Simple Proof that the Usual Transformations of the Electric and Magnetic Fields are not the Lorentz Transformations and EDM Searches

TL;DR

This paper demonstrates that the common 3D transformations of electric and magnetic fields are not the true Lorentz transformations of the relativistically correct 4D fields, impacting the interpretation of EDM and quantum phase shift experiments.

Contribution

It provides a simple proof that the standard 3D field transformations differ from the true Lorentz transformations of 4D fields, highlighting a fundamental conceptual correction.

Findings

Standard 3D transformations are not Lorentz transformations of 4D fields

Implications for EDM experiments and quantum phase shift interpretations

Emphasizes the use of 4D geometric quantities over 3D fields

Abstract

The usual transformations of the three-dimensional (3D) fields E and B that are found in [1] ([1] A. Einstein, Ann. Physik \17, 891 (1905)) are always considered to be the relativistically correct Lorentz transformations (LT) of E and B. However, as proved in, e.g., [2] ([2] T. Ivezi\'c, Found. Phys. Lett. 18, 301 (2005)), these transformations drastically differ from the LT of the relativistically correct 4D electric and magnetic fields. In this paper a simple proof of that difference will be presented and the consequences for EDM experiments and for some quantum phase shifts experiments are briefly examined. In all such experiments the usual 3D quantities, e.g., E, B, ... are measured and their relativistically incorrect transformations are used, but not the relativistically correct 4D geometric quantities, e.g., E^a, B^a, ... and their LT.