Simultaneity can be nonrelative

Abstract

Einstein uses a train embankment case to interpret the concept of the relativity of simultaneity. In this article, we present a few situations showing that simultaneity can be nonrelative. Suppose that frame H with coordinates (x, y, z, t) is fixed on a railway, where the x-axis and the railway coincide, and similarly, frame H′ with coordinates (x′, y′, z′, t′) is attached to a train uniformly moving along the railway, where the x′-axis and the train coincide; i.e., the train moves along the x- and x′-axes. On a transverse plane in H, events occurring at points equidistant from the x-axis occur simultaneously, and nearby observers emit light signals toward observer M on the x-axis and another observer M′ on the x′-axis. The distances between M and all event locations are the same. Additionally, M′ is equidistant from all event locations. Clearly, M′ receives all signals simultaneously. Similarly, M perceives that all events occur at the same time; i.e., simultaneity is not necessarily relative. In addition, we perform an elaborate study of the distinction between the occurrence time and the transmission time. The results suggest that when the transmission time is considered for measuring the occurrence time, simultaneity can be nonrelative.