A principle arising from the observation that gravitational and inertial mass have the same value, expanded by Einstein to the principle that, locally, effects of gravitation are equivalent to acceleration. The (strong) equivalence principle states that physical laws in any local free-falling inertial reference frame are the same as in special relativity. The principle is of central importance to the general relativity theory of gravity.
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In relativity, the equivalence principle is applied to several related concepts dealing with gravitation and the uniformity of physical measurements in different frames of reference. Two new principles were suggested, the so-called Einstein equivalence principle and the strong equivalence principle, each of which assumes the weak equivalence principle as a starting point. Many physicists believe that any Lorentz invariant theory that satisfies the weak equivalence principle also satisfies the Einstein equivalence principle.
Tests of the weak equivalence principle
Tests of the weak equivalence principle are those that verify the equivalence of gravitational mass and inertial mass.
| Researcher | Year | Method | Result |
| John Philoponus | 6th Century | Described correctly the effect of dropping balls of different masses | no detectable difference |
| Simon Stevin | ~1586 | Dropped lead balls of different masses off the Delft churchtower | no detectable difference |
| Galileo Galilei | ~1610 | Rolling balls down inclined planes | no detectable difference |
| Isaac Newton | ~1680 | measure the period of pendulums of different mass but identical length | no measurable difference |
| Friedrich Wilhelm Bessel | 1832 | measure the period of pendulums of different mass but identical length | no measurable difference |
| Loránd Eötvös | 1908 | measure the torsion on a wire, suspending a balance beam, between two nearly identical masses under the acceleration of gravity and the rotation of the Earth | difference is less than 1 part in a billion |
| Roll, Krotkov and Dicke | 1964 | Torsion balance experiment, dropping aluminum and gold test masses | difference is less than one part in one hundred billion |
| David Scott | 1971 | Dropped a falcon feather and a hammer at the same time on the Moon | no detectable difference (Not a very good experiment, but it was the first lunar one.) |
| Branginsky and Panov | 1971 | Torsion balance, aluminum and platinum test masses, measuring acceleration towards the sun | difference is less than 1 part in a trillion (most accurate to date) |
| Eöt-Wash | 1987– | Torsion balance, measuring acceleration of different masses towards the earth, sun and galactic center, using several different kinds of masses | difference is less than a few parts in a trillion |
Experiments are still being performed at the University of Washington which have placed limits on the differential acceleration of objects towards the Earth, the sun and towards dark matter in the galactic center. Future satellite experiments – STEP (Satellite Test of the Equivalence Principle), Galileo Galilei, and MICROSCOPE (MICROSatellite pour l'Observation de Principe d'Equivalence) – will test the weak equivalence principle in space, to much higher accuracy.
The Einstein equivalence principle
The Einstein equivalence principle states that the weak equivalence principle holds, and that
Here local has a very special meaning: not only must the experiment not look outside the laboratory, but it must also be small compared to variations in the gravitational field, tidal forces, so that the entire laboratory is moving inertially.
The principle of relativity implies that the outcome of local experiments must be independent of the velocity of the apparatus, so the most important consequence of this principle is the Copernican idea that any of the fundamental physical parameters – other than masses and Newton's gravitational constant – must not depend on where in space or time we measure them.
Schiff's conjecture suggests that the weak equivalence principle actually implies the Einstein equivalence principle, but it has not been proven.
Tests of the Einstein equivalence principle
In addition to the tests of the weak equivalence principle, the Einstein equivalence principle can be tested by searching for variation of dimensionless constants and mass ratios.
| Constant | Year | Method | Limit on fractional change |
| fine structure constant | 1976 | Oklo | 10-7 |
| weak interaction constant | 1976 | Oklo | 10-2 |
| electron-proton mass ratio | 2002 | quasars | 10-4 |
| proton gyromagnetic factor | 1976 | astrophysical | 10-1 |
There have been a number of controversial attempts to constrain the variation of the strong interaction constant.
The strong equivalence principle
The strong equivalence principle suggests the laws of gravitation are independent of velocity and location. In particular,
and
The first part is a version of the weak equivalence principle that applies to objects that exert a gravitational force on themselves, such as stars, planets, black holes or Cavendish experiments.
Tests of the strong equivalence principle
The strong equivalence principle can be tested by searching for a variation of Newton's gravitational constant G over the life of the universe, or equivalently, variation in the masses of the fundamental particles.
Thus, the strong equivalence principle can be tested by searching for fifth forces (deviations from the gravitational force-law predicted by general relativity).
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