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Re: blackbody radiation



Justin Parke asked

How many different ways are there to radiate energy?

At the fundamental level, only one.

> Shouldn't these all be fundamentally the same?

Yes, at the fundamental level.

I can think of:

a) An object with temperature radiating as a blackbody

b) A laser emitting by stimulated emission

c) A hydrogen atom in an excited state spontaneously dropping to a
lower state and emitting

d) Electrons accelerating in an antenna and emitting

Item (d) is the easiest. It can be completely understood
in terms of classical electrodynamics.

In the notation of geometric algebra, the entire basis
of classical electrodynamics can be written as
del F = 4 pi J (Maxwell equation)
d p / d tau = (q/m) p dot F (Lorentz force law)

where F is the electromagnetic field (a bivector in four
dimensions), J is the charge/current (a vector in four
dimensions), p is the energy/momentum, q is the charge,
and m is the invariant mass.
http://www.av8n.com/physics/maxwell-ga.htm

In a matter-free region, del F = 0 describes the free
propagation of electromagnetic waves. But if you want
to emit waves, the source term -- the _only_ source
term -- is J, i.e. the charge/current.

Item (c) is almost the same. It is the same in the
sense that if an atom radiates, it is because there is
a charged particle in there wiggling around.

There is a slight wrinkle in that we must explain why
the atom in its ground state does not radiate, even
though it is still wiggling a little bit due to zero-
point fluctuations. For that we need something
nonclassical, i.e. quantum electrodynamics. That is,
we need a solution that jointly describes both the EM
field and the charged particle. We need
-- initial and final states for the EM field, and
-- initial and final states for the particle, plus
-- a transition from inital to final that involves
a suitable amount of acceleration of the charged
particle.

The third requirement is not to be sneezed at. There
are some transitions that are called "forbidden" because
they are absent or very weak in the observed spectrum.
There are various equivalent ways of explaining this,
but one nice way is to say that the transition doesn't
couple to the field very well. All this can be calculated
to high precision using Fermi's Golden Rule.

Item (d) can be understood in terms of item (c), in the
limit where there is a great abundance of initial and
final states for the particle.

Item (b) is essentially the same as item (c). You can
have a hydrogen hydrogen laser or hydrogen maser. In
any laser or maser, coupling between matter and the EM
field is the same old thing as discussed above for
item (c).

Item (a) is again the same as item (c), possibly in
the limit where item (d) is valid also. The blackness
of the black body depends on charges moving around as
nonthermal light is absorbed and thermal light is
emitted.