On 11/6/2013 5:16 PM, LizR wrote:
On 7 November 2013 14:06, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>>
wrote:
On 11/6/2013 4:15 PM, LizR wrote:
That's very interesting. I'm afraid I can't quite see what is meant by the
entropy
of the universe being maximal but not the local entropy. There is a
claculation
showing that the entropy in a sphere is less than maximal /until /the
sphere equals
the Hubble volume. This is where my understanding breaks down. This is the
sort of
thing I was trying to explain - badly I expect - in my last post. How can
the
entropy of a small sphere be non maximal if the entropy of the entire
observable
universe is maximal (I referred to "information" but entropy is probably
better).
Because the entropy density is roughly constant and depends on the number of
different quantum fields. So the entropy within a volume is proportional
to the
volume. But the Beckenstein bound is proportional to the bounding surface
area. So
for small spheres the maximum possible entropy can be much bigger than the
BB; but
as you consider larger spheres the entropy due to particle fields goes up
as the
cube of the radius while the BB only goes as the square. So at some size
the former
catches up with the latter. And this happens roughly at the Hubble radius;
which
suggests it may be more than a coincidence.
Yes it does rather. The BB is (I believe) supposed to specify the maximum possible
entropy (or information) that can physically exist within a volume - so the fact that
the BB for the Hubble sphere equals the calculated entropy within it implies that the
universe couldn't contain any more information than it does, or equivalently that the
entropy is maxed out overall. Or that the universe is a black hole, or that the
expansion parameter (or whatever it's called) is exactly 1. Or something along those
lines. I'm still not sure I understand how we can have local pockets of low entropy if
the universe is at maxium entropy overall, though. And what happens when the hubble
sphere expands, as it is doing?
You're confusing the *observable universe*, i.e. the Hubble volume, the sphere relative to
us whose surface is being carried away at c due to the expansion of spacetime. This is
NOT *the universe*. It's a tiny part and it's defined relative to us or relative to any
other point. The universe is very likely infinite. Observationally we can only say it's
at least 251 times bigger than the observable universe (because it's so nearly flat). The
Hubble volume is like a black hole in that things come into it but nothing inside can
leave because it's boundary moving away from us at c. But it's not a black hole because
it doesn't contain a singularity.
Brent
Sorry to be so dense but I fear my brain may be not big enough to contain this
particular proof.
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