Standard Grant: Geometric Approaches to Representing the Observable

该奖项支持物理学历史和哲学的项目。PI将产生一个新的历史叙述，纠正帕斯夸尔·乔丹在量子理论中对可观测量（可测量的物理量）的方法的标准但有缺陷的历史叙述，从而阐明他的方法的意义和遗产。PI不仅将表明Jordan的方法具有与量子理论相同的表达能力，它还为构建量子现象的几何模型提供了新的概念见解，这种方式更容易与关于可观测量的常识联系起来。PI在专注和成功的外展方面有着令人印象深刻的记录，它有具体的外展计划，面向研究生、本科生和高中以及公众的受众，明确强调促进多样性。PI还将组织一个研讨会，计划招募初级学者和代表性不足的团体成员，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个新的代数理论，该理论具有与标准量子理论相同的表达能力。然后，该帐户将用于提供关于可观察对象在表示哲学中的作用的新视角。他将使用约旦的帐户作为一个案例研究理解的意义表示定理，并建立一个深刻的新的连接之间的约旦可观的和表达的量子理论的几何语言。他还将探讨几何哲学，因为它适用于量子理论，并澄清了形而上学和实用的意义，重新制定了物理理论的几何语言。将发展的影响，以提供洞察最近的理论等价性的哲学辩论，并探索可能的方式与其他非标准的方法来量子观测。该项目为科学中可观测量的新颖分析奠定了基础，这将对科学的历史和哲学产生潜在的变革性影响，并为这两个领域提供了与当代物理学进行有意义的接触的机会。

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.