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From: throopw@rtp47.UUCP (Wayne Throop)
Newsgroups: net.physics
Subject: Re: speed
Message-ID: <56@rtp47.UUCP>
Date: Sat, 1-Jun-85 08:05:26 EDT
Article-I.D.: rtp47.56
Posted: Sat Jun  1 08:05:26 1985
Date-Received: Thu, 6-Jun-85 12:29:57 EDT
References: <359@osiris.UUCP>
Organization: Data General, RTP, NC
Lines: 55

> I've heard the twin paradox, and until recently I thought I had it
> straight.  I thought of something recently, though.  When one twin
> takes off, leaving the other here, why does the one in space age
> more slowly?  Why can't you use a reference frame travelling with
> him and say that the earth is travelling at a great velocity?  Am
> I missing something?  (Obviously I am.)
>
> 				Rob St. Amant

You may have have heard the twin paradox before, but apparently you just
realized why it is a paradox.  After all, if one twin simply ages faster
than the other, where is the paradox?  The paradox is that *each* twin
ages faster than the other (depending on your point of reference).

To be more specific, imagine two folks of the same age, each traveling
at some large fraction of C with respect to the other.  Each will find
that the other fellow seems to be aging slower.  One way to resolve the
paradox is to note that, unless one or the other fellow accelerates,
they will never meet again, and hence the paradox can never be realized.
On the other hand, if they *do* accelerate, that takes it out of the
realm of special relativity, and *general* relativity accounts for the
situation.  (I have heard this hand-wave from several science
popularizers, including either Arthur Clarke or Issac Asimov, I can't
remember which).

As I understand it, the situation *does* key on the acceleration, but
the resolution of the paradox doesn't require general relativity.  The
key to the thing is what is considered "simultaneous" by each person in
the situation.  Let's tag the people here left-traveling and
right-traveling (where "traveling" is simply in relation to the other
person). The set of events in space-time considered "simultaneous" by
the left-traveling person is *not* the same set of points considered
"simultaneous" by the right-traveling person.

For example, the left-traveling person considers the event "I've aged 1
year", simultaneous with event "the right-traveler has aged
half-a-year".  Also, the right-traveling person considers the event
"I've aged 1 year", simultaneous with the event "the left-traveler has
aged half-a-year".  However, these two "facts" don't conflict, since
they are derived from different reference frames.

Now then, assume that the right-traveler accelerates after having
traveled 1 year, and aquires the same velocity as the left-traveler.
This acceleration changes the set of events that the right-traveler
considers simultaneous.  The right-traveler now considers the event
"I've aged one year" to be simultaneous with "the left-traveler has aged
two years".  One way to look at it is that the right-traveler sees the
left traveler age one-and-a-half years during the acceleration, and the
paradox evaporates in a puff of exhaust gasses. :-)

I hope this clarifies things rather than making them worse.  It is a
little easier to understand with diagrams, but I can't get my space-time
charts to look good using simple character graphics.  Sigh.
-- 
Wayne Throop at Data General, RTP, NC
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