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

• URL: http://arxiv.org/abs/2509.19377v2
• Date: Tue, 07 Oct 2025 13:12:11 GMT
• Title: A unified relativistic path integral origin for noise-activated collapse and decoherence
• Authors: Wei Wen,
• Abstract summary: We construct a relativistic path integral that recovers the Dirac, Klein-Gordon, and Schr"odinger equations.<n>This term dormant in differentiable potentials but is activated by non-differentiable noise, driving outcome probabilities through bounded-martingale process.<n>Because the trigger is the noise spectrum, our work shows that engineering colored'' noise can expedite or steer collapse.
• Score: 6.864380740265179
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Relativity and quantum mechanics are two cornerstones of modern physics, yet their unification within a single-particle path integral and a dynamic explanation of quantum measurement remain unresolved. Historically, these two problems have been treated as separate, but we in this work show they are intimately linked. We construct a relativistic path integral that 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 taking the ensemble average over the noise, 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, coherence preservation, and quantum sensing beyond the standard quantum limit.

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