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Logic Seminar

Wednesday, December 7, 2022
11:00am to 12:00pm
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General relativity does not admit enough observables
Aristotelis Panagiotopoulos, Department of Mathematical Sciences, Carnegie Mellon University,

Please note that the time is PST

One of the biggest open problems in mathematical physics has been the problem of formulating a complete and consistent theory of quantum gravity. Some of the core technical and epistemological difficulties come from the fact that General Relativity (GR) is fundamentally a geometric theory and, as such, it oughts to be "generally covariant", i.e., invariant under change of coordinates by any element of the diffeomorphism group Diff(M)Diff(M) of the ambient manifold MM. The Problem of Observables is a famous instance of the difficulties associated with general covariance, and one directly related to ineffectiveness of classical quantization recipes when it comes to GR. In a nutshell, the problem of observables asks whether GR admits a complete set of smooth observables. That is, whether the family of all diffeomorphism-invariant, real-valued, smooth maps on the space Ein(M)Ein(M) of all Einstein metrics on MM is rich enough to separate all physical spacetimes. So far the only smooth observables known (when M=R4)M=R4) are the constant maps. In this talk, we will employ methods from descriptive set theory in order to answer the problem of observables in the negative. These results are inspired by old discussions with Marios Christodoulou and are based on recent work with George Sparling.

For more information, please contact Math Dept. by phone at 626-395-4335 or by email at A. Kechris at [email protected].