In an effort to formulate a theory of invariance for spacetime expansion and contraction, in 1920, 5 years after Einstein’s formulation of general relativity (GR) and 1 year after GR was experimentally verified by Sir Arthur Stanley Eddington, Hermann Weyl formulated his mathematical theory of length (gauge) invariance in order to unify the classical theory of electromagnetism with GR. Although the word “gauge” is properly referred to “length” in the German language, this word became stuck inside succeeding theoretical circles for naming schemes to simply mean any type of field invariance, whether local or global, for scalar or vector field. Specifically, in the unified quantum fields of Dirac’s electron matter field and the special relativistic electromagnetic field called quantum electrodynamics (QED), the “gauge” concept simply refers to the phase factor of every possible quantum field particle.

Any theory describing a quantum field that is independence of changes in its angular phase displacements is then considered as a theory incorporated with the principle of gauge invariance. Adding or subtracting any phase angle from the electron matter field does not alter the results for any experiment. This was verified by two versions of the double-slit experiment for electrons. One version introduced a 180° phase shift for the diffracted electrons going thru one slit which clearly altered the observed interference pattern. The other version used perpendicular magnetic field with respect to the electron beams and inserted between the slits. Remarkably, the same phase shift is observed even when magnetic shields are arranged such that the magnetic field cannot penetrate the region where the two diffracted electron beams interfere. The second version is known commonly as the Aharonov-Bohm effect or Ehrenberg-Siday-Aharonov-Bohm effect.