Weak equivalence principle
The statement that gravitational mass equals inertial mass for any test particle, regardless of composition — equivalently, that all bodies in vacuum fall with identical acceleration. Galileo's Pisa-tower observation, Eötvös's torsion-balance precision result, and the MICROSCOPE 2017 satellite null result confirm it to ≲ 10⁻¹⁵.
Definition
The weak equivalence principle (WEP) asserts that gravitational mass and inertial mass are the same physical quantity for any test particle. Equivalently: in a vacuum, all bodies fall with identical acceleration regardless of their composition, internal structure, or chemical identity. The classical statement is Galileo's: drop a lead ball and a wooden ball from the Leaning Tower of Pisa, and they reach the ground simultaneously. The relativistic recasting is that a body's response to a gravitational field is determined entirely by spacetime geometry, not by any body-specific charge or coupling — the gravitational analogue of charge-to-mass ratios is universal.
WEP is the cleanest experimental signature of the equivalence principle and the most directly testable. Eötvös's torsion-balance experiments (1889, posthumously refined 1922) constrained any composition-dependent deviation to ≲ 10⁻⁹; the Adelberger group's "Eöt-Wash" experiments at the University of Washington pushed the bound to ~10⁻¹³ in the 1990s; the MICROSCOPE satellite mission (2017–2019) measured platinum and titanium test masses in free-fall around Earth and reported a null result at the ≲ 10⁻¹⁵ level. Lunar laser ranging tests the related Nordtvedt parameter — a combined WEP+SEP constraint — to comparable precision. Any nonzero violation would falsify the geometric interpretation of gravity and force a return to gravity-as-force in some sector. None has ever been observed.