arXiv 2604.032142026-04-08quant-ph

奈尔的随机力学：测量、非局域性与经典极限

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

Tagore Centre for Natural Sciences and Philosophy（塔戈尔自然科学与哲学中心）

Partha Ghose

备注：: 6 pages, no figures; additional supporting paras added

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AI总结：

本文探讨了奈尔随机力学作为非相对论量子力学的随机基础，强调其在解释测量、非局域性和经典极限方面的独特贡献。

摘要：

奈尔的随机力学可被理解为非相对论量子力学的一种随机基础，一旦扩散尺度由$\hbar$固定，并且可接受的状态受限于波函数的通常单值性条件。本文简要指出这条路线所实现的成果以及为何仍具概念吸引力。四个优势被强调。首先，它提供了清晰的配置空间随机图像来描述底层过程。其次，Born规则从一开始就被构建在内，$|ψ|^2$作为底层扩散过程的概率密度$ρ$出现，而不是作为独立的公理。第三，它提供了对测量和非局域性截然不同的视角：特别是，坍缩不必被视为额外公理，与纠缠态相关的非局域性相对于确定性的Bohmian引导图景被弱化。第四，通过将量子性与扩散尺度联系起来，它自然地建议了一种从严格经典到严格量子力学区域的连续物理描述。最后，本文提出了一种自然的距离尺度，并探讨其对检验贝尔相关性的可能极限的影响。

英文摘要：

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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