From: hinson@bohr.physics.purdue.edu (Jason W. Hinson)
Newsgroups: rec.arts.startrek.tech
Subject: Re: Einstein and Warp Speed
Date: 14 Dec 92 06:16:23 GMT
Organization: Purdue University Physics Department

chris@keris.demon.co.uk (Chris Croughton) writes:
>
>In article <1992Dec3.173632.2881@bvc.edu> meierdalepau@bvc.edu writes:
>
>>        I don't know if this thread has already been run, so here goes...
>>According to a friend of mine who studied Einstein's theory of relativity,
>>when a ship reaches the speed of light it becomes infinitely large and time
>>'stops' or 'freezes'.  When it excedes the speed of light, the object or
>>ship goes back in time.  I can understand somewhat how a subspace field
>>projected around a ship would keep it from becoming infinitely large while
>>at warp speed, but how would it keep the ship from going back in time?
>>Does the field distort the time/space continuum in order to prevent the
>>ship from going back in time?  If it doesn't, what is keeping the ship from
>>going back in time?
>
>You're referring to the Lorenz-Fitzgerald contraction equations, which
>state that the *observed* length of an object decreases, and its mass
>increases, as its speed relative to the observer nears te speed of
>light.  Taking the formula beyond lightspeed, it returns an imaginary
>number, which has no meaning that we know of in the 'real world'.
>Several people have interpreted that to mean that time travel could be
>involved...
>

Note that the fact that faster than light travel involves time travel
is not just an interpretation of geting an imaginary number when
substituting v > c into the Lorentz contraction equations.  Consider
the following:
 
An event (event A) occurs right here next to you.  Event B occurs many
light years away from here at the same time in your frame of reference
as event A. (Note here that the light from such an event won't get to
you for many years; however, the event does occure at the same time
in your frame of reference.)  Using Lorentz _Transformations_, one will
find that a frame of reference can exist right next to yours such that
in that frame, event B occured years ago.
 
Normally, this is OK, because in either frame of reference, light cannot
have gotten to this point yet.  So even though it is in one frame's past
and one frame's present, neither of the two observers can know about or
effect the event.
 
Now let's say that you allow for instantaneous travel.  Then in my frame
of reference, it is possible to send a signal to event B.  But in the other
frame of reference, since event B is in his past, I WILL be sending a
signal into his past.  If the other observer could get to me a couple of
seconds before event A occured, he could tell me that event B is going to
occure, and I could send a signal to effect an event that has already
occured in his frame of reference.  That is a violation of causality.
 
So FTL travel does cause time travel in some frame of reference. This we
know is true, because we know how to transform from one frame of reference
to another.  What IS specualtion is what would actually be seen if someone
exceeds the speed of light.  Would we see his/her clocks go backwards? would
he/she see the same of our clocks? would he/she be reverse contracted
so that it looks like he/she is going backwards? These are the questions
that we do not know (and may indeed have no meaning) because the equations
for Lorentz contraction become imaginary if v > c.
 
 
-Jay