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On Mon, 16 Jun 2003, Pentcho Valev wrote:http://www.courses.fas.harvard.edu/~phys16/handouts/textbook/ch10.pdf
On pp. 43 and 57 in
a modified twin paradox is analysed. The conclusion is that, even
in the absence of accelerations, the moving clock is slower.
"the moving clock is slower" is a very imprecise and misleading
notion, one which implies there is this _thing_, called time,
which itself speeds up or slows down. This does not reflect the
concept of time in the standard theory of relativity. In that
theory clocks, in their own reference frame, continue to tick at
their usual rate, as measured by an observer at rest with the
clock. However, observers in relative motion to that clock will,
in general, measure the tick rate of the clock to be different.
This is the notion of time dilation in special relativity, and
while it accounts for _observational_ differences between frames
in relative motion, it does not account for _physical_
differences between synchonized clocks which are reunited after
separation. Any differences in accumulated time between these
reunited clocks is a consequence of their differing paths through
spacetime. Proper time is the time accumulated by a clock --
commonly referred to as wristwatch time -- along its worldline,
and differing paths through spacetime lead to differing
accumulations of proper time.
So there is an important standard theory distinction between
relativistic effects which are considered a matter of
perspective, and effects which are physical differences. Time
dilation and length contraction are in the category of the
former, whereas proper time differences are of the latter.
Proper time refers to the accumulation of time in the observer's
own reference frame, whereas time dilation and length contraction
are a relationship established as a consequence of observation or
measurement amongst different frames. Not understanding this
distinction is quite often the basis for confusion about the
various "twin" scenarios in particular, and the the theory in
general.
In fact, the trip involves an obscure episode. Clarifying it
leads to the opposite conclusion:
Not really. These scenarios are always very clear, precise, and
consistent, unless one obscures the issues with imprecise
terminology and/or misunderstandings.
A.The obscure episode in this story is when "C sets his clock to
read the same as B's". It is not clear how this could happen
without wasting time.
In principle, when they are together at the same event, they
exchange signals at that event. But, regardless, they can
initiate a continual process of exchanging signals prior to the
event.
So let us simplify the problem by assuming that, as B meets C, it
just sets C's clock (which has read zero so far) in motion.
With this simplification, let C's clock read t_C as C meets
The time t_C characterizes the movement of C between B and A. The
respective time on A's clock is T_A / 2. Since no frame is more
fundamental than the other, the conclusion is
t_C = T_A / 2
You have confused the issue. First you mistakenly think that t_C
is somehow related to B, when in fact it is related to how C
moves with respect to A. Second, t_C = T_C/2, not T_A/2.