- E = gamma T f^2,
- with a high frequency cut-off proportional to T,
måndag 11 juli 2011
Blackbody Radiation as a Generic Emergent Phenomenon
A body of temperature T emits radiation with an intensity E similar to that of an ideal blackbody given by Planck's law (Rayleigh-Jeans law with cut-off):
where f is the frequency and gamma is a constant.
The radiation spectrum thus only depends on the temperature and not of the material of the body. This indicates that blackbody radiation is a generic emergent phenomenon resulting from collective atomic vibrations and not from individual atoms or molecules which have different line spectra.
This idea is explored in the upcoming book Mathematical Physics of Blackbody Radiation (and in one of my chapters in Slaying the Sky Dragon) by an analysis of resonance in a wave equation with radiation.
In this model blackbody radiation can be thought of as the sound of a piano with all keys being struck at the same time with the same force: a complex chord which sounds the same for all pianos. An generic emergent phenomenon which cannot be understood by looking at just one key.
It can also be thought of as the complex sound of a big gong with a big range of frequencies. There is an interesting experiment showing that a gong can be made to sound by a short laser pulse kicking the gong atoms into an emergent collective vibrational motion producing sound waves hitting your ear.