From Weyl's scale gauge to London's phase: a consolidation, and a temperature reading of the fields

In 1918 Hermann Weyl proposed that the electromagnetic field is a change of length scale, transported from point to point. Einstein objected that clocks would then carry their history. Within ten years Fock, London and Weyl turned the idea into the gauge principle of quantum theory: what is transported is the phase of the matter wave, not the scale. Part A follows this development in one sequence, from the original papers to the present: the second clock effect and its experimental bounds; integrable Weyl geometry; the Aharonov–Bohm effect; what the gauge account leaves open, above all the value of the fine-structure constant α. It contains standard physics and its history only. Part B reads Weyl's picture in the terms of a separately developed framework (On Pythagoras Within the Universe, doi:10.5281/zenodo.20306533): fields as shifts of a boundary temperature and of a local phase clock. It computes static and moving charges, the force between charges, the field energy, g = 2, Thomas precession and the Rindler horizon of an accelerated charge. It collects the relations into a working set of equations (B.5). From the boundary temperatures that receivers of different charge read at each point, the set determines the scale, the electric and magnetic fields, the forces and the horizons. Each relation reproduces a standard one: the result is a reproduction of established electrodynamics, not new physics, and α remains an input.The numerical programs and their results are included (CC BY 4.0).