— We demonstrate that the relativistic Dirac equation and the non-relativistic Schrödinger equation can be rigorously understood as spinor and scalar representations of the electromagnetic continuity equation and Maxwell's equations applied to spatially localized, standing wave packets. Utilizing the complex Riemann-Silberstein formulation of classical electrodynamics, Maxwell's equations in vacuum are cast into a massless Dirac-Weyl equation. By introducing boundary confinement or phase-locked dual-mode superpositions with a characteristic Compton-de Broglie fundamental frequency ω₀, a rest-mass coupling term emerges naturally from the cross-channel interference of counter-propagating phases. The resulting four-component bispinor equation is identical in form to the Dirac equation with mass m = ℏω₀/c². Furthermore, projecting the conservation of the stress-energy-momentum tensor ∂ᵧTᵵᵖ = 0 onto the non-relativistic velocity regime directly yields the Schrödinger probability continuity equation. This establishes a direct geometric and algebraic bridge between classical field conservation laws and relativistic quantum wave equations without invoking unobservable virtual mechanical media.
No takes yet. Share an insight, caveat, or question.
Wim Vegt (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: