论文标题
量子理论一致的历史表述中古典历史的相反推论
Contrary Inferences for Classical Histories within the Consistent Histories Formulation of Quantum Theory
论文作者
论文摘要
在量子理论的历史公式中，一组粗粒历史，称为一致的，遵守经典的概率规则。有人认为，这些集合可以描述封闭量子系统的半古典行为。大多数物理场景都接受了多个不同的一致集，并且可以将每个一致的集合视为单独的上下文。使用来自不同一致集的命题来推论会导致悖论，例如肯特最初指出的相反推论[物理审查信，78（15）：2874，1997]。一致的历史表述的支持者认为，一个人不应将来自不同一致集合的命题混合在制作逻辑论点时，并且诸如上述相反推论之类的悖论无非是通常的量子上下文悖论，而是Kochen和Specker Theorem首先证明的。 在此贡献中，我们使用一致的历史来描述宏观（半古典）系统，以表明即使在半古典限制中，涉及上下文性（混合不同的一致集合）的悖论仍然存在。这与标准量子理论的上下文是不同的，在标准量子理论中，上下文悖论在半古典限制中并不持续。具体而言，我们考虑了在无限正方形中半经典波数据包的到达时间的不同一致集。出人意料的是，我们会获得一致的集合，这些集合在始于子区域内的半古典系统的运动是否离开该子区域。我们的结果表明，需要约束的必要条件，除了一致性条件之外，还需要在这种形式主义中恢复正确的半古典限制，并导致座右铭“所有一致的集合都是相等的”，但是``一些一致的集合比其他集合更相等''。
In the histories formulation of quantum theory, sets of coarse-grained histories, that are called consistent, obey classical probability rules. It has been argued that these sets can describe the semi-classical behaviour of closed quantum systems. Most physical scenarios admit multiple different consistent sets and one can view each consistent set as a separate context. Using propositions from different consistent sets to make inferences leads to paradoxes such as the contrary inferences first noted by Kent [Physical Review Letters, 78(15):2874, 1997]. Proponents of the consistent histories formulation argue that one should not mix propositions coming from different consistent sets in making logical arguments, and that paradoxes such as the aforementioned contrary inferences are nothing else than the usual microscopic paradoxes of quantum contextuality as first demonstrated by Kochen and Specker theorem. In this contribution we use the consistent histories to describe a macroscopic (semi-classical) system to show that paradoxes involving contextuality (mixing different consistent sets) persist even in the semi-classical limit. This is distinctively different from the contextuality of standard quantum theory, where the contextuality paradoxes do not persist in the semi-classical limit. Specifically, we consider different consistent sets for the arrival time of a semi-classical wave packet in an infinite square well. Surprisingly, we get consistent sets that disagree on whether the motion of the semi-classical system, that started within a subregion, ever left that subregion or not. Our results point to the need for constraints, additional to the consistency condition, to recover the correct semi-classical limit in this formalism and lead to the motto `all consistent sets are equal', but `some consistent sets are more equal than others'.
