Quantum Mechanics from Five-Dimensional Spacetime: Geometric Origins of Probability and Electron Spin

We demonstrate that quantum mechanics emerges naturally from the five-dimensional hydrodynamic spacetime framework developed in the companion paper. The central insight is that quantum probability arises not from fundamental indeterminacy but from observers' confinement to three spatial dimensions. An observer measuring a particle's position integrates over all possible values of the fourth spatial coordinate w (the time density dimension), creating an apparent probability distribution even for particles with definite five-dimensional positions. We show that massive particles execute orbital motion around the w-axis, with angular momentum L = ℏ and orbital velocity v = c. This yields the fundamental mass-radius relation m = ℏ/(cr), providing a geometric origin for rest mass energy: E = mc² is the kinetic energy of motion in the hidden dimension. The Planck constant ℏ emerges as a geometric quantity setting both the orbital angular momentum and the observational window width. A striking consequence is the geometric derivation of electron spin. The observation window intersects the circular orbit at exactly two points, causing observers to perceive half the orbital angular momentum: S = L/2 = ℏ/2. The electron g-factor g = 2 follows directly from the ratio of actual magnetic moment (from full orbital motion) to the moment expected from observed spin. We derive the Schrödinger equation through dimensional projection and show that Heisenberg's uncertainty principle, wave-particle duality, quantum tunneling, and entanglement all follow from the five-dimensional geometric structure without additional postulates. The theory predicts excited states with masses mₙ = (2n+1)m₀ arising from radial oscillations of the orbital motion. For electrons, this predicts resonances at 1.53 MeV/c², 2.56 MeV/c², and higher energies. This work resolves the measurement problem by showing that wavefunction collapse is dimensional projection from five to three dimensions. Quantum mechanics is revealed as the statistical mechanics of observers confined to lower-dimensional hypersurfaces within a deterministic five-dimensional spacetime.