On 8/23/2014 4:58 PM, John Clark wrote:
On Fri, Aug 22, 2014 at 3:47 PM, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
> But entropy is relative constraints, in this case coarse graining.
Yes, entropy is the logarithm of the number of microstates that produce the same
macrostate times a constant; so the entropy of a square foot of steam is Boltzman's
Constant.times the logarithm of the number of ways you could arrange water molecules and
still have the same volume pressure and temperature. Ice would have a lower entropy than
stem because ice is in a rigid lattice of particles so there are fewer ways to arrange
H20 molecules and still have it be ice. There are a lot more ways to arrange H2O
molecules and still have it be steam.
You're assuming there's only one possible constraint (and that it's macroscopic). There
are many possible constraints and one of them would be to specify the complete wave
function, which makes the von Neumann entropy zero and it stays zero under evolution via
the SWE. Or from the standpoint of your more classical example, if you specify the point
in phase space corresponding to all the molecules of the system then that's the only
arrangement satisfying that constraint and it's evolution is deterministic so the entropy
doesn't change.
> If you take the equation of physics seriously, they are time-symmetric
Yes, but that doesn't mean that the world must be time-symmetric because our world is
the way it is because of the laws of physics AND because of initial conditions. As I
said before, if things started out (the Big Bang) with the lowest entropy there could be
then, whatever the laws of physics are and however they change the state of things, that
change must be in the direction of increased entropy because entropy can't get lower
than the lowest it can go.
> (assming MWI)
Assuming anything!
Not assuming collapse of the wave function in a measurement or state
preparation.
The known laws of physics are time-symmetric under any quantum interpretation, but our
world most certainly is not, so if the laws of physics are not responsible for time's
asymmetry there is only one other thing that could be, initial conditions. Things
started out in a super low entropy state 13.8 billion years ago and everything has been
unwinding toward higher entropy ever since. In a billion trillion years or so things
will reach a state of maxim entropy and after that it will be impossible to perform work
in the universe. And that will be that.
> and entropy never changes.
You can't explain entropy's behavior with just the laws of physics alone, in fact it's
more general than that; even if Newtonian physics was 100% correct you couldn't predict
what entropy or anything else will do with the laws of physics alone, just as important
are initial conditions. Physicists started to have a good understanding of entropy about
1880 or so and they had everything they need to have predicted the Big Bang way back
then, but unfortunately they did not.
> But at the coarse-grained level of description, where entropy increases,
But you can't state what you're trying to prove, we're trying to figure out why entropy
increases in one time direction but not the other when the laws of physics work the same
in both direction.
It's because we can only live and read clocks and make records in the direction of
increasing entropy - which is why "entropy increases" is (globally) a tautology.
> there are fewer past states that could produce the present than there are
future
states into which the present can evolve.
I know that, but the question is why there were fewer past states. It's easy to figure
out why the laws of physics will cause the entropy tomorrow to be larger than today,
there are just VASTLY more high entropy stated than low so things will almost certainly
change into one of them. But by using the same reasoning when asked what sort thing
evolved into our present state we'd have to say it almost certainly came from one of
those very very very very numerous high entropy states. And so if we had nothing but the
laws of physics to work with we would state the second law of physics as follows "Things
at the present time are in the lowest entropy state there can be and so entropy will be
higher in the future and was higher in the past".
But this is clearly ridiculous, we must be ignoring something important, and that thing
is initial conditions.
> But that the exact same physics applies to a universe that "collapses"
into a very
very low entropy states. But if we lived in such a universe, we'd live our
lives
and form our memories in the direction of expansion and we'd say we live in
an
expanding universe (as we do) and that's why the 2nd law globally is a
tautology.
But creature in that universe would have something in common with us, we would both note
that the fundamental laws of physics work the same in both time directions but our minds
do not, both of us can only remember things from one time direction but not the other,
and both of us would note that the universe as a whole doesn't behave the same in both
time directions either, it gets larger in one direction and smaller in the other. And
although we remember the past and they member the future we both would have to assume
initial conditions at one end of the timeline to make sense out of things, the laws of
physics alone aren't enough.
Yes, the initial conditions always matter. But whichever state has the lower entropy will
be "the past" because we can't live any other way.
Brent
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