meekerdb wrote:
On 11/6/2014 8:07 PM, Bruce Kellett wrote:
LizR wrote:
On 7 November 2014 14:59, Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote:
I agree that the past hypothesis, while it explains the
thermodynamic AoT, itself stands in need of explanation. This is the
great unsolved problem of cosmology -- at least according to many
cosmologists. The initial big bang might be assumed to be in
thermodynaic equilibrium, but that is essentially the same
assumption as the assumption of low entropy.
It's the opposite assumption. A quark-gluon plasma at a few trillion
degrees should rapidly tend towards thermodynamic equilibrium, given
the chance. Deriving the AOT from the expansion should let the AOT
emerge from almost any initial conditions, because it basically says
that the universe has no need to start in a low entropy state. It can
start in a state near maximum entropy, then chase behind the entropy
ceiling, which is continually raised by the expansion. Another way to
look at this is that expansion makes more states available for the
system to explore. The universe starts with a limited number of
available states and wanders amongst them, probably reaching a state
of high entropy in the process. In the meantime, the expansion brings
more available states into existence - phase space expands, so to
speak, as well as real space. The universe continues to explore its
options, doing a drunkard's walk through the available states for
billions of years, always tending towards higher entropy, while the
number of states available to explore continues to increase.
It is a questionable whether the expansion does give rise to more
states that the system can occupy. If position and momentum are
continuous variables, then the number of possible states is infinite,
even for finite volumes.
Unless Bekenstein's bound applies.
The Bekenstein bound applies to information coded in matter. A system
can have more possible states than can be coded in teh amount of
available matter.
These states might not be quantum mechanically distinguishable, given
the HUP, but the states exist, and eventually become distinguishable
as space-time expands.
There is also the question of Louiville's theorem -- the volume of any
cloud of points moving through phase space remains constant so entropy
cannot increase in this way.
I can because coarse graining is not over fractal grains. Entropy
always depends on how the coarse graining is defined.
Of course, which is why arguments over entropy are always rather
pointless. How can you define a maximum when you have not specified a
graining?
It is rather dubious that the maximum possible entropy increases with
the expansion of spacetime. Entropy is associated with configurations
of matter, and Bekenstein's bound states that the maximum entropy
configuration of any quantity of matter is attained when that matter
is compressed into a BH. The universe in which we live is not a BH, so
it is, and never has been, in a state of maximum entropy.
It's not clear that Bekenstein's bound applies *only* to black holes.
For example it may apply to the relative horizon of the Hubble sphere.
And it might apply to a white hole as just the time-reverse of a black
hole.
Regardles sof what BZ says on the avoid list, the Bekenstein bound does
not apply to the Hubble volume. If it did, entropy could not increase
within the volume, and we know that it does.
The maximum entropy remains constant given that the mass-energy
remains constant, regardless of expansion or the lack of it.
But, as you have pointed out, mass-energy does not stay constant in a
universe without a time-like Killing field.
True, but that only says that you cannot define the total mass-energy of
the universe, or measure it. It does not say that the mass-energy in any
particular co-moving volume is a meaningless concept.
SO the AoT comes from the statistics of increasing entropy and is
quite disjoint from the expansion of the universe. Correlation is not
causation, after all!
The question remains as to why it was in equilibrium. Generic
creation events might actuallybe expected to produce extremely lumpy
universe down to the smallest scaels. I.e., state with very high
entropy.
I don't think anyone is in a position to answer that question, but
certainly inflation (eternal or otherwise) naturally produces a very
smooth background. But somewhat lumpy backgrounds should work. This
is a question of the timescales involved, I imagine - the relaxation
time of a volume of matter against the expansion time. I'm not in a
position to answer that. Maybe someone else can (Brent?) However the
bottom line is that deriving the AOT from the cosmic expansion
doesn't require any particular special starting state. It appears
that the universe did in fact have a special (smooth) starting state,
however, which is why it's a natural assumption that this must be
connected to the AOT. But there's no particular reason for this to be
a necessary condition that I can see - one can get an expansion
derived AOT from many initial conditions, simply because expansion
raises the entropy ceiling constantly. So the smooth start is an
interesting piece of data that may relate to inflation or whatever,
but not necessarily to the AOT. No doubt it affects the way the AOT
plays out - similarly all over the universe, presumably, rather than
some regions being ahead or behind others.
The details of the inflation model come into play when one is thinking
about whether the observed smoothness is uniform or not. Actually,
inflation does lead to smoothness, and zero temperature for the
universe at the end of inflation. All the structure we observe comes
from the re-heating phase, when the energy of the inflaton field
decayed into particles and radiation. There is no reason to suppose
that this was a smooth process. Decays proceeding at different rates
and at different times in different places would be expected to
produce vast non-uniformities of temperature. Models have to be
extremely fine-tuned to give results in agreement with observation.
But regardless of this, the AoT cannot be derived from the expansion
-- it comes from increasing entropy, and the entropy of the universe
was always a long, long way below the Bekenstein bound.
How can you know that?
Because if it were not, it could not increase.
Bruce
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