Lectures on Faster-than-Light Travel and Time Travel

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.

arXiv comment64 pages, 8 figures; updated figures; version published in SciPost Physics Lecture Notes

References in corpus (27)

• Traversable wormholes with arbitrarily small energy condition violations
• The warp drive: hyper-fast travel within general relativity
• Traversable Wormholes via a Double Trace Deformation
• Diving into traversable wormholes
• Averaged Energy Conditions and Quantum Inequalities
• Averaged Null Energy Condition from Causality
• Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
• A Primer on Energy Conditions
• Warp drive basics
• Traversable wormholes from massless conformally coupled scalar fields
• Energy conditions and their cosmological implications
• Closed timelike curves via post-selection: theory and experimental demonstration
• Quantum Field Theory on Spacetimes with a Compactly Generated Cauchy Horizon
• Fundamental limitations on "warp drive" spacetimes
• The unphysical nature of "Warp Drive"
• Achronal averaged null energy condition
• The quantum mechanics of time travel through post-selected teleportation
• Cosmic Strings and Chronology Protection
• Quantum effects in the Alcubierre warp drive spacetime
• Warp Drive With Zero Expansion
• A perturbative perspective on self-supporting wormholes
• Effective Quantum Time Travel
• On the Quantum Stability of the Time Machine
• The time travel paradox
• The Topology of Branching Universes
• Closed Timelike Curves Make Quantum and Classical Computing Equivalent
• Quantum field theory and time machines

Cited by in corpus (8)

• Time Travel Paradoxes and Multiple Histories
• Superluminal local operations in quantum field theory: A ping-pong ball test
• Wormhole Time Machines and Multiple Histories
• Warp Drives and Closed Timelike Curves
• Obstacles from interstellar matters and distortion in warp drive superluminal travel scenario
• Spin Networks and Cosmic Strings in 3+1 Dimensions
• Breaching the light barrier without paradoxes
• Wormhole Nucleation via Topological Surgery in Lorentzian Geometry