Pedagoguery

One of the most useful tools for the high energy physicist is the particle accelerator. With it, physicists probe the realm of the minute, discovering fundamental particles and probing the very nature of matter. As they become capable of generating ever higher energies, an intriguing possibility is arising – the creation of microscopic black holes.

When we think of black holes, we typically think of massive objects formed by the collapse of a star. However, anything can form a black hole if it is compressed enough. To turn the sun into a black hole, its mass would have to be compressed down to a radius of three kilometers, about one four millionth of its actual size. The earth would have to be compressed to a radius of nine millimeters, about one billionth its current size. In general, the smaller the mass, the greater the required compression. In today's universe, the smallest mass that can typically form a black hole is star sized.

This was not always true, however. In the very early universe, conditions were right for the formation of much smaller black holes. Density fluctuations either in the era before inflation, when the average density of the universe was greater than an atomic nucleus, or immediately after inflation, could have conceivably created primordial black holes. However because of Hawking radiation, a quantum effect that causes black holes to evaporate, black holes smaller than about 10¹² kilograms (about the mass of a small mountain) would have already evaporated and exploded. If such black holes exist, we could conceivably observe them exploding right now. In fact, that is one possible explanation for the short duration gamma ray bursts.

According to quantum theory, the smallest black hole that can possibly be formed would have a mass of 10^-8 kilograms, also called the Planck mass. Such a black hole would have a diameter of 10^-35 meters (the Planck length). (The Planck mass and length are so-called because they are derived by multiplying and dividing fundamental physical constants, such as the Planck constant, to arrive at a value that has the dimensions of a mass or a length.) Such an object would have an effective density of 10⁹⁷ kilograms/meter³ – a value far beyond what even the most advanced particle accelerator is capable of. How, then, can we contemplate the possibility of creating them? The answer lies in string theory.

These days, string theory is starting to fall a little out of favor. The biggest problem with it is that it is in fact an infinite number of theories. Each configuration of the extra 7 dimensions of string theory comprises a different universe with a different set of physical laws. The mathematics is so complex that the tools to solve them have not been developed. If, as many physicists expect, the extra dimensions are on the scale of the Planck length, they would not be physically detectable using particle accelerators in the conceivable future. This means that those string theories are not really testable, and therefore, they are not properly scientific theories. However, if the extra dimensions are significantly larger than the Planck length, say around 10^-19 meters, then some interesting possibilities arise.

One of the peculiarities of gravity is that it is very sensitive to the number of physical dimensions. The more dimensions, the faster it drops off with distance. Conversely, the more dimensions, the faster it gets stronger as distances decrease. For this reason, it is possible that if the extra dimensions exist and if they are large enough, at small scales the newer particle accelerators could conceivably have the ability to produce black holes.

How would we know if we had produced a black hole? The detectors in particle accelerators are very sensitive to particles flying away from collision sites. Each kind of particle decay produces a distinctive signature of particle tracks through the detector. A black hole would produce a very distinctive array of particle tracks.

How would a quantum black hole behave? It would pass through a number of stages. Right after the collision, it would be highly asymmetrical, and it would likely have a high spin and probably an electric charge. A famous quote by physicist John Wheeler is “A black hole has no hair.” By this, he meant that black holes have very few observable properties. In fact, they have only three: mass, spin, and electric charge. Immediately after the collision, the black hole quickly sheds all other properties, thus this is called the “balding” phase. Typically, after the balding phase, the first thing the black hole will lose will be its electrical charge, as it emits charged particles that neutralize any charge it may have. At this point, it enters the spin-down phase, as its spin gradually slows as the hole's angular momentum is carried off by emitted particles and gravitational radiation. When its spin is gone, it has entered the Schwarzschild phase, where it becomes perfectly spherical. Eventually, its mass becomes too small to sustain itself, and it goes into the Planck phase, where it explodes. The whole process from formation to explosion would take about 10^-26 seconds.

If this premise is correct, then when the Large Hadron Collider at CERN in Switzerland is operating, it could conceivably create one quantum black hole per second. Upon hearing that, you might think, “Are they crazy!? How could that possibly be safe?” Well, the answer is that if the LHC is capable of producing quantum black holes, then the process of quantum black hole creation has been going on for longer than humans have been around. Cosmic rays hitting the earth's atmosphere are potentially even more energetic than collisions produced by the LCH, so if quantum black holes can be produced in the LHC, they have been produced by cosmic ray collisions in the atmosphere all along. Since the earth hasn't been destroyed by this process, it seems like a good bet that the LHC won't destroy the earth either. In addition, the potential knowledge gained by probing the universe at such scales makes it worth the minuscule risk.

Next issue: Are the laws of physics changing?