The line of sight argument is nice and succinct, and of course in some sense correct, but I've come to view the paradox in a somewhat different way: if all you have in a static and eternal universe are everlasting sources of energy, then of course you're going to run into trouble when considering equilibrium concerning energy, because it won't exist.

So while it is true that the true resolution to the paradox is that our universe is finite in age and expanding, that doesn't mean a static and eternal universe is in principle untenable. One could for example imagine as of yet unknown sinks of energy, or perhaps starlight gets recycled back into new stars as the old stars disappear. Without speculating on the mechanism, basically any universe where conservation of energy holds will have (on a large enough scale) a constant energy density, and hence, a dark sky at night.

The paradox also assumes several things about light, specifically that light propagates forever. Only in recent years have we managed to prove that assumption true. But if light did degrade over astronomical distances, a static and infinite universe could still have a dark sky at night. If one postulates that light degrades into lower and lower frequencies over time/distance, maybe we are indeed living in a non-expanding universe? Given the thermodynamic issues of an accelerating expansion (dark energy) photons that degrade over distance seems at least a less-strange option.

> light propagates forever .... Only in recent years have we managed to prove that assumption true

I thought the dark of night was explained by redshift (given distance, it shifts out of the visual spectrum). I guess the infra-red still continues on so that is in line with light propagating forever

Before we realized the universe was expanding and redshift occurred there was Tired Light

https://en.wikipedia.org/wiki/Tired_light

I am actually intrigued to had never encountered this term when reading Sagan or Hawking or Dawkins - thank you.

In a static universe there would be no redshift, since the redshift comes from the universe expanding.

It also assumes that the density of stars is constant in an infinite universe.

You can have an infinite universe, but with all the stars located in just part of it, i.e. finite mass, infinite space.

Most of the light heads off into empty space, never to be seen again.

>Only in recent years have we managed to prove that assumption true

How? What if after 100 years light has a small chance to disappear.

Because very distant objects describe a very different universe, meaning the light has traveled in time without degrading. For instance, the cmb doesn't match the current universe, proving both that light travels forever and that the universe is not static.

Distant objects also do not show degradation in brightness beyond square area expectations. They are redshifted, but not dimmer than would be normal.

I don’t really see how Olbers’s paradox proves that the Universe is finite, merely that the observable universe is finite. The observable universe is finite because (a) it’s expanding and (b) the speed of light is finite. Both of these can be true in an infinite universe (an infinite universe can still expand everywhere, which can be counterintuitive but it’s true.)

The observable universe is finite because the light started at some point in time (and the corresponding distance in light years).

It says less about the size of the universe, than its age.

It also talks about red-shift. Olbers couldn't know that, but even if our universe was here forever we still wouldn't have a lit night sky.

"and eternal static universe."

Doesn't that assume that an infinite amount of time has already passed? Which seems like a contradiction in terms.

I don't see how it would be a contradiction in terms; we can easily speak of the possibility of an infinite amount of time in the future, why not also in the past?

(It may be factually wrong, but that's not a contradiction in terms).

Why must that be the case? You can sum an infinite series to any arbitrarily small number you want.

Only when you have a free choice over the sum, which you don't in this case: https://en.wikipedia.org/wiki/File:Olbers%27_Paradox.svg