On 11/6/2014 8:30 PM, Bruce Kellett wrote:
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!
But as MWI assumes the projection postulate produces multiple outcomes at the coarse
grained level so will partial traces.
Brent
P.S. Welcome to the everything-list, Bruce. Have you abandoned atvoid-2? :-)
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