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Subsequent edit: Assuming the universe is infinite, is where the problem begins. There is no reason to assume that. Original comment: Is this really not obviou

by rdiddly 11y ago

Subsequent edit: Assuming the universe is infinite, is where the problem begins. There is no reason to assume that. Original comment: Is this really not obvious to people? It's about subtended angles - simple geometry. As the Earth's distance from a star increases, it subtends a decreasing angle in that star's "sky." Assuming radiation does indeed proceed radially and in straight lines, at increasing distance the Earth is capable of catching a decreasing portion of that star's radiation. As the distance approaches infinity, the subtended angle approaches zero and the amount of light reaching us approaches zero. The star is just as bright, but most of its radiation goes somewhere else besides Earth. Imagine building a giant spherical shell around a star. Its radius equals the distance between earth and the star. It catches 100% of that star's radiated energy. Now paint the Earth on the inside of the shell, actual size. It looks, to someone standing on the surface of that star, like the real earth, i.e. a tiny dot. Now divide the surface area of the dot, by the surface area of the sphere (4)(pi)(r^2). That's how much of that star's energy our planet catches. Assuming zero degradation across space. So imagine you're in a forest of trees the closest of which are 800 miles away from you. You'd see the goddamned sky just fine.

samstave 11y ago
Is was an amazing conceptual comment - thank you
gpsx 11y ago
You are correct in your geometry, but you forgot one thing. The earth receives a smaller portion of light for stars that further away, but the number of stars at that radius goes up by the exact same amount. So from any shell the amount of light we get is the same. If the shells go out to infinity, the light becomes infinite (well, according to the naive argument).
- meric 11y ago
  The nearest star is the Sun. With a giant Sun nearest to Earth, it's impossible for the number of stars to go up proportionally as distance to Earth increases. There isn't 4 suns at 2 AU, and at 100000 light years wide, with 63000 AUs per light year, the milky way does't contain (63000 * 100000)^2 stars. There needs to be 4 billion times more stars in the milk way for there to be proportionally as many stars as in our solar system. You can fill the entire sky with AA battery torches and they won't be as bright as the one stuck right up to your eye. The night sky is dark, but it doesn't mean it isn't full of rays of lights heading our way. It's darker than the day sky due to the Sun being so close, yes, but the night sky is full of light, everywhere we look. It's only because the way our minds perceive relatives, we call the night sky "dark".
rdiddly 11y ago
BTW that's (4)(pi)(a gazillion light-years ^ 2) in case the point wasn't obvious!
lutusp 11y ago
Your explanation is correct for individual stars, but it doesn't take universal expansion into account, which independently reduces the energy available from distant sources (apart from the 1/r^2 law). The reason? Same energy, more space, so a reduction in energy per unit of volume. Also, setting aside the issue of expansion and redshift, if you imagine a sphere with a uniformly illuminated interior (imagine a surface composed of so many stars that counting them individually makes no sense) and an observation point at the center, if you increase the radius of the sphere, there's no change in the energy received at the center. This idea works for an infinite plane as well, and is a bit easier to grasp. Imagine an infinite plane with a fixed optical brightness, and an observation point at some distance d. Now double the distance -- no change in received energy because the plane is infinite in extent.
pdonis 11y ago
> As the Earth's distance from a star increases, it subtends a decreasing angle in that star's "sky." But the number of stars at a given distance increases as the distance increases, and this increase exactly cancels out the decrease in the amount of light from a given star that reaches the Earth. So your argument does not explain why the night sky is dark. > Now divide the surface area of the dot, by the surface area of the sphere (4)(pi)(r^2). That's how much of that star's energy our planet catches. Now do it the other way: draw a sphere around the Earth with some radius r. Calculate how many stars are on that sphere. The number increases as r^2; and, as you have shown, the amount of light reaching Earth from a given star decreases as r^2. So, as I said above, the increase in the number of stars exactly cancels out the decrease in the amount of light from each star that reaches the Earth; thus, the total starlight reaching Earth from a given radius r is a constant, independent of r.
- rdiddly 11y ago
  There's no reason to believe the universe is infinite nor that stars are evenly distributed throughout its volume. So "the number of stars increases as r^2" is the part that doesn't hold and is causing the paradox.
  - mannykannot 11y ago
    This is Kepler's theory, and it gets into philosophical trouble, as cosmologists generally take it as axiomatic that the laws of physics are the same everywhere, and so don't have much time for theories that depend on us being in a special place in the universe. A universe having a lower density of stars everywhere above some radius from Earth does put us in a special place, is hard to reconcile with universal laws, and there is no empirical evidence for it. An explanation that derives from the universe evolving over time, however, has none of the philosophical problems and does have supporting empirical evidence.
  - pdonis 11y ago
    > There's no reason to believe the universe is infinite nor that stars are evenly distributed throughout its volume. There is if you believe General Relativity is correct as applied to the universe as a whole. And if you don't, you have no model at all with which to make any predictions about what we should observe, so there's no reason to believe anything.
cousin_it 11y ago
Nope. A ball of radius R around Earth contains R^3 stars. The angular size of Earth as seen from each star is 1/R^2 or more. So the total light coming to Earth is proportional to R. As R goes to infinity, you get Olbers paradox. If you insist on talking about trees, in an infinite forest of trees that are 800 miles apart and 1mm thick, you wouldn't see the sky.
- rdiddly 11y ago
  Yup. The universe was declared infinite not because it is, but because it repeatedly defied our hubris. "If we can't find the end of it, it must be endless!" Kind of like "If she doesn't like me she must be a lesbian!"
gaur 11y ago
> Is this really not obvious to people? It's about subtended angles - simple geometry. If the universe is infinite and filled uniformly with stars, the 1/r^2 falloff in the radiation captured from each star is cancelled by r^2 dependence on the number of stars at radius r. So as you integrate r from 0 to ∞, you accumulate an infinite amount of radiation. Is this really not obvious to you? It's all about infinitesimals - simple calculus.
- rdiddly 11y ago
  As with others here, your problems start with "if the universe is infinite."
  - gaur 11y ago
    Yes, we are all aware of that. Nobody is saying that Olbers's paradox is unsolved; we are saying that your comment doesn't make sense. Olbers's paradox assumes from the outset that the universe is infinite. You cannot solve the paradox by invoking the inverse-square law.
  - rdiddly 11y ago
    You cannot solve Olbers' paradox at all, because it is a malformed question, that leads to a paradox.
    - gaur 11y ago
      Correct. Now could you please edit your top-level comment some more, so that it actually makes sense? First you fake incredulity about how people aren't finding it "obvious", although it's unclear exactly what you think is obvious (the paradox? its resolution? modern cosmology?). Then you launch into an explanation of the inverse-square law for a single point source. What's your intention here? By itself it doesn't demonstrate how to resolve the paradox. (As you say, the resolution is that the universe is not infinite. Thanks for adding that in the edit.) Overall, your top-level comment was incomprehensible, as evidenced by the large number of people who thought you were trying to use the inverse-square law to resolve the paradox.
deleted 11y ago
[deleted]

by rdiddly 11y ago

samstave 11y ago

Is was an amazing conceptual comment - thank you

gpsx 11y ago

You are correct in your geometry, but you forgot one thing. The earth receives a smaller portion of light for stars that further away, but the number of stars at that radius goes up by the exact same amount. So from any shell the amount of light we get is the same. If the shells go out to infinity, the light becomes infinite (well, according to the naive argument).

meric 11y ago
The nearest star is the Sun. With a giant Sun nearest to Earth, it's impossible for the number of stars to go up proportionally as distance to Earth increases. There isn't 4 suns at 2 AU, and at 100000 light years wide, with 63000 AUs per light year, the milky way does't contain (63000 * 100000)^2 stars. There needs to be 4 billion times more stars in the milk way for there to be proportionally as many stars as in our solar system. You can fill the entire sky with AA battery torches and they won't be as bright as the one stuck right up to your eye. The night sky is dark, but it doesn't mean it isn't full of rays of lights heading our way. It's darker than the day sky due to the Sun being so close, yes, but the night sky is full of light, everywhere we look. It's only because the way our minds perceive relatives, we call the night sky "dark".

rdiddly 11y ago

BTW that's (4)(pi)(a gazillion light-years ^ 2) in case the point wasn't obvious!

lutusp 11y ago

Your explanation is correct for individual stars, but it doesn't take universal expansion into account, which independently reduces the energy available from distant sources (apart from the 1/r^2 law). The reason? Same energy, more space, so a reduction in energy per unit of volume. Also, setting aside the issue of expansion and redshift, if you imagine a sphere with a uniformly illuminated interior (imagine a surface composed of so many stars that counting them individually makes no sense) and an observation point at the center, if you increase the radius of the sphere, there's no change in the energy received at the center. This idea works for an infinite plane as well, and is a bit easier to grasp. Imagine an infinite plane with a fixed optical brightness, and an observation point at some distance d. Now double the distance -- no change in received energy because the plane is infinite in extent.

pdonis 11y ago

> As the Earth's distance from a star increases, it subtends a decreasing angle in that star's "sky." But the number of stars at a given distance increases as the distance increases, and this increase exactly cancels out the decrease in the amount of light from a given star that reaches the Earth. So your argument does not explain why the night sky is dark. > Now divide the surface area of the dot, by the surface area of the sphere (4)(pi)(r^2). That's how much of that star's energy our planet catches. Now do it the other way: draw a sphere around the Earth with some radius r. Calculate how many stars are on that sphere. The number increases as r^2; and, as you have shown, the amount of light reaching Earth from a given star decreases as r^2. So, as I said above, the increase in the number of stars exactly cancels out the decrease in the amount of light from each star that reaches the Earth; thus, the total starlight reaching Earth from a given radius r is a constant, independent of r.

rdiddly 11y ago
There's no reason to believe the universe is infinite nor that stars are evenly distributed throughout its volume. So "the number of stars increases as r^2" is the part that doesn't hold and is causing the paradox.
- mannykannot 11y ago
  This is Kepler's theory, and it gets into philosophical trouble, as cosmologists generally take it as axiomatic that the laws of physics are the same everywhere, and so don't have much time for theories that depend on us being in a special place in the universe. A universe having a lower density of stars everywhere above some radius from Earth does put us in a special place, is hard to reconcile with universal laws, and there is no empirical evidence for it. An explanation that derives from the universe evolving over time, however, has none of the philosophical problems and does have supporting empirical evidence.
- pdonis 11y ago
  > There's no reason to believe the universe is infinite nor that stars are evenly distributed throughout its volume. There is if you believe General Relativity is correct as applied to the universe as a whole. And if you don't, you have no model at all with which to make any predictions about what we should observe, so there's no reason to believe anything.

cousin_it 11y ago

Nope. A ball of radius R around Earth contains R^3 stars. The angular size of Earth as seen from each star is 1/R^2 or more. So the total light coming to Earth is proportional to R. As R goes to infinity, you get Olbers paradox. If you insist on talking about trees, in an infinite forest of trees that are 800 miles apart and 1mm thick, you wouldn't see the sky.

rdiddly 11y ago
Yup. The universe was declared infinite not because it is, but because it repeatedly defied our hubris. "If we can't find the end of it, it must be endless!" Kind of like "If she doesn't like me she must be a lesbian!"

gaur 11y ago

> Is this really not obvious to people? It's about subtended angles - simple geometry. If the universe is infinite and filled uniformly with stars, the 1/r^2 falloff in the radiation captured from each star is cancelled by r^2 dependence on the number of stars at radius r. So as you integrate r from 0 to ∞, you accumulate an infinite amount of radiation. Is this really not obvious to you? It's all about infinitesimals - simple calculus.

rdiddly 11y ago
As with others here, your problems start with "if the universe is infinite."
- gaur 11y ago
  Yes, we are all aware of that. Nobody is saying that Olbers's paradox is unsolved; we are saying that your comment doesn't make sense. Olbers's paradox assumes from the outset that the universe is infinite. You cannot solve the paradox by invoking the inverse-square law.
- rdiddly 11y ago
  You cannot solve Olbers' paradox at all, because it is a malformed question, that leads to a paradox.
  - gaur 11y ago
    Correct. Now could you please edit your top-level comment some more, so that it actually makes sense? First you fake incredulity about how people aren't finding it "obvious", although it's unclear exactly what you think is obvious (the paradox? its resolution? modern cosmology?). Then you launch into an explanation of the inverse-square law for a single point source. What's your intention here? By itself it doesn't demonstrate how to resolve the paradox. (As you say, the resolution is that the universe is not infinite. Thanks for adding that in the edit.) Overall, your top-level comment was incomprehensible, as evidenced by the large number of people who thought you were trying to use the inverse-square law to resolve the paradox.

deleted 11y ago

[deleted]