On 7 November 2013 14:48, meekerdb <meeke...@verizon.net> wrote: > On 11/6/2013 5:16 PM, LizR wrote: > > 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? > > 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. However that volume contains 15,625,000 hubble spheres. How is that possible?

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