On 7 November 2013 14:06, meekerdb <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?
Sorry to be so dense but I fear my brain may be not big enough to contain
this particular proof.
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