A clock on the ground is at rest but a train is moving to and fro so that the clock on the ground formally commutes between the front and the back of the train. The speed of the train is constant except for the turn-arounds when clocks on the train suffer sharp acceleration. Will the clock on the ground run slower or faster than clocks on the the moving train? What does relativity say?

First of all it should be noted that the acceleration suffered by moving clocks cannot be responsible for time dilation effects:

http://www.damtp.cam.ac.uk/research/...tivity2010.pdf
Gary W. Gibbons FRS: "In other words, by simply staying at home Jack has aged relative to Jill. There is no paradox because the lives of the twins are not strictly symmetrical. This might lead one to suspect that the accelerations suffered by Jill might be responsible for the effect. However this is simply not plausible because using identical accelerating phases of her trip, she could have travelled twice as far. This would give twice the amount of time gained."

It should also be noted that a clock at the front of the moving train coincides with the travelling twin's clock in the classical twin paradox scenario. Accordingly, relativity predicts that the clock at rest on the ground runs FASTER than the clock at the front of the train.

On the other hand, relativity predicts that, ALL ALONG, observers on the moving train measure the clock at rest on the ground to run SLOWER than clocks on the train.

This is called REDUCTIO AD ABSURDUM. The underlying postulate, the principle of constancy of the speed of light, is false and should be rejected.

Pentcho Valev