Re: [Phys-l] Blackbody radiation

[John Denker <jsd@av8n.com>]

Michael Edmiston wrote:

> Basically I don't understand the standing wave approach to BBR.  I know 
> it is historic, but the historic approach doesn't yield the correct 
> result.

Huh?

> Although I understand standing waves in excited cavities such 
> as klystron tubes and magnetrons, using standing waves for a heated 
> cavity doesn't seem right once we know about quantized atomic structure 
> and emission of photons from atomic transitions.
>
> First of all, hot objects that are not cavities will emit radiation that 
> is nearly BBR.  That is, the cavity is not really necessary for getting 
> the basic BBR curves.  The sun is not a cavity radiator.  So what do 
> standing waves have to do with BBR from hot objects that don't have 
> cavities?

The criterion is that they be optically thick.

A big cavity with a small hole in it (the canonical "black body"
architecture) is sufficient but not necessary.  It is sufficient
because the light bounces many times before finding the small hole.

Feynman volume I chapter 41 calculates the correct formula without
saying boo about cavities or standing waves.


> Second, the idea that the cavity walls must be electric field nodes 
> doesn't seem quite right if the source of the photons is electronic 
> transistions in the atoms on the surface of the walls.

When calculating the wavelength, it is reasonable to assume that the
size of the box is large compared to the skin depth ... especially when
the size of the box drops out of the final answer.

> Modern physics textbooks on my shelf explain the historic standing wave 
> approach leading to the Rayleigh-Jeans result, but then continue using 
> the standing wave approach when switvhing over to the Planck quantum 
> picture.  That doesn't make sense to me.  Am I missing something?

a) I have no idea what books are on other people's shelves.

b) I don't know what the "historic" approach is, and I don't much care,
but I suspect the true history is that Planck obtained the right answer
via a valid argument.

There are many independent valid ways of getting the same answer;  when
talking to freshmen (volume I) he does it by doing the statistical mechanics
of an oscillator, and then arguing that the field is in equilibrium with
the oscillator.  Later (volume III) he obtains the same result by studying
the field directly.

There are innumerable other ways ... all linked by the principle that
radiation in equilibrium with system X will be in equilibrium with any
other system at the same temperature.

Standing waves are not, per se, very important.  You can perfectly well
use running waves.  What really matters is being able to enumerate the
modes.  Standing waves are an expedient way to convince yourself that
you have counted modes correctly.

=========

FWIW if you are going to study the field directly (the voulme III approach,
as opposed to the volume I approach), it may be worth remarking that this
is a quantum field theory calculation.  It is typically the first (and often
the last) quantum field theory calculation people see.  You probably don't
want to call it that, at least not until afterwards, lest you scare off the
customers ... but it is what it is.

In the continuum limit, "counting the standing waves in a box" becomes
"knowing the density of states".

Have you ever wondered why the partition function is called Z?  I'm told
it stands for Zustandsumme : literally, the sum over states.  You can't
do statistical mechanics unless/until you know how to count states.