6 - The Commensurability of Classical and Relativistic Mechanics

Abstract

This chapter elaborates the commensurability of classical and relativistic mechanics. The concept of the four-velocity, while quite extraneous to Newtonian mechanics, is wholly definable in classical terms. A new primitive concept namely, the proper mass of a particle which is specific to theory of relativity is presented. In many elementary presentations of relativistic mechanics, it is customary to deduce from Newton's second law through the erroneous identification of Newtonian and relativistic mass. Anyone who makes the mistake of confusing physical laws with definitions is likely to object to on the ground that it involves the mixing of concepts from semantically distinct theories. In particular, it may be argued that the left-hand side of contains a relativistic concept while the right-hand side contains the classical force which is defined in terms of Newtonian mass. Newtonian force is not defined in terms of Newtonian or classical mass but is a distinct physical quantity which constitutes part of the external environment of physical objects which possess mass. The two concepts are related by a testable law, and not by definition.