Derivation of the Pauli equation using the principle of minimum Fisher information

Asher Yahalom A

B. Roy Frieden

The Klein–Gordon equation for spinless particles, as well as the Weyl–Pauli and Dirac equations for particles with spin, may be derived from one information-theoretic principle. Consider a gedanken experiment whereby the mean position of a particle in a central force field is to be estimated by means of one position measurement. An efficient (optimum) estimate obeys a condition of minimum Fisher information, or minimum precision, according to the second law of thermodynamics. When the Fisher information is minimized subject to a constraint on the mean-square kinetic energy for the particle, the solution is a probability law on position whose corresponding wave amplitude obeys the Klein-Gordon equation, the Weyl–Pauli equation, or the Dirac equation, depending on whether scalar (without spin) or vector (with spin) solutions are sought. The minimized Fisher information is proportional to the mean-square kinetic energy, minus the rest energy of the particle.

Marcel Reginatto

The many-particle time-dependent Schr\"odinger equation is derived using the principle of minimum Fisher information. This application of information theory leads to a physically well motivated derivation of the Schr\"odinger equation, which distinguishes between subjective and objective elements of the theory.

Victor F. Weisskopf

David Böhm, Ralph Schiller, J. Tiomno

Ágnes Nagy

The Euler equation of the density functional theory is derived from the principle of minimum Fisher information. Both time-independent and time-dependent cases are analyzed. It is shown that Fisher information is a measure of the quality of the approximate density.