From: Xela@yabbs
To: JasonLee@yabbs
Subject: warp speed dude...
Date: Mon Mar  7 22:02:28 1994

Because of experiments in the late 1800's, it was found that the speed of 
light is independent of the velocity of the instrument measuring it.  So 
if a spaceship travels away from the sun at 100,000 mps (miles per second) 
and measures the speed of light...the result would be the familiar old 
value of 186,000 mps and *not* 86,000 mps.  So Einstein came up with a way 
of relating changing coordinate systems in "space-time."  It's known today 
as his special theory of relativity.

So I'll start off with some definitions are work from there:
1) We have two nonaccelerating coordinate systems S and S' in three-space 
(R^3, or 3-D).  Because there is no acceleration, S' moves at a constant 
velocity relative to S.

2)The corresponding axes of S and S' (x,x',y,y',z, and z') are parallel.  
The origin of S' moves in the positive direction along the x-axis of S, at 
a constant velocity v > 0 relative to S.

3)Two clocks C and C' are placed in space.  C is placed stationary 
relative to S, and C' placed stationary relative to S'.  The time unit is 
in seconds.  At the point where the origins of S and S' are the same, the 
clocks both read zero.

4)The unit of length is the light second (the distance light travels in 
one second).  So the speed of light (in respect to these units) is one 
light second per second.

Because I'll need to use some matrix stuff, a column vector will be 
written as [x1,x2,...,xn]; each component separated by a comma.