exchemist, I have a question for you regarding how the whole thing of CBR started 80 years ago.
Back in the late '30s and early '40s, some "cosmologists" (it wasn't an stablished branch of astronomy yet) theorized about the average
temperature of the whole universe, discounting the hot spots that galaxies were.
Out of our earthly understanding of temperature, related to the kinetic theories of gaseous atmosphere, to talk about temperature in the
space is a very tricky subject, because only theories of radiating heat can apply (as far as I know).
There are two formulae which are used in astrophysics, when temperature is an issue, and both are related directly to radiation.
The oldest one (Stefan, 1879) is very simple and connect radiating power per unit area with the fourth power of temperature (in °K). It was used
by Stefan himself to estimate the Sun's surface temperature 150 years ago, and remain as an undisputed tool in astrophysics to derive a lot of
info about stars (temperature, size, luminosity) even today.
The second one (Planck, 1901) is quite more complex because it involves statistical behaviors (Maxwell-Boltzmann-Gibbs statistical mechanics).
The complexity lies in its three components: 1) the amount of resonance modes of EM waves inside a cavity (independant of temperature); 2) the
unit energy quantum of a given EM wave (h.f) and 3) the statistical distribution of energy along the spectrum, which is the exponential part that
makes the difference between Rayleigh's PDF (flat) and Planck's PDF (gaussian like curved shape being function of f and T).
I'd like very much if you help to reconstruct the history of the current CBR behavior, starting with the original thoughts of the first ones who dared
to approximate a value of average temperature for the whole universe. The values that appeared between the 30's and the 50's varied in a wide
range between 4°K and 50°K.
My question to you is this: What theory did the early cosmologists used to estimate the temperature of the universe?
I think that they should have worked very hard to discount "singularities" in the isotropic conception of the universe, like the billion-trillions of galaxies
which were not meant to be considered. It was already known by then that distances between galaxies were huge, in the order of tens of Bly. So,
assuming that they discounted the accumulated energy of such hot-spots into the "volume" of the universe, the above question is:
Did they approximated results by Stefan? Did they averaged part of the Planck's spectrum (area under the curve)? Another theory that I'm not aware of?
I'd really appreciate your comments about the early stage of the development of the CBR theory that we know today.