[{"_1":2,"_3":-5,"_4":-5},"loaderData",{"_5":6,"_7":8},"actionData","errors","root",{"_28":-5,"_38":-5,"_39":40,"_41":42,"_43":44,"_45":46,"_47":48,"_49":50,"_51":52,"_53":54,"_55":56,"_57":58},"routes/_store+/_readers+/email_author.$slug/route",{"_9":10,"_11":-5},"book",{"_12":13,"_14":15,"_16":17,"_18":19,"_20":21,"_22":23},"currentUser","id","Z2lkOi8vbGVhbnB1Yi9TdG9yZTo6Qm9va1Byb2R1Y3QvNzc5OTQ","title","Wave Relativity","state","published","contactAuthorMethod","email","aboutText","

Wave Relativity 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.

**v4.0 integrates the dark-matter sector.** The neutrino sector's realised sterile slot forces a 4×3 neutral mass matrix of rank at most three, which makes one active eigenstate exactly massless to all orders in the effective theory and predicts a vanishing neutrinoless-double-beta-decay rate under B−L preservation, while the heavy mostly-sterile eigenstate of that same matrix reads as a conditional cold-dark-matter candidate at mass scale m_s ~ 10^12 GeV through gravitational production. Two further results ship in this edition: the Clay Yang-Mills existence and mass-gap question is reframed on the substrate ontology, where pure Yang-Mills is the projection of the matter substrate onto the gauge-only sector and substrate positivity together with the matter-mode-trace spectrum deliver a structural mass-gap statement with gap scale Λ_QCD; and the metric response functional g_μν = 𝒢_μν[Ψ] is displayed in closed form, forced to Einstein-Hilbert plus a cosmological term by Lovelock's four-dimensional uniqueness theorem.

Earlier editions established the forward-prediction and holographic-anchor content this edition builds on: matter-wave self-gravity gives a closed-form breathing-mode frequency ω = √(4πGρ/3) depending only on material density, with a silica-versus-gold discriminator √(ρ_Au/ρ_SiO₂) ≈ 2.96 at fixed mass that falsifies the matter-wave-sources-COM-gravity reading if absent; non-product Ψ-configurations require a connected scaffold, so an observed Bell-violating correlation absent any scaffold falsifies the one-substrate-with-one-history ontology; Bekenstein-Hawking entropy and Hawking radiation recover as horizon-localised Ψ-mode content with no graviton-loop contribution; and the classical-GR Schwarzschild and FLRW singularities sit beyond the projection-validity boundary, so the inference from classical curvature divergence to substrate-level singularity does not transfer by default.

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.

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