🚀 go-pugleaf

     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.
     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.

     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|-

-- 
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.