onsdag 12 mars 2014

Blackbody Radiation as Collective Vibration Synchronized by Resonance

There are two descriptions of the basic phenomenon of a radiation from a heated body (blackbody or greybody radiation) starting from a description of light as a stream of light particles named photons or as electromagnetic waves.

That the particle description of light is both primitive and unphysical was well understood before Einstein in 1905 suggested an explanation of the photoelectric effect based on light as a stream of particles later named photons, stimulated by Planck's derivation of Planck's law in 1900 based on radiation emitted in discrete quanta. However, with the development of quantum mechanics as a description of atomistic physics in the 1920s, the primitive and unphysical idea of light as a stream of particles was turned into a trademark of modern physics of highest insight.

The standpoint today is that light is both particle and wave, and the physicist is free to choose the description which best serves a given problem. In particular, the particle description is supposed to serve well to explain the physics of both blackbody radiation and photoelectricity. But since the particle description is primitive and unphysical, there must be something fishy about the idea that emission of radiation from a heated body results from emission of individual photons from individual atoms together forming a stream of photons leaving the body. We will return to the primitivism of this view after a study of the more educated idea of light as an (electromagnetic) wave phenomenon.

This more educated view is presented on Computational Blackbody Radiation with the following basic message:
  1. Radiation is a collective phenomenon generated from in-phase oscillations of atoms in a structured web of atoms synchronized by resonance.
  2. A radiating web of atoms acts like a system of tuning forks which tend to vibrate in phase as a result of resonance by acoustic waves. A radiating web of atoms acts like a swarm of cikadas singing in phase. 
  3. A radiating body has a high-frequency cut-off scaling with temperature of the form $\nu > \frac{T}{\hat h}$ with $\hat h = 4.8 \times 10^{-11}\, Ks$,where $\nu$ is frequency and $T$ temperature in degree Kelvin $K$, which translates to a wave-length $\lambda < \hat h\frac{c}{T}\, m$ as smallest correlation length for synchronization, where $c\, m/s$ is the speed of light. For $T =1500 K$ we get $\lambda \approx 10^{-5}\ m$ which is about 20 times the wave length of visible light.   
We can now understand that the particle view is primitive because it is unable to explain that the outgoing radiation consists of electromagnetic waves which are in-phase. If single atoms are emitting single photons there is no mechanism ensuring that corresponding particles/waves are in-phase, and so a most essential element is missing.

The analysis of Computational Blackbody Radiation shows that an ideal blackbody is characterized as a body which is (i) not reflecting and (ii) has a maximal high frequency cut-off. It is observed that the emission from a hole in a cavity with graphite walls is a realization of a blackbody. This fact can be understood as an effect of the regular surface structure of graphite supporting collective atom oscillations synchronized by resonance on an atomic surface web of smallest mesh size $\sim 10^{-9}$.


4 kommentarer:

  1. I don't think that your point 1. isn't really compatible with observations.

    In the this paper

    Donges Eur. J. Phys. 19, 245 (1998),

    the correlation length of a black body is empirically determined to follow

    l_c * T = 3.6 mm K.

    For 300K this corresponds to a monochromatic correlation time of

    t_c = 3.6e-3 mK/ (300 K* 3e8 m/s) = 4e-14 s

    In graphite the speed of sound is about 3070 m/s. Correlated motion on this
    scale is then on the length scale

    t_c * 3070 = 1.228 Å

    This is less then the interatomic separation between any carbon atom (1.42Å) and layer separation (3.35Å).

    The black body radiation can not originate from any correlation over many atoms...

  2. Because that is the scale for acoustic waves, and relates to the linear behavior of the dispersion near the Gamma point.

    They are also the speed limit for a lattice wave since the dispersion typically flattens out approaching the Brillouin zone boundary, lowering the group velocity of the waves close to zero.

    Correlated movement over a lattice could not be the source of thermal radiation, it seems like an empirical fact looking at the correlation in radiation similar to black body radiation.

    The calculation above is for the humble case of room temperature. Any higher temperature lower the possible range as 1/T.