Estimation of distribution laws, and physical laws, by a principle of extremized physical information

Abstract

A new method of estimating physical probability laws is given. This arises from a new form of information, which in turn follows from four physically based axioms. Extremization of this “physical information” gives rise to the required probability laws. As verifications of the approach, the following statistical (and non-statistical) laws of physics are derived: the complex Schrödinger and Helmholtz wave equations, relativistic quantum mechanics in the Klein-Gordon, Dirac, and Weyl-Pauli formulations, the Boltzmann energy- and Maxwell-Boltzmann velocity distributions, the Lorentz transformation group of special relativity, and Maxwell's equations. Also derived are inequalities defining a class of uncertainty principles (e.g., Heisenberg's). Finally, the Einstein equations of motion (but not the fields) of general relativity are derived, along with an equivalence d I / dτ ∞ mc 2 between information flow rate and matter energy.