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*From*: rjensen@ualberta.ca*Date*: Sun, 22 Jun 2014 10:02:13 -0600

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.

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**Follow-Ups**:**Re: [Phys-L] error in Feynman § I-50-5 : wave energy "theorem"***From:*John Denker <jsd@av8n.com>

**Re: [Phys-L] error in Feynman § I-50-5 : wave energy "theorem"***From:*John Denker <jsd@av8n.com>

**References**:**[Phys-L] error in Feynman § I-50-5 : wave energy "theorem"***From:*John Denker <jsd@av8n.com>

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