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University of London Professor Herbert Dingle showed why special relativity will always conflict with logic, no matter when we first learn it. According to the theory, if two observers are equipped with clocks, and one moves in relation to the other, the moving clock runs slower than the non-moving clock. But the relativity principle itself (an integral part of the theory) makes the claim that if one thing is moving in a straight line in relation to another, either one is entitled to be regarded as moving. It follows that if there are two clocks, A and B, and one of them is moved, clock A runs slower than B, and clock B runs slower than A. Which is absurd.
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This is not even original, it's simply the twin paradox.
The moving clock will run slower.
The key to the problem is that the moving clock needs to be returned to it's original position in space (not space time) in order to compare the times elapsed on each clock. This destroys the symmetry aspect of the paradox.
The stationary clock's world line "moves" along a straight line in space time (along the t-axis), the moving clock moves along an oblique worldline (including the t and x axis) but inside the light cone of space time.
Here is the full explanation involving Minkowski space time diagrams.
http://en.wikipedia.org/wiki/Twin_paradox
Regards
Steven