Olbers’ paradox states that given a static, inifinitely old universe with an infinite number of stars distributed in an infinitely large space our sky would be bright rather than dark.
The mainstream explanation of the paradox is that it requires both finite age of the universe and redshift due to the expansion of spacetime to be explained.
This is such a crock of shit.
If the stars are no longer shining, then after an infinite number of years we should have an isotropic radiation soup corresponding to the energy density of the “initial” universe.
On the other hand, if you want stars shining after an infinite number of years, you seem to be forced to choose between:
a) An infinite amount of energy for the stars or
b) an entropy reversing process
If you have b), then we can resolve the paradox with an infinite universe by having the radiation “recycled” and absorbed into new stars an infinite number of times.
If we select a) then the energy density of the universe is by definition infinite, which is an untenable assumption.
Despite that, a lots of books tend to shamelessly suggest that a) is a possible option!
There is a choice c) though: fractal star distribution.
If the distribution of stars is such that the density of stars decreases as the region increases then again we solved the paradox, since the universe can then be assigned a finite energy density, but we can regionally have extremely high energies. Incidentally this also seems to agree with observation.
Conclusion
Olbers’ paradox is based on the hidden assumptions of infinite energy density. Such an assumption will naturally lead to other absurd results.
What we can surmise is basically simply that at least one of these hold true:
- There are entropy reversing processes at a large scale
- The universe is finite in time and space
- The distribution of energy and matter in the universe is fractal
This is far from the paradox ruling out an infinite universe, but the worst part is not pointing out the obvious hidden assumption that causes the “paradox” to begin with.