Periodic boundary conditions in special relativity

Abstract

The imposition of periodic boundary conditions on the space-time of special relativity is shown to lead to the existence of a preferred frame of reference. One characteristic of the preferred frame is that it is the frame in which the resulting finite universe has the smallest size. In a frame moving with respect to the preferred frame, global synchronization of clocks cannot be carried out and the transit time to traverse the universe depends on the direction of travel. As measured in a moving frame, a person at rest in the preferred frame can be found at two or more different places at the same time, although the age of the person will be different at each of those places. A ‘‘pole in the universe’’ paradox is presented, the resolution of which requires use of some of these bizarre properties of the universe of periodic boundary conditions.