The time travel paradox

TL;DR

This paper defines the time travel paradox in physical terms, constructs an explicit example to prove its existence, and discusses conditions under which paradoxes do not arise in certain theories like general relativity.

Contribution

It provides a formal definition of the time travel paradox, constructs an explicit example, and analyzes its implications within general relativity.

Findings

Explicit example of the time travel paradox

Paradoxes do not arise in theories with differential equations and initial data

Discussion on conditions avoiding paradoxes in general relativity

Abstract

We define the time travel paradox in physical terms and prove its existence by constructing an explicit example. We argue further that in theories -- such as general relativity -- where the spacetime geometry is subject to nothing but differential equations and initial data no paradoxes arise.