The statistical origins of gauge coupling and spin

U. Klein*
Universitity of Linz
Institute for Theoretical Physics
A-4040 Linz, Austria

September 4, 2010



A previous one-dimensional derivation of Schrödinger’s equation from statistical assumptions is generalized to three spatial dimensions, gauge fields, and spin. It is found that the same statistical assumptions that imply Schrödinger’s equation determine also the form of the gauge coupling terms, and the form of the corresponding local (Lorentz) forces. An explanation for the role of the electrodynamic potentials, as statistical representatives of the Lorentz force, is given. Spin one-half is introduced as the property of a statistical ensemble to respond to an external gauge field in two different ways. A generalized calculation, using the twofold number of variables, leads to Pauli’s equation. The new spin term is again the statistical representative of the corresponding local force. The classical limit ℏ→  0  of Schrödinger’s equation and closely related questions of interpretation of the quantum mechanical formalism are discussed.

1 Introduction
2 Basic equations
3 Statistical conditions
4 Gauge coupling
5 Fisher information
6 Spin - Basic theory
7 Spin - Fisher information
8 The classical limit
9 Discussion
10 Concluding remarks
A Electrodynamical and inertial gauge fields