The Large Hadronic Collider (LHC), which is to be the world’s highest energy particle accelerator, is currently being constructed at the CERN laboratory in Geneva, Switzerland. The machine was designed to be high enough in energy to produce a completely new type of particle, the Higgs boson, which is considered to be the missing puzzle-piece in the Standard Model of particle interactions. According to current theoretical thinking, it is the Higgs particle that gives mass to all the other particles, quarks, leptons, etc., in the current bestiary of fundamental particles.
However, there are new theoretical predictions that when the new accelerator goes into operation, the LHC's proton-proton collisions may also make something even more exotic: black holes. This column is about the possibility of black hole production at the LHC.
Physicists have found only four fundamental forces in our universe. These forces (with their relative strengths in parentheses) are: the strong force (1), the electromagnetic force (1/137), the weak force (10-6), and the force of gravity (10-43). Some current theories suggest that gravity is so much weaker than the other forces, not because it is intrinsically weak, but because gravity is allowed to spread out its lines of force into several extra dimensions, while the other three forces are confined to the 3+1 dimensional "brane" that we perceive as our universe. The implication of this idea is that, at small distances (less than a millimeter) and/or high energies (more than 1 TeV) gravity may become quite a strong force, as discussed in several previous Alternate View columns about extra dimensions for gravity (December-1999, April-2002, and August 2002). The implication of these ideas for the LHC is that the machine may be able to reach collision energies at which gravity becomes a very strong force and small black holes are produced in the collision.
Is this a disaster scenario, with the resulting black hole devouring first the LHC detector in which the collision occurs, then the surrounding French countryside and the city of Geneva, and finally the Earth itself? Fortunately, no. Black holes with masses around 1 TeV don't stay around long enough to devour anything. As Stephen Hawking taught us, they would be super-hot little objects that would dissipate all their energy very rapidly by emitting radiation and particles before they wink out of existence. But that's getting ahead of the story. Let's continue with some questions and answers about black holes.
Q: What is a black hole?
A: It's an object that has acquired enough mass for its size that its accumulated mass is completely confined by gravity, so that the velocity of escape of any mass from its surface exceeds the speed of light. To put it another way, the gravitational force at its surface is so strong that energy cost of moving a lump of mass from its surface to some distance away exceeds the mass-energy of the mass lump.
Q: Do black holes actually exist, or are they just some theoretical fantasy?
A: There is good astrophysical evidence for the existence of black holes from the energy-squandering behavior of quasars and active galactic nuclei, from x-rays emitted from certain binary star systems, and from the high velocities of stars near the center of our own galaxy, which is believed to have a large black hole at its center.
Q: How large can a black hole be?
A: There's no upper limit to the mass and size of a black hole. In a certain sense our entire universe is a black hole, with us inside.
Q: How small can a black hole be?
A: The mass of a black hole can be no smaller than a Planck Mass, which is (hc/2 pG)½, where h is Planck's constant, c is the speed of light, and G is Newton's gravitational constant. Since gravity is weak, G, which sets the scale of the strength of gravity, has a small value (6.67 × 10-11 N m2/kg2). This makes the Planck mass fairly large (22 micrograms or in energy units 1.22 × 1028 eV).
Q: In the Standard Model, could a minimum-size black hole be produced by an accelerator?
A: No. A minimum-size black hole should have a mass of about 22 micrograms, and an accelerator would need an energy of about 1016 TeV to produce it. That energy is many orders of magnitude higher than the few TeV available in the collisions of current accelerators like the FermiLab Tevatron, or accelerators under construction like the CERN LHC, or even accelerators in the planning stages like the NLC (see my column in the February-2002 issue of Analog).
Q: Are there ideas beyond the Standard Model that would allow production of a minimum-size black hole by an accelerator?
A: Yes. New ideas suggest that gravity becomes stronger at small distances because of the effects of extra dimensions used only by gravity. In this scenario, as the effective value of G grows larger, the Planck mass drops, and the energy required to produce black holes can drop to 1 TeV, well within range of the LHC but probably out of reach for the Tevatron. Thus, the LHC may turn out to be a "black hole factory", an accelerator that makes large quantities of minimum-size black holes.
Q: What would happen to such mini black holes?
A: As Steven Hawking showed in the 1970s, a black hole behaves like a hot object with a certain surface temperature that depends on the curvature of its surface. A mini black hole like those that the LHC might produce would have a very small radius (around 2 × 10-19 m) and a correspondingly large temperature (about 1.5 × 1014 K or about 25 billion time hotter than the surface of the Sun). In energy units, this temperature is 80 GeV. At such a high surface temperature, the black hole would "evaporate" very rapidly into lighter particles: photons, electrons, and quarks, with energies ranging from 80 GeV down.
Q: If such mini black holes were produced, what would be seen by the LHC detectors?
A: First, if no black holes were produced, an LHC collision would make a relatively small number of high energy particles that form into back-to-back "jets" or groups of high energy particles going in the same direction. On the other hand, if a black hole was made, the particle count would increase dramatically but the energy of each particle would be much smaller. Instead of making perhaps 100 particles with kinetic energies around 100 GeV or more, a collision event that made a black hole would make thousands of lower energy particles, including many electrons, positrons, and photons with energies around 10 GeV or less. Such a dramatic in the character of an LHC proton-proton collision should be very obvious in the collision data, and should provide a "smoking gun" signal of the production of black holes.
Q: Could such collision-produced mini black holes be "nurtured", prevented from decaying, and made larger?
A: Perhaps, but it's not obvious how that could be done. The black hole evaporation could only be suppressed by surrounding it with a medium that was even hotter than it was, so that it absorbed more radiation than it emitted. No such medium could be sustained. Even the interior of the Sun would be a billion times too cool to do the job. However, if you could immerse the black hole in such a medium, it would grow in mass and radius and cool in temperature as it absorbed mass-energy from the medium. Eventually, it might be cooled enough that it could be removed from the hot environment and become relatively stable.
Q: Would a stable black hole have any uses?
A: Indeed it would. It would be an excellent mass-detector and a wonderful energy source. It could be fed mass, and some fraction of the mass-energy (E=mc2) could be recovered and used. However, as a number of SF writers have pointed out, a "tame" black hole would also represent a certain hazard, since if it were accidentally dropped, if would probably fall to the center of the Earth and devour the planet from the inside.
That’s the LHC black hole scenario. At some energy scale, perhaps as low as 1 TeV, gravity may become a strong force and accelerators with enough energy may become “factories” producing mini black holes in great numbers. The black holes will evaporate away rapidly, in the process radically changing the behavior of the collisions.
Are there any problems with this theoretical scenario? I'm afraid so. The problems revolve around issues of time-reversal invariance and the arrow-of-time problem. In the everyday world we have no difficulty in distinguishing one direction of time from the other. A movie showing a dropped egg hitting the floor or a car crash looks very strange and unphysical if the film is run backwards. But on the macroscopic scale, there is supposed to be no time preference. A movie of the interaction of fundamental particles is expected to represent expected behavior, even if the movie is running backwards. This is called “time-reversal invariance” and it is an important symmetry principle of the microscopic world.
But a mini black hole would strongly violate this symmetry. A movie of a super-hot black hole emitting particles has a distinct time direction and would look strange and unexpected if the movie were run backwards. This means that particle collisions at the LHC should show dramatic violations of time reversal invariance. Moreover, since right-vs.-left handedness and matter-vs.-antimatter asymmetries cannot be expected to compensate, the more fundamental TPC symmetry principle (time-reversal plus matter-antimatter interchange plus reversal of spatial directions) will also be violated. Even at lower collision energies at accelerators like the FermiLab Tevatron, where there may not be enough collision energy to produce free black holes, sub-threshold virtual process involving black holes might be expected to produce time reversal and TCP symmetry violations, (but we note that none have been observed).
Is there any way around this problem that would permit mini black hole production at the LHC? The physics literature is silent on this issue because the time-reversal invariance aspects of black hole production in particle collisions have not yet been analyzed or discussed in detail. However, let me suggest a possible fix.
In general relativity, in addition to the solution to Einstein’s equations that we call a black hole, there is another solution called a “white hole”. It is in effect the time-reverse of a black hole, a black hole running backwards. In a black hole, matter falls in to become completely bound with no possibility of escape, while in a white hole, matter falls out to escape completely with no possibility of binding. If matter runs down the drain of a black hole, it emerges from the fountain of a white hole. In observational astronomy no evidence for white holes has ever been found, despite several searches. Moreover, there are arguments that if cosmological white holes were ever produced, they would have vanished early in the Big Bang.
However, the time-reversal problem of the above scenario could be cured if the LHC produced black holes and white holes in pairs, with most of the particles emerging from the white hole feeding into the black hole. I’m not sure how such a system would evolve, but as in the black hole scenario above, it would probably evaporate into lighter particles and be observed primarily as a change in the character of the spectrum of particles emerging from an LHC collision..
The test of these ideas will come in a few years.. When the LHC goes into operation, we may discover the Higgs boson or we may find that indeed gravity becomes a strong force. Or we may discover other things that on one has even predicted. What this column for further developments.
Production at the LHC:
“Black Holes at the LHC”, S. Dimopoulos and G. Landsberg, Phys. Rev. Letters 87 (2001) 161602, preprint hep-ph/0106295 available at http://arxiv.org ;
“Black Hole Chromosphere at the LHC”, L. Anchordoqui and H.Goldberg, preprint hep-ph/0209337 available at http://arxiv.org .
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