Use of Lorentz Transformations for Noninertial Frames of Reference

Abstract

By analogy with the calculation of the path of a mass point in terms of the integral of the point velocity with respect to time, such that the point has a constant velocity V(ti) within a time interval dti, then changes this velocity stepwise by V(ti+1), moves with this velocity within a time interval dti+1, etc., an accelerated motion of an observer with a clock is represented by alternating states of rest in a sequence of inertial frames of reference and instantaneous jumps from one frame of reference into another. Lorentz transformations are used to calculate the readings of a “resting” clock observed from a noninertial frame of reference represented in this manner, during the rest of a noninertial observer in a next-in-turn inertial frame of reference belonging to the mentioned sequence, and upon a jump. For the observation from a noninertial frame of reference, the relation of the time interval counted by the “resting” clock to the time interval counted by the accelerated clock and to the acceleration has been obtained.