From: aguirre@wigner.physics.upenn.edu (Anthony Aguirre)
Newsgroups: sci.physics
Subject: Re: Twins Paradox Resolved
Date: 22 Jul 92 13:49:06 GMT

In article <BrrztE.J4u@well.sf.ca.us>, metares@well.sf.ca.us (Tom Van Flandern) writes:
|> 
|>      After 25 messages in three days on the Twins Paradox, the silence over
|> the past few days has been deafening.  In the earlier example, there was no
|> mathematical paradox, but there was a logical paradox.  To review:
|> 
|>      Consider an inertial frame containing the Earth and Alpha Centauri (AC),
|> four light years apart and having clocks synchronized within their own frame.
|> And consider another inertial frame containing another two planets, T1 and
|> T2, also four light years apart and synchronized within their own frame.  Let
|> the two frames have a relative velocity of 99% of the speed of light.  [This
|> implies a time dilation and distance contraction of a factor of about seven.]
|> 
|>      Assume that one day T1 and the Earth encounter one another.  Babies are
|> born simultaneously on both planets as they pass, with T1 headed in the
|> direction of AC and T2 still headed toward Earth.
|> 
|>      Eventually, T1 passes close by AC, and they compare notes.  How old will
|> the T1 child be when this happens?
|> 
|>      How old will the Earth child be when Earth passes T2?
|> 
|>      A) 4 years old
|>      B) 7 months old
|>      C) other (explain)
|> 
|>      The significance of this version is its perfect symmetry, and the total
|> absence of accelerations, turn-arounds, or frame changes, either during the
|> journey or at any time in the past or future.
|> 
|>      Now here is the resolution:
|> 
|>      There are four events:
|>      T1 meets E1: both are age zero.
|>      T1 meets E2: T1 age 7 months, E2 age 4 years.

now wait a minute:  Here you have introduced an asymmetry already.  I'll explain:
hypothesize two more children being born, one on AC (or e2) and one on t2.  The
one on AC is born at the same time as on E1 (this synchronization is possible.)
and likewise t2 and t1 are born simultaeneously in their frame.  Now, how old is
AC when t1 passes by?  And how old is t2 then e1 passes by?  

|>      T2 meets E1: T2 age 4 years, E1 age 7 months.
|>      T2 meets E2: both are age 4 years plus 7 months.
|> 
|>      For those unfamiliar with SR, SR implies that events synchronized in one
|> frame will not be synchronized (= simultaneous) in a relatively moving frame.
|> 

exactly.  What we basically have here is 4 clocks, two of which are synchronized
in each reference frame.  This is akin to the classic example in SR of two lines
of synchronized clocks moving at high speed alongside each other-each will claim
the other is running slower.  But there is no meaning in saying that "more time
has passed" in one frame unless one set of clocks stops and turns around so that
is is now in the same frame as the other.  Then, the clocks will show different
times, and it will mean something.
	This is probably fairly equivalent to what you are saying, I guess I
just don't understand what's so paradoxial about it.

|>      So the situation for the twins IS perfectly symmetric for both frames,
|> as the math requires.  Understanding this is the principal key to resolving
|> the logical paradox, and for understanding SR.  The key reason that the twins
|> can be perfectly symmetric, yet show different aging, is this:  In any frame,
|> the apparent rate of progress of time (and distance) for a fast-moving
|> traveler is quite different when the traveler is moving away, from what it is
|> for an approaching traveler.  Naturally, neither the E-frame nor the T-frame
|> runs systematically slower or faster than the other, since they are
|> equivalent.
|> 
|>      If we can agree on the resolution of the paradox, then perhaps we can go
|> on to discuss its significance.  This version of the paradox reveals one or
|> two loopholes in the usual understanding of special relativity with
|> interesting implications for physics.  -|Tom|-

	Could you explain these in more detail?  I don't quite understand what
the difference in approaching vs. receding travelers has to do with it.  I still
claim that there really is no asymmetry.  

|> 
|> -- 
|> Tom Van Flandern / Washington, DC / metares@well.sf.ca.us
|> Meta Research was founded to foster research into ideas not otherwise
|> supported because they conflict with mainstream theories in Astronomy.