In physics, the graviton is a hypothetical elementary particle that transmits the force of gravity in most quantum gravity systems. In order to do this, one theory posits that gravitons have to be always-attractive (gravity never pushes), work over any distance (gravity is universal) and come in unlimited numbers (to provide high strengths near stars). In quantum theory, these requirements define an even-spin (spin 2 in this case) boson with a rest mass of zero.
Gravitons are postulated simply because quantum theory has been so successful in other fields. For instance, the electromagnetic interaction can be very well explained by the application of quantization to photons, a science known as quantum electrodynamics. In this case photons are being continually created and destroyed by all charged particles, and the interactions between these photons produce the familiar effects of electricity and magnetism. In the same way, the strong nuclear force and the weak nuclear force are mediated by gluons and by W and Z bosons, respectively.
Given the widespread success of quantum theory in describing the basic forces in the universe except for gravity, it seemed only natural that the same methods would work well on gravity as well. Many attempts finally led to introduction of a so-far unseen graviton, which would work in a fashion somewhat similar to the photon, the gluon etc. It was hoped that this would quickly lead to a quantum gravity theory, although the mathematics became convoluted and no internally consistent theory has yet emerged.
Gravitons and models of quantum gravity
While the classical theory (i.e. the tree diagrams) and semiclassical corrections (one-loop diagrams) behaved as expected, the Feynman diagrams with two (or more) loops led to ultraviolet divergences - i.e. infinite results that could not be removed because the quantized general relativity was not renormalizable, unlike Quantum electrodynamics. In popular terms, the discreteness of quantum theory is not compatible with the smoothness of Einstein's general relativity. These problems, together with some conceptual puzzles, led many physicists to believe that a theory more complete than just general relativity must regulate the behavior near the Planck length. Superstring theory finally emerged as the most promising solution; it is the only known theory in which the quantum corrections of any order to graviton scattering are finite.
String theory predicts the existence of gravitons and their well-defined interactions which represents one of its most important triumphs. A graviton in perturbative string theory is a closed string in a very particular low-energy vibrational state. The scattering of gravitons in string theory can also be computed from the correlation functions in conformal field theory, as dictated by the AdS/CFT correspondence, or from Matrix theory.
An interesting feature of gravitons in string theory is that, as closed strings without endpoints, they would not be bound to branes and could move freely between them; this "leakage" of gravitons from our brane into higher-dimensional space could explain why gravity is such a weak force, and gravitons from other branes adjacent to our own could provide a potential explanation for dark matter. See brane cosmology for more details.
It should be noted that there exist proposed quantum theories of gravity that do not predict a graviton; for instance, loop quantum gravity has no analogous particle.
Gravitons and experiments
Detecting a graviton, if it exists, would prove rather problematic. Because the gravitational force is so incredibly weak, as of today, physicists were not even able to directly verify the existence of gravitational waves, as predicted by general relativity. (Many people are surprised to learn that gravity is the weakest force. A simple experiment will demonstrate this, however: an ordinary refrigerator magnet can generate enough force to lift a mass against the force of gravity generated by the entire planet.)
Gravitational waves may be viewed as coherent states of many gravitons, much like the electromagnetic waves are coherent states of photons. Projects that should find the gravitational waves, such as LIGO and VIRGO, are just getting started.
Problems with the Graviton
There may well be very good reason the Graviton has not been detected any may not exist, at least in the simplistic manner in which it is envisioned. Superficially speaking, quantum gravity using the gauge interaction of a spin-2 field (graviton) fails to work like the photon and other gauge bosons do.
But more importantly the spin-2, linear wave (classical gravitational wave) is only a perturbation on certain, highly restrictive metrics. In general there are wave-like fluctuations, but they are non-linear, as is often the case in General Relativity. Maxwell's equations always admit a spin-1, linear wave, but Einstein's equations rarely admit a spin-2, linear wave, and when they do it is only perturbative and not exact.
The more analagous gravitational object to the electromagnetic wave is actually the Weyl curvature. In classical electromagnetism you have fields determined by sources along with electromagnetic waves that are source-free. And in gravity you have the Ricci curvature determined by the stress-energy tensor along with the source-free Weyl tensor which contains the gravitational waves.
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