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arXiv 2401.04085quant-phphysics.hist-ph
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量子力学的动态规划解释

A dynamic programming interpretation of quantum mechanics

Adam Brownstein

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AI总结：

提出一种量子相位变换，将量子力学确定性方程转化为随机粒子的拉格朗日参考系，通过求解随机哈密顿-雅可比-贝尔曼方程消除量子势，提供了一种基于动态规划的量子力学局域描述。

摘要：

我们 introduce a transformation of the quantum phase $S'=S+\frac{\hbar}{2}\logρ$,, which converts the deterministic equations of quantum mechanics into the Lagrangian reference frame of stochastic particles. We show that the quantum potential can be removed from the transformed quantum Hamilton-Jacobi equations if they are solved as stochastic Hamilton-Jacobi-Bellman equations. The system of equations provide a local description of quantum mechanics, which is enabled by the inherently retrocausal nature of stochastic Hamilton-Jacobi-Bellman equations. We also investigate the stochastic transformation of the classical system, where is it shown that quantum mechanics with the quantum potential reduced by a factor of $\frac{1}{2}$ has a classical representation, which may have interesting implications. Finally, we discuss the notion of a subsystem correspondence principle, which constrains the ontology of the total quantum system.

英文摘要：

We introduce a transformation of the quantum phase $S'=S+\frac{\hbar}{2}\logρ$, which converts the deterministic equations of quantum mechanics into the Lagrangian reference frame of stochastic particles. We show that the quantum potential can be removed from the transformed quantum Hamilton-Jacobi equations if they are solved as stochastic Hamilton-Jacobi-Bellman equations. The system of equations provide a local description of quantum mechanics, which is enabled by the inherently retrocausal nature of stochastic Hamilton-Jacobi-Bellman equations. We also investigate the stochastic transformation of the classical system, where is it shown that quantum mechanics with the quantum potential reduced by a factor of $\frac{1}{2}$ has a classical representation, which may have interesting implications. Finally, we discuss the notion of a subsystem correspondence principle, which constrains the ontology of the total quantum system.

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