Microscopic black holes from high-energy particle collisions

[Martin]

this is a topic that a new member, jana, raised in another thread

it really deserves a thread of its own

 

I am hoping jana will provide a tutorial on this that several people besides me can enjoy

[Martin]

the "Big Bang" origin of the universe envisions a brief time of very high (planck scale) temperature during which particles could collide (some people think) with enough energy to form microscopic black holes

 

since we dont see a lot of microscopic black holes around us, perhaps they evaporated or dispersed in some fashion.

 

to me this is pretty exotic stuff and i would be happy if someone would

discuss it

 

jana brought this up in another thread so I am hoping jana will

give us an informal tutorial on how high energy collisions can form microscopic black holes

[Martin]

BTW in an earlier post jana said that he (or she) was a student at the University of Toronto planning to take a course for seniors offered this fall on string theory. To me jana seems already quite knowledgeable and well versed about string theory (i hope this is a correct impression). So with luck this could be an informative thread.

[jana]

Since I think you know more than I do about what people working in string theory believe' date=' i would like to ask you about that in particular. Strings are extended objects which limits (by the string scale) how close they can come.

 

Please explain how two strings form a black hole by colliding with each other at high energy.

 

jana seems already quite knowledgeable and well versed about string theory (i hope this is a correct impression)[/quote']

 

 

Truthfully, I don't know much about string processes forming black holes either and am just beginning to learn about strings. I realize that string theory is currently the theory of choice for most guys doing quantum gravity so I think it is important to understand why. But in fact I know more about other approaches to quantum gravity, e.g. loop quantum gravity, euclidean quantum gravity and simplicial quantum gravity since they're a whole lot easier to grasp in full. But this is okay in this case because I wasn't thinking about strings. I was more interested in discussing arguments that bear on any prospective quantum theory of gravity.

 

What I wanted to focus on first was my point number 2, the idea that quantum gravity is a holographic theory.

 

The intuitive argument for black hole creation in high energy collisions requires one imagine that a finite fraction of the energy of the collision remains for some time in a region bounded by something of order the impact parameter. Then we have at large distances from this region a Schwarzchild field with mass M. For large M and fixed impact parameter, the Schwarzchild radius is larger than the region in which the energy is concentrated and so the system must be a black hole. There are a number of arguments consistent with this. For example, one is that the black hole spectrum grows far more rapidly at high energies than any other known class of states.

 

The point is that if we believe this, than taking seriously the lesson from QFT that the true fundamental degrees of freedom of a theory are found at high energies, then these degrees of freedom are, in a quantum theory that includes gravity, those of black holes. If we then take seriously the idea a la bekenstein and hawking that the degrees of freedom of black holes are proportional to their event horizons, then the true fundamental degrees of freedom of any QG theory are area- and not volume-extensive. This argument eliminates all current approaches to quantum gravity except string theory. In fact, even classical arguments from general relativity seem to imply this.

 

So how seriously should we take this argument? The answer is only as seriously as we can take the assumptions on which it depends. There are two that I know of. One is a weak form of the cosmic censorship conjecture which states that singularities formed as a result of scattering are never naked (naked singularities have no event horizons and thus the entropy-area relation doesn’t apply). The other, I think, is a weak form of the dominant energy condition used in proofs of the singularities theorems of GR, that energy can’t flow at superluminal speeds.

 

Then for current nonstring approaches to quantum gravity to be correct requires that two fundamental assumptions made in teaching GR, cosmic censorship and the dominant energy condition, be wrong.

 

Interestingly, I recently learned that there are arguments that nature may allow certain exotic singularities that are naked. This is the gregory-la flamme instability, and I’m not sure but I think it involves aspects of string theory and/or supersymmetry. If so, than if one views superstring theory as excluding the other QG theories, than this doesn't help the latter.

 

I apologize for taking so long to respond. I'm learning as fast as I can. Right now I'm thinking about background independence from a point of view related directly to the above. I'll have to get back to you on this.

[Martin]

...I apologize for taking so long to respond. I'm learning as fast as I can. Right now I'm thinking about background independence from a point of view related directly to the above. I'll have to get back to you on this.

 

No need for apologies on that account! I am glad to take plenty of time to assimilate what you are saying and others may want to as well, rather than trying to play lightningchess with ideas of the universe

 

Take your time. I am looking forward to hearing more.

 

BTW the nonstring quantum gravity pictures I've encountered are almost never holographic.

 

In my experience people talk about 't Hooft's holographic principle more as a conjecture than as an necessary axiom to be satisfied by QG.

 

It seems to me that you are breaking new ground here---opening up a new front in the string/nonstring debate. it is really quite majorleague in a sense. You are arguing that any decent QG theory MUST (because of your reasoning about black holes) be holographic in the sense that the state of the universe must be described on a 2D manifold. To quote your essential point:

" If we then take seriously the idea a la bekenstein and hawking that the degrees of freedom of black holes are proportional to their event horizons, then the true fundamental degrees of freedom of any QG theory are area- and not volume-extensive. This argument eliminates all current approaches to quantum gravity except string theory.."

[swansont]

since we dont see a lot of microscopic black holes around us' date=' perhaps they evaporated or dispersed in some fashion.

[/quote']

 

IIRC the evaporation rate of black holes via Hawking radiation is inversely related to their size. Small ones evaporate fast.

[Martin]

IIRC the evaporation rate of black holes via Hawking radiation is inversely related to their size. Small ones evaporate fast.

 

that's my understanding too! those microscopic BH may have evaporated in a twinkling if there ever were any! but I was hoping jana would go into that. I could use a refresher on the details

[Martin]

...

 

It seems to me that you are breaking new ground here---opening up a new front in the string/nonstring debate. it is really quite majorleague in a sense. You are arguing that any decent QG theory MUST (because of your reasoning about black holes) be holographic in the sense that the state of the universe must be described on a 2D manifold. To quote your essential point:

" If we then take seriously the idea a la bekenstein and hawking that the degrees of freedom of black holes are proportional to their event horizons' date=' then the true fundamental degrees of freedom of any QG theory are area- and not volume-extensive. This argument eliminates all current approaches to quantum gravity except string theory.."[/quote']

 

Yeah jana, the beck and hawk semiclassical analysis of blackholes suggests that the "degrees of freedom" or parameters describing the BH

do live on the surface of it

(everything one can know about the BH can be described by describing minutely its event horizon)

 

so in a vague sense if everything is (fundamentally) black holes then whatever we can know about anything should be projectable onto a 2D screen---the degrees of freedom, as you elegantly put it, are not volume- extensive but area-extensive.

 

Personally I think this is highly conjectural. I personally dont think everything is fundamentally black holes, or that a theory of quantum gravity can be reduced to whatever it says about black holes.

 

I know that isolated horizons (different from event horizons) are an active field of study and people dont yet have a very satisfactory notion of what is inside black holes. or how to describe them quantum theoretically. Ashtekar has a longish run of recent papers on this. Event horizons are a bit elusive and so the tendency has been to study other types of horizon or pairs of horizons surrounding the black hole.

 

So I dont think the word is in yet, about describing BH, and I dont think what Beck and hawk said in 1976 or whenever is the final word. But the idea of holographic description is a fascinating speculation.

 

However I do appreciate your argument, jana, and if you and I really are 2D holograms then Renate Loll's simplicial quantum gravity certainly wouldnt describe us very well, I should think, or Rovelli's loop quantum gravity either! So, unless I am mistaken, you have a point there. Such holographic speculations seem not to have deterred people from continuing to develop nonholographic theories with regular old 3D space and 4D spacetime--but who knows maybe they will in the future.

[jana]

I personally dont think everything is fundamentally black holes, or that a theory of quantum gravity can be reduced to whatever it says about black holes. I think this is highly conjectural.

 

Yes, it is conjectural; we have arguments but no proof. But I'm trying to psyche myself up for the deep waters of string theory. I need more than mere logical possiblility (e.g., for whatever reasons, "I reserve the right to believe in LQG or anything else until I'm shown an airtight proof that it is wrong"). I need believability, and so far, I find these black hole arguments to be quite plausible. In fact I know that they are taken seriously by many (in fact my impression is most) people. Of course there are probably many subtleties that I'm completely missing (maybe I'm missing the boat entirely, which would of course suck greatly).

 

Before I spew out what I learned in relation to all this about background independence, I'll say one more thing. In quantum gravity the measuring apparatus is always coupled gravitationally to the system. This suggets that the only sensible way to define observables in quantum gravity is with respect to measuring apparatus placed at asymptotic infinity. This means that defining quantum gravity is problematic for spacetimes that don't have appropriate asymptotic properties. The point is that it may be that the only observables allowed in quantum gravity are those whose data lives on the boundary at infinity (for spacetimes that have boundaries). In other words, the only sensible observable would be the S-matrix, and this is consistent with holography. This is the case with string theory, but in LQG, area and volume operators serve as fundamental observables.

 

So my next post will be about background-independence. I’ll relate as best I can an argument based on this black hole stuff that suggests that there is no such thing as a background-independent theory of quantum gravity, and in particular, that the idea that M-theory can ever be background-independent is wrong.

[Martin]

[edited part out that seemed too effusive, lacking in reserve]

 

i am looking forward to following your next argument

although I may disagree with the conclusions.

 

go for it

[jana]

i am looking forward to following your next argument

although I may disagree with the conclusions.

 

That's okay since I'm really just trying to reevaluate my own attitudes, and I'm finding bouncing this stuff off of you helps.

 

These next arguments I’ve been reading about require that we consider background-independence in the very general context (e.g., more general than LQG) of the wilsonian RG for QFT. In this framework, the true fundamental degrees of freedom occur at some very high energy represented by an ultraviolet fixed point of the RG beta function defined as usual on coupling constant space. The points along each possible trajectory traced out by the beta function as we move from the ultraviolet to progressively lower energies represent increasingly course-grained approximations of the fixed point theory, eventually reaching in the infrared the various endpoints of each RG flow representing some vacuum or background. In these terms, background-independence means insensitivity of the fixed point theory at high energies to the different possible vacuums at low energies. This is known as “short-distance universality” or just “universality”.

 

For example, LQG is hoped to be an ultraviolet fixed point which flows in the infrared to classical spacetimes whose dynamics is governed by GR. Notice the clean separation between the expression of background-independence here and the idea of relationalism it is somewhat conflated with when discussed in the context of GR. In fact, GR doesn’t come up at all here! As another example, string theorists have believed that all physically admissable backgrounds flow in the ultraviolet to a unique theory at high energy called M-theory which would thus be background-independent. It would then only remain to discover it’s degrees of freedom and precise form. In this case, the question is whether and how the conventional meanings and implications of RG notions like fixed points and flows extend beyond the paradigm of field theory to whatever new paradigm M-theory represents.

 

In fact the argument I studied says that there can be no background-independent QG theories since the (conjectural) domination in quantum gravity of transplanckian scattering processes by the production of correspondingly extremely massive and hence very large black holes (tom banks calls this conjecture “asymptotic darkness”) ruins universality. The idea is simply that asymptotic darkness means that transplanckian scattering instead of probing short distances, instead probes distances of order the size of these very large black holes. The resulting entwining of large scale geometry with the high energy spectrum means that the fundamental degrees of freedom depend on vacuum dynamics thus preventing background-independence. This is an example of the celebrated but still mysterious “UV/IR connection” which is yet another idea intimately related to holography.

 

We conclude from this that in general, different backgrounds correspond to different QG theories so that the aforementioned traditional view that string theory gives rise to a unique QG theory called M-theory is wrong, though this doesn’t mean that string theory is wrong. It goes without saying of course that this isn’t a happy argument from the perspective of the nonstring nonperturbative QG crowd.

 

In my next post I'll discuss a troubling aspect of the LQG black-hole area-entropy argument, and also from a point of view different from the above the claim that LQG is a background-independent and discrete theory of spacetime.

[jana]

.........................

[Martin]

... isn’t a happy argument from the perspective of the nonstring nonperturbative QG crowd.

 

In my next post I'll discuss a troubling aspect of the LQG black-hole area-entropy argument' date=' and also from a point of view different from the above the claim that LQG is a background-independent and discrete theory of spacetime.[/quote'] Hi jana, you may accidentally have posted the same thing (except for the last paragraph, shown here) twice

 

I'm reading your posts with interest though not always responding.

[arivero]

I think it was Doplicher (of axiomatic/algebraic field theory fame) whom ten years ago proposed to get quantum geometry indeterminacy from the postulate of impossibility of microscopic black holes. Ie that geometry has an indeterminacy relation just because too much energy in a space time are creates a black hole.

 

Or perhaps it was Fredenhagen. Oh, memory!

[jana]

I think it was Doplicher (of axiomatic/algebraic field theory fame) whom ten years ago proposed to get quantum geometry indeterminacy from the postulate of impossibility of microscopic black holes.

 

Okay, but the black holes I've been discussing are of transplanckian mass and thus enormous. Martin made an understandable mistake when he entitled the thread "...microscopic black holes..."

[jana]

I believe that the LQG derivation of the proportionality between black hole entropy and area (there appears to be no way in LQG to obtain the coefficient of this proportionality) is invalid since instead of treating complete black holes, microstates of area of their event horizons are counted as if black hole interiors don’t even exist and with no justification that I can see given for identifying these microstates with the fundamental states of black holes themselves. This seems to yield the expected proportionality trivially, as a cheat, their argument in effect assuming the entropy-area proportionality it is suppose to prove.

 

On the other hand, the string demonstration appears to honestly build entire black holes out of D-branes and then counts their true physical states, the result being in complete agreement with the standard formula.

 

One more thing. I now feel that the criticism levelled by LQG people at string theory to the effect that it “only proves this result for extremal and near-extremal black holes” really misses the point, this being that for strings to be correct requires that they at least produce the correct result in every situation in which this calculation can be carried out, and so far it clearly has.

 

Moving on, were you aware that, according to this recent paper, it is in fact not known for sure whether LQG is in fact a description of quantum geometry that is truely background-independent and discrete? I’m going to think about this for a little bit before posting anymore about it.

[Martin]

Okay, but the black holes I've been discussing are of transplanckian mass and thus enormous...

 

Jana could you please explain why a black hole with mass larger than the planck mass (a "transplanckian mass" black hole) must necessarily be enormous?

[jana]

Jana could you please explain why a black hole with mass larger than the planck mass (a "transplanckian mass" black hole) must necessarily be enormous?

 

For example, the schwarzshild radius is R=2GM, so large mass means large hole.

 

 

Here is a illustrative sample of what you wrote in [this] thread:

 

"In fact the argument I studied says that there can be no background-independent QG theories since the (conjectural) domination in quantum gravity of transplanckian scattering processes by the production of correspondingly extremely massive and hence very large black holes (tom banks calls this conjecture “asymptotic darkness”) ruins universality. The idea is simply that asymptotic darkness means that transplanckian scattering instead of probing short distances' date=' instead probes distances of order the size of these very large black holes. The resulting entwining of large scale geometry with the high energy spectrum means that the fundamental degrees of freedom depend on vacuum dynamics thus preventing background-independence. This is an example of the celebrated but still mysterious “UV/IR connection” which is yet another idea intimately related to holography."

 

 

jana this is such tortured reasoning! background independence is something very simple that 1915 gen relativity has in a simple

extremely obvious way---its a fundamental characteristic of GR:

 

there is a basic continuum set of points (a manifold) and you start with no metric on it---so there is no prior commitment to a geometry

 

the metric, which determines the shape by giving distances between points, IS the graviational field---and the point of the theory is that the field (the metric, the geometry) emerges dynamically as a solution to the main equation

 

any theory that wants to be free of a prior commitment to geometry, and let the geometry emerge, can be background indep

 

but string theory isnt background independent so it does not have the fundamental characteristic of General Relativity[/quote']

 

It’s not tortured reasoning. You are talking about background-independence in terms of classical GR. But I had to describe background-independence in the context of QFT in order to make certain arguments, and in particular, to discuss a certain aspect of the AdS/CFT correspondence in connection with the cosmological constant problem (which I didn’t do since it didn’t look like anyone, including you, was interested).

 

Do you agree that the background-independence you learned about in the context of GR can be described in RG terms as they apply to any QFT including LQG, or do you believe that they are unrelated, at least as far as LQG is concerned?

[Martin]

For example' date=' the schwarzshild radius is R=2GM, so large mass means large hole.

 

 

[/quote']

 

I know the formula for the schwarzschild radius!

 

But please answer my question.

 

Why does having a mass M greater than the planck mass (i.e. transplanckian)

mean that the hole is enormous?

 

Suppose it is 10 times planck mass, or 100 times planck mass,

 

how big is it then

 

(I think you will see, if you work it out, that enormous is not the appropriate word)

[jana]

I used the word "enormous" to highlight the fact that I wasn't talking about microscopic holes. The point is that as a hole increases in mass as we go to the ultraviolet, it's exterior goes to the infrared and is therefore described by effective field theory with increasingly good accuracy. In other words, unlike in nongravitational physics where large energies probe short distances, the formation of large black holes as a result of collisions between sufficiently high energy objects means that large energies instead probe the long distances characterizing the region exterior to the hole. This is one aspect of the UV/IR connection I want to discuss.

 

So are you going to answer any of my questions straight up, or are you going to continue with your conspicuously odd (and that is putting it charitably) behaviour?

[Martin]

just tell me, in meters or kilometers or whatever you think is appropriate

 

the radius of a Schwarzschild black hole which is 100 times the planck mass

 

so we can see if it is enormous or microscopic or what

[jana]

just tell me' date=' in meters or kilometers or whatever you think is appropriate

 

the radius of a Schwarzschild black hole which is 100 times the planck mass

 

so we can see if it is enormous or microscopic or what[/quote']

 

"Transplanckian" includes arbitrarily high energies above planck so this exercise is pointless.

[Martin]

Jana you said that transplanckian mass implied enormous

 

if you dont know the basics and make elementary mistakes

then it is clear that when you start slinging around terminology

from quantum field theory it is pretentious, not authentic.

 

Just tell me the size of an ordinary BH with 100 planck mass.

 

Or if that is not "transplanckian" enough for you, 1,000,000 times the planck mass.

[jana]

Jana you said that transplanckian mass implied enormous

 

if you dont know the basics and make elementary mistakes

then it is clear that when you start slinging around terminology

from quantum field theory it is pretentious' date=' not authentic.

 

Just tell me the size of an ordinary BH with 100 planck mass.

 

Or if that is not "transplanckian" enough for you, 1,000,000 times the planck mass.[/quote']

 

Edit in italics:

 

My experience is that the term "transplanckian", though not necessarily meaning arbitrarily high energies above planck, is often used as a matter of convention to indicate such. In fact I've never seen the term used in any other way.

[Martin]

My experience is that the term "transplanckian", though not necessarily meaning arbitrarily high energies, is often used as a matter of convention to indicate such. In fact I've never seen the term used in any other way.

 

it sure is high energy!

 

planck energy is 2 Gigajoules!

a huge whallop for a little thing like a photon to deliver

(speaking very informally)

 

but please answer the question, how big is the BH

your choice 100 planck mass

1,000,000 planck mass

 

it should be easy for you, given who you are