Imagine in empty space there are two objects in where one of them is moving to the other. How we can know which one is moving to the other? If there is an experiment that could tell us, would this experiment violate Einstein's equivalence principle?
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No, and this is the essence of relativity. In an static, empty spacetime, it is impossible to distinguish absolute motion. Only relative motion is a meaningfully measurable quantity; the relative velocity between the two observers matters, but deciding which (if either) of them is stationary is just a choice of coordinates with no underlying physical significance. This doesn't even require the equivalence principle, which is a statement about general relativity; only special relativity is involved here.
Of course, in the real universe, we are actually supplied with an implicit background against which absolute velocities can be measured. This exists because the universe is evolving in time; the expansion of the universe has a unique rest frame in which it is isotropic. We can measure the velocity of the solar system relative to the universe's natural rest frame by observing the dipolar Doppler shift of the cosmic microwave background (which fills the universe like black-body radiation of temperature 2.73 K in the rest frame of the expansion).
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Our universe is so constructed that there is absolutely no way to tell which object in space is standing still and which is coasting past it at a million miles an hour. you are right in stating that if an "absolute speedometer" existed, it would break the equivalence principle in special relativity (i.e., all inertial reference frames are equivalent for formulating equations of motion).
answered Dec 24, 2021 at 20:56