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QFT with respect to general relativity 
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#19
Dec2511, 05:49 PM

Sci Advisor
P: 5,366

As I said, we expect the geometry to be quantized for several reasons  mainly consistency reasons. Quantum effects would then be small far away from the Planck scale, i.e. quantum gravity would be the UV completion of an effective QFT on smooth classical spacetime (however there are proposals for socalled fuzzball blackholes in string theory which indicate deviations from classical metric even far away from the Planck sale)



#20
Dec2611, 06:08 AM

P: 407

Actually to be fair, there are some proposals out that challenge the conventional wisdom. One is classicalization and selfcompleteness. This posits that if one tries to probe the Planck scale, eg by an energetic scattering process, then one creates black holes before one ever enters into the quantum gravity regime. These are classical objects, so in this sense one never would be able to probe quantum gravity near the Planck scale: the theory protects itself. Pumping in more energy just makes the black holes larger and even more classical.
This is not undisputed, however, but some version of this may be true, perhaps only in particular kinematical regimes; see the ref. in my previous post. The key point is unitarity, not renormalizeability. Nevertheless, for consistency, the whole theory needs to be quantum mechanical. This is independent of whether one can probe the Planck scale by scattering experiments or not. 


#21
Dec2611, 08:18 AM

P: 353




#22
Dec2611, 10:28 AM

P: 3,014

I think you guys are running in circles with your discussion. Would you please define what you mean when you say an equation is "quantized", and similar terms. What is "classical" then?



#23
Dec2611, 10:32 AM

P: 353




#24
Dec2611, 10:35 AM

P: 3,014




#25
Dec2611, 10:47 AM

P: 353




#26
Dec2611, 10:48 AM

P: 3,014




#27
Dec2611, 10:59 AM

P: 407

There seems a lot of confusion. So let's do a little thought experiment. Just scatter two electrons  one from the left, the other coming from the right, in some rest frame.
Quantum mechanics is used to describe the scattering matrix. This is like a black box which tells you what comes out from this scattering process, given the incoming particles. And you want to have unitary scattering, so that probabilities do not exceed one. So far so good, I guess nobody objects that QM is the right concept here. To make things easier, the electrons have an offset, or impact parameter, which is large, say 1km. Ordinarily one wouldnt expect that something would be peculiar or problematic. But I didnt tell you that the kinetic energy of the electrons equals to the mass of a large star. A star with such a mass would form a black hole. So what's going to happen is that when the electrons are still, say 2km apart, a large black hole forms. But you dont really want to know the details now; all that matters is the "black box", or SMatrix, and the question is, without caring about the details of what happens in the black box, what are the final states? Is the scattering unitary? This is obviously a quantum mechanical question. And if the scattering is unitary, this implies that the black hole must be able to decay. So Hawking radiation must necessarily occur, if quantum mechanics is supposed to be valid. Note that this involves quantum mechanics and gravity, and ultraplankian energies, but still these questions are insensitive to the Planck scale: small distances are not relevant here. So we talk about highly nonperturbative nonlocal effects. Related problems occur when considering loops of virtual black holes; do these induce nonunitary scattering for lowenergy particle physics? Better not! Obviously one needs to describe gravity and quantum mechanics in one single coherent framework, in order to address this kind of questions. AFAIK a suitable framework to describe this quantitatively is still lacking. Although I know of some attempts using AdS/CFT. 


#28
Dec2611, 12:35 PM

P: 969




#29
Dec2611, 12:44 PM

P: 2,799

The other problem is that it also only makes sense when ensembles can be realized. In cosmological pictures, where the observer is strongly coupled, the observers entire ENVIRONMENT (ie remainder of the universe) is the effective "black box", and here most of the premises in the scattering picture fails. Also an inside observer can hardly encode arbitrary amounts of inforamtion  someting that is usually not cared about in a good way in the scattering pictures as I see it. It's no news that my own view is that QM formalism as it stands is unlikely to be sufficient here. That's not to say the scattering matrix is interesting, it is. But I think it's a good abstraction of observed reality only in limiting/special case. /Fredrik 


#30
Dec2911, 07:25 AM

P: 407

If you dispute the valitidy of QM and the SMatrix  well QM has been proven to be extremely robust against deformations and so far no one, AFIAK, was able to replace it by something else. It is very common (because cheap) to say "according to my opinion QM needs somehow be modified", but very difficult to actually do it ... 


#31
Dec2911, 07:27 AM

P: 407




#32
Dec2911, 12:47 PM

P: 3,014

So, what is the meaning of the operators [itex]g_{\mu \nu}[/itex], and [itex]R_{\mu \nu}[/itex]? 


#33
Dec2911, 04:55 PM

P: 969




#34
Dec2911, 05:00 PM

P: 3,014




#35
Dec3011, 12:52 AM

Sci Advisor
P: 5,366

In canonically quantized GR g and R are field operators with a huge gauge symmetry and therefore w/o a direct physical meaning.



#36
Dec3011, 12:48 PM

P: 3,014

Also, if you canonically quantize the gravitational field, what are the canonical commutation relations? 


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