Einstein equivalence principle

The Einstein equivalence principle (EEP) strengthens the weak equivalence principle by adding two further demands. *Local Lorentz invariance: inside a sufficiently small freely falling laboratory, the laws of physics are isotropic and independent of the lab's velocity — the inertial laws of special relativity hold exactly. Local position invariance*: those same laws are independent of where in spacetime the lab is located — no privileged points, no privileged time. Combined with WEP, these three constituents give the form of the equivalence principle Einstein needed for general relativity: gravity is locally indistinguishable from flat-space inertia, and all sufficiently small free-fall frames are physically equivalent.

EEP is the precise content of "gravity is geometry." If it holds, then any deviation between gravitational and inertial frames is a frame-effect, not a property-effect — something that can always be transformed away by going to free-fall. The geodesic equation that governs free-fall in GR is the natural consequence: bodies follow extremal world-lines through spacetime, and gravitational acceleration is a coordinate-system artefact. Tests of EEP separate the three constituents: WEP via Eötvös-class experiments; local Lorentz invariance via precision Lorentz tests (Hughes-Drever, atomic clocks); local position invariance via precision-clock comparison at different gravitational potentials (Gravity Probe A, optical-lattice clock networks). All current data are consistent with EEP at the most sensitive bounds achievable. Schiff's conjecture, never proven, holds that EEP is logically equivalent to a metric theory of gravity — making EEP the single principle from which GR's geometric content follows.