission asymmetry does not indicate a broken symmetry, but rather the inability to realize the corresponding mirror-configured system. We formalize this idea with a criterion for parity conservation based on the existence of a nonzero phase-space volume for the mirror state: parity is conserved if and only if the mirror configuration occupies a nonzero volume in phase space. This formulation suggests that the Standard Model’s so-called parity asymmetries arise not from dynamically broken laws, but from the absence of complete mirror configurations. Our approach replaces the usual notion of an algebraically reversible symmetry with a focus on the constructive realizability of mirror states, providing a new perspective on symmetry, conservation laws, and experimental tests. In this view, parity is not “broken” in cases where the mirror state cannot exist; instead, parity is simply undefined there.