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Mach's principle is a term (coined by Albert Einstein) for the proposition (considered by Ernst Mach) that the observed effects of rotation are due to all the surrounding mass of the universe. Relativity implies that if the rest of the universe weren't there, an object's velocity would be moot, and Mach's principle extends that notion to the object's rotation. The effects of rotation, i.e., centrifugal force, are due to acceleration, which in the view of general relativity (GR) is identical to gravitation, and Mach's principle is sometimes cited in terms of acceleration and/or gravity rather than rotation.
In fact, in Einstein's development of GR, he searched for an equation that converges with the then-existing laws of mechanics and is also consistent with Mach's principle, but the equation he found that satisfies the former is not consistent with the latter.