On 7 November 2014 15:51, Bruce Kellett <[email protected]> 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)
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
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.
> 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).
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.
>
> 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.
>
> 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.
>
> 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).
> 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.
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