A unified relativistic path integral origin for noise-activated collapse and decoherence

Abstract: Relativity and quantum mechanics are two cornerstones of modern physics, yet their unification within a single-particle path integral and a dynamical account of quantum measurement remain unresolved. Here we show that these puzzles are linked. We construct a relativistic path integral that, from a single action principle, recovers the Dirac, Klein-Gordon, and Schr\"odinger equations, while also exposing a latent nonlocal term in the propagator. This term dormant in differentiable potentials but is activated by non-differentiable noise, driving outcome probabilities through bounded-martingale stochastic process. In this regime, the pointer basis emerges as absorbing boundaries, Born's rule arises from first-passage statistics, and collapse occurs in finite, parameter-dependent time, thereby reducing measurement axioms to dynamical consequences. Crucially, our work recovers the standard GKSL master equation by averaging over the stochastic record, and thus provides a first-principles foundation for decoherence. Because the trigger is the noise spectrum, our work shows that engineering ``colored'' noise can expedite or steer collapse, suggesting practical routes to fast qubit reset, preserved coherence, and quantum sensing beyond the standard quantum limit.