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Re: [Phys-L] error in Feynman § I-50-5 : wave energy "theorem"


I don't have an answer to your question. I have a question.

I believe many of us endeavor to teach in a constructivist manner.
That is, we build on the material taught in junior courses and teach
in a manner that leaves the door open for future course to build on
what we taught. Is "energy proportional to the wave amplitude" stated
in FLP a reasonable simplification for the level of the student FLP is
endeavoring to educate? From another perspective, does the 'correct'
answer for the energy of all waves simplify to "energy proportional to
the wave amplitude" for the conditions in FLP?

Dr. Roy Jensen
Lecturer, Chemistry
E5-33F, University of Alberta

On Thu, 19 Jun 2014 11:29:25 -0700, you wrote:

Hi --

Executive summary: There's a bug. I mostly know the
right answer, but perhaps somebody could suggest a
more elegant way of saying what needs to be said.

Background: For the last 15 years or so, people
have been collecting and correcting errors in
_The Feynman Lectures on Physics_. Hundreds of trivial
punctuation and spelling errors have been caught.

On the other hand, it is astonishing how few /physics/
errors there are. In his preface to _The Definitive Edition_
Kip Thorne wrote "It is remarkable that the errata included
only two inadvertent errors in physics."

This stands in contrast to the textbooks published
nowadays, where a typical 1000-page book contains many
hundreds of nontrivial physics errors.


I claim there is a third physics error in the Feynman
lectures. Volume I chapter 50 section 5 starts by saying:

The energy in a wave is proportional to the square of its amplitude.
For a wave of complex shape, the energy in one period will be
proportional to ? f^2(t) dt. [1]

See for yourself:

The problem is, statement [1] is not reliably true. You
can get away with it for plane waves in the electromagnetic
field, or ideal plane waves in air ... but it's not correct
for waves on a string, or waves in the electromagnetic potential.

There are presumably other counterexamples.

Not coincidentally, my two counterexamples have the property
that you can shift the ordinate of the wavefunction by a
gauge transformation that doesn't change the physics. This
alone is sufficient to guarantee that the simple square
law [1] cannot possibly be correct.

For details, see

If anybody has any clever ideas about how to understand this
bit of physics -- or a more elegant way to explain it --
please let us know.
Forum for Physics Educators