Wave Relativity: Unifying Quantum Mechanics and General Relativity Without New Physics

Wave Relativity re-derives the classical and semiclassical content of physics from one principle: equations for physically-real potentials must be self-consistent. Three structural requirements — frame-independence, index matching, and self-sourcing — are applied to three empirically-grounded starting equations. Maxwell on a physically-real four-potential A^μ yields electromagnetism with special relativity. Newton's law on a physically-real metric potential g_μν yields general relativity through a fixed-point equation iterated to all orders. The Davisson-Germer-anchored matter wave ψ, under the same requirements together with Stern-Gerlach, neutron interferometry under 4π rotation, and Pauli exclusion, yields the Dirac equation in curved spacetime as the minimal Lorentz-covariant first-order wave equation whose square is Klein-Gordon.

The three potentials (g_μν, A^μ, ψ) then assemble as aspect-content of one Dirac-spinor substrate Ψ. The matter wave is Ψ's WKB amplitude reduction on a single-spin mode; the gauge potential and metric are separate fields sourced by Ψ-built objects through Maxwell's and Einstein's equations, with gauge-class freedom and vacuum-sector solutions retained. 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. The conventional quantum-gravity programme was quantising the wrong object.

One master equation — the Dirac equation on curved spacetime 𝒞[Ψ] — governs the coupled system. Under scale limits (v/c, λ_dB/L, λ_dB/ℓ_P) it reduces to classical mechanics, special relativity, general relativity, and standard quantum mechanics. No new physics is introduced, no quantisation programme is applied to gravity, and all empirical inputs are audited.

Intended for readers with undergraduate-or-first-year-graduate familiarity with special relativity, general relativity, and wave-mechanical quantum mechanics. The book requires comfort with four-vectors, tensor indices, and wave equations; it does not require fibre-bundle language or path integrals.