Classical theories of gravitation
Encyclopedia
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
.
, 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:
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.
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
. This is a classical
Classical physics
What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics...
, relativistic
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
field theory (physics) of gravitation
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
. At present, there is no quantum theory of gravitation
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
.
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 gravitationNordström's theory of gravitation
In theoretical physics, Nordström's theory of gravitation was a predecessor of general relativity. Strictly speaking, there were actually two distinct theories proposed by the Finnish theoretical physicist Gunnar Nordström, in 1912 and 1913 respectively...
, which is now known to be incompatible with observation.
Presently, general relativity is compatible with current observations
Tests of general relativity
At its introduction in 1915, the general theory of relativity did not have a solid empirical foundation. It was known that it correctly accounted for the "anomalous" precession of the perihelion of Mercury and on philosophical grounds it was considered satisfying that it was able to unify Newton's...
. 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
Pioneer anomaly
The Pioneer anomaly or Pioneer effect is the observed deviation from predicted accelerations of the Pioneer 10 and Pioneer 11 spacecraft after they passed about on their trajectories out of the Solar System....
, 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 gravityTeleparallelismTeleparallelism , was an attempt by Einstein to unify electromagnetism and 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 gravitationEinstein–Cartan theoryIn theoretical physics, the Einstein–Cartan theory, also known as the Einstein–Cartan–Sciama–Kibble theory or the Cartan–Sciama–Kibble theory is a classical theory of gravitation similar to general relativity but relaxing the assumption that the metric be torsion-free. Introducing torsion allows...
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 principleMach's principleIn theoretical physics, particularly in discussions of gravitation theories, Mach's principle is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach....
. 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 covariantGeneral covarianceIn theoretical physics, general covariance is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations...
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 relativityAlternatives to general relativityAlternatives to general relativity are physical theories that attempt to describe the phenomena of gravitation in competition to Einstein's theory of general relativity.There have been many different attempts at constructing an ideal theory of gravity...
for a more detailed description of alternate classical theories of gravitation. - Classical unified field theoriesClassical unified field theoriesSince the 19th century, some physicists have attempted to develop a single theoretical framework that can account for the fundamental forces of nature – a unified field theory. Classical unified field theories are attempts to create a unified field theory based on classical physics...
describes attempts by Einstein and others to unify gravitation and electromagnetism. - Quantum gravityQuantum gravityQuantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
surveys contemporary work toward creating a quantum theory of gravitation. - Theory of everythingTheory of everythingA theory of everything is a putative theory of theoretical physics that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle....
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. DickeRobert H. DickeRobert Henry Dicke was an American physicist who made important contributions to the fields of astrophysics, atomic physics, cosmology and gravity.-Biography:...
and Carl H. BransCarl H. BransCarl Henry Brans is an American mathematical physicist best known for his research into the theoretical underpinnings of gravitation elucidated in his most widely publicized work, the Brans–Dicke theory....
. - Einstein–Cartan theoryEinstein–Cartan theoryIn theoretical physics, the Einstein–Cartan theory, also known as the Einstein–Cartan–Sciama–Kibble theory or the Cartan–Sciama–Kibble theory is a classical theory of gravitation similar to general relativity but relaxing the assumption that the metric be torsion-free. Introducing torsion allows...
, a theory introduced by Élie CartanÉlie CartanÉlie Joseph Cartan was an influential French mathematician, who did fundamental work in the theory of Lie groups and their geometric applications...
, with contributions from Albert EinsteinAlbert EinsteinAlbert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
. - 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 relativityGeneral relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, our current gold standard theory of gravitation. - Kaluza–Klein theoryKaluza–Klein theoryIn physics, Kaluza–Klein theory is a model that seeks to unify the two fundamental forces of gravitation and electromagnetism. The theory was first published in 1921. It was proposed by the mathematician Theodor Kaluza who extended general relativity to a five-dimensional spacetime...
, 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 gravityLovelock theory of gravityIn physics, Lovelock's theory of gravity is a generalization of Einstein's theory of general relativity introduced by David Lovelock in 1971. It is the most general metric theory of gravity yielding conserved second order equations of motion in arbitrary number of spacetime dimensions D...
, a higher-order gravity theory which comes in several variants. - Ni's theory of gravitation, a theory introduced by W.-T. Ni.
- Nordström's theoryNordström's theory of gravitationIn theoretical physics, Nordström's theory of gravitation was a predecessor of general relativity. Strictly speaking, there were actually two distinct theories proposed by the Finnish theoretical physicist Gunnar Nordström, in 1912 and 1913 respectively...
, a now obsolete theory introduced by Gunnar NordströmGunnar NordströmGunnar Nordström was a Finnish theoretical physicist best remembered for his theory of gravitation, which was an early competitor of general relativity...
. - Rosen bi-metric theory, a theory introduced by Nathan RosenNathan RosenNathan Rosen was an American-Israeli physicist noted for his study on the structure of the hydrogen molecule and his work with Albert Einstein and Boris Podolsky on entangled wave functions and the EPR paradox.-Background:Nathan Rosen was born into a Jewish family in Brooklyn, New York...
. - Parameterized post-Newtonian formalismParameterized post-Newtonian formalismPost-Newtonian formalism is a calculational tool that expresses Einstein's equations of gravity in terms of the lowest-order deviations from Newton's theory. This allows approximations to Einstein's equations to be made in the case of weak fields...
, for a formalism which facilitates comparison of many classical theories. - TeleparallelismTeleparallelismTeleparallelism , was an attempt by Einstein to unify electromagnetism and gravity...
, 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 WeylHermann WeylHermann Klaus Hugo Weyl was a German mathematician and theoretical physicist. Although much of his working life was spent in Zürich, Switzerland and then Princeton, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski.His...
. - Whitehead's theory of gravitationWhitehead's theory of gravitationIn theoretical physics, Whitehead's theory of gravitation was introduced by the distinguished mathematician and philosopher Alfred North Whitehead in 1922.-Principal features of the theory:Whitehead's theory is said to feature a prior geometry...
, a now obsolete theory introduced by Alfred North WhiteheadAlfred North WhiteheadAlfred North Whitehead, OM FRS was an English mathematician who became a philosopher. He wrote on algebra, logic, foundations of mathematics, philosophy of science, physics, metaphysics, and education...
.