============================================================================= Relativity and FTL Travel by Jason W. Hinson (hinson@physicsguy.com) ----------------------------------------------------------------------------- Part 0: Introduction to the FAQ ============================================================================= Edition: 5.2 Last Modified: December 9, 2025 URL: http://www.physicsguy.com/star-trek/ftl-travel/ PDF: http://www.physicsguy.com/star-trek/ftl-travel/pdf/ftl.pdf ------------------------------------------------------------------ Copyright(C) 1995–2025, Jason W. Hinson. All rights reserved. Permission to distribute this document in its entirety (unedited and including this copyright notice) is granted, provided no fees are charged beyond any download or connection costs. A partial distribution is also permitted, but must contain the introduction, Part I, and Part IV. Publication of any portion in a magazine, journal, or other media requires the author’s approval. Star Trek(R), Star Trek: The Next Generation(R), Star Trek: Deep Space Nine(R), and Star Trek: Voyager(R) are trademarks of Paramount Pictures. ------------------------------------------------------------------ Contents of this Introduction: 0.1 What is this FAQ About, and Who Should Read It 0.2 Edition Information 0.3 The Versions A contents of the FAQ is also given below. 0.1 What is this FAQ About, and Who Should Read It The primary purpose of this FAQ is to discuss, in straightforward and simple terms, the relationship between relativity and faster-than-light (FTL) travel. Part I introduces the aspects of special relativity needed to understand the FTL Travel discussion. One of its sections includes an introduction to space-time diagrams, which are used to illustrate several key points later on. If you're not familiar with these diagrams, this will be an especially important section to read. Parts II and III are what I call “optional reading.” You don’t have to read them to follow the FTL discussion, but they may be helpful. Part II provides additional information about special relativity and explains two “solvable paradoxes” associated with the theory, while Part III introduces and explores several major concepts in general relativity, doing so at considerable length. Part IV is the section that directly discusses the question of FTL travel. It addresses two basic problems that arise. Although most science-fiction concepts for FTL travel deal with the first problem (the light-speed barrier), many simply ignore the second (which leads to unsolvable paradoxes). Part IV also examines various conceptual forms of FTL travel (each of which circumvents the “first problem”) and introduces special provisions for avoiding the “second problem.” Finally, because this FAQ was originally written for the rec.arts.startrek.tech Usenet newsgroup, I apply the FTL discussion to show how warp travel, as depicted in Trek, can allow FTL motion while avoiding both problems. As far as I can tell, this provides the best explanation for everything shown in the series. I hope you can learn something from reading this, or at least strengthen your understanding of what you already know. Your comments and criticisms are welcome, especially if they suggest improvements I can make in future revisions. If you ever notice missing or truncated sections in any of the available formats, feel free to let me know, and I can provide the material directly. 0.2 Edition Information This is edition 5.2 of the Relativity and FTL Travel FAQ. The main text has not significantly changed since version 5.1, though I did fix a few issues and made improvements here and there. This edition is published in three versions (or formats): HTML, plain text, and PDF. See Section 0.3: The Versions (below) to learn more about these versions. As usual, I cannot guarantee the FAQ doesn't contains mistakes here and there I have yet to catch. Therefore, as always, if you see any mistakes or if you think that any changes should be made, please let me know. Edition 5.2 was completed on December 9, 2025. Any later modifications involve smaller changes and/or corrections. Here is some information about previous editions: No detailed information was kept concerning changes in editions 1 through 3, but they were all single-part documents concerned mainly with giving the reader a quick introduction special relativity and explaining how FTL travel seemed impossible because of it. They also included only one "special provision" for getting around all the problems of relativity (that provision being the use of a special frame of reference). In edition 4.0b, the FAQ was split into five parts (an introduction and four parts to the FAQ itself). In addition to one part that introduced special relativity and another that discussed FTL travel, two completely new parts were added (one which looked further into special relativity and one which introduced general relativity). In this edition, the FAQ was also made available in an HTML version (though all diagrams and equations were still in ASCII). In edition 4.1b (completed September 8, 1995) I added another "special prevision" in the FTL section. With edition 5.0b1 of this FAQ (completed on July 11, 1997), in addition to a text version and an HTML version with only ASCII graphics, I also made it available in a graphics-rich HTML version and a LaTeX version! In 5.0b1, I also made changes in various chapters (expanding some material and moving some into new sections) to help improve explanations and readability. In general, the basic information included has not changed, but the FAQ was hopefully made even more understandable to its readers. Edition 5.1 (completed on September 6, 1999) added a couple of subsections to the discussion of relativistic energy and momentum, and a few other minor corrections were made over the previous edition. 0.3 The Versions As of edition 5.2, the FAQ is available in three formats. The HTML version includes cross-reference links and vector-based graphics for equations and figures. The FAQ is also provided in its original text-only format—similar to the version once posted to the old rec.arts.startrek.tech Usenet newsgroup. Like the HTML version, the text-only version is divided into an introduction and four parts, but it presents figures and equations using ASCII graphics. Finally, if you prefer to have the entire FAQ as a single document, you can download it as a PDF file. The PDF version is prepared and published using LaTeX. If you are interested in the LaTeX source material used to create it, feel free to contact me and I can send it to you. As a historical note, when I published edition 5.0b1, the FAQ was available in several different formats: a set of plain-text files with ASCII graphics; HTML pages that used ASCII graphics (to support users with limited internet speeds); HTML pages with GIF-based diagrams and equations; a LaTeX package; and a PostScript file (an older print-oriented format that served as a precursor to PDF). For those curious about LaTeX, it is a high-quality document preparation system that uses markup coding to produce professional scientific and technical documents and to handle complex mathematical expressions. You can read more at the LaTeX Project website (URL=https://www.latex-project.org/about/). I also want to give special thanks to Ricardo Aler Mur for his help in converting the original text into a LaTeX version. He provided an excellent foundation for the final LaTeX edition, and without his work I might never taken the time to do the conversion. ---------------------------------------------------------------------------- CONTENTS OF THE FAQ: Part I: Special Relativity Chapter 1: An Introduction to Special Relativity 1.1 Relativity Terminology 1.2 Reasoning for its Existence 1.3 Time Dilation and Length Contraction Effects 1.4 Introducing Gamma 1.5 Energy and Momentum Considerations 1.5.1 Rest Mass versus "Observed Mass" 1.5.2 The Energy and Momentum of a Photon (Where m = 0) 1.6 Experimental Support for the Theory Chapter 2: Space-Time Diagrams 2.1 What are Space-Time Diagrams? 2.2 Time as Another Dimension 2.3 Basic Information About the Diagrams we will Construct 2.4 Constructing One for a "Stationary" Observer 2.5 Constructing One for a "Moving" Observer 2.6 A Quick Comparison of the two Observers 2.7 Interchanging "Stationary" and "Moving" 2.8 "Future", "Past", and the Light Cone Part II: More on Special Relativity Chapter 3: Completing the Space-Time Diagram Discussion 3.1 Comparing Time for O and O' 3.2 Comparing Space for O and O' 3.3 Once Again: The Light Cone Chapter 4: Paradoxes and Solutions 4.1 The "Twin Paradox" 4.1.1 Viewing it with a Space-Time Diagram 4.1.2 Explaining the "First Part" 4.1.3 Explaining the "Second Part" 4.1.4 Some Additional Notes 4.2 The "Car and Barn Paradox" 4.2.1 Viewing it with a Space-Time Diagram 4.2.2 The explanation Part III: A Bit About General Relativity Chapter 5: Introduction to General Relativity 5.1 Reasoning for its Existence 5.2 The "New Inertial Frame" 5.3 The Global Break-Down of Special Relativity 5.4 Manifolds, Geodesics, Curvature, and Local Flatness 5.5 The Invariant Interval 5.6 A Bit About Tensors 5.7 The Metric Tensor and the Stress-Energy Tensor 5.8 Applying these Concepts to Gravity 5.8.1 The Basic Idea 5.8.2 Some Notes on the Physics and the Math 5.8.3 First Example: Back to SR 5.8.4 Second Example: Stars and Black Holes 5.9 Experimental Support for GR Part IV: Faster Than Light Travel--Concepts and Their "Problems" Chapter 6: Introduction to the FTL Discussion 6.1 A Few Notes On The Meaning of FTL Travel Chapter 7: The First Problem: The Light Speed Barrier 7.1 Effects as One Approaches the Speed of Light Chapter 8: The Second Problem: FTL, Causality, and Unsolvable Paradoxes 8.1 What is Meant Here by Causality and Unsolvable Paradoxes 8.2 How FTL Travel Implies Violation of Causality 8.3 How We Get Unsolvable Paradoxes Chapter 9: FTL Concepts with these Problems in Mind 9.1 Tachyons (Without Special Provisions) 9.2 Using a Special Field/Space/etc. (W/o Special Provisions) 9.3 "Folding" Space (Without Special Provisions) 9.4 Space-Time Manipulation (Without Special Provisions) 9.5 Special Provisions 9.5.1 Parallel Universes 9.5.2 Consistency Protection 9.5.3 "Producing" Restricted Space-Time Areas 9.5.4 A Special Frame of Reference for the purpose of FTL Travel Chapter 10: Some Comments on FTL Travel in Star Trek 10.1 Which Provision is Best for Explaining Warp Travel 10.2 Subspace as a Special Frame of Reference 10.3 The "Picture" this Gives Us of Warp Travel 10.4 Some Notes on Non-Warp FTL Travel and Time Travel in Trek 10.5 To sum up... Chapter 11: Conclusion