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There is a lot of discussion on the subject of Mach's principle, and whether it has any place in the theory of relativity. But it seems to me that one could argue that Mach's principle is at the heart of the equivalence principle, in both its forms (weak and strong). The argument would go like this: 1) It is clear that gravitational forces are exerted between bodies of gravitational mass. 2) Thus, The large scale distribution of mass determines the total gravitational force on a body (assuming a perfectly uniform density sphere, for example, around our test particle, would result in zero total force, but if we introduce inhomogeneities that break the spherical symmetry the net force won't be zero anymore). 3) If we suppose that there is no way to locally differentiate between inertial and gravitational motion, it is evident that what the test particle perceives as inertial motion is in fact influenced by the large-scale distribution of matter. In fact, given that the scale of the mass distribution involved is so vast, the fields will be almost perfectly homogeneous, making the aforementioned locality prerequisite almost trivial (meaning it will be very difficult to measure any divergence or tidal forces). 4) Changes in the distribution of matter, as they connect causally with the test particle, will produce changes in its inertial motion, that could be measured by a distant observer.

I think the crux of the argument is that what differentiates gravity, is the divergence, the deviation of geodesics implied by curvature. But a nearly uniform gravitational field, resulting from a large distribution of matter, couldn't in principle be detected.

My understanding of the equivalence principle could certainly do with some improvement, and I hope we could gain some insight from this question.

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