Standard Grant: Geometric Approaches to Representing the Observable

该奖项支持一个关于物理学历史和哲学的项目。PI将产生一种新的历史叙述，纠正pasqual Jordan在量子理论中对可观测（可测量的物理量）的方法的标准但有缺陷的历史描述，从而阐明他的方法的意义和遗产。PI不仅将表明Jordan的方法与量子理论具有相同的表达能力，而且还将为构建量子现象的几何模型提供新颖的概念见解，这种模型更容易与可观测的常识联系起来。PI在专注和成功的外展活动方面有着令人印象深刻的记录，它为研究生、本科生、高中以及普通公众的外展活动制定了具体计划，并明确强调促进多样性。PI还将组织一个讲习班，计划招募初级学者和代表性不足群体的成员，他们将参与各种培训工作。PI将展示约旦方法的历史发展导致了一种新的代数理论，它具有与标准量子理论相同的表达能力。然后，这个解释将被用来提供一个关于可观察物在表征哲学中的作用的新视角。他将使用Jordan的描述作为案例研究，以理解表征定理的重要性，并在Jordan可观测值和量子理论在几何语言中的表达之间建立深刻的新联系。他还将探讨几何哲学在量子理论中的应用，并阐明用几何语言重新表述物理理论的形而上学和实用意义。该研究将提供对最近关于理论等价的哲学辩论的见解，并探索与其他非标准方法连接到量子可观测物的可能方法。该项目为科学中可观测量的新分析奠定了基础，这将对科学的历史和哲学产生潜在的变革性影响，并为这两个领域与当代物理学进行有意义的接触提供了机会。

This award supports a project in the history and philosophy of physics. The PI will generate a new historical narrative that corrects the standard but flawed historical account of Pascual Jordan's approach to observables (measurable physical quantities) in quantum theory, and thereby illuminate the significance and legacy of his approach. The PI will show not only that Jordan's approach has the same expressive capacity as quantum theory, it also provides novel conceptual insights for constructing geometric models for quantum phenomena in a way that connects more readily with common sense ideas about observables. The PI, who has an impressive track record of dedicated and successful outreach, has concrete plans for outreach to audiences at the graduate, undergraduate, and high-school levels, as well as the general public, with explicit emphasis on promoting diversity. The PI will also organize a workshop with plans to recruit both junior scholars and members of underrepresented groups, who are to engage in various training efforts.The PI will show that the historical development of Jordan's approach led to a new algebraic theory that has the same expressive capacities as standard quantum theory. That account will then be used to provide a new perspective on the role of observables in the philosophy of representation. He will use Jordan's account as a case study for understanding the significance of representation theorems, and for establishing a deep new connection between Jordan observables and the expression of quantum theory in geometric language. He will also explore the philosophy of geometry as it applies to quantum theory, and clarify the metaphysical and pragmatic significance of reformulating a physical theory in geometric language. Implications will be developed to offer insight into recent philosophical debates on theoretical equivalence, and to explore possible ways to connect with other non-standard approaches to quantum observables. This project lays the groundwork for a novel analysis of observable quantities in science that will provide a potentially transformative impact on history and philosophy of science, as well as an opportunity for both fields to engage meaningfully with contemporary physics.