2008-09-25: Will CERN create a black hole?

On a forum I visited, some people were getting worried about the LHC at CERN in Switzerland producing a black hole. In fact, this seemed to be a rather common public concern. I couldn't resist the opportunity to respond to all the scaremongering. A real physicist will probably laugh at my calculations, but I don't truly care. Even if I'm off by several orders of magnitude, there will be nothing to worry about.

IANAQP (I Am Not A Quantum Physicist), but I do know a little bit about it. The smallest category of black hole is the one with a mass of less than that of the moon. That's still an awful lot of mass. Although quantum theory says that particles are created and destroyed the whole time, even in a vacuum, the total amount of energy in the universe remains the same.

What Einstein's famous "E=mc²" describes is that energy and mass are interchangeable. This means that you can convert mass into energy (for instance: burn a coal, you get heat. Some of the mass has been converted into energy -- the remaining ash will be lighter than the coal was originally). It is also possible to convert energy into mass, but no easy example springs to mind as this is a more difficult process that requires enormous amounts of energy. For example: 1 gram of mass (think of the weight of a 5 pound banknote) is equivalent to 89.9 terajoules. To produce that much energy, you'd need to save up all the output of a nuclear power plant for 25 hours. Or convert all the energy released by the nuclear bomb dropped on Nagasaki into matter. Now, that's how much energy you need to convert into mass for a banknote.

How much do you guess you'll need to make the mass of the moon? Well, if you're impatient and don't want to take more than those 25 hours, you'd better start construction on some 73 septillion nuclear power reactors. That's a 25-digit number! Of nuclear reactors! If you're not in a hurry or can't afford to build that many reactors (or run out of planets to put them on), let's just use 1 reactor and keep it running for, oh, 209,694,634,703,196,347,031,963 years. (Roughly 15 trillion times the estimated age of the universe).

No man-made object in the foreseeable future will produce that amount of energy.

So, what are we left with? A smaller black hole, consisting of less mass, still using stupendous amounts of energy. Such a black hole would be tiny beyond belief. Even one with the mass of the moon would be about the size of a particle of common house dust. A lighter one would be even smaller.

Now, this mass is all concentrated in that small volume, almost a point. Is that dangerous? Not as much as you might think. Assuming an 8 gram black hole (that's the weight of 2 sugar cubes), what is that going to do? It still only weighs 8 grams. Are those 2 sugar cubes dangerous to you by mere presence? The biggest danger you have of those is offending a passing diabetic. Those sugar cubes won't suddenly suck you in. An 8 gram black hole exerts the exact same gravitational pull as those sugar cubes. That is negligible. It is still a black hole, though, so light can escape from it, and neither can matter. But that is true only within its so-called "event horizon". Outside that, think sugar cubes. For such a small black hole, the event horizon is very tiny. The only way it extends is to attract more matter, e.g. more mass, and become heavier.

An actual "micro black hole" that might be created in the LHC would be a lot lighter than those 2 sugar cubes. 400,000 times lighter, according to accepted theory. To create that, the energy output of the LHC would have to be increased by a factor of, oh, lemme think, 10 trillion! The LHC has a radius of just over 2.5 miles. To get it to be able to create that infinitesimal black hole, you'd have to enlarge it to a radius of nearly 3 quadrillion miles. That's big. That's very big. That is stupendously big. The diameter of that SHC (stupendous hadron collider) would be roughly 250 times larger than the distance from the sun to the nearest other star.

If such a black hole were created, über-egghead Stephen Hawking has theorised that it would actually disintegrate in a flash of gamma radiation anyway. Nasty, but not too much to worry about. People in the direct vicinity might be affected by a small nuclear explosion underground in Switzerland, but the Chernobyl disaster was much bigger. So were the famous nuclear tests.

If you've read this far (and most probably haven't), you'll have seen lots of really large and really small numbers. As said before, I Am Not A Quantum Physicist, but those numbers are of such an unimaginable scale that even if I'm off by a factor of a million on all counts, it'd still be absolutely unlike any thing the people at CERN can produce. In the incredibly unlikely event that a black hole were produced, it'd be pretty much harmless.

You have more chance of getting hit by an asteroid than you have of being affected by the LHC.