 Equivalence principle

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.

The Equivalence Principle is a fundamental concept in physics, particularly in the context of general relativity. It states that the effects of gravity are locally indistinguishable from those of acceleration. In other words, being in a gravitational field and being in an accelerating reference frame are equivalent in terms of the physical effects experienced by an observer.