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Einstein said that the synchronization of two clocks is dependant on the velocity of the observer. But I feel a conceptual contradiction can be made:

There are two observers A and B. Observer 'A' faces direction X, and will be labeled "stationary." Another observer B faces direction X and is travelling rapidly in that direction as well on a collision course with 'A'. Both observers are holding two clocks; One in each hand, with hands held perpendicular to direction X. Both observers hit a "synchronization" button on the clocks before colliding.

My expectation in this case is that when the moving observer B halts to greet observer A - both observers will agree the B-pair clocks are synchronized and the A-pair clocks are synchronized (though all four clocks are not necessarily synchronized with eachother, and is not at issue in this question).

Bottom line: what was considered "synchronicity" by the speedy individual is accepted by the stationary individual. This seems to contradict special relativity.

Now if my scenario were modified slightly, then I believe special relativity would apply. If observer A were to hold the A-pair clocks with one held out before herself and the other held out behind herself (instead of the original left and right perpendicular angles), then finally I would expect there to be disagreement between the two observers when they stop to meet eachother.

All this suggests that position is an unaccounted for primary component of relativity, but from what little I know of SR, it doesn't hardly factor in at all. Can someone explain what I'm missing?

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I don't think you're missing anything. If the two clocks are not separated in the dimension of the velocity of the systems (say this is the x dimension), then they are synchronized with respect to both systems. Try thinking about light clocks held this way. In both systems, light takes the same time to go from B to his left-hand clock back to B as it would for light to go from B to the right-hand clock and back to B. Thus, the clocks are synchronized in both systems. Summary: This does not contradict the two axioms of special relativity.

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I'm not sure but i think you miss something. Special relativity applies only on inertial frames of refernce, so when the two observers are moving relatively to each other with an unchanging velocity, special relativity can be used to determine if the clocks are synchroonized or not. In your example observer B stops moving according to A so his frame of reference becomes non-inertial during his deceleration and therefore during this time special relativity no longer applies (general relativity must be used). As a result this does not contradict special relativity.

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