Counting Steps: A New Approach to Objective Probability in Physics

TL;DR

This paper introduces a novel interpretation of objective probabilities in physics using physical computational complexity, linking state realization difficulty, resource-based distance, and compatible complexity functions to provide a new perspective on statistical physics and quantum mechanics.

Contribution

It presents a new complexity-based framework for understanding objective chances, removing ignorance assumptions and offering fresh insights into quantum mechanics.

Findings

Defines a complexity measure for physical state transitions.

Provides a new interpretation of quantum probabilities.

Connects physical resources to state realization difficulty.

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 set--up 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.