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*From*: John Denker <jsd@av8n.com>*Date*: Thu, 19 Jun 2014 11:29:25 -0700

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.

**Follow-Ups**:**Re: [Phys-L] error in Feynman § I-50-5 : wave energy "theorem"***From:*rjensen@ualberta.ca

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