Nelson's Stochastic Mechanics: Measurement, Nonlocality, and the Classical Limit

Nelson's stochastic mechanics may be understood as a stochastic underpinning, or reconstruction, of nonrelativistic quantum mechanics, once the diffusion scale is fixed by $\hbar$ and the admissible states are restricted by the usual single-valuedness condition on the wavefunction. In this note I briefly indicate what this route achieves and why it remains conceptually attractive. Three advantages are emphasized. First, it supplies a clear configuration-space stochastic picture of the underlying processes. Second, it offers a markedly different perspective on measurement and nonlocality: in particular, collapse need not be treated as an extra axiom, and the nonlocality associated with entangled states is softened relative to the deterministic Bohmian guidance picture. Third, by tying quantumness to a diffusion scale, it naturally suggests a continuum of physical descriptions ranging from the strictly classical to the strictly quantum-mechanical regime. I conclude by proposing a natural distance scale in stochastic mechanics and examining its implications for testing possible limits of Bell correlations.

Source: arXiv:2604.03214v1 - http://arxiv.org/abs/2604.03214v1 PDF: https://arxiv.org/pdf/2604.03214v1 Original Link: http://arxiv.org/abs/2604.03214v1