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QFT with respect to general relativity 
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#1
Dec2111, 08:16 PM

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After recently researching about Quantum Field Theory and more specifically gravitons, I am slightly confused with how this theory of the gravitational force fits in with general relativity. I know it hasn't disproved it so there must be some connection. Do gravitons in 11 dimensions cause curvature in 4 dimensional spacetime that we observe as gravity? I've been thinking hard about this one and its been stumping me



#2
Dec2111, 09:44 PM

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We don't yet have a generallyaccepted theory that combines general relativity and quantum field theory. People are working on different approaches (e.g. string theory, loop quantum gravity) but none of them has won out.



#3
Dec2211, 09:53 AM

P: 21

So string theory is postulating that gravitons are closed loops that can move between branes correct? Would this possibly explain why they would cause curvature in the 4 dimensions that we can observe? If the particles travel between extra dimensions it seems to me that the effects in our 4 dimensions would then be what we observe as general relativity. Just a thought



#4
Dec2211, 08:13 PM

P: 756

QFT with respect to general relativity
A few comments in lieu of a comprehensive explanation...
If you have read about general relativity, you may be aware that the curvature of space is described by the metric, and the metric is described by a tensor field. In quantum field theory, particles (like the graviton) are associated with fields; they arise by applying the laws of quantum mechanics, such as the uncertainty principle, to the field. The original way to get a quantum theory of gravitons, as pioneered e.g. by Feynman, is as follows: You take the dynamical metrical field of general relativity. You express it as a deviation from the constant metric of flat space (Minkowski space). Then you treat this deviation itself as the graviton field. From this perspective, the graviton is a quantized deviation from flat space. You mention 11 dimensions and string theory. Well, before we get to string theory, let's talk about 11 dimensions. The original 11dimensional theory was the 11dimensional form of "supergravity" (which can also be defined for a lower number of dimensions). In supergravity, you have an 11dimensional metric, an extra "3form" field that is a generalized version of the electromagnetic field, and then a "gravitino" field which is a matter (fermion) field. So at the quantum level, you have the 11dimensional graviton (which can be defined in the way I mentioned above), an 11dimensional photonlike gauge boson, and an 11dimensional fermion. If you were trying to get the real world out of 11dimensional supergravity, you would probably treat 7 of the dimensions as "compact" or "closed", with a radius much less than that of an atomic nucleus. Fundamentally, you still only have the graviton, the 3form field, and the gravitino. However, the way that e.g. the graviton manifests itself depends on whether it's traveling in one of the extra, compact, closed directions, or whether it's traveling in one of the 3 "large" directions of space. Gravitons traveling in the large directions show up as gravity in 3 dimensions, while gravitons circulating in the compact directions can show up as other forces. This was part of the agenda of prestring "KaluzaKlein" unification efforts  the other forces would be explained as resulting from higherdimensional gravity. (That idea goes back to about 1921.) In Mtheory, along with the fields I've described, you have "Mbranes" (of 2 and 5 dimensions) which interact with the graviton, the 3form, and the gravitino fields. A string is really an M2brane with one of its internal directions wrapped around the compact dimensions. Anyway, these complexities aside, if we go right back to where we started, the key point is that quantum fields have particles, whose presence indicates a deviation from the ground state of the field, and the graviton is the particle of the metric field, indicating a deviation from flat space. 


#5
Dec2311, 02:07 AM

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some people think the the artificial split into a static background metric + quantized fluctuations on top of it cause severe problems for the whole program, and that no such background must be introduced



#6
Dec2311, 08:02 AM

P: 9

As discovered long ago, this naïve perturbative approach to obtaining a quantum theory of gravity that reduces to General Relativity in the lowenergy limit by simply quantizing the linearized gravitational field doesn`t work because General Relativity cannot be fully understood as just a theory of a selfinteracting massless spin2 field. There is only one known consistent perturbative approach to quantum gravity that does have the proper lowenergy limit, and that`s string theory. In fact, at this point there is no nonperturbative approach (e.g., LQG etc) to quantum gravity that is known to achieve this. 


#7
Dec2411, 01:45 AM

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#8
Dec2511, 07:17 AM

P: 275

Even without going to planck scale. I think the search for physics of wave functions of the metric is a separate thing, isn't it? Or how to quantize the metric.. this is not related to Planck scale, correct?



#9
Dec2511, 09:08 AM

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#10
Dec2511, 10:15 AM

P: 3,014

There is a well developed theory called Quantum Field Theory in curved spacetime. It treats the dynamics of "matter fields" on a background metric caused by massive bodies. Then, you can go ahead and calculate the stressenergy tensor due to these fields and use it in the Einstein's field equations.
In this respect, the "gravitational field" is treated classically, i.e. it develops according to Einstein's equations which minimize the action of the gravitational field. However, the sources of the gravitational field, namely, the stressenergy tensor of various particles is treated in a fully quantum fashion. This partial theory predicts emission of particleantiparticle pairs from the exterior of an event horizon of a black hole. The emitted spectrum looks just like a blackbody spectrum, with the temperature of the black hole being inversely proportional to its Schwarzschild radius (smaller black holes emit more). This causes evaporation of black holes. It is interesting to notice that what was a static, or stationary, problem in General Relativity (we were solving for a metric that does not depend explicitly in time. As a necessary condition, the total massenergy enclosed inside the Schwarzschild radius remains fixed, and the radius remains constant), has become an explicitly timedependent problem, because as the black hole evaporates and looses energy, its radius shrinks. To me, this is very similar to the failure of Classical Electrodynamics when applied to the atomic system, or simply by its own predictions. Namely, in the Rutherford model, the electron used to be in a dynamical balance because the attractive Coulomb force caused centripetal acceleration keeping it in a stable orbit around the nucleus. However, when we apply the laws of Classical Electrodynamics to the model, the accelerated electron, being a charged particle, should emit electromagnetic radiation, and spiral down to the nucleus in a very short time (of the order of 10^{8} s). Nevertheless, this never happens. It took the genius of Niels Bohr to postulate that there are particular orbits on which the electron does not emit electromagnetic radiation. Thus, he essentially modified Classical Electrodynamics. The criterion by which these orbits were chosen was the quantization of the angular momentum of the electron around the nucleus, which also modified the laws of Classical Mechanics. Of course, it was later shown that the latter corresponds to so called semiclassical quantization conditions of the Quantum Mechanics. It took the development of Quantum Electrodynamics to resolve the mystery of the former prediction. QED also solves the absurdity of the prediction of classical electrodynamics that a charged particle should exponentially accelerate once it was accelerated in some external electric field due to its own radiation reaction force. Up to now, there has been no conclusive evidence that Hawking radiation exists. 


#11
Dec2511, 10:24 AM

P: 407

See eg. here for a readable exposition: http://arXiv.org/pdf/1105.2036 Citation: These notes have given sharpened statements that this unitarity crisis is a longdistance issue, and there is no clear path to its resolution in shortdistance alterations of the theory..... 


#12
Dec2511, 11:43 AM

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Dec2511, 12:20 PM

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#18
Dec2511, 04:49 PM

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