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Quantum Causality Relations and the Emergence of Reality from Coherent Superpositions
Foundations of Physics ( IF 1.5 ) Pub Date : 2020-05-18 , DOI: 10.1007/s10701-020-00346-4 Holger F. Hofmann
Foundations of Physics ( IF 1.5 ) Pub Date : 2020-05-18 , DOI: 10.1007/s10701-020-00346-4 Holger F. Hofmann
The Hilbert space formalism describes causality as a statistical relation between initial experimental conditions and final measurement outcomes, expressed by the inner products of state vectors representing these conditions. This representation of causality is in fundamental conflict with the classical notion that causality should be expressed in terms of the continuity of intermediate realities. Quantum mechanics essentially replaces this continuity of reality with phase sensitive superpositions, all of which need to interfere in order to produce the correct conditional probabilities for the observable input-output relations. In this paper, I investigate the relation between the classical notion of reality and quantum superpositions by identifying the conditions under which the intermediate states can have real external effects, as expressed by measurement operators inserted into the inner product. It is shown that classical reality emerges at the macroscopic level, where the relevant limit of the measurement resolution is given by the variance of the action around the classical solution. It is thus possible to demonstrate that the classical notion of objective reality emerges only at the macroscopic level, where observations are limited to low resolutions by a lack of sufficiently strong intermediate interactions. This result indicates that causality is more fundamental to physics than the notion of an objective reality, which means that the apparent contradictions between quantum physics and classical physics may be resolved by carefully distinguishing between observable causality and unobservable sequences of hypothetical realities “out there”.
中文翻译:
量子因果关系和从相干叠加现实的出现
希尔伯特空间形式主义将因果关系描述为初始实验条件和最终测量结果之间的统计关系,由代表这些条件的状态向量的内积表示。因果关系的这种表述与经典观念存在根本冲突,即因果关系应根据中间现实的连续性来表达。量子力学本质上用相敏叠加代替了这种现实的连续性,所有这些都需要相互干扰,以便为可观察的输入-输出关系产生正确的条件概率。在本文中,我通过确定中间态可以具有真实外部效应的条件来研究经典现实概念与量子叠加之间的关系,由插入内积的测量运算符表示。结果表明,经典现实出现在宏观层面,其中测量分辨率的相关限制由围绕经典解的动作的方差给出。因此,可以证明客观现实的经典概念仅在宏观层面出现,由于缺乏足够强的中间相互作用,观察仅限于低分辨率。这一结果表明,因果关系对物理学来说比客观现实的概念更为基础,这意味着可以通过仔细区分可观察的因果关系和不可观察的“外面”假设现实序列来解决量子物理学与经典物理学之间的明显矛盾。
更新日期:2020-05-18
中文翻译:
量子因果关系和从相干叠加现实的出现
希尔伯特空间形式主义将因果关系描述为初始实验条件和最终测量结果之间的统计关系,由代表这些条件的状态向量的内积表示。因果关系的这种表述与经典观念存在根本冲突,即因果关系应根据中间现实的连续性来表达。量子力学本质上用相敏叠加代替了这种现实的连续性,所有这些都需要相互干扰,以便为可观察的输入-输出关系产生正确的条件概率。在本文中,我通过确定中间态可以具有真实外部效应的条件来研究经典现实概念与量子叠加之间的关系,由插入内积的测量运算符表示。结果表明,经典现实出现在宏观层面,其中测量分辨率的相关限制由围绕经典解的动作的方差给出。因此,可以证明客观现实的经典概念仅在宏观层面出现,由于缺乏足够强的中间相互作用,观察仅限于低分辨率。这一结果表明,因果关系对物理学来说比客观现实的概念更为基础,这意味着可以通过仔细区分可观察的因果关系和不可观察的“外面”假设现实序列来解决量子物理学与经典物理学之间的明显矛盾。