The heavens are telling the glory of God;
and the firmament proclaims his handiwork.
Olber’s paradox, also known as the ‘dark night sky’ paradox, is a paradox which is intended to demonstrate that we have empirical evidence that the universe has not always existed (in a steady-state) but had a definite beginning; namely, that we can distinguish the stars in the sky. Of course, the paradox is rarely heard of anymore as mainstream cosmologists have come to recognize that the universe did have a beginning. However, before the Big-Bang hypothesis was widely accepted, this paradox proposed that we could look to the stars for evidence that there has not always existed a universe in a steady-state. What I want to do here is simply think through the logic of the paradox, and critique it.
The paradox can be summarized as follows:
“If the universe is static and populated by an infinite number of stars, any sight line from Earth must end at the (very bright) surface of a star, so the night sky should be completely bright.”
~Wikipedia, Olber’s Paradox
Perhaps Olber’s paradox would work granting certain assumptions about steady-state universes. For example if one grants that in any direction from any point in space, there exists a star at some distance, then this may follow (one would also think to assume that stars do not have half-lives, though perhaps one wouldn’t have to admit even that, so long as at every given time there are infinitely many stars in any given direction from any given point in space).
However, it is logically possible that in some steady-state universe it is not the case that in every direction from any point in space there exists an infinite number of stars. I can imagine a steady-state universe in which there is at least one direction from at least one point in space for which there does not exist an infinite number of stars. So long as that is even logically possible, it would be possible to have some spot of the night sky not illuminated by the light of a star. Then, we might say, it is logically possible that in some steady-state universe we would observe our night sky (a sky ‘identical’ to our night sky – where ‘identical’ is informal).
So, I think that Olber’s paradox is easily dissolved if it is intended to be a logical paradox. However, Olber’s paradox would have made the steady-state model of the universe extremely improbable given the observational evidence of the night sky. In other words, it represents a kind of empirical paradox on the steady-state assumption.