The Relativity of Simultaneity: An Analysis Based on the Properties of Electromagnetic Waves

Abstract

The determination of whether two distant events are simultaneous depends on the velocity of the observer. This velocity dependence is typically explained in terms of the relativity of space and time in a counterintuitive manner by the Special Theory of Relativity. In this paper, I describe a straightforward and intuitive way to explain the velocity dependence of simultaneity in terms of velocity-dependent changes in the spatial (k, {\lambda}) and temporal ({\omega}, {\nu}) characteristics of electromagnetic waves that result from the Doppler effect. Since, for any solution to a wave equation, the angular wave vector (k) and distance vector (r) as well as the angular frequency ({\omega}) and time (t) are complementary pairs (k *r) and ({\omega}t), it is only a matter of taste which members of the pairs (k, {\omega}) or (r, t) one assumes to depend on the relative velocity of the source and observer. Einstein chose r and t and I chose k and {\omega}. I present this electromagnetic wave approach to understanding the velocity dependence of simultaneity as a physically realistic alternative to Einstein's Special Theory of Relativity.