Eötvös parameter
The dimensionless ratio η = (m_g − m_i)/m_i quantifying the fractional difference between gravitational and inertial mass for a given material. Eötvös's torsion-balance experiments constrained η ≲ 10⁻⁹; modern Eöt-Wash and MICROSCOPE measurements push the bound to ≲ 10⁻¹⁵.
Definition
The Eötvös parameter η is the dimensionless figure of merit for tests of the weak equivalence principle. Defined as η = (m_grav − m_inertial)/m_inertial — or, more precisely, as the differential acceleration between two test bodies of different composition divided by the local gravitational acceleration g — it parametrises any composition-dependent violation of WEP. A nonzero η in any direction or for any material pair would falsify the universality of free-fall and the geometric interpretation of gravity built on top of it. The parameter is named for Loránd Eötvös, whose 1889 and posthumous 1922 torsion-balance results established the first precision bound, η ≲ 10⁻⁹, against materials ranging from platinum and brass to glass and asbestos.
Modern bounds have tightened by six orders of magnitude. The Adelberger group's Eöt-Wash rotating-torsion-balance experiments at the University of Washington reached η ≲ 10⁻¹³ in the 1990s and 2000s, comparing aluminium-beryllium pairs against the gravitational pull of the Sun, the Galactic centre, and dark-matter halo gradients. The MICROSCOPE satellite mission, launched in 2016, measured platinum-titanium pairs in freefall around Earth and reported η ≲ 10⁻¹⁵ in 2017 (with refined null results published through 2022) — the current world bound. No nonzero η has ever been observed at any precision. The persistent null result is one of the strongest empirical underpinnings of general relativity's geometric foundation; any future detection would force revision of the equivalence principle and likely point to new physics in the matter-gravity coupling.