Ok, this is a bold question, I know. But, let me explain: After first hearing about Olbers' paradox, I found that something seemed 'off' about it, so I looked into the subject as much as my skills (and time!) would allow. And I came to the conclusion that the paradox was probably kind of like Zen...
Have patience, your post on Astronomy is barely two hours old. You should not expect many responses in that time frame on most SE sites, we are not meant to deliver answers immediately in real-time.
Suggest you first get a bit better informed about what the argument for the paradox is. Basically, the further away you look, the more stars there will be at that distance, on the assumption they are distributed uniformly on average.
Yes, traffic is a bit slower on Astronomy.SE, but most of the Physics L.SE regulars who are into astronomy do watch it. And your question is less likely to get buried by new questions over there, which improves its visibility.
@Wolphramjonny No it's not, both statements are empirical facts: The question has been answered like that when I've asked it, and the human eye is only able to resolve a distinct light at a certain finite distance, you should know this from your own experience..
@AndrewSteane The thing is I'm going from a broad reading of popular science sources. As presented here, youtube.com/watch?v=gxJ4M7tyLRE the 'paradox' seems to be nonsense.
@Wolphramjonny. No. Try it with a pen flash light.
it is because the number of photons reaching the retina is too low, but a ccd will integrate them
In any case, the issue is that you keep getting weaker and weaker sources, but adding them amounts to something, not to zero. and to something infinite!
Not so with zeno. The problem was that the greeks didnt know that an infinite series can add to a finite sum.
@Wolphramjonny, I see no reason why it would be infinite?
BTW, @Wolphramjonny what is 'ccd'?
@Wolphramjonny are you saying that the sum in my thought experiment amounts to infinity?
@Wolphramjonny, anyhow, I'd be happy to find I'm wrong, I just want an answer that makes sense. I don't know why people find this sort of a touchy subject?
As you consider bigger distances, each star contributes less brightness, but there are more stars. To figure out which effect wins, you have to do the math. If you don't actually do the math, you're essentially making the same mistake as Zeno's paradox. An infinite sum can be finite, infinite, or infinitesimal, and you actually have to check which it is.
As you can read in any cosmology textbook, when you do the math, you get infinity. People are getting annoyed at you because you're acting as if you've uncovered some great error in all of cosmology, when in reality your question is answered in the first two pages of any book on the subject.
There appears to be something wrong with the math; which I can demonstrate with a slightly more complex thought-experiment. Would you like to hear it? The issue is that people seem to blindly believe this calculation without thinking it over carefully or thinking about its physical interpretation. Now, again I may well be wrong, but the arguments I've heard don't suggest so.
So, either people are presenting a faulty interpretation of the math, the math has over-looked something, or there's an error in my reasoning. One of these must be true. But, no one has argued very well against my reasoning, so I don't know. Though, I will admit, revolving the lights does involve a kind of flaw, that's why I updated / will update my thought experiment.
@knzhou In short (very short), I'm pretty sure a (well-formulated) visual computer sim would not yield a sky as bright as the sun.
@knzhou, maybe few people understand the paradox too well as I've heard several different arguments on here.
"so long as there were a finite (not too big) number of near-by light sources" What does that even mean here? How close is "near-by", and why does that even really matter for a static eternal universe? All stars should be close enough to interact with us in such a universe... which would be infinite stars.
First thing you need to do is to understand the math, and if you find a flaw there, we can discuss. It is an argument that cannot be resolved without doing the math
but if you do not believe in calculus per se, nobody will bother to discuss
let us see what part of the reasoning you disagree:
1) the light per visual area of a star is independent of distance.
as the star gets farther away, the visual area diminishes but the luminance per unit area does not
once the star is very far away, the area will be so low that the total luminance will be low too. You might get a photon every million years
but if the universe is infinite you will have a star in every direction, so the total area will be the sky. So the luminance of the sky per area must be as bright as that of a star.
Now, keep adding infinite stars on each direction, and the sky will glow infinitely
Why is the inverse square law a red herring? In Olber's model all stars are the same size & absolute brightness, i.e., we have a homogeneous isotropic eternal universe populated by average stars. A star at unit distance occupies an angular area of $a$ with apparent brightness $L$, so its brightness per unit area is $L/a$. A star at distance $d$ occupies an area $a/d^2$ with brightness $L/d^2$ due to the inverse square law, so its brightness per unit area is once again $L/a$. — PM 2Ring7 hours ago
(Pity chat doesn't support MathJax (unless you use a userscript or bookmarklet)).
@Wolphramjonny, in short, the math amounts to arithmetic...., I love math, but this doesn't have to do with the accuracy of a calculation but rather with whether or not it would correspond to any kind of physical reality....
Also note that stars don't actually block the light coming from behind them. Those incoming photons just add to the energy of the star, and that energy gets re-emitted, although some photons are effectively reflected back.
Discussion on question by Jinny Ecckl…
Discussion on question by Jinny Ecckl…