# Lectures on Faster-than-Light Travel and Time Travel

## TL;DR

This paper provides an overview of the theoretical possibilities and limitations of faster-than-light travel and time travel within general relativity and quantum field theory, including exotic spacetime geometries and paradoxes.

## Contribution

It offers a comprehensive educational resource on superluminal travel and time travel concepts, including detailed explanations of advanced relativity topics and analysis of exotic spacetime models.

## Key findings

- Exotic spacetimes like warp drives and wormholes are theoretically possible but have significant limitations.
- Tachyons are introduced as hypothetical particles that travel faster than light.
- Time travel paradoxes are explored with potential resolutions discussed.

## Abstract

These lecture notes were prepared for a 25-hour course for advanced undergraduate students participating in Perimeter Institute's Undergraduate Summer Program. The lectures cover some of what is currently known about the possibility of superluminal travel and time travel within the context of established science, that is, general relativity and quantum field theory. Previous knowledge of general relativity at the level of a standard undergraduate-level introductory course is recommended, but all the relevant material is included for completion and reference. No previous knowledge of quantum field theory, or anything else beyond the standard undergraduate curriculum, is required. Advanced topics in relativity, such as causal structures, the Raychaudhuri equation, and the energy conditions are presented in detail. Once the required background is covered, concepts related to faster-than-light travel and time travel are discussed. After introducing tachyons in special relativity as a warm-up, exotic spacetime geometries in general relativity such as warp drives and wormholes are discussed and analyzed, including their limitations. Time travel paradoxes are also discussed in detail, including some of their proposed resolutions.