The 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 Merit
In 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 Impacts
The 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.
This award funded two trips for the co-Principal Investigator (co-PI), who was then a graduate student, to work with researchers at the Universities of Washington and Pittsburgh. These trips improved the quality of the co-PI's doctoral dissertation by giving him extended, face-to-face interaction with experts on topics relevant for this work. The co-PI gained new perspectives on these trips and broadened the exposure of his ideas, which showed him how to make them more relevant and accessible to a broader part of the philosophy of science community. In part because of this, he was able to successfully defend in dissertation in June, 2014, and acquire a tenure-track position at the Department of Philosophy at the University of Minnesota, Twin Cities, starting in August, 2015. The intellectual goals of the project were to develop technical tools for describing the ways in which different configurations of space and time, as described by our best science, could be similar to one another. Judgments of this kind of similarity play a role in theoretical reasoning and explanation in physics, topics that philosophers of science are interested in giving accounts of. There were three main lines of investigation supported by this award: Giving an analysis of physicists' judgments regarding whether a mathematical model depicting a certain configuration of space and time could be "physical" or "unphysical". It was found that one way in which this terminology is used reflects conditions under which one has warrant to infer a property about the world from a property of the mathematical model. In particular, in order for one to infer any property from a mathematical model, it has to be possessed as well by all mathematical models sufficiently similar to it. Naturally, whether this criteria will be fulfilled will depend on the notion of similarity used! Exploring different notions of similarity, especially their consequences for understanding how one theory can explain the success of another. It was found, for example, that whether Einstein's theory of general relativity can explain Newton's (older) theory of gravitation depends on what kinds of features of the theories one requires to be relevantly similar. This dependence of explanation on the notion of similarity has not been adequately described before. Investigating a new notion of similarity, described by the co-PI, which was designed to capture how a configuration of space and time as a whole could be similar to another whole configuration. This new notion was designed to replace an older notion of similarity that was used in the literature and had some problems. It was found that in many cases the new notion adequately captures the kinds of judgments and conclusions the older notion successfully captured. Besides being of interest to philosophers of science, some of the work supported by this award has been relevant to mathematical physicists, who are interested in general structural relationships within and between theories. Presentations of work done along lines #2 and 3 at physics venues has led to further invitations to present at colloquia in Vienna, Austria and Cologne, Germany. Lastly, the trips supported by this award have engendered more kinds of collaboration than anticipated. The co-PI's visit to the University of Washington reignited a joint project between him and, the PI, and Prof. John Manchak of the philosophy department there. The co-PI's visit to the University of Pittsburgh yielded extended contact with other students there and at Carnegie Mellon University working in the philosophy and foundations of statistics, which has now resulted in a biweekly online discussion group. The establishment of this new small network of researchers may not have been possible without the support of this award.
