If the universe is infinite, for each particular direction there are an infinite number of stars. So even if the probability of a photon coming from a distant star is very low, there are infinitely many stars in that direction, so that direction will still be very bright. So the quantum nature of light does not change the paradox.

The wikipedia article surprises me though.. The actual brightness can be calculated as an infinite sum of start brightnesses getting weaker with the distance. The result of an infinite sum can be finite or infinite. I would have though apriori that the sum is finite because the star density is so low. But at the end of the article they seem to suggest that the universe is dense enough for the sum to be infinite...

From a simple standpoint of energy conservation, it's obvious the observed brightness cannot be infinite; the article questions the brightness value of the sky, not whether it is finite. From conservation of energy, for a homogeneous universe, a region around a star must receive as much energy as it gives out. So the total observed brightness of the sky would sum to the brightness of your own star, approximately (but distributed over a solid angle 4pi).

I think one resolution is the finite speed of light. Even if there are infinite stars in any given direction, they haven't been around long enough for the brightness to be infinite.

This "paradox" is basically just theorizing an aspect of the heat death of the universe.

The paradox says that an universe infinite in space and time would have to be bright in all directions. By infinite in time, I mean that the universe has been around infinitely long, i.e. it has no beginning. The finite speed of light wouldn't matter here since the light would have had an infinite amount of time to reach you.

Huh? We definitely know that that doesn't describe the universe. If two points are so far apart that the expansion of space inflates the distance between them faster than light can cross it, then no light can ever reach from one to the other, even if it travels for an infinitely long time.

The Olbers' paradox is from the 1800s, before we knew about the expansion of space. It's arguing against a static, infinitely old universe. As you point out, we now know that this isn't the case.

> If two points are so far apart that the expansion of space inflates the distance between them faster than light can cross it, then no light can ever reach from one to the other, even if it travels for an infinitely long time

Actually, it can. The issue is quite subtle. What you are saying is true only if the Hubble parameter is constant, it is not. (Hubble constant is such a misnomer! It's only constant across space but not time).

You may want to re-read paragraph 3.3 of the Lineweaver paper (http://arxiv.org/pdf/astro-ph/0310808v2.pdf)

Quotes :

> Photons near the Hubble sphere that are receding slowly are overtaken by the more rapidly receding Hubble sphere.

> The most distant objects that we can see now were outside the Hubble sphere when their comoving coordinates intersected our past light cone. Thus, they were receding superluminally when they emitted the photons we see now.

We know, but Olbers didn't. He died in 1840.

There will be a first star in any direction: photons will be very unlikely to pass throught that star.