Mathematics Colloquia and Seminars

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The process of identifying a time variable in time reparameterization invariant theories results in great ambiguities about the actual laws of physics described by a given theory. A theory set up to describe one set of physical laws can equally well be interpreted as describing any other laws of physics by making a different choice of time variable or ``clock''. I will show how this ``clock ambiguity'' arises and then discuss how one might still hope to extract specific predictions about the laws of physics even when the clock ambiguity is present. As a step in this direction, I will compare the Hamiltonian of a local quantum field theory with a completely random Hamiltonian finding that any random Hamiltonian (constructed in a sufficiently large space) can yield a ``good enough'' approximation to a local field theory. Based on this result I will argue that theories that suffer from the clock ambiguity may in the end provide a viable fundamental framework for physics in which locality can be seen as a strongly favored (or predicted) emergent behavior, and speculate on how other key aspects of known physics such as gauge symmetries and Poincare invariance might be predicted to emerge in this framework.