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The Einstein equivalence principle combines the weak equivalence principle with local Lorentz invariance and local position invariance of nongravitational experiments. In a sufficiently small freely falling laboratory, their results agree with special relativity independently of its location and velocity. The strong equivalence principle extends this claim to local gravitational experiments.

A torsion-balance comparison of the gravitational acceleration of bodies of different composition, testing equality of inertial and passive gravitational mass up to a universal proportionality factor. A universal acceleration law independent of test-body mass and composition agrees with this weak equivalence principle test. It does not by itself establish the strong equivalence principle for self-gravitating bodies.

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 Tong's discussion of normal coordinates and local equivalence.