Re: blackbody radiation

[John Denker <jsd@AV8N.COM>]

Justin Parke wrote:

> > Wien tells us the shape but not the overall magnitude.  The lasers
> > would almost certainly be too bright;  right shape, excessive
> > magnitude.
>
> Suppose the laser light could be attenuated in some manner so the
> magnitude was correct.  Perhaps the mechanism responsible for
> attenuating would heat the box up to the proper black body
> temperature?

That question is not as simple as it might appear.
Things to think about include:

1) There's no such thing as an attenuator that just
attenuates;  it must also be an emitter.  Otherwise
we would have violations of
 -- Liouville's theorem,
 -- the 2nd law of thermodynamics,
 -- the Heisenberg uncertainty principle, and
 -- the fluctuation/dissipation theorem.
(Those four ideas are not quite mutually synonymous, but
are profoundly related.)

2) If you put in enough attenuation, at some point
you don't see the laser light at all, but rather just
the emission from the attenuator.  You can presumably
arrange that this will be thermal ... but that may
take some engineering;  you can't take it for granted.
Not everything has a temperature.  Not all radiation
is thermal.

3) The question mentioned "the proper" temperature.  I
assume that means the temperature one would calculate
by curve-fitting to the shape of the spectrum, ignoring
its magnitude.  But it's not at all clear that that is
the physically-relevant temperature of the laser light,
or even that the laser light has any well-defined
physically-relevant temperature.  It is a chimera,
having a shape that corresponds to one temperature and
a total power that corresponds to another temperature.
(And you can probably find a third way of characterizing
the light that yields a third temperature.)

I suspect that total power is the most fruitful way of
analyzing the situation.  Assuming there are no other
outlets for the energy, the absorber will heat up until
it is thermally emitting enough power to balance the
power it is absorbing from the laser.  Calculating the
exact temperature will depend on geometry (areas and
solid angles) as well as on the incident power.