Standard Research Grant: A Novel Philosophical Analysis of How Modern Gauge Symmetries Can Have Empirical Content

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This award supports a research project that will develop a new philosophy of symmetry. The project diagnoses the challenge of the Galilean paradigm (in which symmetries have empirical content) for gauge symmetry; this is the key symmetry of our best physical theories, but it does not seem to have any empirical content. The researchers will put forward a novel conception of symmetry that can account for the empirical content of gauge symmetry. The project will place this novel account of symmetry in historical perspective by exploring its connection to deep conceptual issues raised by Emmy Noether, Albert Einstein, and Felix Klein. The project will also examine the consequences of the new account for two important topics in the foundations of physics. These results will be incorporated into educational programs at graduate, undergraduate, and K-12 levels; they will be incorporated in undergraduate and graduate courses in the philosophy of science, and in the creation of outreach events for the South Bend School System.This project develops a new philosophy of symmetry. The researchers will analyze how and why physicists' present conception of the empirical content of symmetries outstrips the naive Galilean paradigm. They will use the results of this analysis to develop a new account of how gauge symmetry (the key symmetry of our best physical theories) can be empirical. They will then connect their notion of empirical content to an important episode in the history of symmetry, the Noether-Klein-Einstein correspondence about energy conservation in General Relativity. Noether and Klein famously charged that the conservation laws derived by Einstein for General Relativity were trivial; they do not bear any physical significance. The researchers will show that Noether and Klein's concerns were precisely about the failure of the Galilean paradigm, and that Einstein's rejoinders (though not entirely successful) were important clues towards the project's novel account of symmetry. The researchers will also apply their notion of empirical content to two important topics in the foundations of physics; they will use it to shed light on the possible of existence of boundary observables in Newtonian gravity, and on the phenomena of the quantum Hall effectThis award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.