A New Coordinate Transformation between Inertial Reference Frames S and S′

Abstract

This paper introduces a new coordinate transformation between the two inertial reference frames S and S′, where S′is moving at velocity v relative to S and with the occurrence of an event by which an object starts to move with velocity u′relative to S′. It is assumed that the origin O′of the frame S′coincides with origin O of the first frame S at t=t′=0. The transformation is formulated as t=t′, x=x′+vt), where =1/+vu′/c). We show that using this transformation, the wave equation for electromagnetic waves in frame S′has the same form as that in S. This result thus shows that there exists a transformation with absolute time (t=t′) which conforms to the relativity principle. A strong implication on the time dilation of a moving object is also discussed.