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How Many States Does a Black Hole Have?
There has to be enough room in the black hole. You can't transfer the information. And entropy has to go up. So that's an example of the holographic principle at work. It's surprising not only because it's again weird that gravity knows something about the quantum states of matter. The statement is just true. But also it's surprising because you would have thought that the amount of information you can have in a region should grow like the volume, not like the area. If I make a heap of computer chips that each store a gigabyte of data or something, then the volume of the heap tells me how much information is stored rather than its surface.