Relativistic Paradoxes and Lack of Relativity in Closed Spaces

TL;DR

This paper examines relativistic paradoxes in closed spaces, revealing that global time and effective forces resolve apparent contradictions and restore an absolute rest frame, thus eliminating paradoxes in such geometries.

Contribution

It demonstrates that in closed spaces, global time and effective forces distinguish true inertial frames, resolving twin paradoxes and challenging the relativity of uniform motion.

Findings

Global time exists only in a truly stationary reference frame.

Uniform motion in closed space involves effective forces, contradicting inertial assumptions.

Relativity paradoxes are resolved when considering the geometry and clock synchronization in closed spaces.

Abstract

Some known relativistic paradoxes are reconsidered for closed spaces, using a simple geometric model. For two twins in a closed space, a real paradox seems to emerge when the traveling twin is moving uniformly along a geodesic and returns to the starting point without turning back. Accordingly, the reference frames (RF) of both twins seem to be equivalent, which makes the twin paradox irresolvable: each twin can claim to be at rest and therefore to have aged more than the partner upon their reunion. In reality, the paradox has the resolution in this case as well. Apart from distinction between the two RF with respect to actual forces in play, they can be distinguished by clock synchronization. A closed space singles out a truly stationary RF with single-valued global time; in all other frames, time is not a single-valued parameter. This implies that even uniform motion along a spatial geodesic in a compact space is not truly inertial, and there is an effective force on an object in such motion. Therefore, the traveling twin will age less upon circumnavigation than the stationary one, just as in flat space-time. Ironically, Relativity in this case emerges free of paradoxes at the price of bringing back the pre-Galilean concept of absolute rest. An example showing the absence of paradoxes is also considered for a more realistic case of a time-evolving closed space.