The twin paradox in a cosmological context

TL;DR

This paper investigates the twin paradox in Schwarzschild spacetime, revealing new effects related to vertical motion and rotating frames, and proposes an extended Minkowski spacetime model incorporating cosmic matter for a consistent resolution.

Contribution

It introduces a novel analysis of the twin paradox considering vertical motion and rotating frames, and proposes an extended spacetime model with a cosmic shell to resolve paradoxes.

Findings

Vertical motion reverses the aging order of twins compared to circular motion.

A new relativistic time effect linked to rotating frames is identified.

An extended Minkowski spacetime with a cosmic shell is proposed for consistent paradox resolution.

Abstract

Recently Abramowicz and Bajtlik [ArXiv: 0905.2428 (2009)] have studied the twin paradox in Schwarzschild spacetime. Considering circular motion they showed that the twin with a non-vanishing 4-acceleration is older than his brother at the reunion and argued that in spaces that are asymptotically Minkowskian there exists an absolute standard of rest determining which twin is oldest at the reunion. Here we show that with vertical motion in Schwarzschild spacetime the result is opposite: The twin with a non-vanishing 4-acceleration is younger. We also deduce the existence of a new relativistic time effect, that there is either a time dilation or an increased rate of time associated with a clock moving in a rotating frame. This is in fact a first order effect in the velocity of the clock, and must be taken into account if the situation presented by Abramowicz and Bajtlik is described from the rotating rest frame of one of the twins. Our analysis shows that this effect has a Machian character since the rotating state of a frame depends upon the motion of the cosmic matter due to the inertial dragging it causes. We argue that a consistent formulation and resolution of the twin paradox makes use of the general principle of relativity and requires the introduction of an extended model of the Minkowski spacetime. In the extended model Minkowski spacetime is supplied with a cosmic shell of matter with radius equal to its own Schwarzschild radius, so that there is perfect inertial dragging inside the shell.