Relativity and FTL Travel

by Jason W. Hinson (hinson@physicsguy.com)

Part 0: Introduction to the FAQ

Edition: 5.1
Last Modified: April 8, 2003
URL: http://www.physicsguy.com/ftl/
FTP (text version): ftp://ftp.cc.umanitoba.ca/startrek/relativity/

Other languages (tanslation provided by a third party):
This introduction has been translated into UKrainian for the interested reader.

Copyright©1995, Jason W. Hinson. This document, including all of its parts, is not in the public domain. Permission to distribute this document in its entirety (unedited and including this copyright notice) is granted, provided no fees are charged for the distribution beyond charges for downloading and/or connection time from a commercial information service. Permission to distribute a partial version of this document containing only this introduction along with parts I and IV is also granted under the same restrictions. Publication of any part of this document in a magazine or journal (in any media format) must be approved by the author.

Star Trek® , Star Trek: The Next Generation® , and Star Trek: Deep Space Nine® are trademarks of Paramount Pictures registered in the United States Patent and Trademark Office. Star Trek: Voyager^(TM) is a trademark of Paramount Pictures.

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 straight-forward, simple terms) the relationship between relativity and faster than light (FTL) travel. Part I introduces the information about special relativity which one needs to understand the discussion of FTL travel. One of its sections involves an introduction to space-time diagrams, which are used to make some significant points in the FTL travel discussion. Therefore, if you are not familiar with these diagrams, then this will be a very important section for you to read.

Parts II and III are what I call "optional reading" parts. If you do not want to read them, you can still understand the FTL travel discussion. Part II gives more information about special relativity and explains two "solvable paradoxes" which are associated with the theory, while Part III introduces and explores some of the major concepts in general relativity, and does so at considerable length.

Part IV is the part which discusses the question of FTL travel. There are two basic problems which are discussed, and while most ideas for FTL travel in science fiction address the first problem (the light speed barrier), many simply ignore the second (producing unsolvable paradoxes). Part IV also discusses various conceptual forms of FTL travel (each of which get around the "first problem"), and it introduces special provisions for getting around the "second problem". Finally, because this FAQ is meant for the rec.arts.startrek.tech newsgroup, I will apply the FTL discussion to explain how warp (as it is depicted in Trek) can allow FTL travel while getting around both of the problems mentioned above. As far as I can tell, it presents the best way of explaining everything the series has shown us.

I should also note that various diagrams are used throughout this FAQ, and so the HTML versions provide links to the diagrams when they are mentioned throughout the FAQ for convenience. However, if you are reading the LaTeX or text versions, it may be helpful for you to make a hard copy of the parts you are reading so that you can view the diagrams easily as you read various sections of the FAQ.

I hope you can learn a little something from reading this, or at least strengthen your understanding of that which you already know. Your comments and criticisms are welcome, especially if they indicate improvements that I can make for future posts. If any or all parts of this post do not show up at your site, or if any or all are cut short, let me know and I can e-mail you the parts you want.

0.2 Edition Information

This is edition 5.1 of this FAQ. A couple of subsections have been added to the discussion of relativistic energy and momentum, and a few other minor corrections were made over the previous edition.

As usual, (although I'm no longer calling this edition a "beta" edition) I am sure it still 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 5.1 was completed on September 6, 1999. 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 which introduced special relativity and another part which 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.

As of 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, it was also made available in a gif-graphics-rich HTML version and a LaTeX version! (See Section 0.3: The Versions to learn more about these versions.) 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.

0.3 The Versions

As of edition 5.0b1, this FAQ was made available in the following versions: A plain text version allows for reading the FAQ on a simple ASCII screen, or the reader can print out the FAQ quite easily. All the graphics and equations are in simple ASCII. This is the version of the FAQ which is a regular posting on the rec.arts.startrek.tech newsgroup. It is also available to download via FTP from the site listed at the top of each part to this FAQ.

A non-gif HTML version of the FAQ is also available that includes links used throughout the FAQ which make studying the FAQ easier. All the graphics and equations in this version are in ASCII, which allows for faster download, but which may not be as readable as the gif graphics included in other versions. This version can be accessed from the URL listed at the top of each part of this FAQ.

A new HTML version including gif graphics for diagrams and equations is now available as well. While the parts of this version take longer to download, you will likely find the graphics easier to understand and more informative. This version is also accessible from the URL listed at the top of each FAQ part.

Finally, the FAQ has been converted to a LaTeX version as well. LaTeX is a package used with TeX which in turn is a high-quality typesetting program used to produce various scientific and technical documents. Documents written in LaTeX use a type of scripting language which includes various commands to tell the LaTeX program how to typeset the document. The final product of a LaTeX work is often a postscript file which contains the typeset document and is ready for printing. For more information on LaTeX, I would probably recommend looking at the "Hypertext Help with LaTeX" page.

If you are interested, the LaTeX version can be downloaded as a file ready for processing, or you can download the final postscript file which is ready for printing. Either of these files can be downloaded from the URL listed at the top of each part of this FAQ.

I also want to give a special note of thanks to Ricardo Aler Mur <aler@inf.uc3m.es> for his help in converting the original text into a LaTeX version. He provided a great starting point for the final LaTeX version, and without him I may have never gone through all the trouble.

Well, I hope the reader will find at least one of these formats to his or her liking.

Contents of the FAQ:

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

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

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

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

Before You Go...

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