What are the difficulties of gravitational quantization scheme?

[ndung200790]

I will study gravitation quantization(string theory or canonical quantum gravity),so I want to know what are the difficulties of gravitational quantization scheme.I know that quantization means that calculating commutator of quantum field operators via Poisson brackets.Are the difficulties being the nonrenormalizable?But I hear that it is not hopless,because we can use an infinite number of counterterms.

 

[Simon Bridge]

I will study gravitation quantization(string theory or canonical quantum gravity), so I want to know what are the difficulties of gravitational quantization scheme.

Is this to be a personal study or will you be attending college for this?
It's not a small subject.

Note: the following quoted sentence is incomplete:

I know that quantization means that calculating commutator of quantum field operators via Poisson brackets.

... however, "quantizing gravity" is basically attempting to find the QM that gives rise to GR "on average".
... "calculating commutator of quantum field operators via Poisson brackets" would be a pretty general task in QM, not specific to quantum gravity.

Are the difficulties being the nonrenormalizable?

"The non-renormalizable" what?
Nonrenormalizableness(?) can be a problem but, in a nutshell, the main problem with current quantum gravity approaches is that they don't match reality as well as they need to.
The trouble in coming up with a good scheme seems to lie in deciding how to deal with the ways time is treated in QM vs GR.

If a college study - you will be introduced to the issues in due time. Best advise is to follow the coursework.
If a personal study: you need to get a book - make sure you have the background to read it as this is not an easy field.

 

[marcus]

http://hyperspace.aei.mpg.de/2014/01/10/phd-positions-in-gravity-cosmology-astrophysics-at-fudan-university/

Fudan University (Shanghai) and maybe also Beijing Normal (where the leader is Yongge Ma) are good places

Notice that the announcement of PhD positions mentions COSMOLOGY and ASTROPHYSICS.

To make progress (as Simon Bridge indicated) the quantum gravity (QG) theorists must derive prediction of PHENOMENA in the sky for astronomers to look for. It is the only way to TEST the QG theories and make them better.
This means understanding about "cosmic rays" and about "cosmic microwave background" which is the ancient light from early times.

If I were a young person in China interested in QG, I would go to Shanghai and visit Fudan University. By talking to the leaders and the students there I would learn the right preparation, the right books, the right courses of study. Eventually, after a lot of hard work, I would get into the QG program at Fudan. The leaders there, especially Modesto and Marciano, are very strong researchers.
Bambi and the others may also be, but I don't know them.

In the meantime, have a look at this paper:
http://arxiv.org/abs/1401.6562
Planck stars
Carlo Rovelli, Francesca Vidotto
(Submitted on 25 Jan 2014)
A star that collapses gravitationally can reach a further stage of its life, where quantum-gravitational pressure counteracts weight. The duration of this stage is very short in the star proper time, yielding a bounce, but extremely long seen from the outside, because of the huge gravitational time dilation. Since the onset of quantum-gravitational effects is governed by energy density --not by size-- the star can be much larger than Planckian in this phase. The object emerging at the end of the Hawking evaporation of a black hole can then be larger than Planckian by a factor (m/m_P)ⁿ, where m is the mass fallen into the hole, m_P is the Planck mass, and n is positive. The existence of these objects alleviates the black-hole information paradox. More interestingly, these objects could have astrophysical and cosmological interest: they produce a detectable signal, of quantum gravitational origin, around the 10⁻¹⁴cm wavelength.
5 pages, 3 figures.

Notice that the authors are conceptualizing a "detectable signal of QG origin" and that signal is of "astrophysical and cosmological interest". This kind of move is the future of QG theory, of whatever type. The researchers must bring the theory into contact with observable natural phenomena.

 

[atyy]

1) We do have a theory of quantum gravity as an effective field theory at low energies. http://arxiv.org/abs/1209.3511

2) Having to add an infinite number of counterterms, the theory becomes unpredictive, because of the need to fit an infinite number of parameters. But more seriously, it is unclear if even adding an infinite number of couterterms yields a theory that is UV complete. Asymptotic safety is an approach in which a non-trivial UV fixed point of renormalization is searched for, that would yield UV completeness of gravity. If the non-trivial fixed point lies in a finite dimensional surface, then Asymptotic Safety would be both UV complete and predictive (of course, it could still make wrong predictions, but at least it would be testable). Investigations suggest that a non-trivial fixed point exists, but these suggestions rely on truncations and other approximations which may be misleading. Percacci reviews Asymptotic Safety in http://arxiv.org/abs/1110.6389.

3) Loop quantum gravity is an approach that is like Asymptotic Safety in that it tries to quantize gravity without adding additional degrees of freedom. The current state of the theory is summarized in Rovelli's Zakopane lectures http://arxiv.org/abs/1102.3660 and Engle's article on spin foams http://arxiv.org/abs/1303.4636. Loop quantum gravity has not been shown to yield general relativity in the appropriate limit.

3) If gravity is not UV complete, then presumably additional degrees of freedom must be added to get a UV complete theory. The Weinberg-Witten theorem places very strong constraints on such additional degrees of freedom. These constraints are evaded by AdS/CFT, which is conjectured to give a non-preturbative definition of some sector of string theory. Although AdS/CFT is still a conjecture, it has passed many checks, and is the leading candidate for a theory of quantum gravity in some universe, most likely not ours. However, it may give clues as to how other theories of quantum gravity can be formulated.

 

[tom.stoer]

... so Iy want to know what are the difficulties of gravitational quantization scheme.

One finds that standard textbook quantization (perturbation theory starting with free gravitons and renormalization) fails for gravity, so the conclusion is that one has to modify / enhance / ... this approach; there are several approaches
- add additional d.o.f. (like in SUGRA)
- abandon the QFT approach, use one-dim strings requirier extra dimensions, ...
- use a more general approach to renormalization (like asymptotic safety)
- use different classical variables to start with quantization (LQG)
- ...

Now every approach comes with two types of problems
1) problems specific to that approach, technical problems, consistency, ...
2) problems posed by nature

My impression is that unfortunately we focus on (1) simply b/c there are not so many problems of type (2); we do not have any experimental hint regarding quantum gravity; we cannot probe the QG regime directly; and we know that theories differing in the QG regime may very well have the same semiclassical limit, so QFT + classical GR in a certain limit is not sufficient to decide on the viability of an approach.

So besides the huge technical problems with each individual approach the main challenge seems to be that we have to construct a theory nearly w/o experimental facts.