QED Constraints, Minimal Geometry, and a Differential Atomic Clock Test

This article develops a mathematically explicit framework in which time is treated as an observable emerging from the projection of internal dynamical degrees of freedom rather than as a fundamental parameter. Starting from the operator structure of Quantum Electrodynamics, it is shown that the Dirac algebra and the existence of spin-1/2 representations severely constrain any admissible underlying geometry, uniquely selecting a minimal tetrahedral structure. Within this framework, standard QED observables act as precision probes of internal response channels while remaining insensitive to the geometry itself. The theory leads to a single, falsifiable experimental prediction: a strictly differential, state-dependent gravitational redshift between distinct atomic clock transitions. Existing and next-generation optical clocks, particularly Yb⁺ E2 and E3 transitions, are identified as capable of testing this prediction using the known tidal modulation of the Earth’s gravitational potential.