## Thursday, January 29, 2009 ... //

### LHC: black holes living for seconds?

Yesterday, I had to spend hours with a debate about global warming under my article at The Invisible Dog, a famous Czech personal internet daily of Mr Ondřej Neff, a well-known science-fiction writer, called Rationally About Weather And Climate - a modified Czech version of Weather and Climate: Noise and Timescales.

Yes, it seems that the skeptics have won once again. ;-) The IPCC's proxy, Dr Ladislav Metelka, is an OK chap and he's not even terribly radical. But he has shown his remarkable ignorance in many ways.

For example, a reader asked him why the IPCC seems to predict that the temperature change per CO2 concentration change is speeding up as the concentration goes up, in violation of the logarithmic law. Metelka answered some incoherent nonsense that the IPCC result includes all feedbacks, and it can therefore be accelerating. Of course, the real explanation was that the reader had calculated "temperature change OVER concentration" instead of "temperature change OVER concentration change".

He forgot to subtract 280 ppm from the concentration, and when he did it right, it worked as expected: the influence is slowing down. The reader understood the error (and the correct answer) completely. I am sure that he must have learned the feeling of being sure that his knowledge is more robust than the knowledge of the self-declared best Czech mainstream climatologist.

Black holes at the LHC

But there is one more type of alarmism that began to spread in the media, the LHC alarmism. You know, the LHC will create a black hole that will destroy the Earth. A few days ago, a new wave of this stuff began to penetrate through the media. See e.g.
MSNBC: Study revisits black-hole controversy
FoxNews: Scientists not so sure 'doomsday machine' won't destroy world
and others (Google News). The story is based on a new preprint by Roberto Casadio, Sergio Fabi, Benjamin Harms,

On the Possibility of Catastrophic Black Hole Growth in the Warped Brane-World Scenario at the LHC
Well, these authors do conclude that black holes cannot grow catastrophically at the LHC but they say a lot of "worrisome" things, anyway. For example, they say that the black holes may live for seconds (or minutes) and their evaporation may even be slower than the accretion of matter so that these black holes may grow for quite some time.

What a complete nonsense. Let me explain why.

The LHC is rather unlikely to produce black holes. But if it will, and I estimated the probability to be comparable to one percent, the black holes will be very close to the minimum-size black holes that deserve the name. Why? Simply because we haven't produced black holes yet and the LHC is only going to surpass our current energy frontier by one order of magnitude at the energy scale. Because there have been no lighter black holes, the LHC black holes would be almost the lightest ones that are possible.

But the minimum black holes that deserve the name have the radius that is equal to the higher-dimensional Planck scale - the minimum distance that deserves the name. Depending on your method how you treat the extra dimensions, this distance may be longer or shorter. But it surely can't be longer than 10^{-18} meters because otherwise we would have already seen quantum gravity effects.

Now, if a black hole has this minimum size, the fundamental Planck scale, the evaporation time is comparable to the same fundamental Planck scale - at most 10^{-25} seconds. You know, in the fundamental (higher-dimensional) Planck units, everything - including the black hole size - is of order one, so the evaporation time (being a simple function of other quantities) must clearly be of order one (i.e. a supertiny Planck time), too. That's the simplest dimensional analysis argument you can ever make. As David Berenstein will nicely explain in two days from now :-), estimates and dimensional analysis belong among the most useful and most important skills of a physicist.

Even if you imagine that the Lorentz gamma factor (determining the time dilation) is 10^{4}, like for the protons themselves, the black hole is still going to live for less than 10^{-21} seconds in the lab frame.

This upper bound is enough to travel the distance 10^{-14} meters, the size of the nucleus, but it is not enough to get from one nucleus to another: the atomic radius is about 10,000 times longer. This black hole would be a thousand times heavier than a nucleus, so if it swallowed one whole nucleus (which is already very unlikely), it wouldn't influence its mass substantially. But it is pretty much guaranteed that the black hole won't live long enough to hit another nucleus even if it happened to move in the right direction: it will decay much earlier. As we mentioned, the lifetime is at most 10^{-21} seconds in the lab frame. Seconds are just ludicrous.

Recall that this time, 10^{-21} seconds, is already an amazingly inflated estimate (made possible by the extra dimensions) because the conventional laws of four-dimensional quantum gravity would predict the lifetime of minimum-size black holes to be of order the normal Planck time, 10^{-43} seconds.

We have considered the discrete nature of the matter and argued that such a small black hole can't live long enough to hit several nuclei even if it had the right direction to do so (which is very unlikely). So it can't ever eat macroscopic amounts of matter before it dies. There are many ways to quickly see that such a "worry" is completely absurd.

Cross sections: power in and out

For example, let us compare the cross sections. For the sake of simplicity, we will work in the units where 1 fermi is equal to one and approximately 1 proton mass is also equal to one (which is compatible with c=hbar=1, too). The density of ordinary matter is at most 10,000 kilograms per meter cubed which is about 10^{31} protons per 10^{45} cubed fermi, or 10^{-14} in our dimensionless units. The eating rate (in kilograms per second) is equal to the mass density times the black hole cross section times the velocity (speed of light).

Because the black holes must be smaller than 0.001 of the proton radius, the black hole cross section (or event horizon area, if you wish) is surely smaller than 10^{-6} in our dimensionless units. The product with the matter density is below 10^{-20} in our dimensionless units: that's the upper bound on the eating rate.

On the other hand, the evaporation rate is "area times temperature to the fourth" which goes like "R^2 T^4" = "R^2/R^4" = "1/R^2". This 4D scaling is actually correct for higher-dimensional black holes, too: the temperature is always comparable to the inverse radius.

The black hole radius is 10^{-3} in our dimensionless units, so the evaporation rate (mass per second) is about 10^{6} in the black hole rest frame. Even if you add time dilation, slowing the decay rate in the lab frame, with the gamma factor of 10^{4} inherited from the protons - which is a substantially exaggerated figure because the black holes would be created nearly at rest - you will still get at least 10^{2} for the evaporation rate.

It is therefore at least 10^{22} times faster than the accretion rate which we showed to be below 10^{-20} in the previous text. Those 22 orders of magnitude should allow you to sleep really well (and it should have been really more than 25 orders of magnitude). You may be picky and find various factors of 2.pi at various (five?) places but that could only change the result by a few orders of magnitude, not by 22 orders of magnitude.

Again, the statemenent that such black holes can live for second is exaggerated at least by 20 orders of magnitude. (Even a nanosecond, or a meter, is absurd.) This mistake seems to be related to the truly stupid mistake by R. Plaga who wrote an alarmist paper in August 2008.

As Giddings and Mangano explicitly wrote (but their leadership was surely not needed even for a slightly above-average physics student to see Plaga's mistake) that Plaga overestimated some power output by 23 orders of magnitude, too. How did he do it? Well, he combined some four-dimensional scaling formulae with completely different five-dimensional scaling formulae in an inconsistent way. Well, that gotta hurt. With such mistakes, it is easy to add 23 orders of magnitude wherever you want. You either assume that certain objects follow 4D laws or the 5D laws. Such an assumption may be incorrect but if you assume both of these things at the same moment, your assumption is guaranteed to be wrong. Saying that they follow both is equivalent, in this case, to the statement that 10^{23}=1.

You know, their mistake is so spectacularly wrong that it has nothing to do with any numerical factors or the particular pseudomathematical games they pursue. In such cases, physicists worth the name are simply able to do very fast order-of-magnitude estimates of the result: detailed calculations of integrals and sums can only serve as the "second phase" refinements of the initial estimates. I don't think it makes any sense to go through the seemingly complicated sums written in the paper by Casadio et al. These sums have clearly nothing to do with the discrepancy. Dimensional analysis may sometimes go awry but if it does, it must always be possible to localize the error.

I assure that any major mistake in the scalings and upper bounds explained above would be a spectacular discovery in physics that might be at least on par e.g. with the Randall-Sundrum discovery of a new scenario for extra dimensions. And it would have to be justified by an idea that would be so obviously clever that hundreds of high-energy physicists would immediately work on it. For example, if one could argue that the minimum, very light black holes producable by the LHC might be 1 centimeter in size instead of 10^{-18} meters or less, that would surely be spectacular.

I have no idea how such a dramatic revision of physics could be justified but I am sure that no revolution of this caliber is waiting for the readers in the Casadio et al. paper. The page 1 of their paper indicates that Casadio et al. haven't understood the stupid mistake by Plaga, not even after Giddings and Mangano explained it. The paper is just plain dumb, the authors should return their undergraduate physics diploma for the waste of time they have written, and all the articles about it in the mainstream media are equally silly.

And that's the memo.

P.S.: Similar stupidities are often promoted by male journalists, too. But I predicted that the MSNBC story would have a female author and I was right: Jeanna Bryner.

Update: a sociological paper

To make things worse, arxivblog.com promotes another new preprint about the sociology of estimates,
Probing the Improbable: Methodological Challenges for Risks with Low Probabilities and High Stakes
by three unknown authors from "Future of Humanity Institute" (wow, this pure trash is affiliated with Oxford). They claim that the tiny calculated probabilities of the destruction of the world are not important because there is a non-negligible probability that the "safe" arguments themselves are wrong.

And you know, I must tell you that at a qualitative level, this comment is surely correct. If there exists a high enough probability that an argument is wrong, the tiny probabilities of an event predicted by this argument can't be taken seriously. Space shuttle failures - that were absurdly claimed by some bureaucrats to be as unlikely as 0.001% - are the best example I can think of.

At the same moment, I must tell you that if you apply this meta-observation unreasonably, you may be prevented from breathing or living or anything else, or you may be forced to do really crazy things. Why? Because you may always construct a crazy statement and argue that the argument showing that the statement is crazy has a chance to be wrong.

For example, you may think that your nation won't die tomorrow if you avoid the church tonight. Someone can give you a seemingly rational explanation that your nation won't die. But he may be wrong, after all. Does it follow that everyone must go to the church tonight? Well, one can prepare inconsistent collections of ideas in this way. Imagine that your nation dies if you do visit the church instead! ;-)

Of course, this inconsistency can be imported to the case of the LHC, too. Maybe, the life is going to disappear unless we will be colliding two 7 TeV beams in 2009. For example, an extraterrestrial alien may blackmail us in January 2010, demanding six Higgs bosons: otherwise she will exterminate us. Some people may tell you that the scenario will probably not occur, extraterrestrial aliens may not be around, and the survival of the mankind doesn't require the LHC to run. But what if these people are wrong? People are often wrong, aren't they?

When you abandon all scientific arguments, how are you going to decide that the probability of the doom is higher if the LHC runs than if it doesn't run? By checking whether the LHC is more similar to God who saves us or the Devil who brings us to the hell? In that case, let me assure you that the LHC is God machine! We will all die unless it runs. ;-)

This game can lead to many absurd and inconsistent conclusions. My main point is that every question that is studied rationally must follow some self-consistent methods to estimate the probabilities of various outcomes. There are all kinds of methods - theoretical, phenomenological, historical - showing that the LHC doom is not possible (it is an extremely robust combination of approaches!) and there are no methods to show that it is possible.

You can still say that the LHC doom is possible because the existing arguments are wrong for unknown reasons while the correct arguments are unknown. But if you use such a meta-argument against the LHC and not e.g. about your visit of the church tonight, it only shows your bias.

You may dismiss arguments based on string theory because you're not certain about the validity of string theory. Fine. You may dismiss all arguments based on effective field theory or quantum mechanics in general. Fine. But if you also dismiss the historical arguments that look whether there has been any disaster in the previous 5 billion years, then you simply don't have any rational basis for your thinking. If you reject theoretical, phenomenological, as well as historical arguments, it is absurd to claim, like these three authors do, that "Rather, we need robust estimates that can handle theory, model and calculation errors." There simply can't be any robust estimates of anything if one simultaneously rejects all conceivable kinds of rational thinking.

The LHC project was started in the good old times when nutcases such as these doomsayers were considered to be what they are, namely nutcases. Of course that one can brutally and completely reorganize the society and the decisions about difficult scientific issues so that idiots' opinions may be considered equally important as Frank Wilczek's, Steve Giddings's, my, or other expert opinions - just because there are many idiots, they can write preprints, and many stupid journalists can promote them in the media.

But it would be really sad and costly if the society were reorganized in this way.

#### snail feedback (8) :

Hi Mr. Lubos;
I know nothing about physics, I am just a guy that works in construction and has been unable to sleep or work for 2 days due to the fact that earthquakes around the world have been blamed on the gravity waves created by the hundreds of Black Holes produced by the LHC.
After reading your blog I have calmed down and will sleep more soundly tonight. I still have a couple of questions, that are probably very stupid to you but I would feel grateful if you could answer them.
1. If Hawking radiation does not prove true, and several Plank Black holes are created, merge and migrate to the center of the earth. How long would it take for it to destroy earth. A couple of years, hundreds or thousands.
2. Would there be any warning signs and time for humans to build ships and escape?
3. There are other things called strangelets, what are they, should I worry about it?

Dear Karl,

good fantasies but during the recent earthquakes, the LHC was not even colliding any particles, so it couldn't create any new particles (or black holes) even if they were possible and stable enough etc. ;-)

Collisions will resume on March 30th or so, at 7 TeV total energy, 3 times higher than the previous record.

1. Even if Hawking radiation didn't exist, which is really a physical nonsense, and LHC produced the black holes, it would surely not produce enough of them for even two of them to ever meet and merge. So the idea that such black holes would merge is unrealistic.

You should imagine a few particles whose typical radius is much shorter than the atomic nucleus. And they're created at random times. They don't have any reason to merge. You know, 7 TeV sounds as a great energy, but if you ask how heavy the particles are in normal units, using the E=mc^2 conversion formula, 7 TeV is just 10^13 eV which is 10^{-6} Joules which is something like 10^{23} kilograms, just 3-4 orders of magnitude heavier than a proton.

So the mass of the objects created at the LHC collisions is just comparable to very large nuclei. The mass also determines the gravity. It's clearly negligible - as negligible as gravity created by one heavy nucleus: it's the same mass, after all. Such gravity is not enough to attract things by the force.

The only way how such a thing could grow would be to directly hit the nuclei. But the typical cross section - typical area that you must hit for a reaction to occur - is almost certainly much smaller than the atomic radius because the black holes are made of much smaller stuff. When such an object goes through your body, or the Earth, it would be very unlikely to eat even a few nuclei.

But if the cross section happened to be bigger, for crazy reasons - if all my physics calculations broke down - then, of course, the black hole could grow and swallow more stuff. It would grow pretty much exponentially after some time, and it would swallow the Earth pretty soon. We know that this can't happen because if it could, it would have happened naturally billions of years ago.

...

...

2. It depends on the speed. I can't really answer your question because the right answer of physics is that such a disaster scenario can't happen. To answer that it can happen, you need to modify physics in several new crazy ways. Then the answer whether you're warned in advance depends on the modifications you make.

It's like writing science-fiction - you may choose whether the catchy phenomena in it are moderately sensible or really crazy. I don't want to write science fiction. Whatever remotely sensible modification of the laws of physics I can imagine, still implies that there can't be any threat like this.

3. Strangelets are mutated atomic nuclei that contain a new type of quark, the strange quark, which is heavier. There exist indications to think that such things may prefer to grow much bigger - and be remotely stable - than ordinary nuclei.

The "practical" result would be almost indistinguuishable from black holes, but with different numbers. The general methods to see that they can't be dangerous are similar, especially the astrophysical bounds ("it would have happened already"). See Wilczek and others, 1999, for a discussion of the strangelet speculative scenarios (optimized for RHIC).

It can't really happen in the real world but of course, there are some fun calculations that people may do to get a little bit excited, too.

Strangelets are less popular as the killers today for purely sociological reasons. People just got used to talking about black holes. That doesn't mean that black holes are a bigger threat than strangelets. In fact, one can invent other threats, such as a spontaneous decay of the vacuum etc. ;-) None of them can threaten us in the next billion years, to say the least, but people can still scare each other like children by hiding into closets. :-)

Best wishes
Lubos

Dear Mr. Lubos;
Thank you very much for your information. On my ongoing quest to understand some more about mini black holes. I came across a paper published in the Physical Review Lettters by Dr. Matthew W. Choptuik from the University of British Columbia and Frans Pretorius from Princeton University published this on the site on December 17 2009. Called Ultrarelativistic particle collisions. Where they prove via computer simulations using Einsteins GR that Black Holes are not only posible but very likely to occur by colliding particles at 1/3 of plank speed. Physicist Josehp Likken from Fermilab the American Collider, says that experts on black holes need to look at this very closely. The energy needed of 1/3 of plank can be significantly reduced if more dimensions are involved. Mr. Lubos, I was wondering if you have read this paper and maybe shed some light into it. How much is one third of plank in Tev and if several dimensions are involved how many Tev will be needed to create this black hole in a particle accelerator? Thank you very much.

Dear Karl,

the Planck scale - note that it's spelled with "ck" - is defined as the size or mass of the smallest black hole deserving the name.

So your statement that black holes are produced in Planckian collisions is not only true: it is tautologically true. It directly follows from the definition.

The conventional "four-dimensional" Planck energy, as calculated by Planck, is 1.22 x 10^{16} TeV which is 12,200,000,000,000,000 TeV. So be sure we won't build the required accelerator - which would have to be as big as the visible Universe.

All the discussions about the creation of black holes by the colliders always assume that thare are extra dimensions - otherwise it's just technologically impossible to create black holes at colliders.

With extra dimensions, especially in the Randall-Sundrum scenario, the "fundamental" Planck scale - the energy of the lightest black hole - can be reduced to a few TeV. We know that it can't be lower than that because the signs of such black holes would have already been detected.

Yes, if the higher-dimensional Planck scale is at a few TeV, the LHC will be able to produce such black holes. But it's just nonsensical to imagine that these black holes are completely new objects. Light black holes are just like heavy elementary particles of other types - that just tend to decay to many lighter resulting particles or decay products (like if they evaporate - they do).

They surely do evaporate even if they exist - it follows from the very same theory that calculates that they can exist in the first place.

Even if you assume that physicists like Hawking (or myself who checked him) are dumb, the cross section of such small black holes is too small for them to eat much before they escape from the Earth. Even if they were confined by the Earth and started to eat matter, we know that they can't eat the whole Earth because if the laws of physics tolerated such a thing, the Earth would have been gone for billions of years - because of similar black holes created by collisions of cosmic rays (against the Earth).

Cheers
LM

Dear Mr. Lubos;

Thank you very much for answering the questions I have put forward to you. The more I read about black holes, the more I realize I know nothing. Since I was not able to sleep or work for 2 days as I wrote to you in my first comment. I can honestly say that “Ignorance is no bliss”. From my limited point of view I am still a little uneasy. I would like to ask you several questions if it is ok with you. I will understand if you feel they are not good questions but I think they will clear up many blind spots. I have read that you consider a 1% probability of the LHC creating tiny black holes. These I understand would not be the regular GR-Black Hole, but other type of black holes because they would be created thanks to extra dimensions. Hawking also came up with the 1% chance of the LHC creating this Tiny black holes.
1) How do scientist like you and Hawking know that there is a 1% chance of this event occurring if no one I am aware of has measured the frequency of these Tiny black holes being created. How do scientists know they are created by cosmic rays if no one has observed this natural phenomenon, and there is no known mechanism for them to form via normal processes of stellar evolution?
2) Hawking says that these Tiny black holes end their life in a burst of light and gamma radiation, NASA’s GSLAT satellite is currently searching the cosmos for such flashes, thus, the burst of light and gamma radiation of one of the Micro black holes would be thousands of times brighter than the sun. What would be the impact of one of these Tiny black holes ending its life in the LHC. Should I worry about it?
3) Since the Micro black holes created at the LHC would be virtually stationary vs the ones created on the outer atmosphere and their mass would be insignificantly low. Quantum gravitation would play a significant role on them vs the ones created on the outer atmosphere. What would be the impact on these, the lightest of black holes? Would they rotate, could they hypothetically become stable? I came across this article on Wikipedia which has me up at night, like an owl.
“A Black Hole of mass 1 TeV/c2 would take less than 10−88 seconds to evaporate completely. Of course, for such a small black hole quantum gravitation effects are expected to play an important role and could even hypothetically make such a small black hole stable.” Source WIKIPEDIA
4) Do black holes operate in a spherical 4 dimensional area or in a 2 dimensional way? If they act on 2 dimensions. Would that not affect the amount of tev required to produce one?
5) In the Alice experiment, where the density of the particles will be greatly increased to produce the primordial particles seen only at the start of the Big Bang. Would it not also create the conditions for a primordial black hole?
6) Since Black holes can carry a charge, depending on the particles they gobble up. Could physicists give the black hole a negative charge by firing electrons at it from a cathode ray tube and then trap it within a box lined with negatively charged metal plates; thus having the negatively-charged black hole repelled by the negatively-charged walls. Leaving it suspended inside a vacuum where it could then be jettisoned from earth in a rocket?

Thank you very much Mr. Lubos

Sincerely;

Karl

Dear Karl,

I would like not to add you sleep disorder but because I don't know what's the right algorithm, anyway, let me answer your questions.

First, the LHC-created black holes, if they happen to occur, are not regular 3+1D black holes from GR. But in a more general interpretation of GR, they are solutions to GR - but in higher dimensions. They're solving the very same equations where the coordinates are e.g. 5 instead of 4, and the indices can also have more values.

1) The percentage 1% is my estimate based on the probability that various data describing the size of the extra dimensions fit into the LHC interval etc. This 1% is a purely informal guess and has nothing to do with Hawking's calculations.

There is nothing objective about 1%. Indeed, 1% will be proved wrong in 5 years. The right estimate will be known to be either 0% or 100% because the question will actually be settled. So 1% only reflects a particular calculation of the odds given our incomplete evidence.

My estimate is like this because the likelihood for one extra dimension being parameterically bigger than others is e.g. 20% - five equally big scenarios - and when it is bigger, its size/curvature can be anywhere in 15 orders of magnitude. I take a uniform distribution on the log scale - and end up with 1% or so that the dimension is "behind the corner", detectable by the LHC.

There's no hard science behind this estimate. It's just meant to express the feeling that Randall-Sundrum at the LHC is not excluded but it's less likely than yes.

If these black holes can be created by the LHC, they must also be created by collisions of the cosmic rays against the celestial bodies - and gas. That's because we know, by direct detection, that there are very high-energy cosmic rays, and there are also many protons at rest, and the center-of-mass energy of these collisions, whose rate is substantial and we can calculate it, exceeds that of the LHC. By Lorentz symmetry, only the center-of-mass energy of the collisions matter, and the LHC value is routinely surpassed by the natural collisions. Cosmic rays can have up to 10^{8} TeV, ten million times above the LHC beam energy.

2) A tiny black hole that can be produced by the LHC is similar to a decaying nucleus 100 times heavier than the uranium. It's still an elementary particle of a sort, by its size. It's ludicrous to compare it to stars by its energy output. It's just a somewhat heavy but not too heavy a particle that may decay to 10 others but not a Sun that emits trillions of photons.

Hawking would love somewhat bigger black holes that would emit e.g. visible light. That would be great. They would have to be a micrometer (or 10^{29} Planck lengths) in size. But a black hole that is so big would have mass 10^{29} Planck masses which is 10^{21} kilograms, not far from the mass of the Moon, Clearly, you can't create it by colliding two protons even if their mass is inflated 10,000 times by the relativistic effects.

The black holes emitting visible light would be cute sources of energy but they would still be similar to any piece of metal of this size heated up to the temperature of thousands of degrees - like the solar surface. Nothing too impressive in its output but good enough for Hawking to get the Nobel prize.

So the output of the LHC-created black holes is negligible and surely not a reason for concern. I don't understand what you mean by other black holes' ending their life at the LHC. Even if I knew what black holes you're talking about, why does it matter where they end their life?