[论文解读] Two different physical interpretations of Schroedinger equation

M. V. Lokajíček, V. Kundrát+1 more|arXiv (Cornell University)|May 22, 2013

Quantum Mechanics and Applications参考文献 15被引用 4

一句话总结

本文挑战了量子力学中贝尔不等式的标准解释，认为其推导与应用基于源于经典决定论而非概率性量子系统的错误假设。文章主张，贝尔不等式的违背并不能决定性地支持玻尔的哥本哈根诠释胜过爱因斯坦的隐变量理论，因为该不等式在概率框架（如扩展的薛定谔方程）中不成立，从而削弱了量子纠缠是唯一非经典现象的说法。

ABSTRACT

The assumptions added by Bohr and concerning the Hilbert space (formed by all solutions of Schroedinger equation) changed fundamentally the original physical interpretation of these solutions proposed earlier by Schroedinger. This new alternative was refused by Einstein on the basis of the EPR Gedankenexperiment, but accepted fully for microscopic reality by scientific community. Both the quantum alternatives were discussed, however, again later. Bell tried to find a possibility how to decide between them; he generalized Einstein's Gedankenexperiment assuming that also spins of two detected particles would be measured. He derived then some inequality for a special combination of four coincidence probabilities, and it was commonly assumed that his inequality held for the original Schroedinger interpretation but not in Bohr's Copenhagen quantum mechanics; without any actual proof having been given. Corresponding experiments were proposed and finished in 1982. The violation of Bell's inequality was then interpreted as decisive victory of Bohr's theory. However, it will be shown that Bell's inequality has been interpreted mistakenly. It has been based always on some assumption that does not hold in any probabilistic theory (i.e., in the given spin experiment) but only in deterministic classical theory. There is not any argument for preferring the Copenhagen quantum mechanics and against Einstein's critical standpoint. Some other consequences will be mentioned, too.

研究动机与目标

• 挑战广泛接受的观点，即贝尔不等式违背证明了哥本哈根量子力学优于爱因斯坦隐变量理论。
• 证明贝尔不等式在概率性量子系统中不成立，与认为其仅适用于经典决定性模型的假设相反。
• 主张当扩展以包含非经典特征时，薛定谔方程仍与经典本体论原则及因果性保持一致。
• 质疑宏观与微观物理之间边界的合理性，表明当前解释依赖于未经证实的假设。
• 提倡重新审视基本力，提出接触力与物体尺寸是理解原子稳定性和结构的关键。

提出的方法

• 分析贝尔不等式原始推导，聚焦于概率必须在所有系统中满足确定性界限（B ≤ 2）的假设。
• 将此假设与概率系统对比，表明贝尔不等式在这些情境中失效，特别是在扩展的薛定谔方程框架下。
• 重新审视EPR思想实验及贝尔对纠缠粒子自旋测量的推广。
• 回顾1982年利用原子衰变产生的光子对测试贝尔不等式的实验，强调其违背的解释。
• 重新评估冯·诺依曼无隐变量定理的作用及其对科学界接受哥本哈根诠释的影响。
• 提出基于本体论实在论的物理模型重新评估，强调低能系统中物体尺寸与接触力的重要性。

实验结果

研究问题

• RQ1 贝尔不等式是否在概率性量子系统中成立，还是仅在经典决定性框架中有效？
• RQ2 贝尔不等式违背能否被解释为量子力学非局域性的决定性证据，以及哥本哈根诠释优越性的证明？
• RQ3 薛定谔方程在扩展以包含非经典特征时，与经典本体论原则的相容程度如何？
• RQ4 为何科学界接受了玻尔的诠释，尽管存在爱因斯坦的异议且缺乏明确的宏观-微观边界？
• RQ5 物体尺寸与接触力在解释原子稳定性和低能相互作用中起什么作用，它们如何挑战传统的势能模型？

主要发现

• 贝尔不等式在概率系统（如扩展的薛定谔方程）中不成立，与认为其仅在量子力学中失效的假设相矛盾。
• 实验中贝尔不等式的违背并不能逻辑上推导出必须拒绝爱因斯坦的隐变量方法或接受非局域性。
• 当不施加玻尔的附加假设时，薛定谔方程在本质上仍与经典本体论概念（包括因果性）相容。
• 冯·诺依曼反对隐变量的论点被证明是循环的，因此无效，从而动摇了哥本哈根诠释的关键支柱。
• 仅靠长程势能力无法充分解释氢原子及其他束缚系统的稳定性，暗示需要引入接触力。
• 从高能碰撞中得出的质子尺寸与原子尺寸显著不同，暗示其具有致密核心与周围弱相互作用区域的复合结构，这可能解释低能相互作用。