Is the equivalence principle exact or only approximate?

It holds exactly only in the limit of an infinitesimal region; over any extended region tidal effects from the variation of the real gravitational field appear, and these residual tidal forces are precisely what spacetime curvature describes.

What would it mean if a test found a violation?

A measured difference in the free-fall acceleration of different materials would imply a new composition-dependent interaction, falsifying the simplest form of general relativity and pointing toward extra fields such as those predicted by some unified or dark-sector theories.

Equivalence Principle

The equivalence principle states that the effects of gravity are locally identical to those of acceleration, so that all bodies fall with the same acceleration regardless of their composition.

Definition

The equivalence principle is the statement that gravitational and inertial mass are equal, so that in a sufficiently small freely falling frame gravity is locally undetectable and the laws of physics reduce to those of special relativity.

Scope

This topic covers the weak equivalence principle (universality of free fall), the Einstein equivalence principle that adds local Lorentz and position invariance, the strong equivalence principle extending to gravitating bodies, the thought experiments of falling elevators and accelerating rockets, and the precision tests that constrain any violation.

Core questions

Why do all objects fall with the same acceleration in a gravitational field?
In what sense is a freely falling laboratory indistinguishable from one in empty space?
How precisely has the equivalence principle been tested, and could it fail?

Key concepts

Inertial versus gravitational mass
Universality of free fall
Local Lorentz invariance
Local position invariance
Falling-elevator thought experiment
Eotvos-type tests

Key theories

Universality of free fall: Because gravitational and inertial mass are equal, all bodies fall with the same acceleration independent of mass or composition, the empirical fact that lets gravity be removed locally by going to a freely falling frame.
Einstein equivalence principle: In every local freely falling frame the non-gravitational laws of physics take their special-relativistic form, independent of the frame's velocity and location, which is the precise statement underlying the geometric description of gravity.

Clinical relevance

The equivalence principle is tested ever more precisely because any violation would signal new physics beyond general relativity; torsion-balance and lunar-laser-ranging experiments and the MICROSCOPE satellite constrain composition-dependent forces that could arise from extra fields or modified gravity.

History

The equality of gravitational and inertial mass was checked by Newton and refined by Eotvos around 1900 with torsion balances; Einstein elevated it to a fundamental principle in 1907, calling it his happiest thought, and modern Eot-Wash and space experiments confirm it to parts in 10^15.

Key figures

Albert Einstein
Lorand Eotvos
Robert Dicke

Seminal works

einstein1916
mtw1973

Frequently asked questions

Is the equivalence principle exact or only approximate?: It holds exactly only in the limit of an infinitesimal region; over any extended region tidal effects from the variation of the real gravitational field appear, and these residual tidal forces are precisely what spacetime curvature describes.
What would it mean if a test found a violation?: A measured difference in the free-fall acceleration of different materials would imply a new composition-dependent interaction, falsifying the simplest form of general relativity and pointing toward extra fields such as those predicted by some unified or dark-sector theories.