Counting steps: a finitist approach to objective probability in physics

Abstract

We propose a new interpretation of objective deterministic chances in statistical physics based on physical computational complexity. This notion applies to a single physical system (be it an experimental setup in the lab, or a subsystem of the universe), and quantifies (1) the difficulty to realize a physical state given another, (2) the 'distance' (in terms of physical resources) of a physical state from another, and (3) the size of the set of time-complexity functions that are compatible with the physical resources required to reach a physical state from another. This view (a) exorcises "ignorance" from statistical physics, and (b) underlies a new interpretation to non-relativistic quantum mechanics.