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quote:Originally posted by realmswalkerBlack holes suck in matter, and prevent it from being chaotic, eventually condensing it into a single point, what could be more ordered that that?How does this conform witht he fact that entropy must always increase?As black holes exist more and mroe (as they will when the universe advances) eventually all matter ought to be caught in them, and therefore entropy must not increase...idk maybe im wrong...
quote:Originally posted by DocNStarting from some theorems proved by Stephen Hawking, Jacob Bekenstein conjectured that the black hole entropy was proportional to the area of its event horizon. The black hole entropy is proportional to its area A. The fact that the black hole entropy is also the maximal entropy that can be squeezed within a fixed volume was the main observation that led to the holographic principle.
quote:Originally posted by another_someoneIf the maximal entropy is proportionate to area, then how can it be the maximal for the volume? Volume and area are not the same thing?
quote:Originally posted by lightarrowhttp://en.wikipedia.org/wiki/Holographic_principlequote:"...so the entropy contained in a given region of space cannot be larger than the entropy of the largest black hole which can fit in that volume."So, it's not possible to fix volume and area of that region independently one of the other: if I consider a region of space with a given volume, I cannot arbitrarily increase its area to infinite, for example warping it into a table-like shape, because the largest black hole which can fit inside it couldn't be larger than the table tickness. At least, this is how I have understood it.
quote:Originally posted by another_someoneSorry, I still don't understand.I was not suggesting that the shape would be anything but spherical, but nonetheless, the surface area is proportional to the square of its radius, while the volume proportional to the cube of its volume. This implies that the larger the black hole, the smaller the volume density of entropy, because the entropy is merely increasing quadratically, while the volume continues to expand cubically. In other words, the sum of the entropy of lots of small black holes filling a volume would be less than the entropy of a single black hole filling that same volume, so how can a single black filling a given volume be considered of maximal entropy.
quote:Originally posted by lightarrowIf entropy of ordinary mass (not just black holes) is also proportional to area, then this implies that volume itself is somehow illusory: that mass occupies area, not volume, and so the universe is really a hologram which is isomorphic to the information "inscribed" on its boundaries ."When I read it for the first time, I was upset too.
quote:Originally posted by lightarrowWhy should entropy density be more important than entropy itself? The second law refers to entropy, not to entropy density.