Newsgroups: sci.physics
From: hoey@ai.etl.army.mil (Dan Hoey)
Date: 7 Aug 89 22:13:35 GMT
Subject: Special relativity and FTL and Time travel

m...@v7fs1.UUCP (Mike Van Pelt) writes,
``I keep hearing [that FTL travel (or communication) implies travel
(or communication) into the past]....  However, I'm not convinced.
Maybe I'm missing some vital detail, but the explanations seem to boil
down to [a variation on the paradox of the twins]....''

No, the problem is not due to, or even particularly related to, the
twins' paradox.  The amount of time traveled into the past is not
equal to the time lost by the younger twin, or anything like that.
The problem is that by special relativity, travel/communication that
is FTL in one inertial frame must be into the past in some other
frame.  By use of such travel/communication in two frames, we can
construct travel/communication that is into the past without moving
an inconvenient distance away.  For an explicit construction of
this, I recommend any reasonable published treatment of Lorentz
transformations.  If you are allergic to published works, these things
appear on the network with surprising regularity (e.g., Eric Smith,
<2...@uwovax.uwo.ca>).

He continues, ``By the way, for this one you need general relativity,
as one of the reference frames is under acceleration....''  The idea
that special relativity is needed for the twins' paradox or the FTL =>
into the past construction has also appeared on the net repeatedly,
but the idea is false.

The twins' paradox appears in a version that involves acceleration
only at the beginning and end of long inertial trips.  If we postulate
that the acceleration ages the twin (so as to vitiate the difference
in the rate of aging) we need only increase the length of the trip
enough to overcome the aging due to acceleration.  I assume for this
argument that the amount of aging due to acceleration is independent
of the place and time that the acceleration takes place.

When we convert FTL travel/communication into travel/communication
into the past we must transfer the body/information between points in
the same reference frame, i.e. not accelerated with respect to each
other.  But if we have an FTL effect that arrives in an accelerated
frame, and we postulate that it takes time to decelerate/transmit into
the reference frame, then the time can be made up by making the trip
longer, so as to go further into the past, to make up for the time
lost in changing frames.  I assume that the (subluminal) velocity at
the end of the trip is independent of the length of the trip, and the
time lost in changing frames is independent of the time and place at
which the change is performed.

As for the request from mak...@tukki.jyu.fi (Otto J. Makela) that the
effect be explained ``in simple but still GR-type maths,'' the general
theory of relativity, while perhaps not worked out completely in
all of its details, presupposes the the special theory: SR is GR
restricted to inertial frames.  So these SR arguments are GR, too.

Dan Hoey