Simultaneity, Chronometrology, and the Two Postulates of Relativity

Einstein gave examples whereby simultaneous events recorded by one inertial observer may not be simultaneous for other inertial observers. This paper eliminates a common misconception. Simultaneous events are confused with separated events occurring at the same coordinate time. Simultaneous events are witnessed by all observers, whether inertial or accelerated, because simultaneous events occur when phenomena collide, merge, overlap, or superimpose into one point at the same instant of time. Chronometric events are separated by a nonzero distance and occur at the same coordinate time of a reference frame. Simultaneous events are witnessed identically by all observers, because a point is still a point with an instantaneous time within any reference frame. Chronometric events occur at identical coordinate times, but are usually not simultaneous, because the distances to convey the information to an observer are usually unequal so that arrival times are different. Einstein’s thought experiment to test simultaneity is explained by Newtonian physics without relativity. The mathematics concerning an embellishment of this thought experiment is derived. The contradictory results indicate the two relativity postulates should be revised to establish the correct equations in inertial frames to make identical predictions using the proper transformation.