This paper proposes a clear test of the relativistic assumption of the relativity of simultaneity. Special relativity assumes that two relatively moving observers instantaneously collocated will see light from a distant event at the same place and time. This assumption is embedded in Einstein’s original train embankment thought experiment. It is reconciling this assumption with the presumed constancy of the speed of light that led to relativistic length contraction and time dilation for the moving observer. An uncomfortable by product is that these two observers can no longer agree on where and when an event occurred. If they are viewing two separated events, and one observer concludes the events occurred simultaneously, the other observer will conclude that the two events were not simultaneous—thus the relativity of simultaneity. Two events that are simultaneous in one reference frame are not simultaneous in a different reference frame.
Until recent years, a test of the relativity of simultaneity would not have been possible. A direct test has never been attempted due to the great distances, high speeds and extremely small variances in time to be observed. Even if these could all be overcome, the ability to perform one part of the experiment in the moving frame and obtain results that do not require converting back to the stationary frame are extremely problematical.
But currently, we have many satellites at distances of 20K km and greater, routinely transmitting with carrier signals in the GHz range. We are able to accurately model the ephemerides of these satellites, and even account for atmospheric disturbances. We have very stable oscillators in the same range in lab environments, with the ability to phase-lock their outputs to another signal, and phase detectors able to provide voltage outputs proportional to the difference in phase of signals with wavelengths in the 20 cm and smaller range. Similarly, clock and code signals can be compared in the same manner as phase shifts by combing signals. Phase detection is a much simpler and preferred method for determining subtle differences in light travel times. The most notable example in recent times is the LIGO gravitational wave detector, which uses an interferometer with 2.5-mile arms to detect an extremely subtle phase shift due to the varying gravitational field caused by rapidly orbiting black holes. As will be shown, the proper use of phase measurements eliminates any reliance on clock synchronization between the “moving” and “stationary” frames, or between either of these frames and the source itself, and allows for a realistic test of relativistic simultaneity.
