This problem was originally embedded deep within another topic, and only one person attemped to answer it.
That attempt failed to address the issues. Circular reasoning was the approach used, which is not acceptable in Physics.
THE DILATION OF TIME CONUNDRUM
Two unmoving spaceships: A & B are the same distance from an observation point C.
The observer at point C sends a signal in both directions which will reach A & B after the same
amount of time. This signal thus starts both spaceships moving simultaneously.
Both spaceships accelerate identically and reach the same high velocity on their way to point C.
This velocity is close enough to the velocity of light so that they should apparently be
significantly affected by time dilation according to the principles of Special Relativity.
At the precise point that they pass by C, both spaceships send a signal which is the measurement
of the time on their own clocks to reach point C. These signals are marked AT & BT in the
Both spaceships are in a state of perfect symmetry from the perspective of C.
It is therefore clear regardless of the exact value of AT & BT, that these measurements of their
respective times (including any time dilation) will be equal to one another at the point of passing
C, from the observation point of C.
Thus AT = BT when perceived from the observer at C.
However the signals sent out are also both received by the other ship!
So A receives the signal BT, and B receives AT. There will be a very small delay in the time
that it takes the signals to pass between the ships. Seeing as the measurement is taken before the
signal is sent (as they both symmetrically pass by point C) this will not affect the actual
measurement, and thus the signals sent will be identical.
Both ships each will therefore be able to see that the times of their flight are such that BT = AT
when they arrive at point C.
We do not need to specify any values to see that despite a large effective velocity between A &
B, that there can be absolutely no effective time dilation between A & B!
This proves that time dilation due to relative velocity as specified in the Special Theory of
Relativity can only be a logical and empirical impossibility!!
(clipped from www.flight-light-and-spin.com)
Relativists need to step up and show how SR still can work.