Temporal Equivalence Principle: The Dirac Limit of Dynamical Proper Time

Standard relativistic quantum mechanics, including the Klein–Gordon and Dirac equations, is recovered here as the screened, flat-frame tangent limit of a deeper dynamical proper-time phase transport governed by the Temporal Equivalence Principle (TEP). By treating proper time τ as a dynamical scalar field φ rather than a universal parameter, three foundational structures are derived and two are geometrically reinterpreted. (1) The phase action S = −mc² ∫ dτ̃ emerges as the primitive geometric driver, with mass appearing in the primitive action as the parameter governing the oscillator frequency, ω₀ = mc²/ℏ, modulated by the conformal factor in the causal matter metric g̃μν. (2) The Klein-Gordon equation is derived from the minimal geometric Lagrangian in the causal metric and verified via WKB / eikonal expansion; its eikonal limit recovers the g̃-Hamilton-Jacobi equation, not via operator substitution. (3) The Dirac operator is recovered as the local Clifford/tetrad representation in the isochronous background — it emerges in the limit where temporal shear Σμ and disformal coupling B(φ) are negligible. (4) Spin-1/2 is reinterpreted as temporal-orientation holonomy of the proper-time phase frame, and antiparticles as reversed proper-time orientation within the temporal-orientation bundle, eliminating the need for a macroscopic two-sheeted spacetime. (5) The spinor structure of relativistic quantum mechanics may be reinterpreted geometrically: Dirac's 1928 spinor encoded temporal-orientation holonomy without access to a dynamical proper-time geometry. These results recover standard relativistic quantum mechanics as the screened tangent-space limit of the TEP causal geometry, in the regime where the temporal field is frozen and locally constant over the interaction scale; the saturation scale ρ_T ≈ 20 g/cm³ is empirically calibrated in TEP-UCD (Paper 6). Keywords: Temporal Equivalence Principle, Temporal Shear, Temporal Topology, proper time, conformal metric, disformal metric, synchronization holonomy, clock-sector gravity, scalar-tensor theory, quantum foundations, Dirac equation, phase transport, spin, antimatter, geometric quantum mechanics Website: https://mlsmawfield.com/tep/qfRepository: https://github.com/matthewsmawfield/TEP-QF DOI: 10.5281/zenodo.20572697 Open Science Statement: This work is a preprint and is open to community review, ideas, and collaboration. All manuscripts and analysis code are open source. Feedback and contributions are welcome.