Foundation for Fisher-information-based derivations of physical laws

The principle of extreme physical information (EPI) places physics on an information-theoretic footing. It yields many of the fundamental wave equations of physics (of Klein-Gordon, Dirac, etc.). EPI is based upon the measurement of particle four-vectors θ_n with random errors x_n, n=1,...,N. This leads to an additive Fisher information form whose extremization provides the derivations. However, the model measurement procedure was, in the past, overly restrictive: the real and imaginary parts q_n(x), n=1,...,N of the probability amplitude functions for the fluctuations were required to have nonoverlapping support regions. Here we rederive the requisite information form without this restriction. Our model measurement procedure is simply the efficient collection of four-data, that is, N independent measurements of four-coordinates of particles of the field. In effect, each measurement defines a different degree of freedom q_n(x) of the scenario.