Relativistic Path-Integral Origin of the Dirac Equation, Quantum Collapse, Decoherence and Non-Hermitian Phenomena

Abstract

Relativity and quantum mechanics are two cornerstones of modern physics, yet their unification within a single-particle path integral and a dynamical explanation of quantum measurement remain unresolved. Historically, these two problems have been treated as separate, but here we show they are intimately linked. We construct a self-consistent relativistic path integral that yields the Dirac and other standard wave equations under differetialable potentials. More importantly, we find that this propagator contains a latent, nonlocal correlation that is activated by realistic electromagnetic noise. This correlation unifies unitary evolution and wave-function collapse into a single dynamical mechanism: while differentiable potentials preserve unitary driving, nondifferentiable noise activates a bounded-martingale stochastic process that induces collapse. We show that the characteristics of quantum measurement are naturally derived from this stochastic dynamical process, thereby turning the axioms of quantum measurement from postulates into dynamical consequences. Furthermore, averaging this stochastic evolution over the noise record recovers the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, providing a first-principles derivation of decoherence free from the method of Born-Markov approximation. Extending this approach to composite systems establishes a stochastic foundation for effective non-Hermitian descriptions while preserving relativistic causality. Finally, because the noise spectrum governs the collapse process, engineering ``colored'' noise can actively accelerate or steer state reduction, suggesting new routes toward fast qubit reset and enhanced quantum control.