The Secret of Radiative Heat Transfer vs CMB and Big Bang

A main challenge to physicists at the turn to modernity 1900 was to explain radiative heat transfer as the process of emission, transfer and absorption of heat energy by electromagnetic waves described by Maxwell's equations. The challenge was to explain why real physics avoids an ultra-violet catastrophe with radiation intensity going to infinity with increasing frequency beyond the visible spectrum. 

More precisely, the challenge was to uncover the physics of a blackbody spectrum with radiation intensity scaling with $T\nu^2$ with $T$ temperature and frequency $\nu\le\nu_{max}$ with $\nu_{max}$ a cut-off frequency scaling with $T$, and intensity quickly falling to zero above cut-off. 

Planck as leading physicist of the German Empire took on the challenge and after much struggle came up with an explanation based on statistics of energy taking the above form as Planck's Law, which has served into our time as a cover up a failure to explain a basic phenomenon in physical terms. 

Computational Blackbody Radiation offers an explanation in terms of finite precision physics setting a cut-off (scaling with temperature) on the frequency of emission from coordinated oscillations of an atomic lattice, with uncoordinated atomic motion stored as heat energy.

In this analysis heat is transferred from a body of higher temperature  to a body of lower temperature through a resonance phenomenon analogous to the resonance between two tuning forks. The essence can be described in terms of a  forced acoustically weakly damped harmonic oscillator:

• $\dot v(t)+\nu^2u(t)+\gamma v(t)=f(t)=sin(\bar\nu t)$ for $t>0$                    (1)

where $u(t)$ is displacement at time $t$, $v(t)=\dot u(t)$ is velocity, the dot represents derivative with respect to time $t$, $\nu$ is the frequency of the harmonic oscillator and $\bar\nu\approx\nu$ that of the forcing. For radiation the damping term takes the form $\gamma\ddot v(t)$. 

Mathematical analysis shows assuming small damping with $\gamma << 1$ and near resonance with $\nu\approx\bar\nu$ and integration over a period:

• $Output = \gamma \int v^2(t)dt \approx \int f^2(t)dt = Input$         (2)
• Velocity $v(t)$ out-of-phase with $f(t)$.                                                                (3)

Even if it looks innocent, (2) represents the essence of Planck's Law with (3) expressing basic physics: Out-of-phase means that the interacting between forcing and oscillator corresponds to a "pumping motion" with the forcing balanced mainly by the harmonic oscillator itself and not the damping. In the acoustic case $T=\int v^2(t)dt$ and thus $Output =\gamma T$, which in the case of radiation takes the form $Output = \gamma T\nu^2$ or Planck's Law. 

Sum up:

• Radiative balance between two bodies of equal temperature is expressed by (2).
• Heating of a body B1 with lower temperature from body B2 of higher temperature from frequencies above cut-off for B1.  
• High frequency cut-off effect of finite precision physics and not statistics.
• Blackbody spectrum is continuous (all frequencies) and requires atomic lattice. 
• A gas ha a line spectrum with selected frequencies, which is not a blackbody spectrum.
• Cosmic Microwave Background radiation as a perfect blackbody spectrum of an after-glow of Big Bang without atomic lattice appears as very speculative, with Big Bang itself as even more speculative beyond experimental confirmation.