Self-Completeness of Einstein gravity via Black Hole formation

[S.Daedalus]

I just recently came across this idea, outlined in http://arxiv.org/abs/1005.3497" ). I've looked for some discussion here, but couldn't find any, so I thought I'd start one (if I missed some previous discussion, I'd appreciate a link).

The basic idea is simple: to probe transplanckian physics, one needs to concentrate an energy $$E > 1/L$$ into a spacetime volume of size $$L$$. The Schwarzschild radius of this configuration is $$R(L) = L_{p}^2/L$$, with $$L_{p}$$ being the Planck length. Thus, for $$L < L_{p}$$, a black hole forms, hiding all potentially new physics within its event horizon.

This BH is essentially a (semi-)classical object, which becomes more and more classical (i.e., larger) the harder you try to probe the sub-Planck scale; hence, attempts to probe the deep-UV limit of the theory bounce back to the IR, which is of course well described by the existing theory -- physics on sub-Planck scales just never plays any role at all. Hence, since quantum gravity stays sane up to the Planck length, and the theory just curls back in upon itself on lengths smaller than that, it is essentially self-complete.

So, what's everybody's thoughts on this? Personally, I'm refraining from forming an opinion for the moment, on account of not being informed enough -- which I hope some discussion here will remedy. But I'm definitely intrigued, and I do wonder somewhat that this doesn't seem to have generated more buzz...

 

[tom.stoer]

Sounds interesting; does this go into the direction "UV/IR" of NCG?

 

[shettaruae]

anybody experts can tell me is it possible to repalce electrical motor by hydraulic motor.What r the parametres supposed to be keep in mind?

 

[S.Daedalus]

Sounds interesting; does this go into the direction "UV/IR" of NCG?

I don't think so, though I'm not very familiar with the NCG approach. IIRC, there, the UV/IR mixing is problematic, because interactions at high energies lead to divergences in the infrared behaviour.

Here, it's just that the deep-UV and IR limits of the theory are effectively identified; if you pump sufficiently much energy into a small enough region, you end up with a macroscopic black hole.

 

[tom.stoer]

This is just T-duality known from string theory. But if I understand you correctly, you are looking for something independent from string theory, right?

 

[S.Daedalus]

This is just T-duality known from string theory. But if I understand you correctly, you are looking for something independent from string theory, right?

Yes. The paper I linked to goes into some stringy details (and mentions the similarity to T-duality), but the main argument is derived simply from general considerations about the quantization of gravity.

Basically, if I understand this correctly, you can just treat QG as an effective field theory cut off at the Planck scale, with the IR behaviour 'subbing in' for transplanckian physics; in this way, one can extract physical predictions up to arbitrarily high energy just from quantized general relativity.

 

[atyy]

Basically, if I understand this correctly, you can just treat QG as an effective field theory cut off at the Planck scale, with the IR behaviour 'subbing in' for transplanckian physics; in this way, one can extract physical predictions up to arbitrarily high energy just from quantized general relativity.

In the early paper, I thought he was actually saying that classical Einstein gravity was a limit of string theory at high energies.

At that time it was very handwavy, so I didn't take it any more seriously than Smolin's regular speculations.

I would expect that high energy behaviour to be quantum - especially if AdS/CFT holds, since the CFT is a completely quantum mechanical theory defined to arbitrarily high energies (except that high energies in the CFT may not mean high energy in the bulk). Naively, I'd expect something closer to this line of speculation http://arxiv.org/abs/0811.0263.

 

[S.Daedalus]

In the early paper, I thought he was actually saying that classical Einstein gravity was a limit of string theory at high energies.

I'm somewhat foggy on what exactly the connection proposed in the paper between Einstein gravity and string theory is; as best I can tell, they just note the similarity between the UV/IR connection in the former and the T-duality of the latter, and build the argument (or, as they put it, the suggestion) that string theory is built into Einstein gravity around that.

However, it doesn't seem to me that the connection is necessary for the argument to work -- it is something observed after the fact, not put in upfront.

 

[qsa]

I'm somewhat foggy on what exactly the connection proposed in the paper between Einstein gravity and string theory is; as best I can tell, they just note the similarity between the UV/IR connection in the former and the T-duality of the latter, and build the argument (or, as they put it, the suggestion) that string theory is built into Einstein gravity around that.

However, it doesn't seem to me that the connection is necessary for the argument to work -- it is something observed after the fact, not put in upfront.

This picture is as simple as this, take a line subdivide it into N, consider each subdivsion as Planck length LP you can describe all of physics as probabilities on the points and the distances as energy relations. Now what happens if you divide that LP again infinitly, again you will get the same behavior on these subdivision as original larger ones. It is like a comformal fractal. The secret is that position has to be on points (discrete), real numbers are ambigiuos, and by sheer force we started with LP as unit distance. So choosing one scale and sticking with it is the same as subdividing and only finding that you are where you started from, i.e. no real gain.

I have already discussed this nightmarish issue in an old thread(#31), talking about my own theory(profile). It drove me up the wall as to its meaning.

https://www.physicsforums.com/showthread.php?p=2661278#post2661278