The clock ambiguity and the emergence of physical laws

Abstract

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''. In this article we demonstrate 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. We argue that a requirement of quasi-separability should play a critical role in such an analysis. As a step in this direction, we compare the Hamiltonian of a local quantum field theory with a completely random Hamiltonian. We find 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 we 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. We also speculate on how other key aspects of known physics such as gauge symmetries and Poincare invariance might be predicted to emerge in this framework.

16 Pages including two appendices and 5 figures. V2: Some additional references added for completeness. No other changes. (Final version accepted for publication in PRD.)

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