The clock ambiguity and the emergence of physical laws

TL;DR

This paper explores how the ambiguity in choosing a time variable in reparameterization invariant theories affects the interpretation of physical laws, proposing that locality and other physics features may emerge as favored behaviors despite this ambiguity.

Contribution

It demonstrates the emergence of locality and physical laws from a framework where the clock ambiguity is present, using random Hamiltonians to approximate local quantum field theories.

Findings

Random Hamiltonians can approximate local quantum field theories.

Locality may emerge as a favored behavior despite clock ambiguity.

The framework suggests gauge symmetries and Poincare invariance might also emerge.

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.