[论文解读] Where was the particle?

Sofia Wechsler|arXiv (Cornell University)|Jan 19, 2003

Quantum Mechanics and Applications参考文献 10被引用 3

一句话总结

本文研究了量子力学中的“空/实波”假说，该假说认为探测器的点击信号源于携带某种属性（称为“实波”）的波包，而非局域化的粒子。研究发现，能量守恒意味着实波必须遵循连续轨迹，这在多粒子情形（如哈迪 gedanken 实验）中导致反事实悖论。研究结论认为，除非放松定域性要求，否则该假说与量子理论预测相矛盾，最终指出该假说无法解决诸如“前后循环”等基础性量子谜题。

ABSTRACT

The hypothesis of empty/full waves considers that a click in a detector is triggered by a property carried by the wave-packet that impinges on that detector. Different authors call this property particle, but according to the terminology of this hypothesis, the term full wave is used in this text. The present article discusses the validity of the empty/full waves hypothesis. It is shown that the energy conservation principle imposes for a full wave a continuous trajectory from the source to the detector. That gives legitimacy to the question -- in case the wave function consists in a couple of space-separated branches -- which wave-packet was a full wave before the click in the detector, or, in other authors' terminology, where was the particle before the detector clicked. This question is a counterfactual question. In some multi-particle experiments, e.g. Hardy's thought-experiment with an electron and a positron, the combination of the empty/full waves hypothesis and counterfactual reasoning leads to a contradiction with the predictions of the quantum theory. However, it is shown here that this contradiction is solvable if the locality requirement is relaxed. To the difference from the local hidden variables, it is not possible to prove or disprove the idea of empty/ full waves, at least at present. But it is possible to ask whether this hypothesis offers a solution to the quantum puzzles. The answer is negative. For instance it offers no solution to the before-before loop. The question remains open whether the empty/full waves hypothesis is correct, or "God plays dice".

研究动机与目标

• 评估空/实波假说的有效性，该假说将探测器点击归因于连续波包携带的属性，而非局域化粒子。
• 研究该假说是否能一致地解释多粒子系统（如哈迪 gedanken 实验）中的反事实推理。
• 确定该假说是否能为诸如“前后循环”悖论等基础性量子谜题提供解决方案。
• 评估该假说是否与能量守恒及连续波轨迹相容。

提出的方法

• 分析能量守恒原理，推导出实波必须从源到探测器沿连续轨迹传播。
• 将反事实推理应用于多粒子量子系统，特别是涉及电子与正电子的哈迪 gedanken 实验。
• 考察空/实波假说在空间分离的波函数分支情境下的影响。
• 放松定域性要求，以检验该假说与量子理论预测之间的矛盾是否可被化解。
• 将该假说与局域隐变量理论进行比较，指出目前尚无法证实或证伪该假说。
• 将该假说与已知的量子悖论（包括“前后循环”悖论）进行评估。

实验结果

研究问题

• RQ1 空/实波假说能否在不违反量子理论预测的前提下，一致地解释多粒子量子系统中的探测器点击？
• RQ2 能量守恒对量子力学中实波轨迹有何影响？
• RQ3 在空/实波框架内进行的反事实推理是否会在哈迪型实验中导致与量子理论的矛盾？
• RQ4 放松定域性条件是否能化解多粒子情形下由该假说引发的矛盾？
• RQ5 空/实波假说是否能为量子基础中的“前后循环”悖论提供解决方案？

主要发现

• 能量守恒强制要求实波必须从源到探测器沿连续轨迹传播，从而否定了波包非连续或非局域传播的可能。
• 空/实波假说与反事实推理的结合在哈迪 gedanken 实验中导致与量子理论预测的矛盾。
• 放松定域性要求可化解该矛盾，但此并不能使该假说成立，因为其仍无法通过现有证据验证。
• 该假说无法解决“前后循环”悖论，表明其不能为基础性量子谜题提供解决方案。
• 目前尚无法证实或证伪该假说，其与量子力学的相容性仍是开放问题。