= Equivalence principle
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The equivalence principle states that gravity couples universally to energy-momentum and that a freely falling local frame removes uniform gravitational acceleration at a point. Tidal curvature remains measurable over a finite region.
Imagine releasing a ball inside a small falling elevator. Relative to the cabin it initially floats, because cabin and ball share the same <free fall>. The <weak equivalence principle> says this trajectory is independent of the <test particle>'s composition for identical initial conditions. The <Einstein equivalence principle> further identifies local nongravitational experiments with those of <special relativity>. It is a statement about experiments in a <local inertial frame>, not just equality of two masses.
The word local is essential. Coordinates can make the <metric tensor> equal to the <Minkowski metric> and its first <derivatives> vanish at one event. They generally cannot erase the <Riemann curvature tensor>, which involves second <derivatives>. Two separated balls can therefore approach or recede even inside the falling cabin. A sufficiently extended experiment detects these <tidal forces>; a long observation can accumulate them even when the cabin is small. The <equivalence principle> does not identify an entire planetary <gravitational field> with acceleration in flat <spacetime>. See https://www.damtp.cam.ac.uk/user/tong/gr/grhtml/S3.html[Tong's discussion of normal coordinates and local equivalence].
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