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

[rjensen@ualberta.ca]

John

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?

Thanks,
 Dr. Roy Jensen
(==========)-----------------------------------------¤
 Lecturer, Chemistry
 E5-33F, University of Alberta
 780.248.1808





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."
>  http://www.feynmanlectures.info/flp_errata.html
>
> 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:
>  http://www.feynmanlectures.caltech.edu/I_50.html#Ch50-S5
>
> 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
>  http://www.av8n.com/physics/wave-energy-theorem.htm
> especially
>  http://www.av8n.com/physics/wave-energy-theorem.htm#sec-bug
>
> 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
> Phys-l@phys-l.org
> http://www.phys-l.org/mailman/listinfo/phys-l