LizR wrote:
On 7 November 2014 15:51, Bruce Kellett <bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au>> wrote:
LizR wrote:
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?
Well, from a GR perspective an AOT is a constraint on the world lines of
matter. If you put constraints on the entire contents of the universe at
both ends of time, the possible results are (that I can see)
Why would you put constraints on the entire contents of the universe at
both ends of time? That is not how physics normally works. The usual
picture is that if you specify the complete data on some Cauchy surface,
and given time-symmetric dynamics, you can calculate the entire history
of the universe in both time directions.
a) the contents of the universe reverse motion at max expansion and you
get a mirror image collapse (seen as expansion to its inhabitants)
b) the contents of the universe conspire to arrange themselves in a
manner that gives two different expansion histories that still manage to
meet in the middle (perhaps all matter decays before the reversal or
something)
c) only part of the universe's contents are constrained by each
singularity (maybe matter vs antimatter or something from the viewpoint
of the inhabitants)
d) there is no well-defined AOT in such a universe
Since one does not have a final state constraint in normal physics,
these possibilities are beside the point. The normal expectation is that
entropy increases in normal dynamical evolution for statistical reasons,
and it continues to increase for all time. A re-contraction of the
universe would not change this, but we know from dark energy that the
universe is not going to re-contract anyway.
I am open to other ideas. I was suggesting (d) might be the outcome
since all the others seem to require some extras.
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.
To clarify the vocabulary, I'm assuming there is such a thing as
fundamental physics, described by a yet to be discovered TOE. Anything
not described by the TOE is called emergent. The second law is a
statistical property of large ensembles of particles and hence (ISTM)
not likely to be part of this hypothetical TOE - indeed it is likely to
emerge in many universes with widely varying fundamental physics - and
hence is not "fundamental" under this description.
It then depends on whether your TOE assumes mathematics, and hence
statistics. If it does, then statistics is fundamental in your sense.
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!
I'm using the description above. This makes the outcome of quantum
measurements emergent - they are what is perceived at our level, not
what is going on at the hypothetical TOE level (this probably requires
an Everettian view of QM, come to think of it).
It certainly does! But even the Everettian view (MWI) is not complete.
It requires this pesky thing called the partial trace over environmental
variables in order to explain single outcomes from measurements, and for
decoherence to actually lead to disjoint worlds. This partial trace is
identical to a projection postulate, so even MWI has a quantum AoT built
into it!
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!
No, it does work. The expansion is uniform but if you assume a normal
distribution of particle velocities you can see that only the ones at
rest in a given region are going to stay there, the rest will bleed off
into adjacent regions, and tend to end up in regions where they are at
rest - because they move outwards from their own region, and all volumes
in an expanding universe are moving away from where you happen to be. So
they will tend to drift into regions where they are more nearly at rest.
That is extremely limited in efficacy because of gravitational binding.
You can't turn gravity off while this happens. So there is essentially
no cooling from this source.
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.
I have no argument with that, but I don't see that it affects the basic
argument.
It explains the cooling where your argument does not.
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.
With you so far. Do you think bound states will arise naturally as the
temperature falls? If so that's an early example of the AOT being
generated by expansion and cooling.
Bound states will arise when the local temperature is low enough so that
typical particle energies are below the disassociation energies of the
bound states. But this is true only for particles in low gravitational
fields. Gravitational binding into clumps is independent of the local
temperatures. (The interior of the sun is at a sufficiently high
temperature to form a plasma, but it does not fly apart.)
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.
I don't see from what you've said above why not.
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.
No, that's right, but by now they have been arranged into low entropy
states by what has happened to them earlier. In particular they contain
bound states like nucleons and atoms which are effectively chunks of low
entropy (compared to a quark-gluon plasma).
Bound states of quarks and atoms are not at any particularly low
entropy. As before, entropy is maximized in black holes, not in normal
matter.
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.
Yes.
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.
But not fundamental, in the sense described above.
I have to stop now. I agree that gravity is the kicker especially in
black holes. Of course if you have an alternative theory of the origin
of the AOT I would like to hear it.
It is gravity, not just black holes that the crunch lies. Most of your
arguments ignore the dominant importance of gravity on the cosmological
scale. The origin of the AoT is simply in the past hypothesis -- the
abnormally low entropy of the initial state of the universe. Everything
else is mathematics.
Bruce
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