Sunday, October 21, 2007

Large N Species

One of the talks at the previously mentioned workshop Origin of Time's Arrow was by Gia Dvali. He talked about his recent paper

The idea is really cute. First, let me summarize some basics: Numerous results lead us to expect that black holes emit thermal radiation with a temperature proportional to the inverse of the black hole's mass. This means the more mass the hole looses through the radiation, the hotter it becomes. It is unknown whether a collapse into a black hole, and a subsequent complete evaporation really destroys information about the initial state. This process can also violate certain conservation laws like baryon number. But electric charge, as well as energy and other gauge charges are conserved. However, in standard General Relativity black holes have no 'hair', i.e. the asymptotic solution is completely characterized by only their mass, angular momentum, and electromagnetic charges. So their ability to carry additional gauge charges is limited, unless one allows for quantum 'hair' that resides on the horizon [1]. Though this quantum hair does not have long-range fields, its gauge charge is a conserved quantity.

Now consider a black hole with N different such conserved charges, and assume that these charges are (as is the case for the electric charge as well) each bound to massive particles, the lightest of which has a typical mass Λ. Imagine we set up a black hole that carries these charges, one of each, and we let it completely evaporate. During this evaporation, all the N charges need to be re-emitted somehow. But the black hole's temperature has to be high enough - or the mass has to be small enough respectively - before it can start evaporating off the massive particles. The required temperature is T ~ Λ, or the black hole mass is M~mp2/Λ, where mp is the Planck mass and roughly ~ 1016 TeV. To give you a feeling for these numbers: if we were talking about electric charge, the lightest particle is the electron with a mass of roughly .5 MeV, then the black hole can start evaporating off electric charge if its mass has fallen to ~ 1017 g.

However, there is also an obvious limit to this: the black hole needs to be able to provide the mass of the particles. If the black hole was charged but lighter than an electron it couldn't emit the charge no matter what [2]. If there were many different charges carried by particles with mass scale Λ, one comes to the conclusion that a bound results. The bound arises from the fact that after the black hole started evaporating off the charges, its mass must still have been high enough to provide all the N particles with mass Λ. One thus has N Λ ≤ M, or, if one inserts the above expression for the mass at which the emission of massive particles can start, one finds Λ2mp2/N.

The further argument is now the following. We don't know why the gravitational interaction is so much weaker than the other interactions of the standard model (SM). Or, to put it differently, we don't know why the masses of the SM particles are so much smaller than the Planck mass. If we take Λ to be the typical mass of SM particles (Higgs VEV) then there is a gap of roughly sixteen orders of magnitude. Dvali's inequality says if there were very many species particles, then there would necessarily have to be such a hierarchy. Putting in some numbers one finds the 'large' number is indeed very large, and somewhere around N~1032.

Now, as far as I am concerned this doesn't really 'solve' the hierarchy problem, one has just moved it elsewhere (as one also does with the extra dimensional models). Instead of having to explain the gap in the mass-scales one now has to explain where all the other particles are, and why so many of them? However, one can model these as only gravitationally interacting with our beloved standard model which would then only describe a tiny fraction of all there is. The question is of course why there don't seem to exist many particles of this kind around us. But this must stem from some processes in the very early universe, and inflation can easily make small numbers large, and blow up initially only subtle differences. Though it is hard to say at this stage whether it would actually work as desired, I can imagine that such a reformulation of the problem offers the possibility to find a dynamical explanation.

The signatures of such a scenario are in certain regards quite similar to those of extra dimensional models. One has a lot of only very weakly interacting particles whose coupling is given by the Planck mass. But since there are so many of them, their phase space gets really large, cancels the Planck suppression, and the signatures could become observable somewhere around the scale Λ. In contrast to the KK-tower in extra dimensional models however, here the number of species is really finite, so one doesn't have the problem of divergences in the higher dimensional integrals.

I can't say I particularly like the idea of having 1032 particle species, but I like the paper because it is another example for how thought experiments with black holes can lead to sometimes surprising insights. It's a cute idea to play around with that resides somewhere between General Relativity and particle physics, which is - still - a region of large mysteries.

What that has to do with the arrow of time however, I honestly don't know.

[1] A black hole can e.g. carry quantum hair associated with discrete gauge charges. This can happen when a local continuous gauge symmetry is broken down to a residual discrete subgroup. See ref [1] in Dvali's paper.
[2] However, since the electron mass is so much smaller than the Planck scale, such a black hole would long fall into the quantum gravity regime and no reliable statements can be made anyhow.



  1. "What that has to do with the arrow of time however, I honestly don't know."

    Haha! All the way through, as I read your report, I was thinking, "yeah, interesting, but what on earth does it have to do with the topic of the meeting?". Getting the answer at the end like that was fun...I suppose it is an indication of the difficulty of solving the problem of the arrow of time that people go to a conference and talk about everything else. But surely there were *some* talks that were not entirely irrelevant? :-)

  2. dude! thanks for the summaries of the talks. i felt bad that this conference was out of the question for me. but now i feel like i had front row tickets :)

  3. Isn't black hole evaporation a bit of a paradox, reflecting on the nature of time's arrow? A movie of unitary time evolution would be indistinguishable running forwards or backwards; but black hole evaporation is supposed to conserve information (and thus the process is in some way reversible) and yet the forwards and backwards running of the movie are distinguishable.

  4. Arun: the breaking of an egg when it is dropped would also look funny when reversed, but nobody doubts that that is a unitary process, correct?

  5. Hi Dr. Who:

    Well, you know, I am just currently organizing a workshop and I have the same problem that some of the people don't even seem to care what the workshop actually is about. Half of the time I really had to insist they speak about this or that, but I could picture them grumbling but-I'd-rather-this-or-that, some just ignored me, half haven't yet send a title or abstract anyway. Maybe next time when I organize a workshop I instead make a list of titles, and say those who talk about one of these topics get reimbursement or so?

    Hi Chanda:

    Unfortunately, my memory is very selective. I tend to recall things I did not understand, which accounts for most of the workshop, but isn't helpful to write about it. It also accounts for most of NYC btw.

    Hi Arun, Hi Anonymous:

    Yes, in a certain sense black hole evaporation as every thermal process says potentially something about the arrow of time. I don't think black holes 'destroy' information, so to me this process is no different from the sun radiating, it's just more complicated to understand.

    However, the black holes are different from the broken eggs in the following regard. A broken 'classical' egg can - theoretically - be un-broken by a suitable process, though it's extraordinarily unlikely. A black hole can classically be formed, but it can never be un-formed. The solution is fundamentally not time reversal invariant (the full Schwarzschild solution is, but it is static) because there are allowed curves leading inside the horizon but not out of it. Things look different if one includes quantum effects though, one could then argue if one stuffs Hawking radiation into the hole it will un-collapse or something, though this is extraordinarily unlikely to happen.

    Off topic comment: PI's server is apparently down since the early morning, I don't get any emails to my standard address, so either be patient or use alternate address. Thanks,


  6. Another possiblity: GR is incomplete. GR cannot handle aspects of angular momentum. The obvious astronomic test, PSR J0737-3039A/B (pdf), requires ~20 years of observation. Chemistry can do it in two days in commercial hardware.

    Angular momentum is the absolute arrow of time. Feynman's sprinkler doesn't go backwards in time, nor do whirlpools. Changing hemispheres can reverse swirl but not swirl plus flow.

  7. Great post, Bee, I enjoyed very much reading it!


  8. "Maybe next time when I organize a workshop I instead make a list of titles, and say those who talk about one of these topics get reimbursement or so? "

    Absolutely! Let's face it, most talks are boring enough even when they are on topic! The other thing you could do is to locate the workshop in some place which nobody likes, so as to eliminate the people who are just there for a holiday. "We wish to announce the XXXth workshop on Quantum Maggots, to be held in scenic Newark, NJ....with a satellite meeting on Avatars of Tribology in Mobile, Alabama".

  9. you mean like Somewhere, Ontario maybe? I am actually not sure whether your comment is meant to be ironic or not? I wasn't joking when I wrote the above, I really find it annoying if you go to a workshop on topic X but people talk about topics A,B,C,D instead, just because they like it better or it's a talk they presently have on their laptop. It's even more annoying if it then turns out that you've heard half of the talks previously anyhow, because they have given that same talk the whole year, including the same lame jokes etc. But to come back to our workshop, we have a bunch of good speakers who will give some overview talks which will make for an interesting week. Since we have a very mixed audience, I thought I should make sure there are some introductionary talks. I've tried to get together some particle physics people with the quantum gravity and cosmology guys, we will see how it works out. Best,


  10. Well, you know, I am just currently organizing a workshop and I have the same problem that some of the people don't even seem to care what the workshop actually is about. Half of the time I really had to insist they speak about this or that, but I could picture them grumbling but-I'd-rather-this-or-that, some just ignored me, half haven't yet send a title or abstract anyway. Maybe next time when I organize a workshop I instead make a list of titles, and say those who talk about one of these topics get reimbursement or so?

    Maybe it would make sense to go the other way around, i.e., collect the titles of the topics people want to give, and THEN decide the subject of the workshop so that it retroactively fits the papers you had submitted anyway. Of course, the subject might have to be somewhat contrived if the papers don't have much to do with one another...

  11. Sorry, I was joking about the location part. Certainly it is intensely annoying to go to all the trouble of attending a conference, only to hear that same old boring talk about completely irrelevant stuff, I fully agree. But it is also annoying to find, as I did when I went to a conference in Paris, that a lot of people went just so that they could visit Paris. Believe me, if you run a conference in Venice you will get a much stronger response than if you hold it in Detroit. In other words, a lot of people go to conferences for all the wrong reasons.

  12. Hi Coin:

    I guess it depends on what you organize a workshop for. If you just want to get people together to reach a critical brain mass, then it really doesn't matter what exactly they talk about. If you want - as is the purpose of my workshop - have different people working on related things to get interested in what the others are/have been doing so there is hopefully some kind of congruence in the field, then your suggestion doesn't work.

    Hi Who,

    Depends on how you see it I guess. Every institute of course wants to proudly show off with the local specialities, and if its an interesting place it will naturally attract people. I see a priori nothing wrong with that. As you say, yes, it is annoying if people register to a conference and then only show up for their own talk or so. This gets certainly noticed by the organizers, and if it was me, I wouldn't invite these people again. On the other hand I have to say that a bad conference organization can cause such behavior. If a conference is in an interesting place, of course people want to have time looking around, we all want a life besides work. So better give them some scheduled time to do so, and don't pack too much stuff on the program. As far as I am concerned, my head is full after 3 talks a day anyhow (given that all of them are new).

    The most annoying thing I find about conferences is if the organizers don't take care about accommodation, and do so sufficiently in advance, especially if its a big city etc because people usually don't make their travel plans sufficiently ahead. Like, when I was in Warsaw some months ago, it was almost impossible to find a hotel room (in fact, I did not find one), in NYC I wasn't able to get one < $ 300, same last year in Paris, the previous year in Budapest... I mean, how much time am I willing to spend looking for a hotel room for an appropriate rate before I cancel my participation?



  13. I think I understood the main argument-if you want to evaporate, you have to have low enough mass, but still more mass than the charges. What I don't understand is why does N have to be related to different gauge fields. Why couldn't it be N electrons? Or a mixture of 2, 3, etc of cherges, N in total?


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