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.
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.
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.
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.
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?
Brent
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