PDA

View Full Version : Olbers' Paradox

EckJerome
2002-Jan-18, 06:03 PM
For reference:

It seems to me that Olbers' paradox ignores the possibility of obscuring dust and stuff that would block and/or diminish the light from distant objects. The way it is stated, it appears to make an assumtion that the universe is perfectly clear of obscuring matter.

We can't even see stars behind the Coal Sack, why should we expect to see every bit of light eminating from a possibly infinite universe?

Eric

ToSeek
2002-Jan-18, 06:14 PM
If the universe is old enough, then the light would have heated up the dust until it glowed. So obscuring dust is at best only a temporary solution to the issue.

Marco
2002-Jan-18, 06:15 PM
With an infinite number of stars shining on it, the obscuring dust would heat up until it is just as bright as the stars.

John Kierein
2002-Jan-18, 06:16 PM
Obscuring dust doesn't solve Olbers paradox, because the dust should soon be heated white hot and glow itself. (I have a different solution for Olbers' paradox, but you'll have to wait for the book.)

John Kierein
2002-Jan-18, 06:29 PM
Another way to state Olbers' paradox is to consider an infinite universe with a constant density of light sources, such as galaxies. Note that the number of sources increases as the cube of the distance (the volume is (4/3) (pi)r^3, so the volume increases as the cube of r). But the energy received from these sources only falls off as the inverse square of the distance. So if one integrates this over the infinite distance one sees that the energy received should increase directly with r and we should have an infinite amount of energy being received! Some people like to throw time into the equation (to help sove Olbers' paradox somehow)and assume that galaxies have a limited lifetime; but that is specious if there are as many galaxies being created as destroyed - i.e, mass/energy is conserved. In that case there is an equilibrium constant density of galaxies. The big bang has a bigger problem (in a sense) with Olbers paradox, because they say the density of galaxies increases(!) with distance since they supposedly were all closer together the farther away they are. They solve this, however, by a combination of energy loss from red shift and much more importantly from a loss of flux due to an expansion. Taken to the extreme, objects moving away at the speed of light cannot be seen because the distance between photons has become infinite.
There are other solutions to Olbers paradox for a static universe that has a red shift.

<font size=-1>[ This Message was edited by: John Kierein on 2002-01-18 13:33 ]</font>

MongotheGreat
2002-Jan-18, 08:31 PM
On 2002-01-18 13:15, Marco wrote:
With an infinite number of stars shining on it, the obscuring dust would heat up until it is just as bright as the stars.

In defense of EckJerome, the gas could never be as bright as a star. The gas would radiate the energy received from stars in all directions.
In order for the gas to be as hot and therefore as bright as a star, it would have to undergo fusion to produce energy on it's own which a distended cloud of gas like the coal sack can't do, unless it condenses into a star itself, which has nothing or little to do with light received from other stars.

Mongo

2002-Jan-18, 09:03 PM
On 2002-01-18 15:31, MongotheGreat wrote:
In order for the gas to be as hot and therefore as bright as a star, it would have to undergo fusion to produce energy on it's own which a distended cloud of gas like the coal sack can't do, unless it condenses into a star itself

sure it can, fusion can start once the gas/dust reaches a certain temperature. The dust doesn't need to be conpressed into a star (of course, that helps). Once fusion starts, photons are emitted and you get a bright cloud...

MongotheGreat
2002-Jan-18, 09:14 PM
Temperature required for hydrogen fusion is what, 1 million kelvin? A gas can't get that hot unless it is under emormous pressure, at the center of a star. Not to mention that the energy received is mostly radiated away.
Mongo

DStahl
2002-Jan-19, 05:17 AM
Well and good, but the underlying principle is that a universe of infinite age would come to thermal equilibrium, right?

Don Stahl

EckJerome
2002-Jan-22, 04:02 PM
Thanks for trying Mongo...but I think I was out of my league before I'd even finished typing. I knew that obscuring dust had to be too simple a thing for others to have ignored it. That doesn't mean I buy into modern cosmology, but at least I'm learning where my limits are in refuting the theories. /phpBB/images/smiles/icon_wink.gif

Eric

ASEI
2006-Jan-15, 09:59 PM
Couldn't Olber's paradox also be solved by an infinite, but self similar arrangement of energy sources. A cluster of cluster of clusters...? Then the amount of matter could vary with less than the cube of the radius looked at. If the clustering arrangement is such that the number of stars only varies with the distance squared, then you could have a universe of a constant temperature.

And how about the opaqueness of the stars? Each star must block out all the stars directly behind it, and absorb the energy from them, so, for each particular direction in the sky, only one star at any arbitrary distance can be swept. (assuming no lensing events). If on average, the distance is great enough, then you would get a cooler universe, wouldn't you?

Of course, redshift and universal expansion has to be taken into account for intergalactic distances for a realistic model.

Ilya
2006-Jan-15, 11:44 PM
Couldn't Olber's paradox also be solved by an infinite, but self similar arrangement of energy sources. A cluster of cluster of clusters...? Then the amount of matter could vary with less than the cube of the radius looked at. If the clustering arrangement is such that the number of stars only varies with the distance squared, then you could have a universe of a constant temperature.
Only if clustering is infinite -- there is always a larger structure.

And how about the opaqueness of the stars? Each star must block out all the stars directly behind it, and absorb the energy from them, so, for each particular direction in the sky, only one star at any arbitrary distance can be swept. (assuming no lensing events). If on average, the distance is great enough, then you would get a cooler universe, wouldn't you?

No, you would not. All energy a star absorbed would simply heat it up more and would end up re-radiated. In that sense an obscuring star is no different from obscuring dust.

Ken G
2006-Jan-16, 12:36 AM
The real problem behind Olbers paradox is so much more fundamental, I'm surprised it is not the real paradox that is discussed. Stars convert mass into starlight. End of story, it never goes the other way in a star. So if stars existed forever in every region of space, there could be nothing more to convert into starlight. It's a problem in mass/energy conservation, and now that we know about this, you can stop worrying about Olbers, we don't need 'im anymore.

ASEI
2006-Jan-16, 02:21 AM
So, if the big bang had infinite mass at infinite temperature, but also has infinite redshift because of speed of light recession velocity (or some gravitational GR thing), then would that work out to a finite observed luminosity? Or zero?

Ken G
2006-Jan-18, 07:03 PM
Infinite mass over what scale? Of course if the universe is infinite and homogeneous, then the Big Bang did have infinite mass. The luminosity you refer to would have to work out to be the CMB in any event, but there's no need or ability to extrapolate all the way back to a singularity. More relevant is the energy density at any given epoch.

rnt20
2006-Jan-19, 12:57 PM
For reference:

It seems to me that Olbers' paradox ignores the possibility of obscuring dust and stuff that would block and/or diminish the light from distant objects. The way it is stated, it appears to make an assumtion that the universe is perfectly clear of obscuring matter.

We can't even see stars behind the Coal Sack, why should we expect to see every bit of light eminating from a possibly infinite universe?

Eric

Perhaps it's worth pointing out that "Olbers' paradox" is only a paradox in a hypothetical "Steady State" universe, and is not relevant to the Universe we are in (it assumes that the Universe is infinitely old, with not redshifting of distant objects). Of course we know that our Universe has a finite age, and that the increasing redshift with distance means that the observable Universe ( http://en.wikipedia.org/wiki/Observable_universe ) has a finite size (the observable universe is a sphere a few kiloparsecs larger than the surface emitting the cosmic microwave background -- see e.g. http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation -- no light from outside the observable Universe can ever reach Earth).

Ken G
2006-Jan-19, 06:45 PM
And as I mentioned on another thread, to get Olbers paradox you not only need a universe that has been nearly the same forever, but also it must also continue for effectively an infinite distance. If you simply limit the stars to what we have so far been able to observe, then the night sky would still not be bright, even if the universe were infinitely old. People forget the size issue, which is important because one can only say that Olbers paradox is evidence that the universe is not both infinite in size and infinitely old. You can't just pull out the age issue. Of course, as said above, we have much better reasons now (and in fact we have had since the inception of thermodynamics) to assert that the universe is not infinitely old, and thus there is no way to set a size limit. Bottom line: Olbers paradox is not important at all, and we only create confusion by dragging it along as an explanation for why the universe must have a finite age.

chriscurtis
2006-Nov-03, 12:03 AM
So, if almost all the stars in the universe are currently black holes, the paradox goes away and the universe can be infinite.

Can those blackholes supply the CMB?

Eckelston
2006-Nov-03, 01:25 AM
So, if almost all the stars in the universe are currently black holes, the paradox goes away and the universe can be infinite.

Can those blackholes supply the CMB?

This is probably ruled out by observation. Think of it this way: if almost all of the stars would be black holes there would be a few of them around. They would show up bright points on the CMB map. Also further away they would tend to cluster together like galaxies (or more likely on top of actual galaxies). The result would be a CMB map which is quite unenven, which is not what we see.

Ken G
2006-Nov-03, 01:57 AM
Furthermore, I suspect that if you ever had enough black holes to "eat" away the light that would otherwise lead you to a contradiction with observation, then you'd have enough gravity to close the universe, so it wouldn't be infinite anyway. Remember, a black hole is very small (the size of a city), so if the vast majority of the rays you are looking along find a black hole before they find a star (which is what you'd need to avoid a very bright background), then you'd need a heck of a lot more black holes than stars out there. It's true that the black holes would tend to bend the light rays into themselves, so their effective cross section would be much larger than a city, but I'll wager it would still be a tiny fraction of a star, so you'd still need an awful high percentage of black holes compared to stars. That would be a lot of gravity, though I can't prove it would close the universe, I just suspect geometrically that if most rays find a black hole, that's a closed universe. Nevertheless, you might be able to make a closed universe that is time steady and has been here forever, if you also have a mechanism for generating fresh hydrogen for stars to use, you have a sink for the light enriched matter that stars make (say, those black holes), you have a way to get redshifts, and you have a way to keep the black holes from gaining mass forever. Tall order!

Nereid
2006-Nov-03, 03:49 AM
So, if almost all the stars in the universe are currently black holes, the paradox goes away and the universe can be infinite.

Can those blackholes supply the CMB?No. So many (stellar mass) black holes would leave a very obvious signature - for every line of sight that ends on a BH, how many merely 'pass close to' such BHs? What would these 'close encounter' lines of sight look like, to us, here on Earth?

Aside from the CMB, an infinite universe full of stellar-mass BHs should not produce a complete lack of objects with ages of >15 billion years (say), nor (as KenG has already pointed out) lots and lots of H (and He), and very little else ... unless, of course, some completely new physics rules the universe .... (in which case all bets are off, wrt Olbers)

harlequin
2006-Nov-05, 04:38 AM
The universe has a finite age and is expanding is the solution.

dhd40
2006-Nov-19, 09:28 AM
I donīt understand the paradox at all: Letīs say, in our Milky Way galaxy there are approximately 20 Billion stars. Yet, we can only see some 2000 to 3000 stars with our unaided eyes. Why donīt we see the other 99.99999 %? Forget about redshift, this is negligible in our 30000 to 70000 light years vicinity. Absorption by interstellar gas and/or dust? No, not at all. I know that the photons from these invisible stars are here, right where Iīm standing. I can easily prove this by putting binoculars in front of my eyes.
So, why should the skys be bright at night? Why should we be able to see stars as far as 13 Billion light years away from us if we canīt even see 99.99999% of our own galaxyīs stars? The reason canīt be redshift, or finite size of the universe, or, or The reason must lie in the construction of our viewing system (eyes, brain, etc).
Therefore, I canīt see a paradox, and I canīt take it as a proof for a finite universe (although, it isnīt a proof for an infinite universe, either).
So, are these thoughts just nonsense? If so, where lies my fallacy?

ArgoNavis
2006-Nov-19, 10:45 AM
So, why should the skys be bright at night? Why should we be able to see stars as far as 13 Billion light years away from us if we canīt even see 99.99999% of our own galaxyīs stars? The reason canīt be redshift, or finite size of the universe, or, or The reason must lie in the construction of our viewing system (eyes, brain, etc).
Therefore, I canīt see a paradox, and I canīt take it as a proof for a finite universe (although, it isnīt a proof for an infinite universe, either).
So, are these thoughts just nonsense? If so, where lies my fallacy?

The sky should be bright for the same reason that the milky way is one of the brightest objects in the heavens - millions of stars individually too faint to see but collectively summed to constitute a river of light.

If the Universe was as full of stars and galaxies as the direction of the plane of our galaxy then it should be ablase with light.

dhd40
2006-Nov-19, 03:51 PM
The sky should be bright for the same reason that the milky way is one of the brightest objects in the heavens - millions of stars individually too faint to see but collectively summed to constitute a river of light.

If the Universe was as full of stars and galaxies as the direction of the plane of our galaxy then it should be ablase with light.

Does this mean that, looking in the direction of our galaxyīs plane, I donīt see individual stars but only a "collectively summed" starlight? If so, why donīt I see this when looking through a telescope? There is darkness again between individual stars, the more, the higher the magnification. Or is this a question of exposure time?

antoniseb
2006-Nov-19, 04:09 PM
I don&#180;t understand the paradox at all
Olber's Paradox keeps coming up in this forum. Basically, understanding it is fairly straight-forward. The idea is that IF the universe is infinite in all directions, and has existed in more or less this same state for ever, and photons can travel forever without losing energy in a way that leaves the universe, then the sum of the light coming from all spherical shells around us should be the same as if the entire sky were the surface of an average star.

The trick is that no matter how clumpy luminous matter is locally, eventually you get to a large enough scale that all part of the universe have about the same density of bright things. If the universe is *infinite* and has existed in this form *forever*, and is not expanding (or using some other way to apparently take energy out of photons), then even if only one part in 1080 of the sky in the closest shell is made of of stellar surfaces, the integral of all the shells covers 100% of the sky.

As you probably know Olber's Paradox is not an issue now because:
- we believe that the universe is not infinitely old
- only a few hundred of the uniform density shells have had time to get light to us
- the universe IS expanding, and light from the distant past is redshifted
- the universe has not always been as we see it now.

Nereid
2006-Nov-19, 04:15 PM
Does this mean that, looking in the direction of our galaxyīs plane, I donīt see individual stars but only a "collectively summed" starlight?Well, you certainly see some individual stars!

However, the 'milky' part is summed stars.

The same is true for the LMC and SMC, M31, Omega Cen, 47 Tuc (and whatever globular clusters are visible in the northern hemisphere), ...
If so, why donīt I see this when looking through a telescope?But you do ... well, I do (and, objectively, so do other telescopes - here's M31 (http://antwrp.gsfc.nasa.gov/apod/ap051222.html), for example). Of course, if you look closely enough at a globular cluster, you can resolve (nearly all) the individual stars - example (http://hubblesite.org/newscenter/archive/releases/2006/37/).
There is darkness again between individual stars, the more, the higher the magnification. Or is this a question of exposure time?Yes, and other things as well ....

Spaceman Spiff
2006-Nov-19, 07:07 PM
Here (http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1991ApJ...367..399W&amp;data_type=PDF_H IGH&amp;type=PRINTER&amp;filetype=.pdf)is a technical description of the problem of Olbers' paradox. A less technical article by the same author can be found here (http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1989JBAA...99...10W&amp;data_type=PDF_H IGH&amp;type=PRINTER&amp;filetype=.pdf). This one (http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1990IAUS..139....3H&amp;data_type=PDF_H IGH&amp;type=PRINTER&amp;filetype=.pdf) is both descriptive and technical.

dhd40 finds that the sky is dark and so wonders what's all the hubbub. Paradoxes are such usually because of one or more incorrect assumptions made by those who considered it a paradox. It's no longer considered as such. In fact as mentioned above, the sky is indeed filled with light - the light of the echo of the big bang: the cosmic microwave background. It's just that this light is way out at mm wavelengths.

dhd40
2006-Nov-19, 09:20 PM
Well, you certainly see some individual stars!

Well, yes, of course. My wording wasnīt very precise. What I meant was: Do I see light (photons) in-between individual stars.
And thanks for the links. The M31-photo is simply overwhelming.

dhd40
2006-Nov-19, 09:24 PM
However, the 'milky' part is summed stars.

I didnīt know there was a īmilkyī part. But, most probably, Iīm not aware of this?

dhd40
2006-Nov-19, 09:44 PM
dhd40 finds that the sky is dark and so wonders what's all the hubbub.

Thanks for the links. I will need some time to read all of them. But, so far, I understand, that the finite age of the universe is one important parameter (which has been said before in several posts, and I agree).
Still, I wonder why all the stars of our own milky way galaxy arenīt good enough to make the sky brilliant bright.

Nereid
2006-Nov-19, 10:12 PM
However, the 'milky' part is summed stars.I didn&#180;t know there was a &#180;milky&#180; part. But, most probably, I&#180;m not aware of this?I was a little too terse - the 'milky' part is both 'summed stars' and diffuse nebulae (reflection nebulae (http://antwrp.gsfc.nasa.gov/apod/ap990301.html), planetary nebulae (http://antwrp.gsfc.nasa.gov/apod/ap061112.html), other emission nebulae (http://antwrp.gsfc.nasa.gov/apod/ap050930.html)).

If you've see the Milky Way from a dark site, on a dark moonless night, you'll recognise immediately why it's called that (especially if it stretches up over your head (http://antwrp.gsfc.nasa.gov/apod/ap060801.html) - though this (http://antwrp.gsfc.nasa.gov/apod/ap051004.html) is rather more than you could ever see.). This B&W APOD (http://antwrp.gsfc.nasa.gov/apod/ap060806.html) nicely captures both the Milky Way and both Magellanic Clouds - oh those lucky Chileans! This ING/WHT "photo composition" (http://www.ing.iac.es/PR/archive/wht/whtmw2.gif)also gives a good impression of the overhead MW (don't be fooled by how bright the telescope dome is).

Nereid
2006-Nov-19, 10:59 PM
Thanks for the links. I will need some time to read all of them. But, so far, I understand, that the finite age of the universe is one important parameter (which has been said before in several posts, and I agree).
Still, I wonder why all the stars of our own milky way galaxy arenīt good enough to make the sky brilliant bright.OK, let's do some OOM (order of magnitude; aka back of the envelope) calculations ...

Let's say the MW covers 1,000 square degrees of the sky.

How many square arcseconds is that? Hmm, 3600 seconds to a degree, so 3600 x 3600 square arcsecs/sq degree = 13 million (OOM, remember), and 1,000 square degrees -> 13 billion.

Let's say the MW stars are distributed evenly over these ~13 bn deg^2, and that there are 130 bn such stars. That means there would be ~10 per arcsec^2.

Now how much of the sky does a star subtend? Well, Mira is about 60 milliarcseconds in diameter (http://hubblesite.org/newscenter/archive/releases/1997/26/text/); that's 0.06", and so covers an area of ~0.003 arcsec^2. So ~300 are needed to cover a square arcsec.

But there are only ~10 available! So the "Milky Way sky" is mostly black space. Or, if you prefer, only ~1 in every 30 sightlines towards the MW would end on the surface of a MW star.

Of course, the "MW sky" is much 'blacker' than that ... Mira is one of the biggest stars (in terms of its apparent diameter); the 'average' MW star is much, much smaller.

As this is only an OOM calculation, the answers are only (very) approximate. However, sharpening up the numbers, to the next level of accuracy say, won't change the conclusion in any appreciable way .... the Milky Way stars 'block' very little of sky.

Spaceman Spiff
2006-Nov-20, 12:29 AM
I put this (http://homepages.wmich.edu/%7Ekorista/bigbang-darksky.html) together for a local astronomy club newsletter.

dhd40
2006-Nov-20, 09:48 AM
hello Nereid and Spaceman Spiff, thank you both for excellent contributions. I feel much better now with Olbersī paradox.

Spaceman Spiff
2006-Nov-20, 10:37 PM
hello Nereid and Spaceman Spiff, thank you both for excellent contributions. I feel much better now with Olbersī paradox.

You are welcome. Glad to have been of some help.

Peter Wilson
2006-Nov-21, 10:30 PM
I didnīt know there was a īmilkyī part. But, most probably, Iīm not aware of this?
Most certainly. That's why they call it the Milky Way...