Abstract

The inertial properties of ordinary matter cannot be ascribed solely to the inertial mass appearing in Newton's second law of motion; the contribution made by space-time must also be considered. Herein special relativity is used to show that inertia is ultimately relativistic in origin. Two observers moving relatively in Minkowski space-time are considered. The moving observer accelerates tangentially along a circular path of constant radius, passing by a stationary observer with greater velocity upon each revolution. The stationary observer uses the dilation of time arising between the two observers to derive an expression for the inertial resistance of the moving observer. The form of the resulting expression implies that inertia is chiefly a local relativistic phenomenon. The case in which an arbitrary force acts on an observer undergoing uniform, relativistic translation in Minkowski space-time is then considered. The time dilation approach leads directly to the well-known relativistic form of Newton's second law of motion, derived on the basis of special relativity.