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From: @S1-A.ARPA,@MIT-MC.ARPA:Ghenis.pasa@Xerox.ARPA
Newsgroups: net.space
Subject: Re: Closed Universe and the Twin Paradox
Message-ID: <2110@mordor.UUCP>
Date: Thu, 6-Jun-85 15:14:56 EDT
Article-I.D.: mordor.2110
Posted: Thu Jun  6 15:14:56 1985
Date-Received: Sun, 9-Jun-85 01:44:24 EDT
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From: Ghenis.pasa@Xerox.ARPA

>Wrongo.  How did the twin leave the earth?  How does he return?  If
>two world-lines become separated, then one or both had to accelerate;
hence
>one or both spend some time in non-inertial frames.  Hence there roles
are
>asymmetric.
>
Sigh... I knew I should have been more explicit about the underlying
assumptions. Here they are:

1) The thought experiment starts with the travelling twin already
possesing an initial velocity v and passing by the stationary twin.
Their clocks are synchronized at that moment. The rest of the thought
experiment will deal with their delta times.

2) What you are saying is absolutely true in FLAT space-time. This is
the domain of special relativity. General relativity goes beyond that,
dealing also with CURVED space-time. Without going into details, just
think about the fact that free-falling into a gravitational potential
(ie.  an astronaut floating inside an orbiting space shuttle) is
indistinguishable from inertial travel in space (ie. the same astronaut
floating inside an interstellar probe with velocity v. If there were no
windows he would be unable to tell whether he was still on course or had
been trapped into the orbit of some neutron star)

The buzzwords CLOSED UNIVERSE (*) refer to the theory that overall,
time-space in our universe is curved enough that any trajectory will
eventually close. (The curvature coming from the gravitational field of
the aggregate mass of everything in the universe), so that the light
from a source will return to its point of origin some day. Even if the
universe isn't flat it need not be closed, since it can be "hyperbolic"
(I'm being a bit loose, but try thinking of the planets' elliptic orbits
vs. a hyperbolic orbit that approaches once and leaves, never to return
because it has more than the escape velocity for the local gravitational
field)

(*) Closed universe also refers to whether, within the Big Bang
framework, the expansion of the universe will one day stop and
contraction will start, giving an eventual "Big Crash", the cycle to be
repeated eternally. An open universe would instead expand forever,
slowing down but never stopping. If we can determine the total mass of
the Universe, knowing the expansion rate we would have the answer to
this since it is essentially an escape velocity problem.

This certainly seems to be related to the original problem: would a
closed universe in the Big Bang sense imply that the curvature of the
universe's space-time is closed?