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. 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.
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. The maximum
entropy remains constant given that the mass-energy remains constant,
regardless of expansion or the lack of it. 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.
Bruce
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