The Paradoxical Case of Force-Acceleration Transformation in Relativity

Abstract

During one of my recent classes, an interesting question, never heard before, was posed by one of the students: "How come that the relativistic acceleration transformation transforms zero acceleration into zero acceleration but transforms zero force into non-zero force?" In the current note I will explain this apparent paradox. The proof is not trivial and, to my best knowledge, cannot be found in the literature. The note is intended for undergraduate students and for instructors who teach special relativity, especially the dynamics chapters. PACS: 03.30.+p