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From: js2j@mhuxt.UUCP (sonntag)
Newsgroups: net.physics
Subject: Re: FTL and time-travel -- exercise for the reader
Message-ID: <1013@mhuxt.UUCP>
Date: Thu, 18-Jul-85 09:41:41 EDT
Article-I.D.: mhuxt.1013
Posted: Thu Jul 18 09:41:41 1985
Date-Received: Sat, 20-Jul-85 02:02:23 EDT
References: <375@sri-arpa.ARPA> <851@oddjob.UUCP> <860@oddjob.UUCP>
Organization: AT&T Bell Laboratories, Murray Hill
Lines: 43

> In article <851@oddjob.UUCP> I give an example of how faster
> than light signalling can lead to causality violations.  As
> an exercise for the readers of this newsgroup who think they
> understand special relativity, I pose the following question.
> I provide the answer at the end of this article.

    Can those of us who *don't* think they understand special relativity
play too?  Especially since we're the ones who don't understand how
FTL signalling can cause causality violations?
> 
> Suppose that at time t=0 person A emits a signal with velocity
> u > c in A's own frame of reference.  This signal is received
> by B who at that instant is at a distance d from A (as measured
> by A) and is moving away from A at speed v, with c^2/u < v < c.
> B immediately replies by sending back a signal at speed u in
> B's own reference frame.
> 
> At what time does the reply signal from B reach A?
> 
    Well, the answer I got (which evidently was wrong) was that the time
for the first signal to get to B would be t1=d/(u-v), and that the time
for the second signal to get back to A would be t2=du/(u-v)^2.  Both of
these quantities are positive for u<v.

> Answer:  In A's frame, the reply arrives at time
> 
> 	t = d/u - d*(uv/c^2 - 1)/(u-v).
> 
> Under the assumption c^2/u < v < c, this is negative.

    I can see that.  What I can't see is how you went about deriving this.
I would appreciate seeing that, since *if I could be convinced about the
correctness of the above formula*, I would then understand how FTL signalling
violates causality

> Matt		University	crawford@anl-mcs.arpa
> Crawford	of Chicago	ihnp4!oddjob!matt
-- 
Jeff Sonntag
ihnp4!mhuxt!js2j
   "Well I've been burned before, and I know the score,
    so you won't hear me complain.
    Are you willing to risk it all, or is your love in vain?"-Dylan