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.