Photon Masslessness Theorem and Light Speed Invariance: Unified Formulation via Information Equivalence and Clifford Geometry

Preprint.This paper derives (i) photon masslessness and (ii) invariance of the speed of light as a single theorem package from one operational axiom—Information Equivalence (invariance of reported observables under local phase redefinition)—formulated in Cl(3,1) spacetime algebra with metric signature (−,+,+,+). Information Equivalence enforces the connection shift and minimal coupling, and thereby excludes the Proca photon-mass term without introducing auxiliary fields (no Stueckelberg/Higgs additions). Independently, the free Maxwell equation in spacetime algebra implies that nontrivial vacuum plane-wave solutions are null, placing free excitations on the light cone (k·k = 0). Together these results yield mγ = 0 as a strict vacuum theorem. Given the existence of a massless signal, the paper derives the Lorentz transformation structure and invariant speed c by kinematic uniqueness (linearity, isotropy, homogeneity), without postulating light-speed constancy as an axiom. As an auxiliary unifying statement, wave–particle complementarity is expressed as a rigorous POVM inequality (V² + D² ≤ 1). An optional “observation-layer” rescaling convention is discussed, explicitly non-essential to the core theorems. Related (DOI only) 10.5281/zenodo.18297667 | 10.5281/zenodo.18169038 | 10.5281/zenodo.18159246 | 10.5281/zenodo.18160277