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Olbers' paradox

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Hortensius

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Olbers' paradox
« on: August 18, 2010, 02:42:55 AM »
I always found this a nice one:

If the universe is infinite and filled with stars, you would expect that whatever direction on the sky you are looking at, each line of sight would eventually end at the surface of a star. Or in other words; the sky should be completely filled with stars, causing the night sky to be extremely bright instead of dark. Why is the night sky dark?

http://cmb.physics.wisc.edu/tutorial/olbers.html
« Last Edit: August 18, 2010, 02:44:28 AM by Hortensius »
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Crustinator

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Re: Olbers' paradox
« Reply #1 on: August 18, 2010, 03:32:10 AM »
Because starlight diminishes according to 1/r2? And some stars are closer than others? Probably we do recieve light from stars billions of light years away, but they're so faint as to be indistinguishable from background scatter.
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Hortensius

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Re: Olbers' paradox
« Reply #2 on: August 18, 2010, 04:54:28 AM »
Quote from: Crustinator on August 18, 2010, 03:32:10 AM
Because starlight diminishes according to 1/r2?

Can't be an explanation since the number of stars grows according to r3. So we still have a net increase of brightness as a function of r.
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Parsifal

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Re: Olbers' paradox
« Reply #3 on: August 18, 2010, 11:08:56 AM »
Quote from: Hortensius on August 18, 2010, 04:54:28 AM
Can't be an explanation since the number of stars grows according to r3. So we still have a net increase of brightness as a function of r.

So we can see through stars to other stars behind them?
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Crustinator

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Re: Olbers' paradox
« Reply #4 on: August 18, 2010, 11:30:43 AM »
Quote from: Hortensius on August 18, 2010, 04:54:28 AM
Quote from: Crustinator on August 18, 2010, 03:32:10 AM
Because starlight diminishes according to 1/r2?

Can't be an explanation since the number of stars grows according to r3. So we still have a net increase of brightness as a function of r.

Hmm. Where did you get the r3 from?
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Lorddave

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Re: Olbers' paradox
« Reply #5 on: August 18, 2010, 01:41:02 PM »
Why is this a paradox?

First of all, the Universe can be infinite but that doesn't mean the matter in it is.  You can have an infinite amount of space with a finite amount of matter.

Add to that the rate of universal expansion that is faster than the speed of light, diminished light from the inverse square law, and you get a good explanation.
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bowler

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Re: Olbers' paradox
« Reply #6 on: August 18, 2010, 02:25:04 PM »
Isnt this just evidence that the universe is finite?
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Hortensius

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Re: Olbers' paradox
« Reply #7 on: August 18, 2010, 03:36:03 PM »
Quote from: Crustinator on August 18, 2010, 11:30:43 AM
Quote from: Hortensius on August 18, 2010, 04:54:28 AM
Quote from: Crustinator on August 18, 2010, 03:32:10 AM
Because starlight diminishes according to 1/r2?

Can't be an explanation since the number of stars grows according to r3. So we still have a net increase of brightness as a function of r.

Hmm. Where did you get the r3 from?

If the density of stars is constant (and observations show it roughly is on large scales), the number of stars is proportional to the volume. The volume of space within a distance r is proportional to r3 (4/3 pi r3).
« Last Edit: August 18, 2010, 04:07:18 PM by Hortensius »
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Hortensius

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Re: Olbers' paradox
« Reply #8 on: August 18, 2010, 03:37:14 PM »
Quote from: bowler on August 18, 2010, 02:25:04 PM
Isnt this just evidence that the universe is finite?

No
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Hortensius

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Re: Olbers' paradox
« Reply #9 on: August 18, 2010, 03:42:34 PM »
Quote from: Lorddave on August 18, 2010, 01:41:02 PM
Why is this a paradox?

First of all, the Universe can be infinite but that doesn't mean the matter in it is.  You can have an infinite amount of space with a finite amount of matter.

Observations show that on large scales matter in the Universe is distributed homogeneously and isotropically, which means that the matter density doesn't just drop beyond some distance...

Quote from: Lorddave on August 18, 2010, 01:41:02 PM
Add to that the rate of universal expansion that is faster than the speed of light, diminished light from the inverse square law, and you get a good explanation.

Inverse square law doesn't help you for the reasons explained to Crust.
Universal expansion, although not faster than the speed of light, might be a good hint.
« Last Edit: August 18, 2010, 04:32:14 PM by Hortensius »
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Hortensius

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Re: Olbers' paradox
« Reply #10 on: August 18, 2010, 04:23:40 PM »
Quote from: Parsifal on August 18, 2010, 11:08:56 AM
Quote from: Hortensius on August 18, 2010, 04:54:28 AM
Can't be an explanation since the number of stars grows according to r3. So we still have a net increase of brightness as a function of r.

So we can see through stars to other stars behind them?

No we can't
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iznih

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Re: Olbers' paradox
« Reply #11 on: August 18, 2010, 05:32:35 PM »
Quote from: Hortensius on August 18, 2010, 03:42:34 PM
Universal expansion, although not faster than the speed of light, might be a good hint.

maybe most of the light is redshifted (to the infrared part of the spectrum or even further) so we can't see it
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Parsifal

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Re: Olbers' paradox
« Reply #12 on: August 18, 2010, 06:05:35 PM »
Quote from: Hortensius on August 18, 2010, 04:23:40 PM
Quote from: Parsifal on August 18, 2010, 11:08:56 AM
Quote from: Hortensius on August 18, 2010, 04:54:28 AM
Can't be an explanation since the number of stars grows according to r3. So we still have a net increase of brightness as a function of r.

So we can see through stars to other stars behind them?

No we can't

Then the number of visible stars doesn't grow according to r3.
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Lorddave

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Re: Olbers' paradox
« Reply #13 on: August 19, 2010, 01:56:11 AM »
Quote from: Hortensius on August 18, 2010, 03:42:34 PM
Quote from: Lorddave on August 18, 2010, 01:41:02 PM
Why is this a paradox?

First of all, the Universe can be infinite but that doesn't mean the matter in it is.  You can have an infinite amount of space with a finite amount of matter.

Observations show that on large scales matter in the Universe is distributed homogeneously and isotropically, which means that the matter density doesn't just drop beyond some distance...
But we can't see from a large scale perspective, we can only see from a "in the middle" perspective.  If we could, I'm sure we'd see a lot of white.

Quote
Quote from: Lorddave on August 18, 2010, 01:41:02 PM
Add to that the rate of universal expansion that is faster than the speed of light, diminished light from the inverse square law, and you get a good explanation.

Universal expansion, although not faster than the speed of light, might be a good hint.
I had thought it was faster than the speed of light. 

-Yep it is. 
The metric expansion of the universe allows for two objects to move away from each other faster than the speed of light because the objects aren't moving, space is expanding.  This is how we can see microwaves that are 13 billion years old, which is the current estimated age of the universe.

http://www.astro.ucla.edu/~wright/cosmology_faq.html#ct2

Some good info.


And, of course, the redshift as mentioned earlier.
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Crustinator

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Re: Olbers' paradox
« Reply #14 on: August 19, 2010, 03:47:09 AM »
Quote from: Hortensius on August 18, 2010, 03:36:03 PM
If the density of stars is constant (and observations show it roughly is on large scales), the number of stars is proportional to the volume. The volume of space within a distance r is proportional to r3 (4/3 pi r3).

But you're not concerned about volume, you're concerned about distance. This would equate to the surface area of the sphere, with r measured from the centre of the shell.

This shell area is proportional to r2. (This should make sense, since the inverse square propagation of light is just the inverse of the area the light has to move through)

It still leaves us with a constant though.

But, as Parsifal pointed out, stars can't multiply up their power, which seems to be an underlying assumption.
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bowler

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Re: Olbers' paradox
« Reply #15 on: August 19, 2010, 02:25:51 PM »
Why do I state facts as questions? All it really means is that there are not a infinite number of stars in the universe, or rather it proves there are not an infinite number of luminous stars. Its not really a paradox, or a particularly powerful statement.
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Hortensius

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Re: Olbers' paradox
« Reply #16 on: August 19, 2010, 03:05:50 PM »
Quote from: bowler on August 19, 2010, 02:25:51 PM
Why do I state facts as questions? All it really means is that there are not a infinite number of stars in the universe, or rather it proves there are not an infinite number of luminous stars. Its not really a paradox, or a particularly powerful statement.

It could be that there's not an infinite stars on the heavens, but that's not the explanation for the paradox. The expanding universe causing starlight to redden by the Doppler effect is the true reason. It is observed that at very large distances the number of stars doesn't become less, but in fact their light becomes redder and thereby less luminous.
« Last Edit: August 19, 2010, 03:07:40 PM by Hortensius »
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Crustinator

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Re: Olbers' paradox
« Reply #17 on: August 19, 2010, 04:13:23 PM »
I'd suggest that stars occupy a finite portion of space and the light from that portion will be proportional to the inverse square distance. Light from stars cannot be stacked cumulatively behind one another, so one star at 10 ly isn't the same as 4 stars at 20 ly stacked behind one another.

The depth would be perceptible.

Add in a few million ly3 gas clouds and you've got starlight that in undetectable to the naked eye.

And starlight will also be scattered by gravity...
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SupahLovah

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Re: Olbers' paradox
« Reply #18 on: August 19, 2010, 08:50:53 PM »
Quote from: Parsifal on August 18, 2010, 06:05:35 PM
Quote from: Hortensius on August 18, 2010, 04:23:40 PM
Quote from: Parsifal on August 18, 2010, 11:08:56 AM
Quote from: Hortensius on August 18, 2010, 04:54:28 AM
Can't be an explanation since the number of stars grows according to r3. So we still have a net increase of brightness as a function of r.

So we can see through stars to other stars behind them?

No we can't

Then the number of visible stars doesn't grow according to r3.
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Hortensius

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Re: Olbers' paradox
« Reply #19 on: August 20, 2010, 12:37:30 AM »
Quote from: Parsifal on August 18, 2010, 06:05:35 PM
Quote from: Hortensius on August 18, 2010, 04:23:40 PM
Quote from: Parsifal on August 18, 2010, 11:08:56 AM
Quote from: Hortensius on August 18, 2010, 04:54:28 AM
Can't be an explanation since the number of stars grows according to r3. So we still have a net increase of brightness as a function of r.

So we can see through stars to other stars behind them?

No we can't

Then the number of visible stars doesn't grow according to r3.

At the point that stars start blocking light of stars behind them, there are already so many stars on the sky that the sky will be extremely bright. Before this happens, the number of visible stars grows according to r3 roughly.
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Hortensius

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Re: Olbers' paradox
« Reply #20 on: August 20, 2010, 12:44:18 AM »
Quote from: Crustinator on August 19, 2010, 04:13:23 PM
I'd suggest that stars occupy a finite portion of space and the light from that portion will be proportional to the inverse square distance. Light from stars cannot be stacked cumulatively behind one another, so one star at 10 ly isn't the same as 4 stars at 20 ly stacked behind one another.

The depth would be perceptible.

Add in a few million ly3 gas clouds and you've got starlight that in undetectable to the naked eye.

And starlight will also be scattered by gravity...


You mean the light is absorbed somehow? This can't explain the paradox either. If you absorb the light of so many stars, the absorbing medium must heat up until it radiates like stars. This follows from energy conservation.
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Hortensius

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Re: Olbers' paradox
« Reply #21 on: August 20, 2010, 12:49:51 AM »
Quote from: Lorddave on August 19, 2010, 01:56:11 AM
Quote from: Hortensius on August 18, 2010, 03:42:34 PM
Quote from: Lorddave on August 18, 2010, 01:41:02 PM
Why is this a paradox?

First of all, the Universe can be infinite but that doesn't mean the matter in it is.  You can have an infinite amount of space with a finite amount of matter.

Observations show that on large scales matter in the Universe is distributed homogeneously and isotropically, which means that the matter density doesn't just drop beyond some distance...
But we can't see from a large scale perspective, we can only see from a "in the middle" perspective.  If we could, I'm sure we'd see a lot of white.

Quote
Quote from: Lorddave on August 18, 2010, 01:41:02 PM
Add to that the rate of universal expansion that is faster than the speed of light, diminished light from the inverse square law, and you get a good explanation.

Universal expansion, although not faster than the speed of light, might be a good hint.
I had thought it was faster than the speed of light. 

-Yep it is. 
The metric expansion of the universe allows for two objects to move away from each other faster than the speed of light because the objects aren't moving, space is expanding.  This is how we can see microwaves that are 13 billion years old, which is the current estimated age of the universe.

http://www.astro.ucla.edu/~wright/cosmology_faq.html#ct2

Some good info.


And, of course, the redshift as mentioned earlier.

Nothing in our causally connected Universe moves faster than the speed of light. Beyond that, ok. But your expansion explanation (+ redshift) is the right one I think...
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Crustinator

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Re: Olbers' paradox
« Reply #22 on: August 20, 2010, 06:01:17 AM »
Quote from: Hortensius on August 20, 2010, 12:44:18 AM
You mean the light is absorbed somehow?

Yes, either absorbed or diffused. Just as our planet is absorbing and diffusing starlight.

The point being that there would still be variation in the night sky, as observed.
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Hortensius

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Re: Olbers' paradox
« Reply #23 on: August 20, 2010, 07:40:55 AM »
Quote from: Crustinator on August 20, 2010, 06:01:17 AM
Quote from: Hortensius on August 20, 2010, 12:44:18 AM
You mean the light is absorbed somehow?

Yes, either absorbed or diffused. Just as our planet is absorbing and diffusing starlight.

The point being that there would still be variation in the night sky, as observed.

Clearly some light in the Universe is absorbed, buth this can't explain the paradox for the reason that if so much light was actually absorbed, the absorbing medium would heat up until it would start radiating optical light by itself...
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Crustinator

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Re: Olbers' paradox
« Reply #24 on: August 20, 2010, 08:22:24 AM »
Quote from: Hortensius on August 20, 2010, 07:40:55 AM
Clearly some light in the Universe is absorbed, buth this can't explain the paradox for the reason that if so much light was actually absorbed, the absorbing medium would heat up until it would start radiating optical light by itself...

Yes. Maybe eventually. If it wasn't already doing so. Although I suspect that stars radiate optical light due to some nuclear process and not due to the fact that some stars thousands of light years away are beaming at them. I also suspect that any other matter that may have absorbed light is never given the chance to "heat up" to an extent that it would radiate light. Greater, more immediate forces are probably at work.

This does not remove the fact that such matter has absorbed the light.

So another assumption in this "paradox" seems to be that all things that can happen, do happen instantaneously.
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sokarul

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Re: Olbers' paradox
« Reply #25 on: August 20, 2010, 03:17:14 PM »
Olbers' paradox would require the universe to be infinite in time.  This would probably go hand in hand with an infinite universe. 
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Ocius

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Re: Olbers' paradox
« Reply #26 on: August 21, 2010, 01:55:59 AM »
I'm no astrophysicist, but I was under the impression that there are stars outside of the observable universe.
« Last Edit: August 21, 2010, 01:57:36 AM by Fortuna »
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scientistT

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Re: Olbers' paradox
« Reply #27 on: August 21, 2010, 02:35:38 AM »
actually the universe does expand and at an increasing rate and yes to my knowledge it is quite possible that we cant even see the whole universe because light does fade eventually into nothingness and time is extremely complicated and not nearly understood

ps the universe is not infinite technically but infinitely expanding
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Parsifal

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Re: Olbers' paradox
« Reply #28 on: August 21, 2010, 02:46:51 AM »
Quote from: Fortuna on August 21, 2010, 01:55:59 AM
I'm no astrophysicist, but I was under the impression that there are stars outside of the observable universe.

We can't know if there are. Things outside the observable universe are, interestingly enough, unobservable.
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Ocius

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Re: Olbers' paradox
« Reply #29 on: August 21, 2010, 02:56:17 AM »
Well, not directly observable. But there isn't really any reason why there wouldn't be stars beyond the 13.5 billion light year mark. If I'm not mistaken, the universe is actually much larger than what we can see. Also, I found this article on "dark flow". I first heard about it a few months ago but it doesn't look like there are any further developments on it yet.

http://www.space.com/scienceastronomy/distant-dark-flow-100317.html
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