Re: Entropy, Objectivity, and Timescales

[Leigh Palmer <palmer@sfu.ca>]

David Bowman is amused:

> I find it astonishing (or maybe amusing is a better term) that Leigh seems
> to have changed his mind about the relevance of quantum mechanics for
> understanding entropy in mid-discussion without skipping a beat.

I have not done so. If you will read to the bottom of my posting you
will see where I have introduced quantum indeterminacy to elucidate
the necessary fuzziness in the specification that microstates be
accessible subject to an energy constraint.

What many here seem to forget is that the purpose of statistical
mechanics is to interpret what is an empirical law in microscopic
terms. Quantum mechanics is the appropriate formulation for physics
in the microscopic realm, that's all. Entropy is *not* defined as
k ln W (forgive the symbols); it is defined in classical terms. The
triumph of Boltzmann and Gibbs was to find this microscopic
interpretation of entropy and to demonstrate its equivalence to the
classical definition.

I take it that most everyone here believes the second law of
thermodynamics is well founded. Quantitative expression of the law
requires all the apparatus of classical thermodynamics. Ideal
systems in quantum physics (prepared in pure eigenstates and isolated
from the rest of the universe) are utterly unrelated to the ideal
systems of classical thermodynamics in terms of which entropy changes
are calculated. I doubt that Boltzmann and Gibbs ever said or thought
otherwise.

> > 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.
>
> Notice Leigh's first and last statements in his quote above and compare
> them with his more recent contribution (farther) above.

I guess you didn't read to the bottom of the page, David. Do I have
to include the argument about the volume of a sphere in a phase
space of high dimension being almost entirely contained within
delta E of its surface?* Read my statement again: "Clearly quantum
indeterminacy is central to microscopic interpretation of
thermodynamics." Clearly quantum indeterminacy is *not* central to
thermodynamics itself!

> > You don't have to know anything about quantum mechanics to understand
> > entropy. It can be understood entirely as a macroscopic classical
> > phenomenon.
>
> I'm glad to see that both Dan and Leigh (and me) can now agree on (at
> least) this.

I'm grateful for that confirmation. I was beginning to believe that
you guys thought thermodynamics was a matter of interpretation of
quantum mechanics. I don't understand quantum mechanics (and I am in
good company); I do understand themodynamics. It's easier.

> In the context of Leigh's comments about creationism, postmodernism, his
> (and many other physicists') atheism, objective realism, reductionism, and
> holism he sums it up with:
>
> > I wish to point out that point of view plays a very important role
> > in physics. Understanding the philosophical orientation of a
> > colleague is central to understanding what he means when he says
> > things about physics.
>
> I think what is central is the mathematics that encodes the physics.  When
> physicists can agree on the mathematics, their philosophical differences
> become a matter of personal taste which may influence how they interpret
> or attach meaning to the physical phenomena described by the mathematics.
> When the physicists agree on the math then they agree on what physical
> theory predicts concerning the outcomes of experiments.  That agreement is
> at the level of physics.  Differences in philosophy and religion may
> be present concerning what the ultimate meaning of it all is, but these
> differences tend to remain philosophical and religious, and seldom
> penetrate to the level of the physics of the situation.  For example,
> physicists may differ on their interpretations of quantum mechanics at a
> philosophical level, but they agree on the predictions that QM makes
> concerning the outcomes of experiments because they agree on the
> mathematical formulation of QM.

Here I will depart. I think what is central is Nature. The description of
Nature is best done so far mathematically. Quantum mechanics is a limited
incomplete theory which succeeds in describing many aspects of Nature at
the microscopic level. That it is inadequate to the task of handling the
interpretation of a classical concept, entropy, should be abundantly
clear at this point. In my opinion Dan is confused to the extent that he
has decided entropy is a subjective quantity based on his quantum
mechanical reasoning. Rudolph Clausius didn't know any quantum mechanics,
and I hope we all agree his definition of entropy difference suffices in
the macroscopic limit. It requires no "correction" analogous to the
corrections relativity makes to Newtonian dynamics. The disagreement here
has arisen because *interpretation* of the quantum mechanics has failed,
but that is unsurprising, to understate the matter greatly.

> In light of my belief about the place of philosophy and religion in doing
> physics I want to state that I would rather not see Leigh using this
> physics forum as a platform to spout his religious beliefs.  Such
> statements seem to be gratuitous flame-bait (even if they are not so-
> intentioned.)  There are plenty of flaming newsgroups out there that
> specialize in such religious wars.  I would hope that our discussions here
> continue to remain on a high plane of discourse.

I take strong exception. I didn't "spout" my religious beliefs; I stated
them in order to define my frame of reference. We atheistic reductionist
logical positivist objective realists may be abrasive, but we do not
proselyte. If you knew of my background you would know that I detest
evangelism. I find that a common problem my students have which leads
them to misconceptions is that they do not sufficiently define their
frames of reference. Doing so here is not gratuitous.

> I'm sorry to seem to have dumped so heavily on Leigh here, especially since
> he has been so nice to me in his posts.  (I suppose that after this post I
> may feel the point of his sharp pen in the future.)  I usually appreciate
> Leigh's curmudgeonly style, and his unflinching willingness to call them as
> he sees them in spite of the possible fallout for being on the wrong side
> of political correctness.  I also very much appreciate his considerable
> physics insights (and often agree with them).  Its just that it seems to
> me that his parading of his religous values goes beyond the purview of
> this list.  (But my thoughts are easily ignorable on this matter since I am
> not the list moderator.  If I was I would probably have to censure myself
> for repeatedly posting excessively long posts.)

Good grief. I thought I heard purring! Don't worry, David and Dan. You
guys still know a lot I don't, and I expect to learn more from you in
the future. My Wiley rep gave me a copy of Callen and it occurs to me
that I haven't had a chance to look at it yet. Perhaps I'll see what he
has to say about entropy, since that's why the book was recommended to
me in the first place.

> On another point I have to credit Ludwik for his ability to innocently
> instigate extended (and sometimes heated) discussions by others.

Ludwik is not innocent. He plants these things on purpose; he is the
*agent provocateur* of phys-l!

Leigh

*I am perfectly willing to expand on this point if I need to. It relates
to the rubber worm problem I presented some time ago, of course. While
that problem doesn't appear in Reif, the higher dimensional geometric
argument does (I think).