Logical Dependence of Physical Determinism on Set-theoretic Metatheory

Abstract

Baroque questions of set-theoretic foundations are widely assumed to be irrelevant to physics. In this article, I demonstrate that this assumption is incorrect. I show that the fundamental physical question of whether a theory is deterministic, whether it fixes a unique future given the present, can depend on choice of set-theoretic axiom candidates over which there is intractable disagreement. This dependence is not confined to hypothetical examples. It reaches into mainstream, discrete, and frontier physics, including the dynamics of Kerr black hole interiors. One upshot is that either physical theories must be relativized to set-theoretic metatheories (in which case physics itself becomes relative), or the search for new axioms to settle undecidables may admit of empirical input.