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From: ptb@ukc.UUCP (P.T.Breuer)
Newsgroups: net.physics
Subject: Re: Re: speed
Message-ID: <5258@ukc.UUCP>
Date: Mon, 24-Jun-85 19:07:11 EDT
Article-I.D.: ukc.5258
Posted: Mon Jun 24 19:07:11 1985
Date-Received: Sun, 23-Jun-85 13:49:11 EDT
References: <359@osiris.UUCP> <56@rtp47.UUCP> <28@ucbcad.UUCP>
Reply-To: ptb@ukc.UUCP (PUT YOUR NAME HERE)
Organization: Computing Laboratory, U of Kent at Canterbury, UK
Lines: 31

In article <28@ucbcad.UUCP> vallath@ucbcad.UUCP (Vallath Nandakumar) writes:
>> > I've heard the twin paradox ...
>> 
>> The paradox is that *each* twin
>> ages faster than the other (depending on your point of reference).
>>... 
>
>I have a followup question.  Excuse the imprecise language.
>
>If the universe is closed (I mean space is of the type where
>all straight lines meet), wouldn't the twins be able to meet
>without either of them having undergone acceleration?
>Who would then be older?
>Or does all this need the addtional math of general
>relativity?  Or isn't our universe closed anyway?  Or should I
>just go home and sleep it off?
>
>Vallath Nandakumar
>ucbvax!ucbesvax!vallath,  esvax.vallath@berkeley.arpa

   This had me worried for a while about a year ago. General relativity isn't
relevant since you can put the twins in a hypothetical universe which is flat
but closed (say a cylinder with cooordinates (x,y,z,t) identified with 
(x+1,y,z,t)). If one twin sits at (0,0,0,0) and the other goes past him with
speed v in the x-direction, they will certainly meet again without either having
accelerated. 
   In fact there's no paradox. If you work out the elapsed times for each twin
(which is very easy once you refuse to be worried by the rather weird-looking
coordinates the second twin uses if she thinks of herself as at rest), you'll
see they're the same.