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Re: [Phys-l] Quantum of action

On 01/07/2012 09:22 AM, Moses Fayngold wrote:

How come then did Plank, Sommerfeld and others conclude that h was a
quantum of action?

That's an interesting question. I've been thinking about it some more.

1) First of all, an amusing trivia question: Do you know what first
got Planck thinking along the lines that led to quantum mechanics?
What got him interested in the black body spectrum?

Answer: It was an industrial application question. Some guys
from the light-bulb industry asked him to help optimize the energy
efficiency of light bulbs.

It may take a moment for this to sink in: The #1 most abstruse,
fundamental, counter-intuitive part of theoretical physics started
out as applied physics. A lot of people find this ironic and
surprising.

As for me, I do not consider it surprising. I reckon that throughout
history, a great deal of the best physics has been closely tied to
real-world applications. One criterion for "great physics" is that
it have long-lasting importance. However, that does not mean it
should have long-delayed importance. Let's be clear:
-- long-lasting importance is a virtue
-- long-delayed importance is not a virtue!

Delay is part of the cost, not part of the payoff. We will sometimes
accept delays and other costs, if the ultimate payoff is worth it
... but other things being equal, the less delay the better.

IMHO there should not be a distinction between physics and applied
physics. Alas, not everybody agrees. The Cornell physics department
is in the college of arts and sciences, while applied physics is in
the college of engineering. Similarly, at Caltech, physics is in
the division of physics, math, and astronomy, while applied physics
is in the engineering division. This has never made sense to me. I
still think there should be no distinction between physics and applied
physics. At least some people agree with me. Feynman had a lifelong
interest in applied physics and all sorts of hyphenated-physics (e.g.
bio-physics).

I find it amusing that the guys from the light-bulb industry got
rather more than they bargained for. The asked for a formula for
energy efficiency and got it ... plus a physics revolution that is
still going on. For Christmas I got a new headlight for my bicycle.
It is small, very bright, and very energy-efficient. A lot of
physics went into that LED, including a lot of quantum mechanics.

As a point of history: Nowadays the "history" you see in physics
textbooks makes a big fuss about the ultraviolet catastrophe, which
is a nice Gedankenexperiment that tells you the unquantized theory
has a problem. As usual, the textbook "history" is bogus. The
term "ultraviolet catastrophe" did not appear in the literature
until many years after the dawn of quantum mechanics. Planck did
not need a qualitative catastrophe, and he did not need a Gedanken-
experiment, because he was up to his ears in real quantitative
experimental data that told him the Wien equation was incorrect.

2) Now for a little bit of physics. Planck had spent years thinking
about the light given off by light bulbs. Everybody's favorite
model for a material system that radiates is a charged harmonic
oscillator.

Long before 1900, Planck knew everything there was to know about
harmonic oscillators. He was not some village idiot who made a
lucky guess about the quantum of action; he was professor of
physics at the University of Berlin, and had been for many years.
That was the pretty much the top of the physics pecking order.
Years earlier, Helmholtz -- who wasn't the village idiot either --
said that he (Planck) had a "comprehensive overview of the various
areas of science." He was also a very accomplished musician. His
father had been a professor. His grandfather had been a professor.
His great-grandfather had been a professor.

In particular, Planck must have known about the phase space of
a harmonic oscillator. For any particular oscillator, its
trajectory in phase space is an ellipse. If you have another
oscillator with the same frequency but more energy, its ellipse
is bigger. The energy scales like x^2 and like p^2 ... where
x and p are the axes in phase space. In other words, the energy
scales like area in phase space. Planck must have known that
at any given frequency ν, a series of ellipses equally spaced
in energy were also equally spaced in action, i.e. area in
phase space. If the Δ(action) is h then the Δ(energy) is hν,
for any h.

I am not a historian, and I have no direct documentary proof
that Planck was drawing ellipses in 1900 ... but to me it is
almost inconceivable that he would not do so.

So, here is my answer to the original question: I reckon that
many years *before* quantum mechanics came along, Planck must
have known that the "quantum of energy per unit frequency" was
also the "quantum of action". I cannot imagine how he could
not know that.

3) Some supporting bits of history: We know that Planck was a
quick study. Minkowski invented spacetime in 1908. Einstein
didn't understand it at first, and wasn't interested. OTOH
by 1909, Planck was giving lectures that used the Minkowski
spacetime approach to the exclusion of the FitzGerald, Lorentz,
Poincaré contraction/dilation approach.

Quickness is relevant because the second volume of Boltzmann's
_Vorlesungen über Gastheorie_ had come out in 1898. We know
Planck was up to speed on it ... including the part where
entropy is computed in terms of area in phase space ...
because he credited Boltzmann when he calculated the entropy,
in 1900, in the first QM paper.

Again: We absolutely know that quantum mechanics was born
/already/ connected to thermodynamics. It seems a safe bet
that it was already connected to phase space. The only
alternative is to hypothesize that Planck used the equation
for entropy without understanding where it came from, which
strikes me as exceedingly implausible.

4) Nowadays, students may be introduced to a little bit of
quantum mechanics in high school. They see some more QM in
the introductory college physics course. If they go on to
major in physics, they learn about canonical *classical*
mechanics much later, maybe in their junior year: Lagrangians,
Hamiltonians, Poisson brackets, et cetera. The non-majors
may never see classical mechanics at all, even if they wind
up in a field such as chemistry or opto-electronics that
requires them to do quantum mechanics every day for the
rest of their lives.

In contrast, Planck already knew classical mechanics, long
before QM came along. People paid good money to go to Berlin
to learn everything there was to know about classical mechanics
... to learn it *from* Planck and his buddies.

I mention this because there are people -- including some who
subscribe to this list -- who still argue that "history" is
a good way to motivate and organize the teaching of physics.
Really? You are going to teach everybody (physics majors and
non-majors alike) everything there is to know about classical
mechanics before you teach them anything about quantum mechanics?
Really????

To me that sounds unkind. It sounds like monumentally bad
pedagogy, or monumental ignorance of the history, or both.

Every so often somebody tries to publish something in the
PER literature about the virtues of "the historical approach",
or about the "energy spreading" model of entropy, or about
the "two kinds" of electrical charge, et cetera ...
/and sometimes they get away with it./ Whenever that happens,
it discredits the entire field.

===================

Also:

[....talking about Joyce's daughter, Buffy....]

JOYCE: I-I know she's having trouble with history. I-is it too
difficult for her or is she not applying herself?

GILES: She lives very much in the 'now', um, and, uh, history,
of course, is, is very much about the, uh... the 'then'.

As a rule, old folks are much more interested in history than
young folks are. Just because *you* are interested in history
doesn't mean your students are.