Information Theory of Action : Reconstructing Quantum Dynamics from Inference over Action Space

TL;DR

This paper reconstructs quantum dynamics using an information-theoretic approach based on inference over action space, deriving core quantum features like unitarity and interference from minimal assumptions.

Contribution

It introduces a novel reconstruction of quantum mechanics from finite-resolution inference over action space, deriving unitarity and interference without postulates.

Findings

Quantum interference and unitarity emerge from inference assumptions.

The Schrödinger equation and Hilbert space structure are derived from the framework.

The action scale is empirically fixed to Planck's constant, .

Abstract

We develop an information-theoretic reconstruction of quantum dynamics based on inference over action space. The fundamental object is a density of action states encoding the multiplicity of dynamical alternatives between configurations. Maximum-entropy inference introduces a finite resolution scale in action, implying that sufficiently close action contributions are operationally indistinguishable. We show that this indistinguishability, together with probability normalization and action additivity, selects complex amplitudes and unitary evolution as the minimal continuous representation compatible with action additivity, probability normalization, and inference under finite resolution. Quantum interference and unitarity therefore emerge as consequences of these assumptions rather than independent postulates. From the resulting propagator, the Lagrangian, Hilbert-space structure, and Schr\"odinger equation follow as derived consequences. In the infinitesimal-time limit, action differences universally fall below the resolution scale, making coherent summation the minimal consistent description at every step. The numerical value of the action scale is fixed empirically and identified with $\hbar$.