Equivalence principle

The equivalence principle is the foundational axiom from which Einstein constructed general relativity. In its sharpest form: no local experiment performed inside a sufficiently small, freely falling laboratory can detect the presence of a gravitational field. A clock, a spring, a beam of light, a chemical reaction, a nuclear decay — all behave inside the falling lab exactly as they would in inertial flat-space conditions. Equivalently, the laws of physics in a freely falling frame are the laws of special relativity, with no gravitational corrections. This is what allows gravity to be reinterpreted as the geometry of spacetime: if free-fall trajectories in a gravitational field are locally indistinguishable from inertial trajectories in flat space, then "freely falling" is the relativistic generalisation of "inertial," and gravity is not a force but a property of the spacetime manifold itself.

The principle comes in three increasingly strong forms. The weak equivalence principle (WEP) demands only that all test particles fall identically — m_grav = m_inertial regardless of composition. The *Einstein equivalence principle* (EEP) adds local Lorentz invariance (no preferred frames inside the falling lab) and local position invariance (no preferred locations); EEP is the form that implies gravity is geometric. The strong equivalence principle (SEP) extends EEP to self-gravitating bodies, demanding that even objects whose own gravitational binding energy is significant (planets, stars) free-fall identically. WEP is constrained to ≲ 10⁻¹⁵ by MICROSCOPE 2017+; EEP and SEP are tested by precision-clock experiments and lunar laser ranging, with no deviation observed at any scale.