Temporal Emergence Theory: A Self-Complete Derivation of Spacetime, Quantum Mechanics, Gauge Fields, Fermion Masses, Dimensional Selection, and CPT-Conjugate Two-Sheet Structure

Abstract

We present Temporal Emergence Theory (TET), a self-complete framework in which a single four-dimensional hyperbolic manifold H_τ, carrying exclusively temporal geometry, gives rise to all observed physics. A complex 3×3 Hermitian matrix-valued scalar field φ on H_τ undergoes spontaneous symmetry breaking SO(3,1)×SU(3)×U(1) → SO(3)×SU(3)_c×U(1)_em. From this single condensation event the following are derived: (i) three spatial dimensions as coordinates of the Goldstone coset SO(3,1)/SO(3) = H³; (ii) the physical identification of the four-dimensional Lorentzian metric structure; (iii) the Planck constant ℏ via Nelson stochastic mechanics; (iv) Newtonian and Einsteinian gravity; (v) the cosmological constant Λ as brane curvature; (vi) quantum mechanics from the stochastic–Schrödinger equivalence, with the stochastic ensemble itself derived: the present is the front on which the condensate is being laid down, the past is frozen and the future is not yet space, and the Brownian motion of matter is the Gaussian, SO(3,1)-invariant, Markovian granularity of that laying-down (Bunch–Davies state at the Gibbons–Hawking temperature T_GH = 1/(2πR_τ)); (vii) SU(2)_L×U(1)_Y×SU(3)_c gauge fields; (viii) Dirac fermions; (ix) SU(2)_L chirality from T-parity of broken boost generators; (x) the fermion mass hierarchy from Casimir-scaled warp factors; (xi) the two-sheet CPT-conjugate structure of H_τ with rigorous suppression of inter-sheet electromagnetic mixing to ε = 1.95×10⁻²³ via the exact Pöschl–Teller propagator; (xii) the inter-sheet gravitational coupling κ = √2/(2πμ_EW M_5³). The complete parameter set of TET is three real numbers (μ, λ, M5): the condensate mass scale μ, the dimensionless self-coupling λ, and the ultraviolet cutoff M5 of the brane EFT (not a separate 5D bulk Planck mass — see Sec. 2.2b). The curvature radius R_τ is not an independent input but a derived quantity, fixed dynamically by the Israel–Lanczos brane equation of motion. In v8 the former Postulate P4 is itself a theorem (Sec. 8.4), reducing the axiom count to three (H_τ, φ, V), and the coefficient matching fixes the self-coupling to λ = 2π² through the two geometric conditions m_φR_τ = 1 and φ₀ = T_GH. Three open problems are explicitly identified. The theory makes five falsifiable predictions: dynamical dark energy with w₀ = −0.819 (thawing quintessence from the inter-sheet axion, w₀ ∈ [−0.820, −0.817] for Ω_m,0 ∈ [0.30, 0.32]); an ultra-light scalar of mass m_φ = √(Λ/3) = (1.20±0.01)×10⁻³³ eV (the radial mode of the cosmological condensate, with Compton wavelength equal to R_τ); a ~30% enhancement of G_eff at the Hubble scale ~1.64 Gpc; a Kaluza–Klein graviton tower at n×196 GeV; and dark photon mixing ε = 1.95×10⁻²³. This is an independent research preprint, not peer-reviewed. Mathematical derivations, numerical computations, and document elaboration were developed with the assistance of AI language models. The physical ideas and theoretical framework are the author's original work. See Section 23 of the paper for full disclosure.