Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Entropy, Objectivity, and Timescales



Ok, here's my next reply to Leigh...

Dan says (and I omit much I do not choose to argue further)...:

In other words, you're refusing to answer some of my honest questions.
I still want to know precisely how large a system has to be before
we're allowed to talk about its entropy. I've now asked you three
times.

The time-dependent Schrodinger equation is fully
deterministic and allows one to predict a future state with precision,
provided that the initial state is also known with precision.
In any case, the issue of quantum indeterminacy surely is not
relevant to understanding entropy. (If you think it is relevant,
then please elaborate.)

It is certainly relevant. It is a cognitive error to believe that
any fully deterministic equation describes Nature in a valid
fashion when applied to predicting the future over the timescales
I mentioned. That view has not been responsibly held by anyone
since early in this century. Perhaps Creationists still hold to a
Cartesian world view, but no serious physicists do. What we are
discussing here is the description of the real world; physics is
the topic at hand, not epistemology. Clearly quantum indeterminacy
is central to microscopic interpretation of thermodynamics.

Look, I don't want to argue quantum mechanics here. But I've never
before heard anyone claim that you need to understand quantum
indeterminacy to understand entropy. Let's go back to 1880, shortly
after Boltzmann introduced the statistical view of entropy and long
before anyone knew anything about quantum indeterminacy. Are you
saying that Boltzmann could have believed that entropy is subjective,
but now that we know about quantum indeterminacy (which in your
view is what makes all those states "accessible" even though most
of them will never be realized), we should realize that entropy is
actually objective? This is a very interesting viewpoint, and one
that I've never considered carefully. I don't think I agree with
it, but I'll think about it some more.

My point is not that we should rely on authority, only
that intelligent people who have thought very carefully about entropy
are *not* in agreement over whether it is objective or subjective.
So let's be a little more polite to each other, ok?

I'm sorry if I seem impolite, but you seem obtuse. How can you
possibly challenge the authoritative view of entropy when it is
a definition!?* The postmodernists may believe that entropy is
a mutable thing, but I really don't want to participate in the
committee that redefines it.

Did these other intelligent people reflect at liesure or did
you badger them like you seem to enjoy badgering me? Or do I
not qualify as an intelligent person? I give up; you win. The
entropy is a subjective quantity. (Eppur si muove.)

I'm honestly not sure what "the authoritative view of entropy" is,
nor do I believe that the question should be decided by appeal
to authority. Please read what I said. I'm making no claims
about your intelligence. I'm simply countering your implication
that all the authorities are on your side.

For the record, I am neither a creationist nor a postmodernist.

As for the methodology of my poll, I simply stuck my head in each
office and, without any context, announced that I was taking a
poll: "Is entropy objective or subjective?". All but one answered
"objective". Then I e-mailed my former instructor, again with
no context, and he answered "subjective" (with a nice brief
explanation along the lines of what I've been arguing). I only
"badgered" one person, the one who changed his answer from objective
to subjective (though with some reservations that he's still
thinking about).

Will someone else please chime in here? A voice of sanity?

I also would like to hear from some others. It's becoming clear
that further exchanges between Leigh and myself are not likely to
get us much further.

Would you insert comments about the
subjective nature of entropy into such a course? I'll wager that
the texts cited here would not support your view.

In my course I raised the issue very briefly, several weeks ago,
and said it's controversial. Then this morning, as students were
coming in before class, I briefly mentioned this debate to them
and asked if they had an opinion. (Most of them did not.) But I
didn't spend any more class time on it.

I've never seen a text that even raises this question, much less tries
to answer it. If you know of one that does, please tell me. Landau
and Lifshitz *almost* touch on the question, especially in their discussion
of timescales on page 27 (statistical physics, part 1, 3rd edition).
They say that there's no such thing as an "instantaneous" entropy,
but rather that entropy is always understood to be relative to some
relaxation timescale. But I'm making a stronger claim, that even
over very long timescales, most "accessible" states will never
be realized and so the conventional entropy also factors in our
large degree of ignorance (which could be somewhat less, yielding
a smaller value of the entropy).

Some other books define "accessible" in terms of "constraints". But
they're usually nebulous about what, exactly, qualifies as a constraint.
I understand how the total energy and volume of a system can be
constrained, but surely we should also allow constraints that come
from initial conditions: the deck of cards is currently in a certain
order and there's just no mechanism that's likely to interchange two
cards with each other while the deck is sitting on the table. OK, but
if you allow this initial condition to be a constraint, what's to keep
me from specifying the precise initial state of all the molecules in
a gas, and saying that this state "constrains" the molecules to explore
only a tiny fraction of the states you thought were accessible?
The only answer I can think of would be some intrinsic randomness or
unpredictability in the behavior of the molecules; that is, quantum
indeterminacy. If this is your position, Leigh, then please say so
once again so I can be sure. Then I'll think about it some more.

-dan