Man-Made Universality of Blackbody Radiation 2

Man-made Universality of Shape

This is a clarification of the previous post on the perfect Planck blackbody spectrum of the Cosmic Microwave Background Radiation CMB as a 14 Billion years afterglow of Big Bang as the leading narrative of cosmology physics today. See also this recent post and this older illuminating post.

The Planck spectrum as the spectrum of an ideal blackbody, takes the form 

• $E(\nu ,T) =\gamma T\nu^2\times C(\nu ,T)$                                         (1)

where $E (\nu ,T)$ is radiation intensity depending on frequency $\nu $ and temperature $T$, $\gamma$ a universal constant, and $C(\nu ,T)$ is a universal high frequency cut-off function of the specific form 

• $C(\nu ,T)=\frac{x}{\exp(x)-1}$ with $x = \frac{\nu}{T}\times\alpha$       (2)

where $\alpha =\frac{h}{k}$ with $h$ Planck's constant and $k$ Boltzmann's constant as another universal constant, with the property that 

• $C(\nu ,T)\approx 1$ for $x<<1$ and $C(\nu ,T)\approx 0$ for $x>>1$.  

We see that radiation intensity proportional to $T$ increases quadratically with $\nu$ in accordance with deterministic wave mechanics, and reaches a maximum shortly before a cut-off scaling with $T$ in accordance with statistics of energy quanta, which kicked off an idea of atom physics as quantum mechanics also based on statistics.    

Computational Blackbody Radiation offers a different version of high frequency cut-off motivated by finite precision physics/computation instead of statistics of quanta opening to a deterministic form of atom physics as real quantum mechanics. The underlying physics model in both cases is that of an atomic lattice capable of generating a continuous spectrum of vibrational frequencies.

The basic assumptions behind a Planck spectrum as an ideal are:

1. Model: Atomic lattice.
2. Equilibrium: All frequencies take on the same temperature.
3. High-frequency universal cut-off: Statistics of energy quanta.  

Observation show that most real blackbody spectra substantially deviate from the Planck spectrum and so have their own signature reflecting specific atomic lattice, non-equilibrium and specific high frequency cut-off lower than the ideal. Graphite is just about the only substance showing a Planck spectrum. 

This was not welcome by physicists in search of universality, and so the idea was born of deciding the spectrum of a given material/body by putting it inside an empty box with graphite walls and measuring the resulting radiation peeping out from a little hole in the box, which not surprisingly showed to be a graphite Planck blackbody spectrum. 

Universality of radiation was then established in the same way as universality of shape can be attained by cutting everything into cubical shape as was done by the brave men cutting paving stone out of the granite rocks of the West Coast of Sweden, which is nothing but man-made universality.  

The line spectrum of a gas is even further away from a blackbody spectrum. The idea of CMB as an afterglow of a young Universe gas cloud with a perfect Planck blackbody as measured by the FIRAS instrument on the COBE satellite, serves as a corner stone of current Big Bang + Inflation cosmology. 

It is not far-fetched to suspect that also the COBE spectrum is man-made, and then also Big Bang + Inflation.