A Theoretical Study of the Conceptual, Mathematical, and Explanatory Interconnections at the Foundations of Classical Field Theories

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OverviewThis STS Scholars Award is to support research on a project in the conceptual foundations of physics. The standard view concerning the fundamental postulates of a physical theory is that they are independent assertions about the nature of space, time, matter, and their mutual interactions. The proposed alternative hypothesis to be examined by the principal investigator (PI) holds that physical theories are better understood as a network of mutually inter-dependent principles and assumptions. The proposed study will focus on the central principles of classical field theories, particularly theories of gravitation. Those principles include conservation principles, energy conditions, and field equations.Intellectual MeritWhile it well known that some principles of classical field theories may be derived from others, the idea that this inter-derivability is ubiquitous (or nearly so) and that this is essential to understanding the foundations of physical theories are novel claims. Also novel is the proposal to systematically explore these interconnections. If the alternative hypothesis of the PI is correct, then the basic postulates of our best physical theories are mutually supporting and constraining in ways that have not previously been systematically recognized; in that case, understanding these interconnections is essential to a full account of the philosophical and mathematical foundations of these theories. Testing the hypothesis will involve new technical work in the mathematical foundations of classical field theories as well as conceptual and philosophical analysis of both new and previously known results. Results will be communicated in physics and mathematics journals as well as philosophy journals, and will form the basis of a monograph on the foundations of classical field theory.Broader ImpactsThe PI will also explore the implications for topics in general philosophy of science, including explanation and theory change, provided that the hypothesis turns out to be correct. In addition, it would be expected that the hypothesis applies more broadly to include quantum theories and perhaps scientific theories more generally. In addition, the proposed project will integrate research with graduate education. The project includes many small, well-defined problems that will provide opportunities for collaborative work with graduate students. These collaborations will form the basis for the development and implementation of a hybrid model of graduate education, drawing from education traditions in philosophy and in theoretical physics, to facilitate broader participation in research by early graduate students from under-served groups. To that end, the PI will partner with existing organizations that are working to increase diversity in philosophy and the sciences such as Hypatia, which aims to improve retention and recruitment of women in philosophy.