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Olbers' Paradox

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Re: Olbers' Paradox

#21

Post by mlinksva »

bjornedstrom wrote: post #8
thih9 wrote: post #6

Earlier quoted context omitted.

I don’t have Chrome, could you elaborate? Where is the highlighter and what does it do?

The link points to " https://en.wikipedia.org/wiki/Olbers%27_paradox#:~:text=In%2... ." In case that renders as a link by Hacker News, I've added a space here and removed the https part: en.wikipedia.org/wiki/Olbers%27_paradox #:~:text=In%20astrophysics%20and%20physical%20cosmology,infinite%20and%20eternal%20static%20universe. What it does is that it highlights that text in the page, with a yellow background color. M…

I love it, and have been manually creating such links every day since discovering the feature. One should be able to link to any portion of a page, and now one can, largely. The highlighting ought to be something a browser allows a user to customize, but I really wish Firefox (which I use about half the time) had the feature.

Re: Olbers' Paradox

#22

Post by colanderman »

pontus wrote: post #11

Isn't this just an issue of comparing a countable and uncountable infinity? The number of points on the unit sphere is uncountable, but the number of stars is countable. As such there are in some sense more points on the sphere than there are stars, even though there are an infinite number of each. Take this together with the fact that intensity falls off as the square of the distance and it seems like the sky should…

Fall-off of light intensity does not factor in: while the amount of light reaching an observer from any given star does indeed fall off with the square of the distance, so does the apparent size of that star; its apparent surface brightness thus does not change with distance. (Think of day-to-day experience: people who walk away from you do not darken!)

I agree that countability vs. uncountability seems like it should come into play.

Re: Olbers' Paradox

#23

Post by jessermeyer »

avian wrote: post #12
jessermeyer wrote: post #9

The Hubble was pointed at what appeared to be a black void of space, and revealed lush fields of stars and galaxies. So at one degree of perception, we have an empty void, and at another, a bright flush of light and activity.

There is still plenty of space between the individual stars in the Hubble Deep Field image. From that point of view it just confirms the paradox - even with a powerful telescope stars don't fill up your entire field of view. I think a more fitting example of "an empty void yet a bright flush of light" would be the microwave background. With eyes sensitive to longer wavelengths the entire sky is indeed bright.

> even with a powerful telescope stars don't fill up your entire field of view.

Suppose the experiment is repeated on a black pixel from the Deep Field image, and another swell of stars are observed, hinting at a kind of fractal distribution.

Were the universe eternal and static, why could this pattern not repeat indefinitely in infinite time, space and matter? The paradox seems to assume a kind of infinite level of sensitivity of the observer.

Re: Olbers' Paradox

#24

Post by Arnavion »

thih9 wrote: post #6
bjornedstrom wrote: post #5

That "#:~:text=" highlighter is so annoying it has made me switch from Google Chrome to Firefox.

I don’t have Chrome, could you elaborate? Where is the highlighter and what does it do?

More details at https://chromestatus.com/feature/4733392803332096 and https://github.com/WICG/scroll-to-text-fragment/

Re: Olbers' Paradox

#27

Post by DiogenesKynikos »

kmm wrote: post #19

While it's true that the finite age of our universe and the expansion of space explain the paradox in the universe we live in, I don't think those are necessary conditions, nor is the dark sky proof our universe is not infinitely old. What I feel is the core of the resolution of the paradox is (global or local) conservation of energy. Even in an infinitely large eternal steady state universe, if we assume the total e…

Energy is not conserved on the scale of the Universe. General Relativity has no energy conservation law (it has a stress-energy tensor conservation law). Two examples of this: expansion of the universe causes the total energy contained in radiation to decrease, and the total amount of dark energy to increase.

Re: Olbers' Paradox

#28

Post by pontus »

colanderman wrote: post #22
pontus wrote: post #11

Isn't this just an issue of comparing a countable and uncountable infinity? The number of points on the unit sphere is uncountable, but the number of stars is countable. As such there are in some sense more points on the sphere than there are stars, even though there are an infinite number of each. Take this together with the fact that intensity falls off as the square of the distance and it seems like the sky should…

Fall-off of light intensity does not factor in: while the amount of light reaching an observer from any given star does indeed fall off with the square of the distance, so does the apparent size of that star; its apparent surface brightness thus does not change with distance. (Think of day-to-day experience: people who walk away from you do not darken!) I agree that countability vs. uncountability seems like it shoul…

Great point, thanks! Makes perfect sense. Turns out though that the intensity actually falls off faster than 1/r^2 toward the end due to quantization effects. Feels silly to include quantization, but I guess when were talking about stars that may be arbitrarily far away this would need to be part of the story.

Re: Olbers' Paradox

#29

Post by avian »

jessermeyer wrote: post #23
avian wrote: post #12

Earlier quoted context omitted.

There is still plenty of space between the individual stars in the Hubble Deep Field image. From that point of view it just confirms the paradox - even with a powerful telescope stars don't fill up your entire field of view. I think a more fitting example of "an empty void yet a bright flush of light" would be the microwave background. With eyes sensitive to longer wavelengths the entire sky is indeed bright.

> even with a powerful telescope stars don't fill up your entire field of view. Suppose the experiment is repeated on a black pixel from the Deep Field image, and another swell of stars are observed, hinting at a kind of fractal distribution. Were the universe eternal and static, why could this pattern not repeat indefinitely in infinite time, space and matter? The paradox seems to assume a kind of infinite level of…

No, the paradox as described in the Wikipedia article doesn't assume the infinite level of sensitivity.

The figure explains it visually - the further away you go from the observer, the more stars you capture in your camera's field of view and the apparent brightness stays the same. The 1/r^2 term for light intensity is cancelled by the r^2 for the number of stars.

It's interesting think what an experimental result you describe would imply. It either contradicts the nature of light or that we're in the center of a cloud of stars where the density of stars falls with distance from us.

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