LizR wrote:
On 7 November 2014 13:29, Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote:
meekerdb wrote:
On 11/6/2014 4:08 PM, Bruce Kellett wrote:
meekerdb wrote:
You seem to overlook that the "expansion" is very likely
just tautological, i.e. it is nomologically necessary
that the AoT points in the direction of bigger.
No, it points in the direction of higher entropy.
Sure, but the physics is such that entropy must increase in the
direction of expansion - the two are linked (that's what I meant
by "nomologically necessary").
I disagree. There is no necessary connection between the expansion
and the increase in entropy. The total possible entropy might
increase with expansion, but if we are always a long way below the
total possible for a given volume, the entropy could increase
whether the universe were actually expanding or contracting.
Anything else and you are necessarily committed to a reversal of the
arrow of time if the universe begins to re-contract at some point.
This may be why the AOT exists, now that we've discovered dark energy. A
recontracting universe may not have one, because the two cancel out, so
anthropically we find ourselves in a U with Dark Energy. (Just a thought.)
I don't think that makes much sense -- how can arrows-of-time cancel out?
As far as we know the thermodynamic AOT isn't due to fundamental
physics. That is, entropy isn't a fundamental feature of physics
(despite that famous quote from Arthur Eddington) but an emergent
one. Below a certain .level of "coarse graining" it disappears. At the
very fine scale (eq particle) all interactions are reversible and it is
impossible to define entropy (except for bound states - these emerged at
an earlier stage of the universe from a collection of unbound states in
which all interactions were time-symmetric - see below).
Just because something is emergent does not mean that it is not
fundamental. Sure, the AoT arises, with entropy, when you coarse-grain
things. But there is very probably a deep connection with QM here -- you
only get definite results for quantum experiment when you coarse-grain.
That is what the partial trace of the density matrix, needed to go from
the initial pure state to the final state mixture, is actually doing. It
amounts to ignoring certain information because it is lost in the
coarse-graining. Entropy arises in the same way -- you ignore certain
microscopic information in the interests of the larger picture. The
second law -- increasing entropy -- then follows as a matter of
statistics. So it is as fundamental as getting a particular result in a
quantum experiment -- and it is hard to get more fundamental than that!
Hence logically you need to connect the thermodynamic AOT to something
that *is* fundamental, or at least more so, to explain why it exists.
The expansion is a possible reason and given that it's THE major feature
of the entire universe that is time-asymmetric, it looks like an obvious
candidate. Plus, even to a bear of little brain like me, the links
aren't particularly obscure, although there are some obscure details
involved (but that's only because we, or at least I, don't know
everything about everything).
Generically, expansion cools aggregates of particles. It does this by
separating out particles according to velocity - a particle that is
moving faster than average in a region tends to leave it and move to a
region where the average speed is nearer to its own velocity. This
effectively cools the particle, and hence all the particles cool as
expansion proceeds. Also, matter gets less dense, which is also
important in generating an AOT since it allows structures like galaxies
to form from an almost uniform matter background.
This is not how it works in cosmology. The expansion is uniform, so it
does not separate particles according to velocity. That would probably
not even work if the expansion were of a hot gas into empty space. And
the cosmological expansion most definitely is not like that!
Cosmological expansion works in different ways depending on whether the
matter in the universe is in the form of radiation, or of particles. If
it is radiation, the expansion stretches the wavelength as well as
decreasing the density, so the energy content falls off like r^{-4}
rather than r^{-3} that we have for particles. The density of particles
decreases because they get spread out, but their relative velocities do
not change.
In the beginning, all matter was very energetic, in the extreme
relativistic domain, so everything was effectively radiation, and cooled
by that law (1/r^4). But since matter and anti-matter annihilated to
produce photons, the number of photons dominated over the number of
particles, so the 1/r^4 cooling continued. Once it reached a temperature
below the ionization energy of Hydrogen atoms, atoms were able to form.
The universe suddenly became transparent. The radiation from this time
is what we now see as the CMB.
Let's start at the quark soup era. Things are a big vague before that.
Expansion cools the soup, and eventually collision energies drop enough
for nucleons to form without being blown apart by subsequent collisions.
This is an early (perhaps the earliest) example of how a system that is
in equilibrium, and in which all interactions are time-symmetric, can
change to one in which there is some structure simply by expanding and
hence cooling it.
Expansion cools the nucleons, until nuclei can form...
Expansion cools the nuclei, until ionised atoms can form...
Expansion cools the atoms, until neutral atoms can form...
As outlined above, this is not really correct.
Expansion now allows a more or less uniform gas to clump into larger
scale structures by amplifying any existing inhomogeneities. This allows
stars etc to form, and eventually us, without introducing any new
physics; all the large scale structure is emergent from time-symmetric
physics operating on mass-energy during a non-time-symmetric
cosmological expansion.
Again, the facts are rather different. Gravity comes into the picture,
and gravity can only work on pre-existing inhomogeneities. But the large
scale clumps are gravitationally bound, so they take no more part in the
overall expansion. They do not, therefore, cool further because of
expansion. The only way primeval clouds of gas can clump further is if
they lose energy. Charged particles can lose energy because when they
collide they can radiate. The radiation is not gravitationally bound, so
that energy is lost to the system, which cools - ultimately enough to
coalesce into stars and planets. Electromagnetic interactions producing
radiation are essential for this further cooling and clumping. We see a
dramatic instance of the effect of not having a simple cooling mechanism
in the more-or-less uniform distribution of dark matter throughout
galaxies. Dark matter was part of the initial inhomogeneities that gave
rise to galaxies, but it lacked the possibility of radiating away
energy, so it could not clump further. It does cool very slowly by
evaporative processes, but it is essentially unclumped, even now.
These process are all described by time-reversible dynamics, of course,
but quantum-level coarse graining is still necessary, so statistics and
the thermodynamic arrow are universal in these processes.
(Another way to look at this is that the expansion is producing more
available states for the universe to move into, effectively raising the
entropy ceiling. This means an expanding universe can never reach a
state of equilibrium - this is particularly clear during the BB
fireball, which I would say is very near to equilibrium for a lot of the
time.)
As mentioned above, that homogeneity assumption is as unjustified as the
past hypothesis of low entropy in the initial state.
The above sketches how you get the components of the entropy gradient.
Each stage is reversible except for black hole formation (which is
another topic since it may also violate unitarity, and may generally
need more investigation). But if we ignore gravitational collapse, we
can definitely get an AOT from expansion + time-symmetric physics.
PS as a side issue, note that in gravitational collapse, you effectively
get a mini-big-crunch which illustrates some of the features of time
reversal. In particular, note that in normal time, objects are
constrained to have certain types of pasts - what we can lower entropy.
In gravitational collapse, objects are constrained to have a certain
type of future - it is physically impossible to avoid certain outcomes
(at least assuming GR is correct "all the way down" - which admittedly
violates the BH information paradox...) With the usual caveats, this at
least suggests that time would indeed reverse in a collapsing universe.
Black hole formation does not lead to reduced entropy. One of the
fundamentals of BH physics is the Bekenstein bound, which states that
the BH is the highest entropy state for an amount of matter equal to the
mass of the BH.
But even this is overturned by Hawking radiation. Hawking radiation also
increases the total entropy of the system, so in the very far distant
future, when everything has collapsed into BHs and evaporated again, the
entropy is even higher than if the total universe were a single black
hole! The final state of the universe is a very high entropy deSitter space.
Cheers,
Bruce
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