Abstract
This chapter is about using curvilinear coordinates to investigate the physics in a noninertial frame, consistent with the special theory of relativity. We first introduce curvilinear coordinates and study the conditions for the coordinates to be acceptable as time and space coordinates. Then we present the concept of extended observer, or frame of reference, as a collection of point observers with a scheme to synchronize clocks and define a coordinate time. We then investigate in detail the concepts of distance and time and measuring distance with radars, which is dictated by special relativity. We introduce Einstein's synchronization scheme and discuss the condition that it can be performed unambiguously on a closed path. As an example, we study a rotating frame and show that the space is curved in a rotating frame. The Sagnac effect is also discussed. We then investigate the Rindler frame, consisting of a set of uniformly accelerated particles. We then study the motion of particles and the equations of electrodynamics in a noninertial frame.
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