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Okay, if the universe were perfectly homogenous, i.e., uniformly dense at all scales, then this argument would be easy to buy. If you allow density variation a

Okay, if the universe were perfectly homogenous, i.e., uniformly dense at all scales, then this argument would be easy to buy. If you allow density variation at some scales, like the difference in density between the interior of a star and interstellar space, then it changes a bit, right? If you're really close to a star, then obviously that star is brighter than the average brightness of the universe. Right? If so, then the night sky wouldn't be "as bright as the sun" (like the video says), as observed from earth. But would the night sky be uniformly bright? Doesn't it depend on the average density of the universe? I.e., if the average density gets low enough, then don't those small-scale density variations start to matter at some point?

jbri 14y ago
It's generally hard to speculate on how things "would" be if the universe were markedly different than it how it actually is. Or rather, it's easy to speculate, but it's nigh-impossible to come up with one solution to the exclusion of others. I can come up with many hypothetical universes where the night sky would be uniformly bright, and many hypothetical universes where there would be substantial amounts of variation. The general statement of the paradox is that the total amount of light coming from distant stars massively outweighs the light coming from a local star, so while the local star might create a slightly brighter patch of sky, that difference is small enough that even in its absence the sky would look "bright".
andrewcooke 14y ago
you're right that it's not going to work out exactly equal to the brightness of the sun. another way to see this is to imagine an alien who lives on a (undiscovered) planet incredibly close to the sun - the sun would appear much brighter to the alien who would, presumably, expect a correspondingly brighter sky everywhere else (which clearly makes no sense since looking in other directions the alien should agree with us). but the effect of variations is most important when you have fewest stars (so the largest variation should be the sun, which seems reasonable). at large distances, with many stars, things will even out despite the fluctuations (for physically reasonable fluctuations). to make the argument rigorous, you need to work out how bright things would be "on average". another (more convincing?) way to understand the problem is to see that if we have an infinite, static universe, full of stars, all burning away, it should get hotter and hotter over time... (and if it's infinitely old, should be infinitely hot by now!). clearly something is wrong with that model.

jbri 14y ago

It's generally hard to speculate on how things "would" be if the universe were markedly different than it how it actually is. Or rather, it's easy to speculate, but it's nigh-impossible to come up with one solution to the exclusion of others. I can come up with many hypothetical universes where the night sky would be uniformly bright, and many hypothetical universes where there would be substantial amounts of variation. The general statement of the paradox is that the total amount of light coming from distant stars massively outweighs the light coming from a local star, so while the local star might create a slightly brighter patch of sky, that difference is small enough that even in its absence the sky would look "bright".

andrewcooke 14y ago

you're right that it's not going to work out exactly equal to the brightness of the sun. another way to see this is to imagine an alien who lives on a (undiscovered) planet incredibly close to the sun - the sun would appear much brighter to the alien who would, presumably, expect a correspondingly brighter sky everywhere else (which clearly makes no sense since looking in other directions the alien should agree with us). but the effect of variations is most important when you have fewest stars (so the largest variation should be the sun, which seems reasonable). at large distances, with many stars, things will even out despite the fluctuations (for physically reasonable fluctuations). to make the argument rigorous, you need to work out how bright things would be "on average". another (more convincing?) way to understand the problem is to see that if we have an infinite, static universe, full of stars, all burning away, it should get hotter and hotter over time... (and if it's infinitely old, should be infinitely hot by now!). clearly something is wrong with that model.