QFT with respect to general relativity

tom.stoer

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

Dickfore

What do you mean by "gauge symmetry" of GR?

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

tom.stoer

Have a lokk at the ADM formulation of GR

http://arxiv.org/abs/gr-qc/0405109
The Dynamics of General Relativity
R. Arnowitt (Syracuse Univ.), S. Deser (Brandeis Univ.), C. W. Misner (Princeton Univ.)
(Submitted on 19 May 2004)
Abstract: This article--summarizing the authors' then novel formulation of General Relativity--appeared as Chapter 7 of an often cited compendium edited by L. Witten in 1962, which is now long out of print. Intentionally unretouched, this posting is intended to provide contemporary accessibility to the flavor of the original ideas. Some typographical corrections have been made: footnote and page numbering have changed--but not section nor equation numbering etc.

The 'gauge symmetry' is related to the diffeomorphism invariance

Finbar

Suprised,

How can you be certain a black hole forms for the two electrons? This is not a kinematical regime that we have any experimental knowledge of and there is not an established theory at transplanckian energies. You cannot simply apply general relativity to two electrons with these energies.

It is a fact that one can only state when a black hole is formed with knowledge of the complete dynamical history of the spacetime. Yes it is true that initially when the two electrons are 2km apart that they should begin to collapse. But since they are transplanckian as they get closer to each other the quantum gravity effects will become important and it is possible that the collapse will cease to continue. So although an apparent horizon will form it is possible that once the electrons reach Planckian distances their coupling to the gravitational field will be vastly altered and a classical spacetime is unlikely to be a valid assumption.


To make rash statements about the formation of black holes one must at least take three quantities into account:

1) The total energy

2) The impact parameter

3) The number of degrees of freedom

The important thing in your example is the number of degrees of freedom is very small, just those of two electrons. Roughly speaking GR is only valid when the number of degrees of freedom is very large. So the normal hoop conjecture rational is good when we assume that there is a large number of degrees of freedom and so we only concern ourselves with 1) and 2). For a star this is fine but in your example it is clearly not.

tom.stoer

I think this is what he wants to show: the usual reasoning of GR and even perturbative QG do no longer apply b/c what you mean by
does not emerge from this ansatz.

What does the asymptotic safety program say about transplanckian scattering?

suprised

Actually one cannot be certain and I should perhaps have said: “So, _according to standard expectations_, what's going to happen is that when the electrons are still, say 2km apart, a large black hole forms.”

There was a paper by t' Hooft in the 80's supporting this idea.
Indeed, this is also the viewpoint of the more recent “classicalization” or “UV-self-completeness” approach to gravity by Dvali & Co, see eg:

arXiv:1006.0984v1:

Physics of Trans-Planckian Gravity
Authors: Gia Dvali, Sarah Folkerts, Cristiano Germani
(Submitted on 4 Jun 2010)

But this is by no means undisputed, and AFAIK no one really knows what is going to happen under these circumstances. So the question about the S-Matrix is a very important one.


With the large impact parameter they will never reach Planckian distances, that was the whole point. I presented this, in the context of the thread, as an example where quantum gravity effects may become important, despite one is _not_ probing distances close to the Planck scale; so this has little to do with the UV completion of gravity.

There are indications that inside of black holes macroscopic quantum effects occur (horizonless “fuzzball states”), that are extremely non-local. So what could happen in the scattering process, roughly speaking, is that one huge extended fuzzball state is created, which decays afterwards in a perfectly unitary way; and no classical black hole is ever formed.

Indeed so, classical GR may not be relevant at all here. This what I would tend to believe. But again, the classicalization approach tries to argue otherwise. Note (tom) that this approach vehemently denies asymptotic safety.

tom.stoer

Do you have a good reference about classicalization?

Isn't AS somthing like "classicalization" as well? It's an effective action (but as such a 'classical' expression) taking into account quantum effects via renormalized couplings - but no new structures or interactions (at least if the usual truncation remains valid).

suprised

I guess the paper cited above and refs. therein, eg. ref.3, is a good start.

No, these authors claim that the regime where AS would take place can never be probed; nothing can ever become weaker coupled than standard gravity.

atyy

Suprised, from the renormalization point of view, unless there is asymptotic safety, new degrees of freedom are expected at high enough energies (and small impact parameter).

But from the unitarity point of view, from the Giddings paper you linked, there seems to be a problem at high energies and large impact parameter, so he says unitarity is really the problem. But shouldn't the two problems somehow be linked, ie. if the new degrees of freedom are properly incorporated, the problem should go away?

suprised

Yes this is likely related and the expectation is of course that the problem goes away in a proper formulation of quantum gravity, but how does this work precisely? There were some attempts from AdS/CFT, but I don't quite recall now as to how far this could be pushed.

On the other hand, the classicalization people claim that new degrees of freedom are not required, since the ultra-high energy regime maps back to classical physics.

Finbar

If we assume that a black hole does form then they do reach Planckian distances when they collapse towards the singularity. The two electrons are attracted to each other my gravity so they will not remain 2km apart. So we can only say that the UV effects can be ignored if they are hidden behind the horizon. But the existence of the horizon really depends on the whole dynamical history of the electrons. So we can't really assume that a black hole does form. So I would say that the idea that we can ignore the UV is actually circular logic.

friend

I just had a thought, perhaps this is the best place for it.

Considering the nature of spacetime and QFT, as I understand it, virtual particles pop into existence, travel about, and then come back together such that the uncertainty principle is not violated. But how much space do the virtual particles travel through before coming back together? And how can you define space without events in the form of particle trajectories that establish the concept of relative distances? It may be that we cannot define one without the other. And the ultimate equations will have to account for both in a single equation.

Dickfore

What specifically should I look for? I don't feel like going through a whole chapter of a textbook.

tom.stoer

The canonical variables and the constraints are defined in section 3-2 and chapter 4

friend

So I'm having trouble with how some quantum gravity programmes make an effort to quantize gravity without matter or other particles of any kind. I guess they expect to couple matter into the equations at a later time. But gravity is the geometry of spacetime, and it seems the only thing that established distance in reality is the relative distance between particles. So what relavance is there to quantizing geometry without respect to particles. Even virtual particles would at least give us a a source of particles between which there is distance, right? So it seems we have to quantize gravity with respect to QFT or we're just quantizing geometry as an exercise.

tom.stoer

Good point.

But of course we know that there are vacuum solutions in GR with non-trivial dynamics (dS spacetime, black holes, brill waves, ...), so it's not totally unreasonable.

friend

That's why I'm thinking that this is where virtual particles come in. At least there are virtual particles in the vacuum to establish relative distances with respect to them. But if geometric quantities are justifiably quantized irrespective of particle quantization, then there is nothing to specify when to quantize and when not to quantize any geometric quantities simply because it is there. If you take away the context of QFT of particles away from the quantization of geometry, then it seems arbitrary to quantize geometry. So I think we need to formulate the problem of quantum gravity by finding geometric quantities as dynamic variables in a more diffeomorphic generalization of the usual QFT.