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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