The One-Way Speed of Light and the Milne Universe

Abstract

In Einstein's Special Theory of Relativity, all observers measure the speed of light, $c$, to be the same. However, this refers to the round trip speed, where a clock at the origin times the outward and return trip of light reflecting off a distant mirror. Measuring the one-way speed of light is fraught with issues of clock synchronisation, and, as long as the average speed of light remains $c$, the speeds on the outward and return legs could be different. One objection to this anisotropic speed of light is that views of the distant universe would be different in different directions, especially with regards to the ages of observed objects and the smoothness of the Cosmic Microwave Background. In this paper, we explore this in the Milne universe, the limiting case of a Friedmann-Robertson-Walker universe containing no matter, radiation or dark energy. Given that this universe is empty, it can be mapped onto flat Minkowski space-time, and so can be explored in terms of the one-way speed of light. The conclusion is that the presence of an anisotropic speed of light leads to anisotropic time dilation effects, and hence observers in the Milne universe would be presented with an isotropic view of the distant cosmos.