Gravity: Graviton
Gravity: Graviton
GravityIntroduction
The work by Max Planck on the blackbody spectrum, and by Albert Einstein on the photoelectric effect convincingly showed that the classical electromagnetic field defined by Maxwell's Equations is quantized in terms of photons. The similarity between gravity and electromagnetism as long-range forces led physicists to propose that gravity may also be quantized, with the force-carrying particle dubbed the graviton. The bad news is that no one has ever seen a graviton, nor any natural phenomena requiring such a particle. Its status is in even worse observational shape that that of the Higgs boson.
Quantum Description
A basic property of a fundamental particle is its spin, so the particle physicist attempting to create a quantum field theory for gravity would reasonably ask what would the spin of the carrier of gravity, the graviton, have to be so that its behavior matched gravity as we know it? In a 1964 paper by Nobel Physicist Steven Weinberg a powerful theorem was announced that related the spin of a force-carrying particle to the conservation laws that it would have to obey to be consistent with special relativity. Spin-1 particles would resemble photons and lead to both attractive and repulsive forces. Gravity was only attractive, so gravitons could not be spin-1 particles. Spin-2 particles, however, would interact in a manner that depends on how much mass was present, and would behave in a consistent, universal fashion between all massive particles. This closely paralleled the way gravity is known to act. For particles with spins higher than 2, no 'static' forces will occur which means that the solar system would not be stable over long periods of time. Gravitons have to be exactly massless so that light from distant stars seen near the limb of the sun would be deflected in exactly the way thatis observed. Massive gravitons would cause a deflection only 75 % of what is seen. But there was more. Not only are gravitons exchanged in large numbers between all forms of matter and energy, but they are exchanged among themselves. Finally, in 1975, a remarkable paper by Boulware and Deser showed how Einstein's equation for gravity is precisely the equation that any good quantum field theorist would be forced to write down based on what we already know about gravity from simple experiences.
Yang-Mills Theory
By 1963, Bryce DeWitt went on to suggest that Yang-Mills theory might be unified with gravity by using Kaluza-Klein's approach. The first complete accounting of just how such a program might be designed was given by Cho and Freund in 1975. The problem with this approach turned out to be that there were no good reasons why the new dimensions which had to be tacked-on to spacetime should be tiny. Still, apart from this technical difficulty, it looked like a unification theory of all forces was close at hand. Had a convincing quantum theory of gravity at last been spotted? Not yet. A collection of ideas is not the same as a rigouous mathematical framework from which real quantitative predictions can be launched.
Abdus Salam has for many years advocated a simple toy model in which gravitons remarkable emerge as the regularizers of the QED infinities. They seem to do so by providing a natural gravitational cutoff to the QED calculations. The basis for all of the calculations is the presumption common to the Covariant Quantum Gravity approach. You start with a flat 'Minkowski' background geometry for spacetime and add one graviton at a time as a perturbation; a similar technique was advocated by Feynmann in the1960's. At no time do any geometric concepts enter as they did for general relativity, but in the end you end up with re-discovering several solutions to Einstein's equation for gravity including the existence of black holes. All, presumably, from the standpoint of a particle physicist's views of what a quantum theory of gravity should look like. Another clue to how particle physicists think about spacetime comes from their efforts in understanding how to wrestle gravity into the same mathematical language used to describe the other three forces; a struggle which has yet to prove successful.
Out of this struggle has come some remarkable new insights expressed by Nobel Physicist Abdus Salam writing in "Impact of Quantum Gravity Theory on Particle Physics."
"...The universe and its quantum topology are determined by WHERE gravitons are and what space-time interaction patterns they give rise to. [p. 507]... The concept of space-like separated points...cannot be defined until AFTER the [theory of quantum gravity] is solved and the [light-cone] structure at each space-time point [is] constructed and specified."
The words, 'where' and 'after', have been emphasized by the author to highlight the unusual aspects of quantum gravity that bare directly on the nature of physical spacetime. Abdus Salam's statement is remarkable and would have warmed the hearts of the Manifold Constructivists, but there was a catch to how this program was implemented that would have caught the attention of the Manifold Substantivists as well.
Spacetime as a quantum system
It was common for particle physicists ca 1975 to begin developing toy models of a quantum theory of gravity expressed by beginning withsome pre-existing flat manifold. A diagram would be drawn of, say, an electron emitting and absorbing a single virtual photon, accompanied by the simultaneous emission and absorption of billions and trillions of virtual gravitons. The gravitational field would in this way be built-up out of the interactions of innumerable virtual gravitons just like the electromagnetic field is built-up out of virtual photons. Salam was quick to point out that "this manifold may have nothing to do with the spacetime of general relativity". This approach was pioneered by W. Thirring in 1968 who also proposed that the manifold was totally unobservable just like the "bare mass" of an electron in the theory of quantum electrodynamics. So the good news for quantum gravity theory is that gravity is fundamentally just like QED and QCD. If we replace the spin-1 gluons with the spin-2 gravitons and replace 'color' with 'mass-energy', wouldn't we get a polite, self-consistent theory? It is not enough to just swap one symbol for another and make a new theory. Humphry Bogart and Harrison Ford are both actors, but you would not want to swap their roles in 'Casablanca' and 'Star Wars'.
But now comes some bad news. Yang-Mills theory applied to gravity still produces infinities that could not be tamed using the by then standard renormalization techniques. A dramatically different variant was invented by Gerard 't Hooft and Veldtman called 'dimensional regularization' in which the calculations were carried out in a spacetime with greater than 4 dimensions, and then converted back to a 4-D answer. For calculations involving pure gravitions interacting only with themselves, this technique provided finite answers. The only problem was that it required that more and more 'counter terms' had to be added to the theory as each new field was included, and this made the whole mess look very ad hoc and inelegant.
By the early 1970's the subject of quantum gravity had reached something of a crossroad. The basic problems involved in creating such a theory along the lines of other familiar quantum field theories were pretty well understood, but there were no answers as to how to circumvent them mathematically. Most significantly, the infinity problem was a glaring indicator that something was lacking in the approaches being taken. Beyond this, there was still no genuine unanimity over which approach to take as the starting point for actually creating a quantum gravity theory.For gravity, there were many features in general relativity that you could 'quantize'.
General relativity posits spacetime as a collectionof points or events that form a 4-D manifold whose shape is determined by Einstein's equation for gravity. You could imagine trying to quantize the 'points', the 'manifold' or the gravitational 'field'. Then again, could it be that spacetime was itself too small an arena? The Kaluza-Klein extension into 5-D had been tried and disgarded because it didn't lead to a sensible theory by 1920's standards. How about the relativistic equation of gravity proposed in general relativity? How much of it should be subjected to the quantization approach? The right-side of Einstein's equation contained an accounting of the mass-energy in spacetime, but these were known to be quantum fields. If these are quantizable, then shouldn't all of those geometric quantities on the other side of the equals sign also be quantizable? But which ones? Should R, $R_{\mu,\nu}$ and $g_{\mu,\nu}$ be quantized together, or just one of them? How about the other geometric fields that are possible in the full Riemannian theory of geometry such as $R_{\alpha \nu \beta \gamma}$ or combinations of all of these quantities that represent different aspects of curvature and the gravitational field? A 'cosmological constant' term could be added to Einstein's equation. Should it be re-instated together with additional 'counter-fields' whose actions might patch-up the infinity problem? Evidently, Einstein's own equation for gravity was not comprehensive enough when attempts were made to re-cast it in the language of quantum mechanics.
Observational Evidence - Gravitons
Upper Limits - Alfred Goldhaber and Michael Nieto at Los Alamos Laboratory outlined the status of the search for a massive graviton ca 1974. Although no quantum gravity theory was available, they decided that the next best thing to do was to establish whether any experiment could decide whether gravitons had to be massive or massless. To weigh the graviton, they used some of the largest collections of matter in the universe: clusters of galaxies, which are believed to be held together by the self-gravity of their constituent stars and galaxies. If gravity is carried by a massive particle, it cannot follow an inverse-square law behavior at all scales. At some critical distance it must begin to die off as the particles reach their maximum distances allowed by Heisenberg's Uncertainty Principle. In the clusters of galaxies Goldhaber and Nieto studied, the typical separations between galaxies were about 118,000 parsecs, with a maximum separation of 580,000 parsecs. Because of the apparent uniformity of the inverse-square behavior of gravity over these scales, this leads to an upper limit for the graviton mass of 2 x 10-62 grams. A limit, by the way, which is even more restrictive than the current best upper limit for the mass of the photon, 4 x 10-48 grams, alsodetermined by Goldhaber and Nieto. About this curious result they reflected that,
"...whether or not gravity should be quantized, one can say that the graviton's rest mass is less than 2 x 10-62 grams. Therefore, somewhat paradoxically, one has experimental evidence on the rest mass of a particle which may not exist"
Heavy Gravitons - Recently, new approaches to quantum gravity based on string theory have rejuvinated the search for gravitons. Lisa Randall and Sundrum (Randall, L. & Sundrum, R. Phys. Rev. Lett. 83, 3370–3373 (1999).) have proposed a brane theory in which ordinary particles and fields are confined to a 3-D brane, but that gravity operates freely along higher diomensions. In particular, gravitons connect a high-density brane ( Planck Brane) with our low-density brane along an additional short-length dimension.
This idea has now been tested at the Tevatron, Fermilab's 2-TeV proton–antiproton collider. The D0 detector, positioned at a collision point, is a large and sophisticated machine that effectively takes an electronic snapshot of the particles that emerge. If nature is like the Randall–Sundrum model, the high-energy collisions could produce a heavy mode of the graviton, called a Kaluza–Klein (or KK) mode, which couples to matter more strongly than ordinary gravity does. However, the additional gravitational force that arises from the KK mode is so short-range that it would not affect any observations of macroscopic gravity. The KK mode created in high-energy collisions would immediately decay into a particle and an antiparticle.
The team searched their data for electron–antielectron, muon–antimuon and photon–photon pairs. Such pairs can, however, be produced by decays of ordinary particles — a Z boson, for instance. When the number of pairs seen is plotted as a function of the invariant mass of the pair (related to their energy and momenta), the distribution falls off steadily above an invariant mass of 100 GeV c-2. But if some pairs are produced by the KK mode, the invariant mass of those pairs is close to the mass of the heavy graviton, creating a tell-tale bump in the spectrum
No bump was seen in the D0 data, meaning that gravitons lighter than 600 GeV c-2 do not exist. It is possible, however, that gravitons have masses of up to several TeV c-2 and that the experiment has not collected enough data yet to see them. The Tevatron collider is still running, so the sensitivity of this search will increase when more data are added to the analysis. Even if no KK modes are observed by the Tevatron experiments (D0 and its sister detector CDF), CERN's Large Hadron Collider will be able effectively to cover all of the interesting mass range for these particles. [Nature Physics 1, 15 - 16 (2005)]
Observational Evidence - Space quantization
Each spot is a gamma ray burst detected by the BATSE instrument on NASA's GRO satellite.
Each spot is a gamma ray burst detected by the BATSE instrument on NASA's GRO satellite. (Source: NASA CGRO.)
Photon Propagation - Gamma ray bursts occear each day, and arrive from distances in excess of one billion light years. In 2005, Ellis et al (Astropart.Phys. 25 (2006) 402-411), used the propagation of gamma ray photons to place an upper limit to spacetime graininess. The refractive index of free space is a function of the scale at which quantum spacetime effects become important. These effects will cause gamma ray photons of different energies to arrive at slightly different times, thereby violating Lorentz-Invariance of empty space.
"Using the weighted averages of the time-lags calculated using correlated features in all the GRB light curves, we find a systematic tendency for more energetic photons to arrive earlier. However, there is a very strong correlation between the parameters characterizing an intrinsic time-lag at the source and a distance-dependent propagation effect. Moreover, the significance of the earlier arrival times is less evident for a subsample of more robust spectral structures. Allowing for intrinsic stochastic time-lags in these features, we establish a statistically robust lower limit: M > 0.9x1016 GeV on the scale of violation of Lorentz invariance."
Related EoC Articles
- Gravity: Canonical Quantization
- Gravity: Covariant Quantization
- Gravity: Dimensionally-Extended
- Gravity: Gauge Field
- Gravity: Graviton
- Gravity: Kaluza-Kline Theory
- Gravity: Quantization ca. 1990
- Gravity: Quantum
- Gravity: Renormalization
- Gravity: String Theory
- Gravity: Superspace Quantization
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- Gravity: What is Gravity?
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Gravitational waves are propagating gravitational fields, "ripples" in the curvature of space-time, generated by the motion of massive particles, such as two stars or two black holes orbiting each other. Gravitational waves cause a variable strain of space-time, which result in changes in the distance between points, with the size of the changes proportional to the distance between the points. Gravitational waves can be detected by devices which measure the induced length changes. Waves of different frequencies are caused by different motions of mass, and difference in the phases of the waves allow us to perceive the direction to the source and the shape of the matter that generated them. (Source: NASA-The Laser Interferometer Space Antenna (LISA).)
Citation
Odenwald, Sten, Ph.D. (Contributing Author); Bernard Haisch (Topic Editor). 2008. "Gravity: Graviton." In: Encyclopedia of the Cosmos. Eds. Bernard Haisch and Joakim F. Lindblom (Redwood City, CA: Digital Universe Foundation). [First published February 12, 2008].
<http://www.cosmosportal.org/articles/view/135646/>
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