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 ofthe universe being maximal but not the local entropy. There is a claculation showingthat the entropy in a sphere is less than maximal /until /the sphere equals the Hubblevolume. This is where my understanding breaks down. This is the sort of thing I wastrying to explain - badly I expect - in my last post. How can the entropy of a smallsphere be non maximal if the entropy of the entire observable universe is maximal (Ireferred 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.`

Brent

It doesn't seem to make physical sense. But then the whole BB surface area thing doesn'tseem to make sense, to me at least, because if you consider a sphere and move outwardsyou are including matter / information / entropy proportional to the cube of the radius, but the amount of information and entropy allowed to exist inside the sphere goes upat the radius squared. At some point - apparently the Hubble sphere - surely somethinghas to give!What am I missing here?On 7 November 2013 13:03, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>>wrote:On 11/6/2013 2:46 PM, LizR wrote:On 7 November 2013 11:31, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote: On 11/6/2013 2:09 PM, LizR wrote: That's similar to my pet theory for explaining the Beckenstein bound - information capacity only goes up as volume in the multiverse. The volume of the multiverse is generally thought to be infinite. Even the volume of our universe may be infinite. If you want to apply the Beckenstein bound, consider the observable universe since its boundary forms an horizon relative to us. Yes. The BB has to be applied to a finite volume. Indeed it seems ridiculous, intuitively - the volume of the universe is quite likely infinite, so we can apply the BB on larger and larger scales for as long as we like (in theory) - and if we do so, we will presumably find that we reach a point where the information content we derive for the interior of that volume is insufficient to account for its contents. (Or does something always prevent that happening in practice - is this the point at which we reach a "cosmic horizon" ? Does the BB have an "information protection conjecture" that makes the universe safe for information theoreticians?)If you estimate the entropy of the visible universe (i.e. our Hubble volume) as being the Beckenstein bound it comes out the right order of magnitude corresponding to an estimate from particle physics. http://www.colorado.edu/philosophy/vstenger/Origin/EntropyCosmol.pdf Brent

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