The Invariant Set Hypothesis: A New Geometric Framework for the Foundations of Quantum Theory and the Role Played by Gravity

A new hypothesis is proposed about the nature of physical reality at its most primitive level. The hypothesis is framed in terms of invariance, a concept that forms the very bedrock of physics. Specifically, the Invariant Set Hypothesis proposes that states of physical reality are precisely those belonging to a non-computable fractal subset I of state space, invariant under the action of some subordinate deterministic causal dynamics D. The Invariant Set Hypothesis provides a geometric framework for a new perspective on quantum physics.