I think it has been proved repeatedly

Every time we find a red and blue shift accelerating for example, and Pound–Rebka–Snider experiments have found its equivalence on earth, and NIST do it so beautifully. But if you mean proved without ever more being able to be questioned? I don't know, but it fits what physics we see so far, as I know I better add. And the easiest test is in your imagination, have you found a reason to doubt that you actually weight more when accelerating on Earth. Just try to move your hand and see in a linear acceleration. I'm quite convinced that it is more than coincidence that uniform acceleration and mass (gravity) fit together so well, as a hand in a glove.

There are in fact two definitions of the equivalence principle. "The Strong Principle of Equivalence states all the laws of nature are the same in a uniform static gravitational field and the equivalent accelerated reference frame. The Weak Principle of Equivalence states all the laws of motion for freely falling particles are the same as in an unaccelerated reference frame." The first one we tested, each by itself, you might say, on accelerations and mass, the other (Wep) is still being polished to a high degree. "If a Gamma Ray Burster occurs at a distance of about 100 MPc (326 million light years), observation of both the time of arrival of the gamma rays (via a GRB monitoring satellite such as currently operating GRO) and detection of ultra-high energy neutrinos (e.g PeV energy) would allow a test of the Weak Equivalence principle to about the 10^{-11} level on cosmic scale in a direct test of the uniqueness of free fall. " Why the weak equivalence is so interesting for physicists today seem to go together with what ways QM and string theory can find to describe gravity from a 'quantum/string' perspective, as I gather it.

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To really get it you need to consider it from Pete's description of 'transforming ones coordinate system'. Because as you do it, in a 'free fall', gravity disappear, locally measured (no tidal influences allowed for this)

And that is as correct for your spaceship in a geodesic as it is on Earth. Tidal influences, as Earths frame dragging (due to rotating) have also been measured recently and found to exist. So relativity have a extremely elegant way of connecting gravitational mass, and uniform accelerations, to a distorted (bent) space. And it's been testable from the beginning on Earth, and later in space. Blue and red shifts are a natural effect from it, and we find them both from Earth and from the inside of that spaceship.

All together it connects into one he* of a description that no one have succeeded to get close to in a hundred years. But you ...must... accept observer dependencies if you try to 'advance' it to something else, or another scale. And so also find some way to translate macroscopic definitions to, for example quantum effects, or strings. And those descriptions better fit our macroscopic definitions too, to work. No wonder so many find Einstein frustrating, and want him to be wrong.