From: David Roberson
I have been attempting to understand if or why there is a difference in the behavior of high frequency photons as compared to those that we can easily measure. ' There is, but it is not easy to follow. It involves going from inverse 4th to 5th powers. Here is a long version of Planck's derivation, since the other link I had is dead. In short, we are comparing photon power (spectral radiance) to temperature (or wavelength) http://bado-shanai.net/map%20of%20physics/mopPlancksderivBRL.htm Planck's law describes radiation emitted by a blackbody and can be written as an inverse 5th Law. Wien's power law also implies that emissive power is proportional to temperature to the 5th power. But Stefan-Boltzmann says emissive power is proportional to temperature to the 4th power. How can all of these be true? The usual explanation given is that Stefan-Boltzmann applies to the total emissive power (the integration of the emissive power density, or the area under the curve) while Wien's power law applies to the peak. When we look at these laws in action for stars of different surface temperature, there is a strong narrowing of the spectrum with increasing temperatures such that the peak is spiked and the distribution is compressed. Wien explains the shift of the peak to shorter wavelengths, while the Stefan-Boltzmann explains the abrupt growth in the height of the curve, but eventually the two become problematic. IOW - going from a 4th to a 5th power may not be accounted for in terms of expectation. One way to verbalize this is in trying to explain the oddities of GRBs, where radiation seems to be more powerful than it should be (penetration depth) it can be said that these rays act as if they are exponentially greater in power. And there is some truth to that. http://en.wikipedia.org/wiki/Gamma-ray_burst
