On 11/6/2013 6:22 PM, LizR wrote:
On 7 November 2013 14:48, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>>
wrote:
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.
OK, but that doesn't alleviate the confusion. If anything it makes it worse. What
exactly can we deduce from the entropy of the observable universe being approximately
maximal when measured by other means, given that the BB apparently places a bound on the
entropy that can exist inside a given volume? Assuming the universe to be, say, 250
times larger than the hubble sphere (for the sake of argument) the BB would say that the
maximum entropy it can contain is 62,500 times the entropy of the hubble sphere.
No it doesn't say that. The BB applies to an event horizon, not just any spherical
volume. In an expanding universe there is only one specific radius where the boundary is
moving away at c, and that's an event horizon.
As to what we can deduce from it...that's a good question.
Brent
However that volume contains 15,625,000 hubble spheres. How is that possible?
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