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I've always been puzzled by this paradox. More particularly, I'm baffled that apparently the mainstream explanation involves cosmological arguments such that t

I've always been puzzled by this paradox. More particularly, I'm baffled that apparently the mainstream explanation involves cosmological arguments such that the expansion of the Universe. Is it really that complicated? Take Hubble's deep field image, for instance. It was shot in a tiny area of the sky that looks completely black. But with enough exposure, Hubble found that it's actually full of galaxies. Can't I just conclude that if this part of the sky if completely black, it's not because space is expending, but just because our eyes are not sensitive enough? Olber's Paradox points out that wherever we look at, at some distance our line of sight will meet the surface of a star. But that does not mean that this point will register as a light for our eyes. Our eyes would have to be sensitive enough.

nostromo 11y ago
Imagine Hubble's deep field image again, but this time imagine you can see towards infinity (beyond the observable universe). If the universe is infinitely big (and old), then there would be so many stars in the image that there would be an infinite amount of light in the image. In this hypothetical universe, the Sun would actually be a dark spot in the sky -- because it would be blocking the infinite amount of light coming from an infinite amount of stars behind it. That's the paradox -- that we do not see that. No matter how sensitive our eyes are, we would be able to see infinite light. (Actually, our eyes would be melted... and all current forms of life impossible... but you get the picture.)
- grondilu 11y ago
  But stars are getting fainter and fainter as they are further and further away. I get that there would be an infinite amount of them, but then it's an infinite times a zero. The limit is not obvious and I've never seen anyone discussing the actual maths of this. I don't know those maths, but it seems reasonable to me that since the sky is indeed black, then it has to be that it's because the dimness of stars prevails over their number and/or density.
  - nostromo 11y ago
    > But stars are getting fainter and fainter as they are further and further away. I get that there would be an infinite amount of them, but then it's an infinite times a zero. No, it never goes to zero, it just gets fainter. An infinite number of small numbers adds up to infinity. > since the sky is indeed black, then it has to be that it's because the dimness of stars prevails over their number and/or density. As the article mentions, the sky is black because we cannot see infinity. We can only see the observable universe.
    - grondilu 11y ago
      > No, it never goes to zero, It never goes to infinity either. Zero and infinity are the limits. > An infinite number of small numbers adds up to infinity. Well, no. It depends. For instance the sum of 1/n goes to infinity, but not the sum of 1/n². And since the luminosity of a star decreases with the square of the distance, I incline to believe the sum does converge. But again, that would require some serious, albeit probably not very hard maths. I've never seen anyone discuss this. Instead everyone seems to immediately assume the sum would diverge. That's not obvious at all.
    - czinck 11y ago
      An infinite number of small numbers does not always add up to infinity! Since the apparent brightness of a star is an inverse-square law, if you assume there are an infinite number of stars, each 1 light year further away from you in a line and all the same brightness, you end up with that area being only 64%[1] brighter than it would seem with only the first star. Seems like a pretty simple resolution to this paradox to me. [1] https://en.wikipedia.org/wiki/Particular_values_of_Riemann_zeta_function https://en.wikipedia.org/wiki/Particular_values_of_Riemann_z...
      - tamana 11y ago
        I am going to guess that physicists have considered your resolution and it is incorrect in the face of current measurements and models.

nostromo 11y ago

Imagine Hubble's deep field image again, but this time imagine you can see towards infinity (beyond the observable universe). If the universe is infinitely big (and old), then there would be so many stars in the image that there would be an infinite amount of light in the image. In this hypothetical universe, the Sun would actually be a dark spot in the sky -- because it would be blocking the infinite amount of light coming from an infinite amount of stars behind it. That's the paradox -- that we do not see that. No matter how sensitive our eyes are, we would be able to see infinite light. (Actually, our eyes would be melted... and all current forms of life impossible... but you get the picture.)

grondilu 11y ago
But stars are getting fainter and fainter as they are further and further away. I get that there would be an infinite amount of them, but then it's an infinite times a zero. The limit is not obvious and I've never seen anyone discussing the actual maths of this. I don't know those maths, but it seems reasonable to me that since the sky is indeed black, then it has to be that it's because the dimness of stars prevails over their number and/or density.
- nostromo 11y ago
  > But stars are getting fainter and fainter as they are further and further away. I get that there would be an infinite amount of them, but then it's an infinite times a zero. No, it never goes to zero, it just gets fainter. An infinite number of small numbers adds up to infinity. > since the sky is indeed black, then it has to be that it's because the dimness of stars prevails over their number and/or density. As the article mentions, the sky is black because we cannot see infinity. We can only see the observable universe.
  - grondilu 11y ago
    > No, it never goes to zero, It never goes to infinity either. Zero and infinity are the limits. > An infinite number of small numbers adds up to infinity. Well, no. It depends. For instance the sum of 1/n goes to infinity, but not the sum of 1/n². And since the luminosity of a star decreases with the square of the distance, I incline to believe the sum does converge. But again, that would require some serious, albeit probably not very hard maths. I've never seen anyone discuss this. Instead everyone seems to immediately assume the sum would diverge. That's not obvious at all.
  - czinck 11y ago
    An infinite number of small numbers does not always add up to infinity! Since the apparent brightness of a star is an inverse-square law, if you assume there are an infinite number of stars, each 1 light year further away from you in a line and all the same brightness, you end up with that area being only 64%[1] brighter than it would seem with only the first star. Seems like a pretty simple resolution to this paradox to me. [1] https://en.wikipedia.org/wiki/Particular_values_of_Riemann_zeta_function https://en.wikipedia.org/wiki/Particular_values_of_Riemann_z...
    - tamana 11y ago
      I am going to guess that physicists have considered your resolution and it is incorrect in the face of current measurements and models.