Extended time-travelling objects in Misner space

TL;DR

This paper investigates the behavior of extended objects in Misner space, revealing self-collision risks in 2D but identifying collision-free time-travel paths in a 4D generalization, with implications for understanding causality.

Contribution

It introduces a 4D generalization of Misner space and demonstrates the existence of safe, collision-free time-travel orbits for extended objects.

Findings

Self-collisions are inevitable for extended objects in 2D Misner space.

A 4D generalization allows for safe, collision-free time-travel trajectories.

The study enhances understanding of causality and time-travel in relativistic spacetimes.

Abstract

Misner space is a two-dimensional (2D) locally-flat spacetime which elegantly demonstrates the emergence of closed timelike curves from causally well-behaved initial conditions. Here we explore the motion of rigid extended objects in this time-machine spacetime. This kind of 2D time-travel is found to be risky due to inevitable self-collisions (i.e. collisions of the object with itself). However, in a straightforward four-dimensional generalization of Misner space (a physically more relevant spacetime obviously), we find a wide range of "safe" time-travel orbits free of any self-collisions.