Quantum Mechanics from Five-Dimensional Spacetime: A Geometric Origin of Probability

We show that the five-dimensional hydrodynamic spacetime frameworkdeveloped in the companion paper naturally reproduces quantummechanics as the effective description seen by observers confinedto three spatial dimensions. The central insight is that quantumprobability arises not from fundamental indeterminacy but from theobserver's inability to access the w-coordinate and the w-t orbitalphases of particles. Electromagnetic coupling is a binary contactcondition at w = w_max; measurement outcomes are selected by theorbital-phase alignment at the instant of contact, with unresolvedphases producing the observed statistics. Starting from theclassical geodesic equations in five-dimensional spacetime, wederive the Schrodinger equation through dimensional projection andthe characteristic orbital radius Δw ~ hbar/(mc) of the w-t motion.The Planck constant hbar emerges as a geometric quantity relatingmass to orbital radius in the w-direction. Heisenberg's uncertaintyprinciple, wave-particle duality, quantum tunneling, andentanglement all follow from the five-dimensional geometricstructure without additional postulates. The measurement problem isresolved: wavefunction collapse is the phase-selective w_max-contactthat couples one branch while leaving the others phase-mismatched.Spin-1/2 arises from the five-dimensional Dirac equation, withchirality identified as w-orbital direction and 4π periodicityestablished through holonomy. Bell inequality violations (S = 2√2)are reproduced through non-separable shared w-t orbital states, withno-signaling preserved. The theory predicts that every particle possesses excited states inthe w-direction with masses m_n = n·m_0 (n = 1,2,3,...). Forelectrons, this predicts states at 1.02 MeV/c^2, 1.53 MeV/c^2, andhigher energies. Laboratory production of these states is stronglysuppressed by viscous flattening of the w-field and dilution of thew-potential by cosmic expansion; the most promising observationalsignatures may be cosmological imprints of early-universe particlecreation. The five-dimensional structure yields quantitative connections tothe Standard Model with minimal free parameters. From the universalReynolds number Re = 2 (a geometric identity: diameter/radius) andthe base vortex coupling g_0 = 1/(8π), we derive: the strongcoupling constant alpha_s = 3/(8π) ≈ 0.119 as a parameter-freeprediction (1.2% agreement with experiment); the fine structureconstant in closed form to the full precision of its experimentaldetermination, α⁻¹ = 128π/3 + 3 − 32π·α²·(1 − 27α/16)= 137.035999067 versus the measured 137.035999084(21) (0.8σ;relative precision 1.3×10⁻¹⁰), from the channel decompositionD_eff = 4×(4/3) + 3/(8π) (four transport channels x,y,z,w atradiation-enthalpy weight, plus three gated w-planes), an exactgate self-consistency, and two orders of transport back-reactionwhose coefficient is fixed by the doubly measured ledger exchangerate t = 3/4; the Weinberg angle sin^2(θ_W) = 3/8 from countingeight force output vectors; the Higgs field identified with thew-field (v/m_H = Re = 2, 1.7% agreement; lambda_H = 1/8, 3.4%agreement); and a particle-internal partition 4/Re = 2 from thedrawing cost of four w-faces, numerically close to thepresent-epoch Omega_DE/Omega_m ≈ 2.17 (the cosmological ratio istime-dependent and the numerical proximity at the present epoch isa coincidence). Parity violation follows from boundary conditionsat w=0, and color confinement arises as the local version of thesame drawing cost. Two further closed-form results complete theset: the gravitational hierarchy from budget equipartition,m_e/M_P = y_e^4/√π (0.03%) and alpha_G = y_e^8/π (0.06%),finalizing the prediction that Newton's constant lies within theCODATA cluster; and the vacuum quantumness derived from thevacuum's two-fluid metabolism, ε = (2m_e/m_H)^(1/3) = 0.0202.