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From: Jason W. Hinson <[e-mail]>
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Subject: Relativity and FTL Travel--Introduction
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=============================================================================
                          Relativity and FTL Travel

               by Jason W. Hinson ([e-mail])
-----------------------------------------------------------------------------

                      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/




     ------------------------------------------------------------------
          Copyright(C) 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(R) , Star Trek: The Next Generation(R) , and Star
     Trek: Deep Space Nine(R) are trademarks of Paramount Pictures
     registered in the United States Patent and Trademark Office. Star
     Trek: Voyager(TM) is a trademark 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 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
(URL=http://molscat.giss.nasa.gov/LaTeX/).
     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
<[e-mail]> 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:


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