A computational approach to the twin paradox in curved spacetime

TL;DR

This paper presents a computational method for analyzing the twin paradox in curved spacetime, helping students understand how different paths affect experienced proper time in general relativity.

Contribution

It introduces a novel computational approach for predicting proper time along various paths in curved spacetime, enhancing educational understanding of the twin paradox.

Findings

Geodesic paths do not always maximize proper time in curved spacetime.

The method clarifies the relativistic effects in complex gravitational fields.

Educational tool for visualizing time dilation in general relativity.

Abstract

Despite being a major component in the teaching of special relativity, the twin `paradox' is generally not examined in courses on general relativity. Due to the complexity of analytical solutions to the problem, the paradox is often neglected entirely, and students are left with an incomplete understanding of the relativistic behaviour of time. This article outlines a project, undertaken by undergraduate physics students at the University of Sydney, in which a novel computational method was derived in order to predict the time experienced by a twin following a number of paths between two given spacetime coordinates. By utilising this method, it is possible to make clear to students that following a geodesic in curved spacetime does not always result in the greatest experienced proper time.