Black holes at the LHC

The Planck length: theoretical background

Lenin used to believe that every electron was a galaxy that contained many smaller electrons that were again galaxies with a lot of even smaller electrons and this hierarchy continued indefinitely.



Even though a similar idea of structure and substructure works well at many longer scales, there are many ways to see that this matryoshka-like picture of the world can't be right at the sub-electron level. For example, in reality, all electrons are exactly indistinguishable, even in principle. This is experimentally seen in various proofs of the antisymmetry of their wavefunctions - for example, via the Pauli exclusion principle that controls the atoms. Any internal structure that is not uniquely determined would make two electrons distinguishable and the Pauli exclusion principle would become impossible.

Another reason why these infinite hierarchies can't exist is quantum gravity itself. It is easy to prove a qualitative conclusion that distances must be longer than the Planck length if they can be interpreted via the usual geometric intuition. At shorter distances, quantum phenomena and new physics strongly influence the behavior of objects and prevent us from understanding them in terms of events that occur at well-defined positions in space. Moreover, geometry can no longer be separated from other kinds of existence. Because the uncertainty principle makes the geometry fluctuate so violently, distances shorter than the Planck scale don't exist in the operational sense of the world.

Alternatively, you may say that the information can't be stored in balls that are smaller than the Planck scale because the number of bits inside such balls would have to be smaller than one bit. Information smaller than one bit is too tiny and doesn't allow you to say "something is here" or "something is not here".

Particle physics used to study the internal architecture of particles at ever shorter length scales by pumping ever greater amounts of energy into the particles. The more energy they have, the closer they can get together and the better resolution your collider - a fancy gigantic microscope - can have.

But this rule according to which the characteristic distance is inversely proportional to the characteristic energy doesn't work forever and cannot work forever. As the energy reaches the Planck energy that is connected with the Planck length and you continue to increase the energy, the experiment will no longer allow you to probe shorter distances. Instead, the collisions will produce ever more massive black holes whose size increases as the mass grows: your resolution will bounce and becomes poor again.

The Planck length is the smallest length scale that can be resolved by any experiment one can think about. More generally, the Planck scale is the ultimate cosmic limit for many other quantities, too. The Planck time is the shortest time you can measure, the Planck density is the maximum density that you should ever talk about, the Planck temperature is the highest temperature you can achieve, and so on.



How big are these Planckian quantities? If you set the universal constants $\hbar, c, G_{Newton}$ equal to one - which is what quantum, relativistic, gravitational adult physicists usually do - the Planck quantities are simply equal to one. In normal units, you can thus write them as appropriate products of powers of $\hbar, c, G_{Newton}$ that have the right units. For example, the usual Planck length is equal to $(G_{Newton}\hbar / c^3)^{1/2}$. Numerically it is about $10^{-35}$ meters. A very short distance.

Planckian transition

So what happens when your colliders reach the Planck energy, normally about $10^{19}$ GeV? If the energy of colliding particles is below the Planck energy, the old-fashioned rules of particle physics work. Higher energies translate to higher frequencies, shorter timescales, and corresponding shorter distances. However, as you reach the Planck energy, what you produce no longer looks like ordinary elementary particles. If your center-of-mass energy is well above the Planck energy, the colliding particles get closer to one another than the Schwarzschild radius if they interact at all which is why they produce a black hole. If you keep on increasing their energy, the resulting black hole will grow in mass and radius.



So how does Nature decide whether you produce a normal particle or a black hole?

Actually, there is no qualitative difference between the two. The transition between elementary particles and black holes is smooth. When the elementary particles are much lighter than the Planck mass, you should talk about them in terms of concepts of particle physics. However, as their energy surpasses the Planck scale, these elementary particles inevitably start to act as microstates of black holes. The heavier they are, the more accurately they can be described by classical general relativity.

The particles whose energy is comparable to the Planck scale are the lightest black holes that deserve the name. These baby black holes have a Planckian radius, mass, and energy. The Hawking process decomposes them into a small number of particles of radiation - a number comparable to one. The Hawking evaporation process makes their lifetime very short - comparable to the Planck time. The Planckian black holes evaporate so quickly that it looks like they are shrinking almost by the speed of light.

Only if black holes are larger, their evaporation slows down. They emit a much larger number of the Hawking thermal particles - a number that grows with the black hole mass as a positive power law - and their lifetime becomes much longer than their radius in Planck units. Black holes that are large but not too large can be described by the classical general relativity and quantum or stringy phenomena add tiny corrections. Note that in both limits - very light objects as well as very heavy objects - we know the right zeroth approximation.

In particular vacua of string theory, all the players in the previous paragraphs become very well-defined objects that obey very clear rules of mathematics. In all realistic or semirealistic vacua of string theory, the qualitative rules above hold. But it is fair to say that even quantum gravity theorists who are not string theorists realize that the general picture of the transition from particles to black holes is valid. We know these things without any direct experiments.

You can listen to Peter Woit, Lee Smolin, and one million of additional crackpots whose net IQ exceeds 60 million points and who complain that any conclusion that relies on the human brain or mathematics can't be trusted - it is not even wrong, they will tell you. The number 60 million seems high but it is certainly not enough to change the conclusion by a millimeter. The laws of physics, mathematics, and logic are unbreakable and the only thing that the crackpots can do against them is to brainwash each other and make idiotic journalists write hundeds of moronic newspaper articles.

Can the Planck be closer?

The Planck energy is very high. It is about 15 orders of magnitude higher than the LHC can squeeze into its colliding particles. That will make an artificial production of black holes - even baby black holes - very difficult. Isn't it possible that the black holes are actually much easier to create?

The answer is that the it may be possible even though it looks unlikely: we estimated the probability that black holes would be produced by the LHC at 0.2 percent. The Planck quantities were calculated by dimensional analysis. The easiest way to change the dimensional analysis is to change the dimension. More precisely, you dismiss the usual Newton's constant as a constant in a bad effective theory and you better switch to the higher-dimensional description that doesn't neglect additional dimensions of space. You thus change the dimension of $G_{Newton}$ because the new constant will appear in Newton's law in a different spacetime dimension, with a different power of the distance. That will force you to compensate its dimension by different powers of $\hbar$ and $c$ in order to get the new Planck length.

If there are additional dimensions of space, the fundamental higher-dimensional Planck scale may be much longer than $10^{-35}$ meters advertised above. If you look at all possibilities - old large dimensions and warped dimensions - you will find out that the fundamental Planck length may be as long as the distances accessible to the LHC, about $10^{-19}$ meters. In other words, the LHC could be able to produce baby black holes as long as it simultaneously brings us evidence for extra dimensions - a necessary pre-requisite for the validity of the dimensional analysis we used.

What happens?

Well, if the LHC has enough energy to produce small black holes - but larger than baby black holes - they will go through spindown; Schwarzschild phase; Planckian phase. During the spindown, the angular momentum is rather quickly reduced by emitting many Hawking particles with the angular momentum preferrentially aligned with the black hole's angular momentum.

This will leave us with a black hole that looks almost like a Schwarzschild black hole. You shouldn't forget that such a black hole has many - about $exp(S)$ - quantum microstates that can be interpreted as elementary particles but that are guaranteed, by consistency of quantum gravity, to obey the laws of general relativity. The Schwarzschild black hole will radiate many Hawking particles in all directions. Such a decay into a large number of products looks like fireworks and its signatures are very different from other models of physics beyond the Standard Model.

As the black hole emits and shrinks, it ends up as a baby black hole that is already indistinguishable from ordinary but heavy elementary particles. Details of the processes depend on the scenario - old large dimensions vs warped dimensions and perhaps other details - and the "ordinary" elementary particles can still organize themselves into new phenomena at different energy scales that look like excited strings, branes, or strings moving in additional dimensions.

The black holes discussed in this article shouldn't be confused with the black holes at RHIC whose character is very different from the kind of black holes that you learn about in courses of general relativity because these RHIC black holes only exist in massively curved spaces and they are consequently equivalent to physics of non-gravitational systems such as QCD.

More details about black holes at the LHC may be found e.g. in:

Dimopoulos + Landsberg (over 400 citations, analysis in the context of old large dimensions)
19 more preprints about black holes at the LHC
Report on a recent talk by Steve Giddings
Man-made black holes and global catastrophes

Enjoy and don't be afraid of a global catastrophe caused by the LHC! ;-)

Al Gore & Live Earth

Posted on 07/07/07 at 07:07:07. See also 06/06/06 06:06:06 and 11/11/11 years after the birth of 11-dimensional M-theory at 11:11:11.

Hundreds of musicians have demonstrated that there is much stronger consensus about global warming among rock musicians than among scientists: all of them want to look like saviors of the world while all of them want to live in the most expensive hotels and mansions and to fly in private jets. All of them may be used as textbook examples of hypocrites.

They should better try to be saviors of modern music because saviors of the world usually cause a lot of troubles if they're morons at the same moment, and sometimes even if they're not.

I am not a fan of this particular kind of music and listening to most of those unknown musicians for hours would be a pain for me. The format and goal of Live Earth was a classical advertisement - attempts to connect show industry with unrelated products - but a good advertisement of this type is 24-seconds-long, not 24-hours-long. (A long chain of these concerts was broadcast by the 2nd program of the Czech public TV station - the weakest among 4 major national TV channels. I suppose that the number of people who watched it was negligible.)

It would be much more pleasant for me to listen to one approved hit - such as "All I wanna to is have some fun with one square of toilet paper" by Sheryl Crow or some songs by Madonna - for many hours.

In some sense, I feel that the event could have had a positive impact - it may return "global warming" its well-deserved status of a fashionable ad supported mainly by people who don't have too much stuff in their skulls and whose ideas don't have a lasting value and by their weird audiences who often live on drugs and whom you don't want to live with or even listen to.

That's why I not only subscribe to Martin Durkin's quote below but I even think that most people whom I call sensible surely agree with it:

I think [the concert is] a combination of hypocrisy and ignorance because the idea of Al Gore and Madonna telling us the world is consuming too much makes the mind boggle. But ignorance because so few people are prepared to actually look at the evidence and there is so much evidence now that flatly contradicts the notion of man-made global warming. I think this is political prejudice rather than science.

We have also learned from organizers of the concert in South Africa that the poor attendance in Johannesburg was caused by global warming, too, because extreme cold weather is always caused by global warming, much like normal weather in the other cities.

Jan Hus: burned at stake in 1415

When I left the U.S., both your humble correspondent as well as America celebrated the Independence Day.

That was no coincidence because the air tickets for all other dates were sold out too early. People apparently think that July 4th is the most likely date for a new large terrorist attack against the U.S. soil. Well, the terrorists think that July 4th is the most attractive day for such an attack but because others know what these terrorists dream about, I feel that July 4th is not such a likely date for a terrorist attack, after all.

There would have been lots of things to write about that have something to do with my transfer to Europe but I personally find blogs filled with similar topics boring. But you may expect that such things will appear later.

When I arrived to Prague, July 5th, it was another holiday: in 863, two orthodox missionaries, Saint Cyril and Methodius, arrived to Great Moravia, an ancient edition of Czechoslovakia, and brought the nation scripture and Christianity translated into a Slavic language. The German Catholic influence from the West has later diminished the religious impact of their visit on Czechoslovakia but the scripture has probably had a more lasting impact.

In order to continue with this holiday rule, July 6th is a Czech national holiday, too. Mr Jan Hus - I chose this name because he is actually referred to as "mistr Jan Hus" - a Czech early protestant - was burned at stake in 1415. He invented diacritics - the accents you find in Czech texts, e.g.

• Žluťoučký kůň úpěl ďábelské ódy.

This is a standardized sentence - "Cutely yellow horse was groaning devilish odes" - with a high concentration of special characters that was chosen to test diacritics and find out what coding system a given file/server uses. Fortunately, the problems with various incompatible trans-ASCII coding systems have mostly disappeared and they haven't influenced me in any way for years. Mr Jan Hus has also discovered that the sum of angles in a triangle is always equal to three. ;-)

Even though Hus was a religious preacher and about 60% of Czechs don't believe in any God, he has been viewed as a national hero for quite some time. Many Czechs associate him with the building of the Czech national self-confidence against Germany. Communists liked him because of many additional reasons, especially because the hussite movement that was promoting Hus' ideas after he was executed was living according to the rules of communism.

(The hussites were both communists and terrorists who were singing majestic songs to defeat their enemies - but let me admit that I am still more proud about them than ashamed of them.)

And many people like myself like Hus because he was fighting against numerous bad moral characteristics of a certain fashionable establishment of his era and especially against the gigantic hypocrisy of the 15th century Catholic Church - hypocrisy that was only surpassed by Al Gore and his Church around 2005.

The religious impact of both Cyril and Methodius as well as Mr Jan Hus was limited - the Czech nation was mostly catholic one for centuries because it became one of the two most secular nations in the world - but people like Cyril, Method, and Hus are always needed.

And that's the memo.

LHC: horrible girls from CERN are back

Most readers of this blog don't have to be introduced to

Les Horribles Cernettes,

the horrible girls from CERN, a high-energy rock band whose picture was incidentally the first image on the web and whose music has been played on this blog as background sound for more than a month.



After 6 years of absence, Les Horribles Cernettes (WWW) are back on the planks of the CERN Hardronic Festival. On July 21st, they will rock their fans out at CERN Restaurant 3 (Prevessin), with three new songs adding to their physics inspired repertoire: "Big Bang", "Mr. Higgs" and "Every proton of you". Since the release of "Collider", their classic hit song in 1990, the Cernettes have become the queens of "High Energy Music", a branch of High Energy Physics that many physicists cannot live without. Dear to over 20 thousand physicists worldwide, the girl trio has been featured in world class press, including the New York Times, the Herald Tribune, Wired etc., and has performed at numerous physics related events around Europe, official and not, singing about quarks, detectors, the web, networks, microwaves, and the Large Hadron Collider. In fact the LHC, whose acronym was derived from the band name, became famous as a seating appliance for the singers, before becoming a particle accelerator. The band was in fact photographed while sitting on an LHC dipole, 10 years before being built, in what became the first picture ever published on the web. The Cernettes, in the current line up with Michele, Anne, and Victoria, will sing again with their live band (in more recent appearances they had sung over a recorded base), and promise to rock the place down, as is their standard, and to get absolutely everybody at the festival dancing and shaking madly to their sixties sounding doo-wop rock & roll tunes.

Via Silvano de Gennaro, The LHC Management Office