Simultaneity in cylindrical spacetime

Abstract

In cylindrical spacetime which is flat like Minkowski spacetime but is spatially closed, two twins can part and reunite, while none of them go through any acceleration. Still, the twins are aged differently upon their reunion (except for some special occasions). The key to understanding what happens in cylindrical spacetime lies in clock synchrony. In cylindrical spacetime, the Round-trip Axiom (that two light signals sent simultaneously in opposite directions along a closed path return simultaneously) fails to hold, and so distant clocks cannot be consistently synchronized following the standard procedure proposed by Einstein except for those under some privileged motion. We propose an alternative method of synchrony utilizing the one-way speed of light traveling around the universe, which can be measured with one clock and varies from inertial frame to inertial frame. This alternative synchrony renders simultaneity not relative but absolute and makes it possible to consistently describe both the local and global phenomena in cylindrical spacetime.