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

• URL: http://arxiv.org/abs/2604.03214v2
• Date: Wed, 08 Apr 2026 14:46:04 GMT
• Title: Nelson's Stochastic Mechanics: Measurement, Nonlocality, and the Classical Limit
• Abstract summary: Nelson's mechanics may be understood as an underpinning, or reconstruction, of nonrelativistic quantum mechanics.<n>It supplies a clear configuration-space picture of the underlying processes.<n>It offers a markedly different perspective on measurement and nonlocality.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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. Four advantages are emphasized. First, it supplies a clear configuration-space stochastic picture of the underlying processes. Second, the Born rule is built in from the outset, with $|ψ|^2$ arising as the probability density $ρ$ of the underlying diffusion process rather than as an independent postulate. Third, 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. Fourth, 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.

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