Universality of Radiation with Blackbody as Reference

One of the unresolved mysteries of classical physics is why the radiation spectrum of a material body only depends on temperature and frequency and not on the physical nature of the body, as an intriguing example of universality. Why is that? The common answer given by Planck is statistics of energy quanta, an answer however without clear physics based on ad hoc assumptions which cannot be verified experimentally as shown by this common argumentation. 

I have pursued a path without statistics based on clear physics as Computational Blackbody Radiation in the form of near resonance in a wave equation with small radiative damping as outgoing radiation, subject to external forcing  $f_\nu$ depending on frequency $\nu$ , which shows the following radiance spectrum $R(\nu ,T)$ (with more details here) characterised  by a common temperature $T$,  radiative damping parameter $\gamma$, and $h$ defines a high-frequency cut-off.  Radiative equilibrium with incoming = outgoing radiation shows to satisfy:

• $R(\nu ,T)\equiv\gamma T\nu^2 =\epsilon f_\nu^2$ for $\nu\leq\frac{T}{h}$,
• $R(\nu ,T) =0$ for $\nu >\frac{T}{h}$,

where $0<\epsilon\le 1$ is a coefficient of absorptivity = emissivity, while frequencies above cut-off $\frac{T}{h}$ cause heating. The radiation can thus be described by the coefficients $\gamma$, $\epsilon$ and $h$ and the temperature scale $T$. 

Here $\epsilon$ and $h$ can be expected to depend on the physical nature of the body, with a blackbody defined by $\epsilon =1$ and $h$ minimal thus with maximal cut-off. 

Let us now consider possible universality of the radiation parameter $\gamma$ and temperature $T$.

Consider then two radiating bodies 1 and 2 with different characteristics $(\gamma_1,\epsilon_1, h_1, T_1)$ and $(\gamma_2,\epsilon_2, h_2, T_2)$, which when brought into radiative equilibrium will satisfy (assuming here for simplicity that $\epsilon_1=\epsilon_2$):

• $\gamma_1T_1\nu^2 = \gamma_2T_2\nu^2$ for $\nu\leq\frac{T_2}{h_2}$ 
• assuming $\frac{T_2}{h_2}\leq \frac{T_1}{h_1}$ 
• and for simplicity that 2 reflects frequencies $\nu > \frac{T_2}{h_2}$.    

If we choose body 1 as reference, to serve as an ideal reference blackbody, defining a reference temperature scale $T_1$, we can then calibrate the temperature scale $T_2$ for body 2 so that 

• $\gamma_1T_1= \gamma_2T_2$,

thus effectively assign temperature $T_1$ and $\gamma_1$ to body 2 by radiative equilibrium with body 1 acting as a reference thermometer. Body 2 will then mimic the radiation of body 1 in radiative equilibrium and a form of universality with body 1 as reference will be achieved, with independence of $\epsilon_1$ and $\epsilon_2$.

The analysis indicates that the critical quality of the reference blackbody is maximal cut-off (and equal temperature of all frequencies), and not necessarily maximal absorptivity = emissivity = 1. 

Universality of radiation is thus a consequence of radiative equilibrium with a specific reference body in the form of a blackbody acting as reference thermometer.  

Note that the form of the radiation law $R(\nu ,T)= \gamma T\nu^2$ reflects that the radiative damping term in the wave equation is given by $-\gamma\frac{d^3}{dt^3}$ with a third order time derivative as universal expression from oscillating electric charges according to Larmor.

In practice body 1 is represented by a small piece of graphite inside a cavity with reflecting walls represented by body 2 with the effect that the cavity will radiate like graphite independent of its form or wall material. Universality will thus be reached by mimicing of a reference, viewed as an ideal blackbody, which is perfectly understandable, and not by some mysterious deep inherent quality of blackbody radiation. Without the piece of graphite the cavity will possibly radiate with different characteristics and universality may be lost.

We can compare many local currencies calibrated to the dollar as common universal reference.  

• All dancers which mimic Fred Astaire, dance like Fred Astaire, but all dancers do not dance like Fred Astaire.     

PS1 The common explanation for the high frequency cut-off is that they have low probability, which is not physics, while I suggest that high frequencies cannot be represented because of finite precision, which can be physics.  

PS2 Note that high-frequency cut-off increasing with temperature gives a 2nd Law expressing that energy is radiated from warm to cold and to no degree from cold to warm, thus acting like semi-conductor allowing an electrical current only if a voltage difference is above a certain value.