Knocking on Heaven's Door - Lisa Randall [86]
Such scenarios would imply that when we explore smaller distances at which the effect of the extra dimensions can in principle appear, a very different face of gravity could emerge. Theories involving additional dimensions suggest that the physical properties of the universe should change at the larger energies and smaller distances that we will soon explore. If extra-dimensional reality is indeed responsible for observed phenomena, then gravitational effects could be much stronger at LHC energies than previously thought. In this case, LHC results would not simply depend on gravity as we know it, but also on the stronger gravity of a higher-dimensional universe.
With such strong gravity, protons could conceivably collide in a sufficiently tiny region to trap the amount of energy necessary to create higher-dimensional black holes. These black holes, if they lasted long enough, would suck in mass and energy. If they did this forever, they would indeed be dangerous. This was the catastrophic scenario that the worriers envisioned.
Fortunately, however, classical black hole calculations—those that rely solely on Einstein’s theory of gravity—are not the whole story. Stephen Hawking has many accomplishments to his name, but one of his signature discoveries was that quantum mechanics provides an escape hatch for matter trapped in black holes. Quantum mechanics allows black holes to decay.
The surface of a black hole is “hot,” with a temperature that depends on its mass. Black holes radiate like hot coals, sending off energy in all directions. They still absorb everything that comes too close, but quantum mechanics tells us that particles evaporate from a black hole’s surface through this Hawking radiation, carrying away energy so that it slowly goes back out. The process allows even a large black hole to eventually radiate away all its energy and disappear.
Because the LHC would have at best just barely enough energy to make a black hole, the only black holes it could conceivably form would be small ones. If a black hole started off small and hot, such as one that could potentially be produced at the LHC, it would pretty much disappear immediately. The decay due to Hawking radiation would very efficiently deplete it to nothing. So even if higher-dimensional black holes did form (assuming this whole story is correct in the first place), they wouldn’t stick around long enough to do any damage. Big black holes evaporate slowly, but tiny black holes are very hot and lose their energy almost right away. In this respect, black holes are rather strange. Most objects, coals for instance, cool down as they radiate. Black holes, on the other hand, heat up. The smallest ones are the hottest, and therefore radiate the most efficiently.
Now I’m a scientist—so I have to insist on rigor. Technically, a potential caveat to the above argument based on Hawking radiation and black hole decay does exist. We understand black holes only when they are sufficiently big, in which case we know precisely the equations that describe their gravitational system. The well-tested laws of gravity give a reliable mathematical description for black holes. However, we have no such credible formulation of what extremely small black holes would look like. For these very tiny black holes, quantum mechanics would come into play—not just for their evaporation, but in describing the nature of the objects themselves.
No one really knows how to solve systems in which both quantum mechanics and gravity play an essential role. String theory is physicists’ best attempt, but we don’t yet understand all its implications. This means that in principle there could be a loophole. Extremely tiny black holes, which we will understand only with a theory of quantum gravity, are unlikely to behave the same way as the big black holes we derive using classical gravity. Perhaps such very tiny black holes don’t decay at the rates we expect.
Even this isn’t a serious loophole however.