The Edge question for 2012 is “What is your favorite deep, elegant or beautiful explanation?” There are lots of interesting answers given but my favorite is not included. That’s partly because they did not have the foresight to ask me, but never mind I can post it here.
My favorite explanation is Stephen Hawking’s argument for why the area of a black hole horizon increases. This is a very non-trivial result from gravitational dynamics and yet the explanation can be summarized almost rigorously in words without any equations. Not only is it elegant but it is also very deep since it leads to the idea that the area of a black hole is related to entropy, a hunch that Hawking later clarified with his theory of black hole radiation and thermodynamics. This in turn led to the information loss paradox which was explained by the holographic principle. It is a remarkably persuasive train of thought that takes us on a journey far beyond anything that experiment or observation can currently reach, an amazing demonstration of the power of the human mind. I am sure I do not need to describe the details of these ideas to most readers of this blog. Any of you that are not familiar can read about them in Wikipedia when it comes back from its anti-anti-piracy sulk.
Anyway, here is Hawking’s beautiful explanation quoted from “a Brief History of Time”
“I had already discussed with Roger Penrose the idea of defining a black hole as the set of events from which it was not possible to escape to a large distance, which is now the generally accepted definition. It means that the boundary of the black hole, the event horizon, is formed by the light rays that just fail to escape from the black hole, hovering forever just on the edge. It is a bit like running away from the police and just managing to keep one step ahead but not being able to get clear away!
Suddenly I realized that the paths of these light rays could never approach one another. If they did, they must eventually run into one another. It would be like meeting someone else running away from the police in the opposite direction – you would both be caught! ~ But if these light rays were swallowed up by the black hole, then they could not have been on the boundary of the black hole. So the paths of light rays in the event horizon had always to be moving parallel to, or away from, each other. ~ If the rays of light that form the event horizon, the boundary of the black hole, can never approach each other, the area of the event horizon might stay the same or increase with time but it could never decrease because that would mean that at least some of the rays of light in the boundary would have to be approaching each other. In fact, the area would increase whenever matter or radiation fell into the black hole. ~ This nondecreasing property of the event horizon’s area placed an important restriction on the possible behaviour of black holes.”