Classical theories of gravitation

The current Gold Standard Theory of Gravitation is the general theory of relativity. This is a classical, relativistic field theory (physics) of gravitation. At present, there is no quantum theory of gravitation.

Discussion

General relativity was not the first relativistic theory of gravitation, or even the first metric theory of gravitation — that was Nordström's theory of gravitation, which is now known to be incompatible with observation.

Presently, general relativity is compatible with current observations. However, this might not be the case for future experiments. Moreover, it is generally believed that general relativity requires quantum corrections at high curvatures or in other extreme conditions; but this Planckian regime appears to be experimentally inaccessible for the moment. It is conceivable that general relativity might turn out to fail at lower energies; in other words, while it is almost universally expected that the classical limit of any reasonable quantum theory of gravitation should be general relativity, this expectation could be wrong. There are in fact some currently mysterious phenomena, particularly the well-known Pioneer anomaly, which might eventually turn out to require a revision of even our classical notions of gravitation.

Since its introduction, various classical relativistic gravitation theories have been suggested as alternatives to general relativity. Such theories have had various theoretical motivations, in addition to the obvious motivation just described (general relativity might not after all be the best possible classical theory for describing how gravitation works in Nature). These motivations include:

• General relativity is fundamentally awkward in the way it handles how energy/momentum is exchanged between the gravitational field and everything else; teleparallel gravity is an alternative theory motivated in part by an attempt to remedy this theoretical flaw.
• General relativity is awkward in the way it handles the coupling of spin to gravitation at the level of test particles; Einstein-Cartan gravitation is motivated in part by an attempt to remedy this flaw.
• Despite Einstein's initial hopes in 1913–1916, general relativity does not clearly or fully validate a precisely formulated Mach principle. This is an umbrella term for a collection of loosely formulated proposals to the effect that the definition of inertial motion depends upon the presence and distribution of matter in the observable universe. One reason for the difficulty is that this notion seems to resist a covariant formulation.

Recently the Italian physicist Christian Corda has shown that the interferometric detection of gravitational waves will be the definitive test for General Relativity or, alternatively, a strong endorsement for alternative relativistic gravitation theories in his paper "Interferometric detection of gravitational waves: the definitive test for General Relativity" which was an Honorable Mention Winner at the 2009 Gravity Research Foundation Awards http://www.worldscinet.com/ijmpd/18/1814/S0218271809015904.html

This article discusses some of these issues, and attempts to compare how various popular alternative classical field theories of gravitation fare in dealing with them.

See also

• Alternatives to general relativity for a more detailed description of alternate classical theories of gravitation.
• Classical unified field theories describes attempts by Einstein and others to unify gravitation and electromagnetism.
• Quantum gravity surveys contemporary work toward creating a quantum theory of gravitation.
• Theory of everything surveys contemporary work toward unifying gravitation with the other known fundamental interactions of physics.

Articles on specific classical field theories of gravitation

• Bergmann-Wagoner theory of gravitation, a theory introduced by Peter Gabriel Bergmann and R. V. Wagoner.
• Brans–Dicke theory, the best known competitor of general relativity, introduced by Robert H. Dicke and Carl H. Brans.
• Einstein–Cartan theory, a theory introduced by Élie Cartan, with contributions from Albert Einstein.
• Fourth-order gravity (FOG), a theory recently championed by Hans-Jürgen Schmidt, Christian Corda and others; this is an example of a higher-order gravity theory.
• General relativity, our current gold standard theory of gravitation.
• Kaluza–Klein theory, for a notion which appears in many recent theories in one guise or another.
• Kustaanheimo's theory of gravitation, a theory introduced by P. Kustaanheimo.
• Lovelock theory of gravity, a higher-order gravity theory which comes in several variants.
• Ni's theory of gravitation, a theory introduced by W.-T. Ni.
• Nordström's theory, a now obsolete theory introduced by Gunnar Nordström.
• Rosen bi-metric theory, a theory introduced by Nathan Rosen.
• Parameterized post-Newtonian formalism, for a formalism which facilitates comparison of many classical theories.
• Teleparallelism, a class of theories deriving in part from work by Albert Einstein and recently championed by Yakov Itin and others.
• Weyl's gauge theory of gravitation, a now obsolete theory introduced by Hermann Weyl.
• Whitehead's theory of gravitation, a now obsolete theory introduced by Alfred North Whitehead.

References

• Misner, Thorne and Wheeler ("MTW") Gravitation (Freeman, NY, 1973), chapter 39: "Other theories of gravity and the Post-Newtonian approximation"
• C.M. Will, Theory and experiment in gravitational physics
• C. Corda, Interferometric detection of gravitational waves: the definitive test for General Relativity, Int. J. Mod. Phys. D18, 2275-2282 (2009)