Olbers' Paradox and Cosmic microwave background radiation?

Yes, it could...

Olber's Paradox was devised in a time when it was believed that space was a true vacuum which would allow light to travel an infinite distance. Even if this *was* the case, the brightness of the sky would depend on photon density which would depend on the matter density of the universe, and so would not be as bright as the sun anyway. But space is not a true vacuum...

The intergalactic medium contains ionised plasma which is redshifting the light that passes through it (which many people mistake for a doppler effect and imagine the galaxies are generally flying away from each other). This plasma has a very low temperature, i.e. 3°K, which makes it opaque to any radiation that is redshifted down to this temperature. This means that light only gets to travel a certain distance through intergalactic space before it becomes thermalised. At 3°K, it is absorbed by the matter of the intergalactic medium and re-emitted as the thermal radiation that we detect as the CMB. Hence, our visibility is limited and detail from beyond these limits is lost.

I am not sure how you can compare Olbers' paradox to the cosmic microwave background. In any case, the former is "old story." Today we know (we think we know) that the CMB is the "left-over" of the Big Bang, a few thousand years after, when space became transparent. As for the infinite universe that must show an entirely bright sky, we think that there are two horizons to our universe:

The past one, of the objects that move from us faster than the speed of light (adding speed and expansion) that their light will never reach us again, and

The future horizon, of the objects who's light hasn't reached us yet.In any case, the Olbers' paradox assumes a static universe and an euclidean space. But, at the scale of the universe, everything is different. We observe in both space and time. The sun is where it was 8 minutes ago, Proxima Centauri where it was 4.5 years ago and distant galaxies, where they were billions of years ago.

There is no center nor edge to this universe and the notion of "infinite" as explained by Olbers, is simply something we can't ask. Descartes wrote that the shortest distance between two points was a straight line, but what is it, at the scale of the universe? Imagine we were to build a tower from earth to Proxima Centauri. What would it look like? A spiral, right? Yes, because during those 4.5 years its light comes down to earth, we have gone around the sun 4.5 times!

Those were not in the mind of Olbers.

"Could the CMBR be equivalent to an Olbers' effect?"

No. The CMBR was not an emission from the surface of stars (a grey body, with emissions spectra), it was a pure black body.

"Without the need to include cycles (Stars /Galaxies and their life and death) Olbers ' Paradox presumes us to have eyesight far superior to that which we really have."

Fail. The "size" of an infinite Universe is infinite, the number of light sources is infinite, the age of the Olber's Universe is infinite. Therefore we *must* see the bare surface of stars in every direction.

"An infinite universe would look no brighter from Earth than a finite universe"

False. We would in fact have the surface of stars as the coldest surface with which to radiate heat.

"With Hubble telescope as "the observer"

Can you describe the differences between an Olbers' Paradox "effect"and the CMBR?"

Olber's... no red shifting, older objects should not be anomalously larger, the spectra should be grey body, not black body.

CMBR... red shifted, self-pumped, hydrogen plasma, the only way we know to produce anything like a black body radiator. Other observations provide that older galaxies look larger, because they subtended a larger part of a smaller Universe. Additionally, red shifting cannot be explained by tired light, nor by us "classically moving away from stars in every direction".

In Olbers paradox , the light did not change its wavelength with increasing distance , just its intensity.

The MBR ,however, does not only display a low intensity due to "distance" --- but is red shifted because of the expansion of the universe

The Olber's Paradox means that the universe is finite.

In fact, this mass is 10^54 kg..

YES¡ GOOD QUESTION¡

But the visible universe would be a thermal anomaly, the universe beyond the cosmological horizon would have the temperature of the CMB, no other way to explain

oblers paradox aint a paradox any more

It was based on a number of assumptions which have since been proved to be incorrect