Doctoral Dissertation Research: Using Topology to Answer Philosophical Questions About General Relativity

项目概述PI建议使用拓扑学和相对论中的工具对物理性概念进行概念性分析，因为它是在物理学的哲学基础的背景下使用的；他计划开发一个数学框架来解释物理性相对于模型的含义。这笔赠款将支持前往匹兹堡大学和西雅图华盛顿大学这两个地点的研究人员研究与他工作的各个方面相关的主题。智力上的优点在匹兹堡，这名学生计划与两名资深教授合作。其中一个，他的目标是为史蒂芬·霍金提出的将拓扑稳定性与模型的“物理意义”属性联系起来的提议奠定概念基础；另一个他的目标是探索将拓扑学应用于理论间的约化。在西雅图，这名学生计划与另一位资深教授合作，扩展拓扑学的已知结果，以进一步发展他的框架。与这些学者的互动将有助于提高他的学位论文研究的质量。潜在的更广泛的影响国际和平研究所计划将他的研究成果传播到除科学哲学界之外的物理界；他计划通过在物理期刊上发表技术成果和在物理会议上发表演讲来实现这一目标。他明确提到，他将在美国物理学会3月和4月的年度会议以及2014年第29届太平洋海岸重力会议上公布他的研究成果。

Project OverviewThe PI proposes to engage in a conceptual analysis of the notion of physicality as it is used in the context of the philosophical foundations of physics using tools from topology and relativity theory; he plans to develop a mathematical framework for explicating the meaning of physicality in relation to models. The grant will support travel to two locations where researchers are working on topics related to aspects of his work, the University of Pittsburgh and the University of Washington, Seattle. Intellectual MeritIn Pittsburgh, the student plans to work with two senior professors. With one, he aims to develop the conceptual basis for a proposal by Stephen Hawking to connect topological stability with the "physically meaningful" properties of a model; with the other he aims to explore applying topology to inter-theoretic reduction. In Seattle, the student plans to work with another senior professor to extend known results in topology to further develop his framework. Interacting with these scholars will serve to enhance the quality of his dissertation research. Potential Broader ImpactsThe PI has plans to disseminate his research to the physics community in addition to the philosophy of science community; he plans to do so through publication of technical results in physics journals and through presentations at physics conferences. He explicitly mentions presenting his results at the annual March and April meetings of the American Physical Society and the 29th Pacific Coast Gravity meeting in 2014.