LizR wrote:
Well, yes, I knew someone would mention that when I typed it! And yes, I
agree, the Beckenstein bound implies that - although isn't that dealing
with information, rather than quantum states (leaving aside any
it-from-bitness, at least) ? Or maybe the two are equivalent.
I'm not sure how (or if) Max got around that one when he did his
calculation of the distance of the nearest duplicate, but given that the
answer came out as something like 10 ^ 10 ^ 28 metres, that makes the
surface area to volume ratio awfully low for any sphere enclosing both...
Max also calculates the distance to the nearest identical 100-lightyear
sphere and nearest identical Hubble volume, and it looks to me as though
he's assuming 3D space operates as Euclidean geometry would predict. To
be exact, he says that
These are extremely conservative estimates, derived simply by
counting all possible quantum states that a Hubble volume can have
if it is no hotter than 10^8 kelvins. One way to do the calculation
is to ask how many protons could be packed into a Hubble volume at
that temperature. The answer is 10^118 protons. Each of those
particles may or may not, in fact, be present, which makes for
2^10^118 possible arrangements of protons. A box containing that
many Hubble volumes exhausts all the possibilities.
FYI the article is here
http://space.mit.edu/home/tegmark/PDF/multiverse_sciam.pdf
Whatever the merits of that argument, it has little to do with the
maximum possible entropy. Rember, that occurs when all of the
mass/energy is in the form of black holes.
Bruce
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