An Ambiguity in the Relativistic Dynamics and Electromagnetism Regarding Force Transformation

Abstract

Einstein’s relativity has always been the subject of considerable controversy among  physicists. So far, a few scientists have tried to demonstrate an inconsistency in the  theory, whereas the majority of the academics believe that finding a real paradox via,  e.g., designing a thought experiment is something absurd and impossible. Although  many of the paradoxes introduced in the framework of relativity have truly been  resolved using precise mathematical expressions, the paradox introduced in this  article can be considered as an exception. A simple thought experiment is indeed  carried out through which it is shown that the accepted transformation for the  electromagnetic (EM) fields, as well as the same transformation for force, culminates  in possible inconsistencies in the framework of the special theory of relativity. A tiny  charge in a uniform electric field is set in motion over a charged lid located in a  compartment shielded against electromagnetic fields within which there is a similar  electric field. It is shown that the observer at rest with respect to the tiny charge  claims that the lid is easily pushed downward as the charge passes over it, whereas the observer in the compartment’s rest frame claims otherwise.