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arXiv quant-ph/9505025quant-phchao-dyngr-qcnlin.CD
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量子自旋测量的局域确定性模型

A Local Deterministic Model of Quantum Spin Measurement

T. N. Palmer

摘要:

传统的观点,即爱因斯坦错误地认为量子物理学是局部的和决定性的,受到了挑战。本文提出了自旋1/2粒子在测量过程中态矢演化的参数化模型Q。Q利用了最近在动力系统理论中所谓的“满洞盆地”的研究成果,它是局部的、确定性的、非线性的和时间不对称的。此外,状态矢量演化为两个混沌吸引子(用来表示观察到的自旋状态)之一实际上是不可计算的。这个模型的动机来自彭罗斯对量子引力的性质和作用的推测。虽然Q的状态矢量的演化是不可计算的,但系统演化到两个吸引子之一的概率是可计算的。这些概率在数量上对应于自旋1/2粒子的统计。在系综意义上的状态向量的演化朝着吸引子可以描述为一个扩散随机游走。本文讨论了Bell定理和一个版本的Bell-Kochen_specker量子纠缠佯谬。证明与局部性的不一致性要求某些反事实命题存在确定的真值。在Q中,这些确定性命题在物理上是不可计算的,并且没有已知或怀疑的非算法解决方案。适应数学形式主义的方法,不存在确定的真值,这样的反事实命题的假设。与实验结果没有矛盾,因此Q不一定受Bell不等式的约束。

英文摘要:

The conventional view, that Einstein was wrong to believe that quantum physics is local and deterministic, is challenged. A parametrised model, Q, for the state vector evolution of spin 1/2 particles during measurement is developed. Q draws on recent work on so-called riddled basins in dynamical systems theory, and is local, deterministic, nonlinear and time asymmetric. Moreover the evolution of the state vector to one of two chaotic attractors (taken to represent observed spin states) is effectively uncomputable. Motivation for this model arises from Penrose's speculations about the nature and role of quantum gravity. Although the evolution of Q's state vector is uncomputable, the probability that the system will evolve to one of the two attractors is computable. These probabilities correspond quantitatively to the statistics of spin 1/2 particles. In an ensemble sense the evolution of the state vector towards an attractor can be described by a diffusive random walk. Bell's theorem and a version of the Bell-Kochen_specker quantum entanglement paradox are discussed. It is shown that proving an inconsistency with locality demands the existence of definite truth values to certain counterfactual propositions. In Q these deterministic propositions are physically uncomputable and no non-algorithmic solution is either known or suspected. Adapting the mathematical formalist approach, the non-existence of definite truth values to such counterfactual propositions is posited. No inconsistency with experiment is found. Hence Q is not necessarily constrained by Bell's inequality.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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