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[–] ghotioninabarrel ago 

This says nothing about time though, only the frequency at which cesium atoms vibrate in different scenarios

The thing is that the scenarios aren't actually different.

The earth orbits the sun, the sun orbits the galactic core, the galaxy itself is moving through space. In every reference frame other than the Earth's, the Earth's velocity is not constant, and varies by far more than the speed of an aircraft. So if the first postulate of special relativity (laws of physics are the same in all inertial frames) is false in this way, then the Earth is somehow a privileged reference frame.