Constructing Time Machines

TL;DR

This paper examines three theoretical proposals for time machines involving cosmic strings, shock waves, and superluminal light, demonstrating that none of these constructions can produce actual time machines, thus highlighting the importance of causality constraints.

Contribution

The paper analyzes and refutes three different theoretical models for time machines, emphasizing the causal self-consistency constraints in classical and quantum gravity.

Findings

None of the proposed models produce a working time machine.

Causal self-consistency is crucial in evaluating time machine proposals.

Insights gained may inform future theories of gravity and causality.

Abstract

The existence of time machines, understood as spacetime constructions exhibiting physically realised closed timelike curves (CTCs), would raise fundamental problems with causality and challenge our current understanding of classical and quantum theories of gravity. In this paper, we investigate three proposals for time machines which share some common features: cosmic strings in relative motion, where the conical spacetime appears to allow CTCs; colliding gravitational shock waves, which in Aichelburg-Sexl coordinates imply discontinuous geodesics; and the superluminal propagation of light in gravitational radiation metrics in a modified electrodynamics featuring violations of the strong equivalence principle. While we show that ultimately none of these constructions creates a working time machine, their study illustrates the subtle levels at which causal self-consistency imposes itself, and we consider what intuition can be drawn from these examples for future theories.