[论文解读] Relativity, signal locality and the uncertainty principle (or How Bohr could have replied to Einstein if he knew about Bell)

Eric G. Cavalcanti|arXiv (Cornell University)|Nov 12, 2009

Quantum Mechanics and Applications参考文献 15被引用 3

一句话总结

本文主张，信号局部性（即不存在超光速通信）与贝尔不等式的实验违背共同表明，自然本质上是不可预测的。通过区分认识论上的可预测性与本体论上的决定论，本文表明，仅凭相对论本身，无需引入量子假设，即可强制得出量子力学的不可约不可预测性。

ABSTRACT

In the early stages of the famous debates between Einstein and Bohr on the foundations of quantum mechanics, Einstein attempted to devise thought experiments aiming at showing that arbitrarily accurate predictions of incompatible physical quantities was possible, in violation of Heisenberg's uncertainty principle. Bohr was able to defend quantum mechanics from those attacks by showing that a careful application of the uncertainty principle to the experimental apparata as well as the measured system lead to consistent results. Could Bohr have given an independent argument for the irreducible unpredictability implied by the uncertainty principle? The celebrated 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the ontological concepts of locality and determinism. However, nothing can be concluded from Bell's theorem alone about locality by itself or determinism by itself--it is possible to reproduce quantum-mechanical predictions with deterministic models which violate locality as well as indeterministic models which satisfy locality. On the other hand, there's almost universal agreement that the epistemic form of locality--signal locality, or the impossibility of faster-than-light communication--must hold in a relativistic universe. By making a similar distinction between determinism and the epistemic concept of predictability, I show that signal locality plus the bare observed phenomena of Bell inequality violations lead to the remarkable conclusion that Nature is fundamentally unpredictable. This result grounds the quantum-mechanical prohibition of arbitrarily accurate predictions on the principle of relativity, regardless of any postulates of quantum mechanics.

研究动机与目标

• 探究不确定性原理是否可仅从相对论和信号局部性推导而出，而无需引入量子力学。
• 澄清在量子基础的语境下，决定论与可预测性之间的区别。
• 表明信号局部性与贝尔不等式违背的结合，意味着自然本质上是不可预测的。
• 为不确定性原理所隐含的不可约不可预测性提供一种相对论性的辩护。

提出的方法

• 将信号局部性（无超光速通信）作为相对论物理中的基础约束，分析其认识论概念。
• 应用贝尔1964年的定理，将局域性与决定论的概念分离开来，聚焦于信号局部性作为物理原理。
• 以贝尔不等式的实验违背作为实证输入，推导出对可预测性的约束。
• 区分本体论决定论与认识论可预测性，表明即使在决定论模型中，只要尊重信号局部性，也必须是不可预测的。
• 构建一个逻辑论证，表明信号局部性与贝尔不等式违背共同导致根本不可预测性。
• 证明不确定性原理对精确预测的禁止，可从相对论推导而出，而无需依赖量子假设。

实验结果

研究问题

• RQ1 是否可仅从相对论与信号局部性推导出量子力学的不可预测性，而无需量子理论？
• RQ2 信号局部性如何约束那些再现量子统计规律的物理理论的可预测性？
• RQ3 贝尔不等式违背与超光速信号不可能性之间的逻辑关系是什么？
• RQ4 若一个尊重信号局部性的决定论理论违反贝尔不等式，它是否仍可具有经验上的充分性？
• RQ5 如果我们接受信息不能超光速传播，不确定性原理是否可从相对论推导而出？

主要发现

• 信号局部性与观测到的贝尔不等式违背共同意味着自然本质上是不可预测的。
• 量子力学的不可约不可预测性可从相对论与信号局部性推导而出，而无需引入量子假设。
• 能够再现量子预测的决定论模型必须违背局域性，但即使此类模型也无法在信号局部性成立时实现精确预测。
• 决定论与可预测性之间的区分表明，量子力学的不可预测性并非源于非决定性本身，而是源于相对论因果性。
• 不确定性原理对任意精确预测的禁止，其根源在于相对性原理，而非量子力学本身。
• 当贝尔定理由信号局部性补充时，可得出结论：没有任何理论能一致地以确定性方式预测所有结果。