Wave Relativity

*Wave Relativity (v3)* re-derives the classical and semiclassical content of physics, and the architecture of the Standard Model, from one principle: equations for physically-real potentials must be self-consistent.

Applied three times, three structural requirements (frame-independence, index matching, and self-sourcing) produce electromagnetism with special relativity from Aharonov-Bohm, general relativity from Newton's law, and matter-wave quantum mechanics from Davisson-Germer. The three potentials (g_μν, A^μ, ψ) then assemble as aspect-content of one Dirac-spinor substrate Ψ, and the apparent incompatibility of quantum mechanics and general relativity dissolves: it was the artefact of treating g_μν and ψ as independent fields requiring separate quantisation.

Lorentz covariance is forced rather than postulated. Einstein's equations are reached by iterating a fixed-point equation for a real metric potential. The Dirac equation on curved spacetime is the master equation, and classical mechanics, special relativity, general relativity, and standard quantum mechanics fall out as its scale-regime corners.

A second arc derives the Standard Model's internal-component architecture from Ψ's structure as a Dirac-spinor substrate. The internal directions on which Lorentz-scalar self-consistency closes pick out the Standard Model gauge group with no postulated factors. Hypercharge ratios follow from chiral-anomaly cancellation on the matter-mode trace. The composite chiral background, identified as Ψ's only L-R, xyz-singlet, SU(2)_W-doublet bilinear channel, plays the role of the Higgs without a postulated scalar field. Tree-level Standard Model phenomenology recovers at the bosonic precision frontier through master-integral residues, gauge cancellation, UV finiteness, and hierarchy theorems.

Written for readers who have seen special relativity, general relativity, and wave-mechanical quantum mechanics at a standard undergraduate-or-first-year-graduate level and want to see them re-derived from a single methodology rather than assembled from separate postulates. Comfort with four-vectors, tensor indices, and wave equations suffices; fibre-bundle language and path integrals are not required. Readers curious about why c, G, and ℏ play the structural roles they do will find that question treated directly.