Belief that the universe can't be infinite seems to contradict simple logic

Question

Physics professors I have had (including Dr. Feynman in 1962) contend that an infinite universe would produce a fairly uniform "glow" from our point of view, which is not present. This seems to be contradicted by a few simple factors:

1. The light from a star reaching the earth decreases as the cube of the distance, so light from sufficiently distant stars would have an ever decreasing probability of reaching us and as the distance increases approach zero.
2. As the distance from earth increases, there is an ever increasing probability that light producing objects would be blocked by non light producing objects (planets, etc.).
3. The light from some distant stars can also be blocked by nearer stars.
4. Some light from distant stars can be absorbed by nearer black holes or scattered by gravitation effects and not reach us.

Answer 1

As has been mentioned in the comments, this is Olbers' paradox. As we are fairly certain that the Big Bang really happened (and does not preclude an infinite universe), the paradox can be resolved by the expansion of the universe. Stars that are far enough away from us will be moving away at more than lightspeed, and hence invisible to us. In other words, an infinite universe is possible.

Now I'll explain why your arguments are wrong.

1. Light from stars decreases as the square of the distance (the inverse square law).
2. If objects like planets absorb light from stars, those objects will heat up. If the entire sky were covered in stars, all planets would have the same temperature as the stars, and would appear equally bright.
3. Same as for the previous problem, except now the blocking object is already as bright as a star - because it is a star.
4. This is correct. Black holes would block light. However, it would appear that there are far more stars than black holes. Hence, with the observed star/BH ratio, the sky would still be uniformly bright.

Answer 2

In addition to hdhondt's comments above, note the following:

When we are looking at extremely distant objects, we are usually not looking at stars: we are looking at either 1) entire galaxies consisting of billions of individual stars in a clump, 2) a jet from an active galactic nucleus which by chance is aimed straight at us, or 3) a single star caught in the act of exploding as a supernova- which will be brighter than an entire galaxy. At those distances, individual stars are indeed too dim to see.

We know that we cannot search for these distant objects that lie in the plane containing the disc of the milky way, because of the amount of dust there that dims out any light reaching us from those directions. So we look in different directions where there is little dust instead, and we indeed see extremely distant objects in those dust-free directions.

Occlusions of one distant object by another undoubtedly occur, but if we are talking about extremely distant galaxies sitting behind concentrations of mass, the galactic light is not blocked- it is gravitationally lensed and therefore still visible, even though the lensing mass sitting in the way is itself invisible.

The fact that very few galaxies get lensed suggests that occlusions at the galaxy level are relatively uncommon.