# Asymptotic darkness in string theory

1. Nov 26, 2009

### atyy

Is Asymptotic Darkness explicitly known to be realised in string theory?

2. Nov 26, 2009

### marcus

Well both are kind of indefinite ideas so it would be hard to say for sure.
Asymptotic darkness is a conjecture of Tom Banks according to which high energy particle scattering is increasingly dominated by black holes as you ramp up the energy.

Here's from his 2003 paper, starting at the middle of page 4:

"...Arguments to be reviewed below suggest that high energy scattering processes
are dominated by black hole production. The result of these considerations is a radical
new principle, which I consider to be the ultimate form of the UV/IR correspondence :
High Energy Dynamics is dominated by large black holes, some of whose properties can
be calculated using the semiclassical Lagrangian formulation of general relativity.
At the
Davidfest in Santa Barbara, I called this principle Asymptotic Darkness."

[Banks' italics. I added color to his emphasis.]

"...At very high energy densities, space is ﬁlled
with black holes
and the area scaling of entropy becomes manifest."

[my emphasis]

http://arxiv.org/abs/hep-th/0306074
A Critique of Pure String Theory: Heterodox Opinions of Diverse Dimensions
T. Banks (SCIPP, U.C. Santa Cruz, Nhetc, Rutgers U.)
82 pages
(Submitted on 9 Jun 2003)
"I present a point of view about what M Theory is and how it is related to the real world, which departs in certain crucial respects from conventional wisdom. I argue against the possibility of a background independent formulation of the theory, or of a Poincare invariant, Supersymmetry violating vacuum state. A fundamental assumption is black hole dominance of high energy physics..."

[my emphasis, I thought the points were interesting.]

Last edited: Nov 26, 2009
3. Nov 26, 2009

### marcus

David Gross' 60th birthday party (the Davidfest) would have been February 2001, so that was when Banks says he coined the idea.

It's not merely the simple observation that you can get from the formula for the Schwarzschild (1916) radius, namely if you concentrate enough energy in a small volume you get a black hole.

My impression is Banks' idea has not gone anywhere. You wouldn't find many people currently taking it seriously. I could be wrong---maybe you can find some contemporary papers. There is a drawback that immediately occurs.

I remember reading this in 2003:
"...At very high energy densities, space is ﬁlled with black holes..."

and thinking "WHAT SPACE???" At very high energy densities you need a mathematical model of quantum geometry and matter at very high energy densities...obviously. You need a mathematical model of the regime that replaces cosmological and black hole singularities.

You can't assume that you have ordinary space, peppered with black holes. It is a misleading mental image. Ordinary space does not have an independent existence. Geometry and matter are probably inseparable at very high density, at least there is no reason to assume that you can treat them as separate entities.

Anyway, so far as I know, Banks' image of high density space didn't catch on. What got researchers' attention is what Abhay Ashtekar calls the "Planck regime" (of geometry and matter) which occurs in QG models of the big bang and of gravitational collapse to black hole.

There are solvable analytical models, and also computer models, of behavior in the Planck regime and people run them and study them quite a lot these days. One trend is to gradually remove simplifying assumptions---relax the conditions of homogeneity and isotropy, another is to connect to covariant QG formalism. It may be right or wrong, I don't know, but that is how people are studying physics at very high energy density nowadays.

For whatever reason they don't appear to be studying Banks' picture: the idea of classical space peppered with classical black holes.

Last edited: Nov 26, 2009
4. Nov 26, 2009

### marcus

Banks says he first presented the AD idea at the Davidfest, which would have been 2001.
Here are the slides and audio for Banks talk at Davidfest (the first proposal, according to him, of the Asymptotic Darkness idea)
http://online.itp.ucsb.edu/online/gross_c01/banks/

This looks like a light witty suggestive talk with charming cartoon illustrations. Wanting something more subsantial and definite from the same 2001 period, I went back and found a paper which has been withdrawn from arxiv, called Black Crunch. Fortunately only the final version of the Banks "Black Crunch" paper has been withdrawn. There is still an abstract for the earlier version 1, which we can read:

http://arxiv.org/abs/hep-th/0111170v1
Black Crunch
T. Banks, W. Fischler
9 pages
(Submitted on 20 Nov 2001 (this version), latest version 5 Dec 2001 (v2))
"We study the growth of fluctuations in collapsing cosmologies, generalizing old work of Lifgarbagez and Khalatnikov to a general class of linear equations of state. We find that fluctuations dominate the homogeneous background for every equation of state but $$p=\rho$$. This leads us to hypothesize that the generic final state of any Big Crunch is a dense gas of black holes. In a companion paper we have shown that such a fluid indeed has equation of state $$p=\rho$$. We explore some of the consequences of these results."

In the above, Banks refers to this earlier 2001 paper

http://arxiv.org/abs/hep-th/0102077
M-theory observables for cosmological space-times
T.Banks, W.Fischler
29 pages
(Submitted on 14 Feb 2001)
"We discuss the construction of the analog of an S-matrix for space-times that begin with a Big-Bang and asymptote to an FRW universe with nonnegative cosmological constant. When the cosmological constant is positive there are many such S-matrices, related mathematically by gauge transformations and physically by an analog of the principle of black hole complementarity. In the limit of vanishing Lambda these become (approximate) Poincare transforms of each other. Considerations of the initial state require a quantum treatment of space-time, and some preliminary steps towards constructing such a theory are proposed. In this context we propose a model for the earliest semiclassical state of the universe, which suggests a solution for the horizon problem different from that provided by inflation."

Not sure there is any relevance to present day physics research but may be of some historical interest. You can see them groping for some way to model conditions around bang, just as in the paper I mentioned first they are trying to model crunch.

Last edited: Nov 26, 2009
5. Nov 26, 2009

### atyy

In my understanding, AD is only named by Banks, but has roots in arguments by Bekenstein. Let me give some references which state or use the idea is a powerful heuristic. The basic argument is given in the paper below by Smolin.

http://arxiv.org/abs/0910.3140
Beyond the Planck scale
Steven B. Giddings
"In the general ultraplanckian Gedanken experiment, the basic control parameters are the energy, and the impact parameter, b – after all, these are essential parameters in our high-energy experiments at real colliders. At E ≫MD, there are good reasons to believe that some important features of the scattering are given by a semiclassical picture. Classically, for sufficiently small impact parameter, one expects to produce a black hole, plus some radiation as this black hole “balds.” Quantum corrections discovered by Hawking tell us that the black hole then evaporates. So, we expect an initial state of two high-energy particles, and a final state approximated by Hawking radiation. ... The trouble is, this leads to an apparent paradox seemingly driving at the heart of the problem of reconciling quantum mechanics with gravity."

http://arxiv.org/abs/0908.0333
Lectures on String Theory
David Tong
"Firstly, there is a key difference between Fermi’s theory of the weak interaction and gravity. Fermi’s theory was unable to provide predictions for any scattering process at energies above sqrt(1/GF). In contrast, if we scatter two objects at extremely high energies in gravity — say, at energies E ≫ Mpl — then we know exactly what will happen: we form a big black hole. We don’t need quantum gravity to tell us this. Classical general relativity is sufficient. If we restrict attention to scattering, the crisis of non-renormalizability is not problematic at ultra-high energies. It’s troublesome only within a window of energies around the Planck scale."

http://arxiv.org/abs/0709.3555
A pedagogical explanation for the non-renormalizability of gravity
Assaf Shomer
"However, our experience with gravity has shown that once enough energy is concentrated in a given region a black hole will form. As far as our understanding goes, the high energy spectrum of GR is dominated by black holes. More technically, it is expected that in theories of gravity, black holes will provide the dominant contribution to the large energy asymptotics of the density of states as a function of the energy."

http://arxiv.org/abs/gr-qc/9510063
Structural Issues in Quantum Gravity
Chris Isham
"This has been emphasised recently by several people and goes back to an old remark of Bekenstein: any attempt to place a quantity of energy E in a spatial region with boundary area A—and such that E > √A—will cause a black hole to form, and this puts a natural upper bound on the value of the energy in the region (the argument is summarised nicely in a recent paper by Smolin)."

http://arxiv.org/abs/gr-qc/9508064
The Bekenstein Bound, Topological Quantum Field Theory and Pluralistic Quantum Field Theory
Lee Smolin
"This suggests that, ultimately, a quantum theory of gravity will not be formulated most simply as a theory of fields on a differential manifold representing the idealized-and apparently nonexistent-“points” of space and time. To put this another way, the space of fields-the basic configuration space of classical field theory-has been replaced in the quantum theory by abstract Hilbert spaces. At the same time, ordinary space, in these formulations, remains classical, as it remains the label space for the field observables. This perpetuates the idealization of arbitrarily resolvable space-time points, that the results of string theory, non-perturbative quantum gravity and semiclassical quantum gravity (through the Bekenstein bound) suggest we must give up."

Last edited: Nov 26, 2009
6. Nov 26, 2009

### marcus

Atyy, I already responded when you gave the same references in the other thread. I don't believe that Banks was simply giving a catchy name to what everybody has known for at least 50 years---that if you concentrate enough energy in a small space you get a black hole.

Maybe you could listen to the audio of Banks' talk, where he says he introduced the AD idea?

And maybe paraphrase what exactly you think the idea was that Banks believed he introduced at that talk?

====================

We've probably all wondered why, at conditions around the big bang, these particles with enormous kinetic energy wouldn't have all formed black holes. At big bang temperature, particle energies are presumably near planckian, to the extent that one can say particles exist at such high temperature. I've certainly wondered about that myself---why don't all those energetic particles crowded together like that form black holes?

I think of Banks as a brilliant and creative guy*. I find it hard to believe that he was presenting an idea that everybody knows---that two particles colliding with sufficient energy would (at least in our nearly flat classical space) form a black hole---and that he thought he had presented an original idea.

So just what do you think Banks was trying to say? You might be right and it might be exactly what Isham said, or Smolin said, earlier before 2001! I'm skeptical of that. I tend to suspect it was different---not necessarily right, but intended to be trail-blazing. For sure you might be right though, we'll have a better idea when we get a paraphrase of Banks Davidfest message.

*whether or not his work, say, on M-theory is of lasting value.

========================

My computer cannot play the vintage 2001 audio, but I have looked at the slides to the Davidfest talk:
http://online.itp.ucsb.edu/online/gross_c01/banks/

It is a highspirited talk with much drollery and wonderful adaptations from La Divina Commedia of Dante.
Slide 13 is where he says what he means by Asymptotic Darkness.
It begins "Black holes as partons."

It harks back to 2001 when the well-known blogger LM was Banks' star graduate student, and recalls some joint work by LM and Banks.

Last edited: Nov 26, 2009
7. Nov 26, 2009

### Haelfix

The idea is very old..

I'm guessing its probably Kip Thorne, or someone like 'T Hooft. In many ways it more or less seems obvious once you buy the no hair theorem and once you knew the dynamics of shock waves, and things like the Hoop conjecture.

Banks makes it popular b/c he specifically implements it as a type of cosmology (black hole gas)

8. Nov 27, 2009

### atyy

http://arxiv.org/abs/0712.1209
Towards an S-matrix Description of Gravitational Collapse
D. Amati, M. Ciafaloni, G. Veneziano

"Extending our previous results on trans-Planckian (Gs ≫ hbar) scattering of light particles in quantum string-gravity we present a calculation of the corresponding S-matrix from the region of large impact parameters (b ≫ G√s > λs) down to the regime where classical gravitational collapse is expected to occur."

"The perturbative resummation diverges at a critical value of the impact parameter b = bc ∼ R = 2G√s, which separates the class of real-valued (b > bc, sec.4) and complex valued (b < bc, sec.7) solutions, all satisfying the boundary condition ρ(0) = 0 which plays the role of quantization condition of the problem. We also find that our estimates of the bc/R ratio are compatible with the classical lower bound for CTS formation, suggesting that our non-perturbative regime is likely to be in correspondence to classical collapse."

http://arxiv.org/abs/0807.2117
http://arxiv.org/abs/0909.4523

These are the closest I could find to explicit calculations, so it looks like the answer is not definitively known within string theory?