Equivalence principle
The weak form, known for centuries, relates to masses of any composition in free fall taking the same trajectories and landing at identical times.
Highly precise experimental tests of the principle limit possible deviations from equivalence to be very small.
The equivalence principle is the hypothesis that this numerical equality of inertial and gravitational mass is a consequence of their fundamental identity.
[2] Newton, just 50 years after Galileo, investigated whether gravitational and inertial mass might be different concepts.
He compared the periods of pendulums composed of different materials and found them to be identical.
[2] A version of the equivalence principle consistent with special relativity was introduced by Albert Einstein in 1907, when he observed that identical physical laws are observed in two systems, one subject to a constant gravitational field causing acceleration and the other subject to constant acceleration, like a rocket far from any gravitational field.
[3]: 153 He connected the equivalence principle to his earlier principle of special relativity: This assumption of exact physical equivalence makes it impossible for us to speak of the absolute acceleration of the system of reference, just as the usual theory of relativity forbids us to talk of the absolute velocity of a system; and it makes the equal falling of all bodies in a gravitational field seem a matter of course.Soon after completing work on his theory of gravity (known as general relativity)[6]: 111 and then also in later years, Einstein recalled the importance of the equivalence principle to his work: The breakthrough came suddenly one day.
Suddenly a thought struck me: If a man falls freely, he would not feel his weight.
Three main forms of the equivalence principle are in current use: weak (Galilean), Einsteinian, and strong.
[11] Instead, the weak equivalence principle assumes falling bodies are self-bound by non-gravitational forces only (e.g. a stone).
What is now called the "Einstein equivalence principle" states that the weak equivalence principle holds, and that: Here local means that experimental setup must be small compared to variations in the gravitational field, called tidal forces.
The two additional constraints added to the weak principle to get the Einstein form − (1) the independence of the outcome on relative velocity (local Lorentz invariance) and (2) independence of "where" known as (local positional invariance) − have far reaching consequences.
[14]: 9 Around 1960 Leonard I. Schiff conjectured that any complete and consistent theory of gravity that embodies the weak equivalence principle implies the Einstein equivalence principle; the conjecture can't be proven but has several plausibility arguments in its favor.
The Einstein equivalence principle has been criticized as imprecise, because there is no universally accepted way to distinguish gravitational from non-gravitational experiments (see for instance Hadley[15] and Durand[16]).
[8] Thus this is a version of the equivalence principle that applies to objects that exert a gravitational force on themselves, such as stars, planets, black holes or Cavendish experiments.
[8] Some of the tests of the equivalence principle use names for the different ways mass appears in physical formulae.
An obvious test is dropping different objects and verifying that they land at the same time.
Historically this was the first approach – though probably not by Galileo's Leaning Tower of Pisa experiment[18]: 19–21 but instead earlier by Simon Stevin,[19] who dropped lead balls of different masses off the Delft churchtower and listened for the sound of them hitting a wooden plank.
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.
[47] With the first successful production of antimatter, in particular anti-hydrogen, a new approach to test the weak equivalence principle has been proposed.
Experiments to compare the gravitational behavior of matter and antimatter are currently being developed.
[48] Proposals that may lead to a quantum theory of gravity such as string theory and loop quantum gravity predict violations of the weak equivalence principle because they contain many light scalar fields with long Compton wavelengths, which should generate fifth forces and variation of the fundamental constants.
Heuristic arguments suggest that the magnitude of these equivalence principle violations could be in the 10−13 to 10−18 range.
Non-discovery of equivalence principle violation in this range would suggest that gravity is so fundamentally different from other forces as to require a major reevaluation of current attempts to unify gravity with the other forces of nature.
Time-based tests search for variation of dimensionless constants and mass ratios.
[50] For example, Webb et al.[51] reported detection of variation (at the 10−5 level) of the fine-structure constant from measurements of distant quasars.
[52] The present best limits on the variation of the fundamental constants have mainly been set by studying the naturally occurring Oklo natural nuclear fission reactor, where nuclear reactions similar to ones we observe today have been shown to have occurred underground approximately two billion years ago.
A tight bound on the effect of nearby gravitational fields on the strong equivalence principle comes from modeling the orbits of binary stars and comparing the results to pulsar timing data.
[14]: 49 In 2014, astronomers discovered a stellar triple system containing a millisecond pulsar PSR J0337+1715 and two white dwarfs orbiting it.
Studies of Big Bang nucleosynthesis, analysis of pulsars, and the lunar laser ranging data have shown that G cannot have varied by more than 10% since the creation of the universe.
