Ultraviolet Catastrophe / Rayleigh-Jeans Black Body Cavity

mrjeffy321

In reading about the “Ultraviolet Catastrophe” in dealing with black body radiation, my book says that at the ultraviolet frequencies and beyond, the Rayleigh-Jean equation for the energy density of the radiation would be infinite (and thus a catastrophe).
If this is the Rayleign-Jeans equation:
p(v)dv = (8 * pi * v^2 * k * T * dv) / c^3
with v being the frequency of light…how does this number come out to be infinite at some finite frequency?
For example, 1 E16 Hz would be well within the ultraviolet part of the EM spectrum. If I plug this value into the above equation I will get a very large number to be sure, but it will not be infinity. Or do they just mean that as the frequency goes to infinity, so does the energy, when we know otherwise experimentally.

jtbell

Objects don't radiate at a single frequency only. The problem is the total energy that you get when you integrate over all frequencies. In the classical Rayleigh-Jeans analysis, there's no upper limit on the frequency.

Haelfix

Correct, and its ironic in fact that quantum mechanics was given birth by the observation that you had to cut the divergence off in just about the most naive way imaginable to a theorist. So Planck basically curve fitted and found that the only way to do this was by adding an arbitrary h in integer units to the equation.

No one until Bohr believed for a second this adhoc curve fitting had anything to do with reality, except that it was a convenient semi empirical law, good for handwavey arguments. And then, even then, his model was quite obviously flawed so it took an extra 10 years (and many experiments) before people took it seriously and QM became accepted lore.

mrjeffy321

OK, I see. Thanks.