情境性的微分几何

IF 1.5 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Sidiney B. Montanhano
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引用次数: 0

摘要

长期以来,上下文性一直与拓扑特性联系在一起。在这项工作中,这种关系被提升到广义语境的更广泛框架中的识别。我们将通常的状态、效果和转换识别作为向量空间中的向量,并将它们编码到切线空间中,将非上下文条件呈现为离散封闭路径在估值中隐含零相的一般条件,并立即扩展到连续情况。在这种形式主义中,语境行为有两种等价的解释。在称为“Schrödinger”的几何或内在现实主义观点中,平坦空间被强加,导致上下文行为被表示为概率函数的非平凡完整,类似于电磁张量。作为评价函数的修改,我们使用曲率将上下文性与干扰、非交换性和有符号测度联系起来。在被称为“海森堡”的拓扑或参与现实主义观点中,评估函数必须满足经典度量公理,导致上下文行为需要被表示为事件结构中的拓扑缺陷,从而导致非平凡的单一性。我们利用这些缺陷将情境性与非嵌入性联系起来,并构造了一个广义的Vorob 'ev定理,该定理形式化了非情境性的必然性。我们在这种形式中确定了具有结果决定论的模型的上下文分数,并提出了一种途径来解决本体论模型中作为非平凡转换映射的干扰。最后,我们讨论了这两种关于编码语境的观点如何与量子理论的解释相关。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Differential Geometry of Contextuality

Contextuality has long been associated with topological properties. In this work, such a relationship is elevated to identification in the broader framework of generalized contextuality. We employ the usual identification of states, effects, and transformations as vectors in a vector space and encode them into a tangent space, rendering the noncontextual conditions the generic condition that discrete closed paths imply null phases in valuations, which are immediately extended to the continuous case. Contextual behavior admits two equivalent interpretations in this formalism. In the geometric or intrinsic-realistic view, termed “Schrödinger,” flat space is imposed, leading to contextual behavior being expressed as non-trivial holonomy of probabilistic functions, analogous to the electromagnetic tensor. As a modification of the valuation function, we use the curvature to connect contextuality with interference, noncommutativity, and signed measures. In the topological or participatory-realistic view, termed “Heisenberg,” valuation functions must satisfy classical measure axioms, resulting in contextual behavior needing to be expressed as topological defects in the structure of events, leading to non-trivial monodromy. We utilize such defects to connect contextuality with non-embeddability and to construct a generalized Vorob’ev theorem, which formalizes the inevitability of noncontextuality. We identify in this formalism the contextual fraction for models with outcome-determinism and propose a pathway to address disturbance in ontological models as non-trivial transition maps. Finally, we discuss how these two views for encoding contextuality relate to interpretations of quantum theory.

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来源期刊
Brazilian Journal of Physics
Brazilian Journal of Physics 物理-物理:综合
CiteScore
2.50
自引率
6.20%
发文量
189
审稿时长
6.0 months
期刊介绍: The Brazilian Journal of Physics is a peer-reviewed international journal published by the Brazilian Physical Society (SBF). The journal publishes new and original research results from all areas of physics, obtained in Brazil and from anywhere else in the world. Contents include theoretical, practical and experimental papers as well as high-quality review papers. Submissions should follow the generally accepted structure for journal articles with basic elements: title, abstract, introduction, results, conclusions, and references.
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