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doc33
2008-Nov-05, 02:47 AM
Can anyone explain to me how the answer to Olbers' Paradox is ''the light from distant sources has not yet arrived here.'' It seems to me a more practicle explanation would be due to the inverse square law: i.e. the light from all of those shinning objects is just too dim to light up the night sky. I think the paradox is created from a defective assumption that the visible light from all shinning objects should reach Earth.

George
2008-Nov-05, 02:57 AM
Where would reduced light be coming from, then? Every spot in the sky would be filled with a star's disk. The inverse square law works proportionately with the size of the disk, too; doubling a star's distance will not only reduce the total amount of light by 25% entering the eye but also reduce the apparent size of the disk by 25%, thus the surface brightness remains the same. But, there are more stars that would fill in any gaps.

Also, any nebulae would "see" all this ubiquitus energy and also glow at the same temperature, so even clouds would not help.

timb
2008-Nov-05, 03:05 AM
Can anyone explain to me how the answer to Olbers' Paradox is ''the light from distant sources has not yet arrived here.''

I thought the explanation was that the universe does not in fact contain an infinite number of stars.

Jerry
2008-Nov-05, 05:57 AM
Simply stated, Obler's paradox is that if the universe is infinite, there should be an infinite stream of photons towards us: The sky should be light; but it is not. Ergo the universe must be limited in size. Notice that dust does not solve the problem; as the dust would be heated by infinite sources of light, too. (you can get around this a bit, since there is an infrared background, and also an xray background, but an infinite universe also require as-yet to be identified energy sinks.)

timb
2008-Nov-05, 07:35 AM
Maybe it's the rivers of light headed for Northian black hole (http://www.bautforum.com/against-mainstream/80287-black-holes-do-they-have-two-event-horizions.html)s.

George
2008-Nov-05, 06:21 PM
Simply stated, Obler's paradox is that if the universe is infinite, there should be an infinite stream of photons towards us: ...Would it have to be an infinite amount? If every star were the same as the Sun, then the spherical shell seen would have an effective surface temperature of about 6000K, which is not infinite.

AndreasJ
2008-Nov-05, 06:50 PM
Would it have to be an infinite amount? If every star were the same as the Sun, then the spherical shell seen would have an effective surface temperature of about 6000K, which is not infinite.

The Sun's atmosphere is kept at that temperature because of an equilibrium between energy radiated away and new energy input from deeper layers. If the whole sky was radiating at the same temperature, the energy radiated away by the solar atmosphere would be balanced by radiation absorbed from outside, and the energy from below would go to heating up the atmosphere. Now the same applies to every star, so they heat up too, meaning the Sun's new surface temperature is matched by the new effective temperature of the sky, meaning the input from below again goes to heat up the solar atmosphere. Repeat.

The cycle will only stop when stellar fusion runs out of fuel, by which time the sky won't be at infinite temperature, but way way way above 6000 K.

William
2008-Nov-05, 07:14 PM
An expanding universe, seems to solve Obler's paradox from the standpoint of an infinite universe vs a finite universe.

With an expanding universe of finite age but infinite size, there is a maximum sphere about each location in the universe which is the limit that light can travel. Also the light is redshifted to infinite redshift.

I would think an expanding universe could also be infinitely old.

George
2008-Nov-05, 09:08 PM
The Sun's atmosphere is kept at that temperature because of an equilibrium between energy radiated away and new energy input from deeper layers. If the whole sky was radiating at the same temperature, the energy radiated away by the solar atmosphere would be balanced by radiation absorbed from outside, and the energy from below would go to heating up the atmosphere. Now the same applies to every star, so they heat up too, meaning the Sun's new surface temperature is matched by the new effective temperature of the sky, meaning the input from below again goes to heat up the solar atmosphere. Repeat. Thanks, I wondered if that was the take on it.


The cycle will only stop when stellar fusion runs out of fuel, by which time the sky won't be at infinite temperature, but way way way above 6000 K. This is a quirky puzzle in itself as how does one determine the energy density of the universe given a fixed number of fixed output energy sources (somehow renewable) yet over an infinite amount of time? Fortunately, the sky is dark. :)

Jens
2008-Nov-06, 03:42 AM
Simply stated, Obler's paradox is that if the universe is infinite, there should be an infinite stream of photons towards us: The sky should be light; but it is not. Ergo the universe must be limited in size.

This is sort of a stock response of mine to these threads, but that is not necessarily true. There is a way to resolve Olber's paradox in an infinitely large universe with infinite stars. Namely, if the universe is fractal. In that case, the density tends toward zero as the scale increases. And AFAIK the question of whether the universe is fractal or not is not yet fully resolved.

StupendousMan
2008-Nov-06, 01:53 PM
This is sort of a stock response of mine to these threads, but that is not necessarily true. There is a way to resolve Olber's paradox in an infinitely large universe with infinite stars. Namely, if the universe is fractal. In that case, the density tends toward zero as the scale increases. And AFAIK the question of whether the universe is fractal or not is not yet fully resolved.

The other "stock response", and in fact the one which is most relevant according to mainstream astronomers, is that the universe has a finite age. It may be unlimited in extent, but the light from all those distant places hasn't had a chance to reach us.

timb
2008-Nov-06, 08:58 PM
The other "stock response", and in fact the one which is most relevant according to mainstream astronomers, is that the universe has a finite age. It may be unlimited in extent, but the light from all those distant places hasn't had a chance to reach us.

I've never (lately) heard mainstream astronomers say that it has infinite mass or infinite observable extent.

StupendousMan
2008-Nov-06, 09:48 PM
I've never (lately) heard mainstream astronomers say that it has infinite mass or infinite observable extent.

Neither have I.

Is there a point to your statement?

timb
2008-Nov-07, 03:36 AM
Neither have I.

Is there a point to your statement?

Yes, to draw attention to the foolishness of yours. If the universe doesn't have infinite mass than the number of stars is finite and the premises of Olber's paradox fail. The age of the universe is irrelevant in that case.

Jens
2008-Nov-07, 03:51 AM
Yes, to draw attention to the foolishness of yours. If the universe doesn't have infinite mass than the number of stars is finite and the premises of Olber's paradox fail. The age of the universe is irrelevant in that case.

But I don't think he was saying anything beyond "whether it is unlimited in extent or not doesn't matter, because the it hasn't existed forever." I don't see any "foolishness" in that.

In any case, though, I think we have put out what I think are the two reasonable explanations for why Olber's paradox exists. Namely (1) the universe has not existed forever, which is the mainstream explanation, or (2) the universe has existed forever, but is fractal. I can't really think of any other way to explain it other than positing a leakage into other dimensions or something like that. But that just gets you back to the beginning, because you'd have to ask why the other dimensions haven't heated up.

Ari Jokimaki
2008-Nov-07, 06:01 AM
This is a quirky puzzle in itself as how does one determine the energy density of the universe given a fixed number of fixed output energy sources (somehow renewable) yet over an infinite amount of time?
I think the energy density is the key issue when considering Olbers' paradox. To me it feels that whatever is the average energy density, we shouldn't expect the night sky to "shine any brighter" than that (even in the case of infinitely large and old static universe).

timb
2008-Nov-07, 08:27 AM
But I don't think he was saying anything beyond "whether it is unlimited in extent or not doesn't matter, because the it hasn't existed forever." I don't see any "foolishness" in that.

In any case, though, I think we have put out what I think are the two reasonable explanations for why Olber's paradox exists. Namely (1) the universe has not existed forever, which is the mainstream explanation, or (2) the universe has existed forever, but is fractal. I can't really think of any other way to explain it other than positing a leakage into other dimensions or something like that. But that just gets you back to the beginning, because you'd have to ask why the other dimensions haven't heated up.

How would it get to be infinitely large if it was finitely old? infinitely fast expansion?

Fractals are another complete red herring.

matt.o
2008-Nov-07, 09:06 AM
How would it get to be infinitely large if it was finitely old? infinitely fast expansion?


Or it was infinite to begin with. Check Ned Wright's FAQ section here (http://www.astro.ucla.edu/~wright/cosmology_faq.html#RB) and have a read through of his tutorial pages while you're there.

Kebsis
2008-Nov-07, 09:29 PM
Wouldn't an infinite universe with infinite stars, also have infinite black holes to absorb the stars' light?

timb
2008-Nov-07, 11:36 PM
Or it was infinite to begin with. Check Ned Wright's FAQ section here (http://www.astro.ucla.edu/~wright/cosmology_faq.html#RB) and have a read through of his tutorial pages while you're there.

Whether there is an infinite amount of empty space is irrelevant to Olber's paradox.

matt.o
2008-Nov-08, 06:14 AM
Whether there is an infinite amount of empty space is irrelevant to Olber's paradox.

It is pertinent to your question:


How would it get to be infinitely large if it was finitely old? infinitely fast expansion?

which is why I wrote it!

eburacum45
2008-Nov-08, 09:58 AM
Up till now I've never understood the 'fractal solution' to Olber's Paradox; but looking at some of the on-line resources
(like this one)
http://www.m-hikari.com/ijcms-password2007/9-12-2007/stasiakIJCMS9-12-2007.pdf
it seems that in a fractal universe an arbritary amount of the sky can be dark. If the places where stars appear is limited to places where other stars appear, that means that there need not be any stars in some, or many, or most parts of the sky.

The fractal solution is amost certainly wrong,, but it can't be ruled out just by considering Olber's conundrum.

timb
2008-Nov-08, 10:46 AM
I think people are making too much of this. The premise of Olber's paradox is that the universe is assumed to contain an infinite number of uniformly distributed luminous stars. There's also an implicit assumption that the universe1 is infinitely old so that the light from very distant stars has had enough time to reach us. Modern cosmology tells us that

(a) the number of stars isn't infinite
(b) the universe is of finite age

RIP Olber's paradox.

Alternatively, you can dream up all sorts of fanciful non-uniform distributions of an infinite number of stars that leave the sky mostly dark. They could all lie in a plane: then the sky would have a very bright line in it and the rest of the sky would be black. The density could fall with distance from the sun. However, the uniformity assumption is the one assumption Olber made which has basically stood up. Cosmological uniformity is one of the principles of the big bang theory. In fact they call it the cosmological principle (http://en.wikipedia.org/wiki/Cosmological_principle).


1. By universe I mean the material universe, not any hypothetical amount of empty space beyond or before it.

matt.o
2008-Nov-08, 11:37 AM
Just a finicky nitpick on point a), I'd change it to say "the number of observable stars isn't infinite" since nothing can be said about the number of stars outside our observable bubble.

RussT
2008-Nov-08, 12:09 PM
Up till now I've never understood the 'fractal solution' to Olber's Paradox; but looking at some of the on-line resources
(like this one)
http://www.m-hikari.com/ijcms-password2007/9-12-2007/stasiakIJCMS9-12-2007.pdf
it seems that in a fractal universe an arbritary amount of the sky can be dark. If the places where stars appear is limited to places where other stars appear, that means that there need not be any stars in some, or many, or most parts of the sky.

The fractal solution is amost certainly wrong,, but it can't be ruled out just by considering Olber's conundrum.

Here are some additional papers on Fractals which are very detailed and extensive...

http://arxiv.org/abs/astro-ph/9611197

http://adsabs.harvard.edu/abs/1988A&A...200L..32C

The CMBR is extremely homogenous and isotropic, BUT the galaxy clusters and Huge Voids in between those clusters is NOT.

I am not vying for a 'Static' Universe, however, it would appear that the statement that...The fractal solution is amost certainly wrong is way stronger than it should be.

And the second paper linked shows how the homogeneity and isotropy has been mathematically manipulated to help make it look that way!


Abstract
The use of the two-point correlation function xi(r) as a description of galaxy clustering requries an a priori assumption of homogeneity on length scales smaller than that of the sample analyzed. In order to verify the validity of this assumption, the CfA catalog was reanalyzed with a more general method. The results show that the galaxy distribution can be described by a fractal which extends up to at least 20/h Mpc without any evidence for a homogeneous distribution. This invalidates one of the principal conclusions based on the use of xi(r) namely, that there is no evidence in the CfA catalog for the existence of the famous correlation length r(0) about 5/h Mpc above which galaxy-galaxy correlations are small. This result is consistent with the observation of voids and superclusters and the existence of high anomalous streaming velocities.

matt.o
2008-Nov-08, 12:15 PM
The CfA catalogue has since been superseded by deeper, larger surveys such as the two-degree field galaxy redshift survey (2DFgrs) and the sloan digital sky survey (SDSS). Has the same study been done on these surveys? If so, what are the results?

agingjb
2008-Nov-08, 12:22 PM
Aren't the largest structures about 1/50 the size of the observable universe?

timb
2008-Nov-08, 12:26 PM
About which we cannot speak thereof let us be silent (apologies to Wittgenstein). Still, the bigbangologists always seem to hypothesize a finite starting mass, which implies a finite number of stars.

matt.o
2008-Nov-08, 12:31 PM
About which we cannot speak thereof let us be silent (apologies to Wittgenstein). Still, the bigbangologists always seem to hypothesize a finite starting mass, which implies a finite number of stars.

Got a link to a paper by a "bigbangologist" stating this? I'd like to see it.

Jens
2008-Nov-08, 03:12 PM
Modern cosmology tells us that
(a) the number of stars isn't infinite
(b) the universe is of finite age


I think it would be better to say that modern cosmology tells us that the number of stars does not appear to be infinite, and that the universe appears to be of finite age. Hubble's law seems to indicate that the universe has a beginning, but this is only an observation, and we cannot say for certain what it means. True, a fractal universe may be a solution to a problem that doesn't exist, but it does mean that Olber's paradox can be solved in a way other than a universe with a beginning. Granted, though, that Hubble's observations tend to discredit the idea of a universe without a beginning.

eburacum45
2008-Nov-08, 04:56 PM
The fractal solution is amost certainly wrong is way stronger than it should be. Well, the reason I said it like that is that the concept of the 'visible universe' seems to overide any effect from fractal disposition.

Whatever causes redshift seems to make stars invisible at a light-travel-time-distance of 13-odd billion light years; it really doesn't matter if the universe is fractally disposed or not, because we simply couldn't see it even if it were.

RussT
2008-Nov-09, 12:54 AM
Well, the reason I said it like that is that the concept of the 'visible universe' seems to overide any effect from fractal disposition.

Whatever causes redshift seems to make stars invisible at a light-travel-time-distance of 13-odd billion light years; it really doesn't matter if the universe is fractally disposed or not, because we simply couldn't see it even if it were.

Sorry, but this is just plain silly. All you are saying is that you/mainstream has the right to assume homogeneity/isotropy to infinity, and unless I can see past the ~13 billion light years to prove you wrong, you must be right.

And, when the Webb telescope sees to 15 billion/20 billion ETC, you can still say the same thing.

As I said, The CMBR IS homogenous/isotropic to infinity (But NOT for the reason you think!) BUT, there are Huge Voids between the Galaxy Clusters as far as we can see out into our big 'ol universe, and beyond to infinty as well, IF the CP (Cosmological Principal) was being invoked correctly!

Spaceman Spiff
2008-Nov-09, 05:11 AM
The Sun's atmosphere is kept at that temperature because of an equilibrium between energy radiated away and new energy input from deeper layers. If the whole sky was radiating at the same temperature, the energy radiated away by the solar atmosphere would be balanced by radiation absorbed from outside, and the energy from below would go to heating up the atmosphere. Now the same applies to every star, so they heat up too, meaning the Sun's new surface temperature is matched by the new effective temperature of the sky, meaning the input from below again goes to heat up the solar atmosphere. Repeat.

The cycle will only stop when stellar fusion runs out of fuel, by which time the sky won't be at infinite temperature, but way way way above 6000 K.

If the Sun were uniformly illuminated from the outside with a radiation field equivalent in energy density of that at its surface, it would take only a few thermal time scales for it to adjust its structure (in the face of zero net leak of energy) to move toward a new equilibrium as a substantially larger entity, the result of which nuclear fusion would slow and eventually shut down. Stars exist as they do because of the enormous temperature gradient between their interiors and the effective radiation energy density temperature of the cosmos.

You don't need infinite stars in an infinite universe to reach a paradox in which our sky would glow as if the Earth were placed at the surface of our Sun, as George mentioned above. This really boils down to a radiation energy-density argument (essentially solved by Lord Kelvin in 1901, but somehow largely overlooked). And invoking significant non-uniformities in the average star number density distribution as a function of distance only makes the paradox that much easier to solve in a universe which has contained stars for a finite amount of time. Ditto by including the effects of an expanding universe.

Edgar Allen Poe made some remarkably illuminating remarks concerning the "paradox", in his prose poem Eureka (http://en.wikipedia.org/wiki/Eureka_(Edgar_Allan_Poe)):


"Were the succession of stars endless, then the background of the sky would present us a uniform luminosity, like that displayed by the Galaxy –since there could be absolutely no point, in all that background, at which would not exist a star. The only mode, therefore, in which, under such a state of affairs, we could comprehend the voids which our telescopes find in innumerable directions, would be by supposing the distance of the invisible background so immense that no ray from it has yet been able to reach us at all."Wikipedia (http://en.wikipedia.org/wiki/Olbers%27_paradox) has a decent discussion of the paradox.

The paradox is that it isn't a paradox at all -- apparently, we are and have always been bathed by a uniform radiation field -- the cosmic background radiation, but one whose energy density temperature has been reduced to 2.725K by expansion, and was already ~100x lower than the surface temperatures of stars as the first generations of stars came into existence. The universe at epochs prior to a redshift of ~10,000 was dominated by radiation and opaque thereto, similar to the interior of a star. Olbers' universe was realized then, but no longer.

eburacum45
2008-Nov-09, 06:41 AM
. All you are saying is that you/mainstream has the right to assume homogeneity/isotropy to infinity, and unless I can see past the ~13 billion light years to prove you wrong, you must be right.
Well, I was trying hard not to make assumptions as to the cause of redshift, but since it does increase with distance (whatever the cause), there will come a distance where the luminosity of the stars is shifted into invisibility.

If the universe does in fact stretch far beyond the 13.7 year light-travel-time-distance, then Olbers Paradox remains, but only for radio waves of ever-increasing wavelength.

timb
2008-Nov-09, 08:38 AM
If the Sun were uniformly illuminated from the outside with a radiation field equivalent in energy density of that at its surface, it would take only a few thermal time scales for it to adjust its structure (in the face of zero net leak of energy) to move toward a new equilibrium as a substantially larger entity, the result of which nuclear fusion would slow and eventually shut down. Stars exist as they do because of the enormous temperature gradient between their interiors and the effective radiation energy density temperature of the cosmos.


In Olber's universe that's true for all stars. If all the stars shut down, where would the energy be coming from? :)


You don't need infinite stars in an infinite universe to reach a paradox in which our sky would glow as if the Earth were placed at the surface of our Sun, as George mentioned above. This really boils down to a radiation energy-density argument (essentially solved by Lord Kelvin in 1901, but somehow largely overlooked). And invoking significant non-uniformities in the average star number density distribution as a function of distance only makes the paradox that much easier to solve in a universe which has contained stars for a finite amount of time. Ditto by including the effects of an expanding universe.


So what is the resolution of the paradox that does not invoke the finiteness of the number of stars, the finite age of the universe, the expansion of the universe, or non-uniformities in the average star number density?

Kwalish Kid
2008-Nov-09, 04:39 PM
About which we cannot speak thereof let us be silent (apologies to Wittgenstein). Still, the bigbangologists always seem to hypothesize a finite starting mass, which implies a finite number of stars.
No, that is simply not correct. The standard cosmological model can accommodate an infinitely large universe with an infinite amount of mass-energy within that universe. Cosmologists who work within the standard model assume that the mass-energy density is finite.

timb
2008-Nov-09, 09:39 PM
Got a link to a paper by a "bigbangologist" stating this? I'd like to see it.

Sory, I don't have one.

hhEb09'1
2008-Nov-09, 11:20 PM
Edgar Allen Poe made some remarkably illuminating remarks concerning the "paradox", in his prose poem Eureka (http://en.wikipedia.org/wiki/Eureka_(Edgar_Allan_Poe)):
Wikipedia (http://en.wikipedia.org/wiki/Olbers%27_paradox) has a decent discussion of the paradox. The BA, in his new book Death From The Skies, gives Poe credit for the first solution to Olber's Paradox. Thanks for the link, I wouldn't have looked it up myself, even though I just finished the book.

matt.o
2008-Nov-10, 08:33 AM
Sory, I don't have one.

I suspected as much.

Perhaps RussT would like to answer my question addressed at this post of his:


Here are some additional papers on Fractals which are very detailed and extensive...

http://arxiv.org/abs/astro-ph/9611197

http://adsabs.harvard.edu/abs/1988A&A...200L..32C

The CMBR is extremely homogenous and isotropic, BUT the galaxy clusters and Huge Voids in between those clusters is NOT.

I am not vying for a 'Static' Universe, however, it would appear that the statement that...The fractal solution is amost certainly wrong is way stronger than it should be.

And the second paper linked shows how the homogeneity and isotropy has been mathematically manipulated to help make it look that way!

and my question:



The CfA catalogue has since been superseded by deeper, larger surveys such as the two-degree field galaxy redshift survey (2DFgrs) and the sloan digital sky survey (SDSS). Has the same study been done on these surveys? If so, what are the results?

Jens
2008-Nov-10, 09:56 AM
The CfA catalogue has since been superseded by deeper, larger surveys such as the two-degree field galaxy redshift survey (2DFgrs) and the sloan digital sky survey (SDSS). Has the same study been done on these surveys? If so, what are the results?

I really don't know how reliable this is, but there is apparently a paper (http://space.newscientist.com/article/dn14200-galaxy-map-hints-at-fractal-universe.html?DCMP=ILC-hmts&nsref=news1_head_dn14200)done from the SDSS that argues that it seems fractal up to 100 million LY.

RussT
2008-Nov-10, 11:35 AM
Yes, thanks Jens...



According to their latest paper, which has been submitted to Nature Physics, Sylos Labini and Pietronero, along with physicists Nikolay Vasilyev and Yurij Baryshev of St Petersburg State University in Russia, argue that the new data shows that the galaxies exhibit an explicitly fractal pattern up to a scale of about 100 million light years.

And they say if the universe does become homogeneous at some point, it has to be on a scale larger than a staggering 300 million light years across. That's because even at that scale, they still observe large fluctuations – a cluster here, a void there – in the matter distribution.

And as I have said several times now, the CMBR is homgenous/isotropic to infinity, BUT the galaxy clusters with the huge voids between them is Fractal as far as we can 'see'. And I'll amend that now to...as far as we will ever see...;)

And...


The wager
But according to their paper, Sylos Labini's team says the Bull's-eye effect is only relevant on very small scales, about 16 million light years and below, and has no influence on the clumpiness at the large scales in question.

Melott disagrees, saying it should magnify clumpiness at any scale. But he adds that the effect only "enhances structures that [already] exist".

What's at stake if the universe is indeed a fractal on the largest scales? Besides a radical rethink of the laws and history of the cosmos, researchers have placed something more down-to-Earth on the line.

More than a decade ago, Sylos Labini and Pietronero wagered a bet with physicist Marc Davis of the University of California, Berkeley, US. The bet, refereed by Turok, held that if the galaxy distribution turned out to be fractal beyond scales of approximately 50 million light years, Davis would owe Sylos Labini and Pietronero a case of California wine.

Should the fractal pattern begin to disintegrate at scales less than 50 million light years, Davis would receive a case of Italian wine – which some would say is a better deal. Turok has yet to declare a winner.

I like it:) It would appear the Mr, Turok should be administering Kudos to Sylos Labini and Pietronero soon :)

PraedSt
2008-Nov-10, 12:02 PM
My bold:
More than a decade ago, Sylos Labini and Pietronero wagered a bet with physicist Marc Davis of the University of California, Berkeley, US. The bet, refereed by Turok, held that if the galaxy distribution turned out to be fractal beyond scales of approximately 50 million light years, Davis would owe Sylos Labini and Pietronero a case of California wine.

Should the fractal pattern begin to disintegrate at scales less than 50 million light years, Davis would receive a case of Italian wine – which some would say is a better deal.
Everyone in the whole world, except perhaps Californians. :)

Spaceman Spiff
2008-Nov-10, 10:52 PM
In Olber's universe that's true for all stars. If all the stars shut down, where would the energy be coming from? :)

Stars shine because they're hot, not because they're fusing hydrogen into helium (or anything else). Fusion merely allows them to stabilize their structures so that no net energy loss (in from fusion, out from photons streaming away from the star's surface) results. Star's (or at least those things we call stars) aren't allowed in Olbers' universe, and maybe that should be a point that is emphasized. As a matter of fact, I did (indirectly) mention it above (http://www.bautforum.com/astronomy/80909-olbers-paradox-2.html#post1361181) (towards the bottom of the post).




So what is the resolution of the paradox that does not invoke the finiteness of the number of stars, the finite age of the universe, the expansion of the universe, or non-uniformities in the average star number density?

Hmmm...again, what I said was:

You don't need infinite stars in an infinite universe to reach a paradox in which our sky would glow as if the Earth were placed at the surface of our Sun, as George mentioned above. This really boils down to a radiation energy-density argument (essentially solved by Lord Kelvin in 1901, but somehow largely overlooked). And invoking significant non-uniformities in the average star number density distribution as a function of distance only makes the paradox that much easier to solve in a universe which has contained stars for a finite amount of time. Ditto by including the effects of an expanding universe.I was saying that you don't need either an infinite amount of stars or an infinite shining time to confront Olbers' paradox (i.e., the equivalent of staring face to face with the surface of a star). You only need to have sufficient energy density of glowing matter to raise the radiation energy density level to a large value, and my point was that Kelvin had reasoned correctly way back in 1901 that this value is WAY too small to produce a bright sky in our universe, thus placing a limit on the time span of shining stars -- despite lacking knowledge that we have today regarding stellar evolution, the expanding universe, etc.

Spaceman Spiff
2008-Nov-11, 01:15 AM
Structures spanning > 300 million light years ("the End of Greatness (http://en.wikipedia.org/wiki/Large-scale_structure_of_the_cosmos)") are rare in the large scale structure, and most of the power is on smaller scales. The galaxy supercluster walls and voids and walls are the largest structure we see in the galaxy surveys. Whether structure from individual galaxies to clusters to superclusters is fractal is still open to debate. As far as I am aware the only group making the claim is that one from Russia... Even if it is fractal (and I doubt it is, mathematically), the structure does not continue in both larger and smaller scales. So, what does it matter?

The other point to be made is that it is well established that galaxy clusters have been undergoing evolution in number, size, mass, contents, you name it, with redshift. And the SDSS galaxy and quasar data surveys are already indicating (although I don't know if it's a definitive result -- we may need to go deeper in apparent magnitude) that the supercluster sheets and voids are a relative new-comer to our universe. But this is moving away the point of this thread.

grav
2008-Nov-11, 02:32 PM
I'm not sure how a fractal universe would solve Olber's paradox. As long as every line of sight from an observer falls upon a star, the universe would still be as bright as the surface of an average star, either directly or by reheating over a long period of time as the temperature of all matter in the universe reaches equilibrium. How far we place the stars or whatever complex pattern we make of them wouldn't matter. The only way to solve Olber's paradox that I can see offhand is to limit one or more of the factors involved, such as cutting off the size or age of the universe entirely. Or perhaps the light could lose energy to particles that don't easily interact with ordinary matter in order to re-radiate readily. The time that the stars actually burn is also limited to about fifteen billion years, so the universe cannot reach equilibrium of temperature easily for all matter, which now that I think about it, sounds like it could possibly be more than coincidence that that is also the age of the universe as found according to the temperature of the CMB.

doc33
2008-Nov-12, 03:21 AM
Thanks for all the in put. It may take me a while to digest it all.
I read in Guth's book on the Inflationary Universe that when the universe was 300,000 years old, it was 900,000 ly in diameter. ? due to inflation ? metric expansion ?

Spaceman Spiff
2008-Nov-12, 06:47 PM
Thanks for all the in put. It may take me a while to digest it all.
I read in Guth's book on the Inflationary Universe that when the universe was 300,000 years old, it was 900,000 ly in diameter. ? due to inflation ? metric expansion ?

That number makes no sense to me at all. Whatever the correct number is, it is NOT speaking of some "actual diameter of the universe" (which could be infinite, or extend greatly beyond our current particle horizon), but rather something related to the size of that cosmic horizon (http://en.wikipedia.org/wiki/Observable_universe) at that time. And yes, due to "metric expansion". Inflation, assuming it occurred (and there is good evidence that it or something like that did occur) stretched space-time far, far beyond our horizon.

Jens
2008-Nov-13, 01:40 AM
I'm not sure how a fractal universe would solve Olber's paradox. As long as every line of sight from an observer falls upon a star, the universe would still be as bright as the surface of an average star, either directly or by reheating over a long period of time as the temperature of all matter in the universe reaches equilibrium.

A fractal universe solves the problem by ensuring that not every line of sight falls upon a star. I don't know how well I can explain it, but basically, as you increase the scale, the density of stars falls. So the density of stars tends toward zero, like a limit in mathematics. So it is only on a small scale, i.e. in our own galaxy, that a line of sight will tend to fall on a star.

grav
2008-Nov-13, 03:21 AM
A fractal universe solves the problem by ensuring that not every line of sight falls upon a star. I don't know how well I can explain it, but basically, as you increase the scale, the density of stars falls. So the density of stars tends toward zero, like a limit in mathematics. So it is only on a small scale, i.e. in our own galaxy, that a line of sight will tend to fall on a star.In an infinite universe, the line of sight should always fall upon a star eventually, regardless of the star density, unless that density cuts off to zero at some point with absolutely no stars thereon forever, basically rendering it the same as a finite universe.

Jens
2008-Nov-13, 05:42 AM
In an infinite universe, the line of sight should always fall upon a star eventually, regardless of the star density, unless that density cuts off to zero at some point with absolutely no stars thereon forever, basically rendering it the same as a finite universe.

No, it doesn't drop to zero. It just approaches zero. The larger the scale, the closer it gets to zero, but it never gets there. It's sort of an interesting idea, because it means that on the universe essentially has zero density, even though it has density.

doc33
2008-Nov-14, 04:21 AM
I have read all the posts. I think most people make this question too complicated.

doc33
2008-Nov-14, 04:33 AM
The conjecture that the total universe is larger than the observable universe is based on what ?

doc33
2008-Nov-14, 04:34 AM
The conjecture that the total universe is larger than the observable universe is based on what ?

''often wrong but never in doubt.''

Sp1ke
2008-Nov-14, 09:34 AM
The conjecture that the total universe is larger than the observable universe is based on what ?

Well, I could ask you in return why the total universe just happens to be exactly the same size as the observable universe?

PraedSt
2008-Nov-14, 09:38 AM
I have read all the posts. I think most people make this question too complicated.
That often happens. :) The upside is you learn a lot. As I have.

Spaceman Spiff
2008-Nov-14, 01:56 PM
The conjecture that the total universe is larger than the observable universe is based on what ?

It's not at all conjecture, but a natural conclusion resting on two sets of observations: the finite speed of light coupled with the observation of Hubble's Law (so-called "expanding universe").

Spaceman Spiff
2008-Nov-14, 02:01 PM
I have read all the posts. I think most people make this question too complicated.

And...so...what contribution would you like to make toward answering the question?

doc33
2008-Nov-20, 05:34 PM
re Olbers: A star with insufficient magnitude to be seen on Earth accounts for the dark areas in the night sky.

timb
2008-Nov-20, 07:56 PM
It's not at all conjecture, but a natural conclusion resting on two sets of observations: the finite speed of light coupled with the observation of Hubble's Law (so-called "expanding universe").

I don't see what differentiates the "unobservable Universe" from parallel universes, God, and the fairies that only poor Aunt Mavis can see, ie speculations outside the realm of science. Science is hypotheses testable by observation, and that excludes hypotheses about the unobservable.

Jens
2008-Nov-21, 01:23 AM
re Olbers: A star with insufficient magnitude to be seen on Earth accounts for the dark areas in the night sky.

If the universe is infinite, that would not be a solution.

Gigabyte
2008-Nov-21, 02:42 AM
Yes it is.

Spaceman Spiff
2008-Nov-21, 04:44 AM
I don't see what differentiates the "unobservable Universe" from parallel universes, God, and the fairies that only poor Aunt Mavis can see, ie speculations outside the realm of science. Science is hypotheses testable by observation, and that excludes hypotheses about the unobservable.

I am not talking about parallel universes or fairies or leprechauns or orbiting teapots, but simply our universe, And if it is part of the same universe we inhabit, then science can address it. The question was:


The conjecture that the total universe is larger than the observable universe is based on what ?Our cosmic horizon is not a fixed distance as time progresses. Thus some objects that were once beyond (or "below") that horizon will have come up above it, and if the accelerated expansion is actually happening then some of what is currently above our horizon will fall below. How large our universe is at a "cosmic now" we do not presently know -- but it is in principle knowable once or if we understand the physics of what led to its "inflation".

Why would you think that our universe is exactly as large as the cosmic horizon dictated by the speed of light? Or maybe that's not what you were getting at, timb, but at least one person was.

Have a look at this (http://en.wikipedia.org/wiki/Observable_universe) and the links therefrom.

Spaceman Spiff
2008-Nov-21, 05:01 AM
Yes it is.

Elaboration?

For roughly constant number density of stars (or galaxies) with distance r, the volume element r^2*dr contains ever more stars (or galaxies) within, compensating exactly for the 1/r^2 dilution of flux. Adding infinite shells sums to infinite incident flux. That was essentially the original argument put forth.

Gigabyte
2008-Nov-21, 05:18 AM
Doesn't matter. The facts of the matter are simple, in regards to the original paradox. It all hinges on one huge assumption that is made about the Universe.

Gigabyte
2008-Nov-21, 05:20 AM
This assumption is even stated as fact, within Olber's paradox, as it is usually stated.

Let me see if I can find it.

Ah, well Wikipedia is the fastest source, and it is pretty much taken from the other sources, so it should do.

Which isn't really the same as being too far away, but one thing at a time. It is still a huge assumption.


An alternative explanation, which is sometimes suggested by non-scientists, is that the universe is not transparent, and the light from distant stars is blocked by intermediate dark stars or absorbed by dust or gas, so that there is a bound on the distance from which light can reach the observer.

However, this reasoning alone would not resolve the paradox given the following argument: According to the second law of thermodynamics, there can be no material hotter than its surroundings that does not give off radiation and at the same time be uniformly distributed through space. Energy must be conserved, per the first law of thermodynamics. Therefore, the intermediate matter would heat up and soon reradiate the energy (possibly at different wavelengths). This would again result in intense uniform radiation as bright as the collective of stars themselves, which is not observed.
http://en.wikipedia.org/wiki/Olber%27s_paradox#Absorption

Here is the huge assumption: Therefore, the intermediate matter would heat up and soon reradiate the energy (possibly at different wavelengths). This would again result in intense uniform radiation as bright as the collective of stars themselves, which is not observed.

The nearest and brightest source of stars, and one that is without a doubt large enough to be a solid mass of starlight, is our own galaxy. The Milky Way (MW). Yet the MW is blocked by clouds of dust and gas, so it is not as bright as the sun, even though it should be. Sections of it are with out a doubt solid stars.

If we go with "the intermediate matter would heat up and soon reradiate the energy", then the intermediate matter should certainly be radiating light like the stars themselves. That is what the assumption says.

Obviously the dust and gas is not. In fact, if the nearest giant mass of stars is blocked by dust and gas, and the dust and gas is not glowing as bright as the stars, then the whole explanation falls apart.

Remember, the reasoning against light being blocked was "the intermediate matter would heat up and soon reradiate the energy". I'm not sure how old our galaxy is, but the word "soon" certainly would fall a few billion years ago. Yet we see no glowing dust and gas, as bright as the stars themselves.

So the whole thing starts to look, well, it looks wrong.

Gigabyte
2008-Nov-21, 05:38 AM
Now as to the light being too far away, so it is too dim to see, the same thing happens with light right here on earth.

Imagine you are sitting in the middles of a ring of candles. They could be, it doesn't matter, 10 feet away, a complete ring of them around you. Hundreds of candles. It would be quite bright. Light enough to read by.

Now move the circle of candles farther away, but increase the number so it is still a solid ring of candles around you. Say, a hundred feet away. (We are going to need a lot of candles). Still think you can read by the light?

Lets move them several miles away to make a point. Yeah, we might need several million candles to make the circle now, but you certainly couldn't read by them. You might not even be able to see most of them. If you could, it would be a very faint flickering ring of light.

Now move them a hundred miles out. But use more candles so it is still a solid ring of candles.

You wouldn't see a thing. Even though there are billions of candles burning. (The human eye can not see a candle flame that far away, it doesn't matter how many of them there are).

Does this prove anything? Probably not. But that is reality for you. It is just there.

eburacum45
2008-Nov-21, 05:47 AM
A solid, flat ring of candles represents one of the possible solutions to Olbers' paradox. If all the stars were arranged in a flat ring then the rest of the sky would look dark.
But the universe is three dimensional, and stars are apparently arranged all over the sky, so there is no obvious reason that any one part of the sky should look darker than any other.

Jens
2008-Nov-21, 05:58 AM
Lets move them several miles away to make a point. Yeah, we might need several million candles to make the circle now, but you certainly couldn't read by them. You might not even be able to see most of them. If you could, it would be a very faint flickering ring of light.


You should be able to, eventually. If the sphere of candles is solid, then the inside should eventually get as bright as the individual candles. Which is essentially what Olber's paradox is about. If any line of sight goes to a star, no matter how dim, then eventually the whole universe should be as bright (and hot) as the surface of a star.

Gigabyte
2008-Nov-21, 02:28 PM
If we go with the assumption that a solid mass of stars would be as bright and as hot as our local star, the sun, then looking at the obvious example, the Milky Way (MW), it is obvious that even after billions and billions of years, dust and gas, or whatever it is blocking out the starlight, does not glow as hot and as bright as the stars themselves.

If a solid mass of stars quite close to us don't look bright, then why would a Universe full of very very very very distant stars look bright?

This question seems obvious to me. And illustrates the difference between reality, where you go look at the Milky Way at night, and armchair physics, where people sit around and imagine stuff. With out doing any observation or experiments to see if it could be true.

There is another obvious problem with the starlight thing.

George
2008-Nov-21, 02:52 PM
If a solid mass of stars quite close to us don't look bright, then why would a Universe full of very very very very distant stars look bright? Are you suggesting the Milky Way is a solid mass of stars?

Consider this.... if you took all the estimated mass of the observeable universe and brought it to our Solar system, and magically kept it at the density of water, its radius would be less than our Solar system.

If we were fish in an infinite ocean and an infinite number of chunks of molten iron were placed in this ocean, then we should be boiling, right? Yet, not only are we not boiling, the water is quite cold.

Gigabyte
2008-Nov-21, 03:08 PM
The nearest and brightest source of stars, and one that is without a doubt large enough to be a solid mass of starlight, is our own galaxy. The Milky Way (MW). Yet the MW is blocked by clouds of dust and gas, so it is not as bright as the sun, even though it should be. Sections of it are with out a doubt solid stars.


In case you are unfamiliar with the Milky Way, looking at the core, from an edge on view, (from our planet), there is nothing but stars, there are so many of them, that we can't see what is on the other side. (A great annoyance to astronomers btw). This means, IT APPEARS as a solid wall of stars. It is not "solid" in the sense of no space between them. Please.

This great glowing mass of stars is for practical purposes, a solid mass of starlight. But it doesn't appear that way (in visible light).

And the dust and gas blocking the light doesn't glow as bright as the starlight it is blocking. Which is what most people predict will happen.

After billions and billions of years, the dust and gas blocking out the vast light from the core of our galaxy, is still dark.

If a nearby galactic center doesn't appear bright, why would an entire sky full of very very distant galaxies appear bright?

Spaceman Spiff
2008-Nov-21, 03:44 PM
This assumption is even stated as fact, within Olber's paradox, as it is usually stated.

Let me see if I can find it.

Ah, well Wikipedia is the fastest source, and it is pretty much taken from the other sources, so it should do.

Which isn't really the same as being too far away, but one thing at a time. It is still a huge assumption.


http://en.wikipedia.org/wiki/Olber%27s_paradox#Absorption

Here is the huge assumption: Therefore, the intermediate matter would heat up and soon reradiate the energy (possibly at different wavelengths). This would again result in intense uniform radiation as bright as the collective of stars themselves, which is not observed.

The nearest and brightest source of stars, and one that is without a doubt large enough to be a solid mass of starlight, is our own galaxy. The Milky Way (MW). Yet the MW is blocked by clouds of dust and gas, so it is not as bright as the sun, even though it should be. Sections of it are with out a doubt solid stars.

If we go with "the intermediate matter would heat up and soon reradiate the energy", then the intermediate matter should certainly be radiating light like the stars themselves. That is what the assumption says.

Obviously the dust and gas is not. In fact, if the nearest giant mass of stars is blocked by dust and gas, and the dust and gas is not glowing as bright as the stars, then the whole explanation falls apart.

Remember, the reasoning against light being blocked was "the intermediate matter would heat up and soon reradiate the energy". I'm not sure how old our galaxy is, but the word "soon" certainly would fall a few billion years ago. Yet we see no glowing dust and gas, as bright as the stars themselves.

So the whole thing starts to look, well, it looks wrong.

You bet something's wrong, but not what for reasons that you think...

If the energy density of the radiation is sufficiently high, the heating time of gas clouds is not billions of years. How do you think HII regions glow? Their gases are nowhere near in thermodynamic equilibrium with the incident radiation field, so the gas' emissivity is far below that of a blackbody of the same temperature, although the dust grains contained within emit with a much higher emissivity, in some cases almost a blackbody. However, hat radiation field from nearby hot stars is sufficiently intense and energetic to heat their skins to ~10,000K, but not so intense to heat their deep interiors, which are exposed mainly to cosmic ray heating. There is also a background diffuse galactic radiation field (mainly from stars) which is weak, but still important to understanding energy balance in HII region environments.


Yet the MW is blocked by clouds of dust and gas, so it is not as bright as the sun, even though it should be. Sections of it are with out a doubt solid stars.Do you want to place bets on that last claim?

If the stars are too few per cubic light year, the collective radiation fields of the stars will not appreciably heat the intervening gas/dust. But the reason is that because of their sparseness their collective radiation field is too feable! (which is to say, the sky is dark :whistle:). So there is nothing "wrong" about that argument given regarding the paradox, at all. It's just a statement of the conservation of energy.

Now, one could consider a radiation "fill up" time scale of the universe...i.e., how long before the radiation of stars could raise the energy density in radiation to some value of significance. If this time scale is for any reason FAR longer than the time that stars have been around, then there's the solution to the "paradox".

This then boils down to the fact that there are FAR too few stars per cubic mega light year (or far too little matter consisting of protons and electrons with couple strongly to the electromagnetic field) to result in a radiation "fill up" time scale that is comparable in any way to the finite amount of time that stars have been around (apparently, ~14 billion years minus ~0.1 billion years).

But consider too, that if the radiation energy density were large enough to give us a bright sky, stars would not have formed or those that had before the universe "filled up" with radiation would cease to exist as objects we call stars in several stellar thermal time scales. The very existence of stars (and all that comes with their formation -- planets for instance) depends on the very fact that they are FAR out of thermodynamic equilibrium with the thermodynamically cold (low radiation energy density) environments. Current models of the formation of the first stars have them forming when the radiation energy density in the cosmic background radiation (the photons of the big bang) had fallen to a value of ~ 10^8x lower than that found just below the surface of a typical star (where matter and radiation are in local equilibrium). This isn't a coincidence, although the energy density in the background radiation field isn't the only issue.

So, again, the simplest solution is one to do with radiation energy density. It's presently WAY too small -- for a number of reasons, and it's been that way since sometime after the radiation energy density (due to photons of the big bang) fell below that of the matter energy density, some ~10,000 years after the big bang. At times before, the "sky" was uniformly bright, not with starlight, but with the light of the big bang. That same light now glows at a very low intensity in the far infrared, as a blackbody at 2.725 K, due to the expansion of the universe over the intervening time. So in some sense, the sky is bright, and virtually uniformly so, but way out in the energetically feeble far infrared.

Gigabyte
2008-Nov-21, 04:03 PM
This does not address the assumption as I quoted it. Using the example of the Milky Way, the matter blocking out the light from the Galactic center is not glowing as bright as the stars. Looking directly at our galaxies center, we would see a solid mass of stars, which according to theory should look as bright as the sun.

It doesn't. The matter blocking out the light also is not glowing as bright as the stars. So the Milky Way looks dark.

The Andromeda galaxy is another example. Looking at the center of that galaxy, we see a solid mass of stars, because of the density there. According to theory, it should look as bright as the sun.

Or, if light is being blocked by matter between us and the galaxy core, it should be glowing as bright as the starlight it is absorbing. It isn't.

Somewhere in all the theory, reality shows up. If a nearby galaxy, or our own galaxy, does not look bright, it is obvious that objects very far away are not going to. No matter how many stars and galaxies there are.

To make it very simple, forget about the entire sky, the entire Universe.

Why doesn't the center of the Milky Way look as bright as the sun? If it is because of matter blocking the light, why doesn't it glow? After billions and billions of years of absorbing radiation?

No matter what the answer is, reality still shows that a solid mass of stars will not appear as bright as the sun. It has nothing to do with an expanding Universe, or redshift, or anything else that cosmic. Because both our galaxy, as well as Andromeda, are not moving away from us. There is no expanding space-time on that relationship.

So why doesn't our galaxy, where the density of stars is great enough to appear as a solid wall of starlight, appear to be bright?

Gigabyte
2008-Nov-21, 04:06 PM
Remember, I am speaking to this claim about Olber's paradox.


According to the second law of thermodynamics, there can be no material hotter than its surroundings that does not give off radiation and at the same time be uniformly distributed through space. Energy must be conserved, per the first law of thermodynamics. Therefore, the intermediate matter would heat up and soon reradiate the energy (possibly at different wavelengths). This would again result in intense uniform radiation as bright as the collective of stars themselves, which is not observed.

It is obvious from looking at nearby sources of intense and constant starlight, that this is not a true statement.


Therefore, the intermediate matter would heat up and soon reradiate the energy (possibly at different wavelengths).

This is not what we see when we look at the matter blocking the Milky Way core.


This would again result in intense uniform radiation as bright as the collective of stars themselves, which is not observed.

This is not what we observe when looking at the Milky Way core. Or at nearby Andromeda. If it isn't true for nearby sources, why would it be true for very distant sources?

That is the huge assumption that is stated. That the Universe doesn't look dark because of matter blocking out the light.

I observe nearby sources of very intense light, and see that this is not the case.

Spaceman Spiff
2008-Nov-21, 04:22 PM
Remember, I am speaking to this claim about Olber's paradox.



It is obvious from looking at nearby sources of intense and constant starlight, that this is not a true statement.



This is not what we see when we look at the matter blocking the Milky Way core.



This is not what we observe when looking at the Milky Way core. Or at nearby Andromeda. If it isn't true for nearby sources, why would it be true for very distant sources?

That is the huge assumption that is stated. That the Universe doesn't look dark because of matter blocking out the light.

I observe nearby sources of very intense light, and see that this is not the case.

I tried to explain why, above. It's because the starlight for the given concentration of stars is too feeble: there aren't enough stars per cubic light year or per cubic mega light year, either locally or in the universe as a whole. You're keen observation is simply a restatement of "the sky is dark". So all you're claiming is that the "sky is dark because the sky is dark".

Ramp the number of stars in the MW up suddenly by some enormous factor, and think about what would eventually happen. The present stellar content in the MW produces starlight that IS too feeble to heat up the vast majority of those dusty gas clouds much above ~100K. In fact spiral galaxies emit a significant amount of light at ~20-100+ microns for just this reason. The visually dark, dusty gas clouds in the disks of spiral galaxies glow brightly at these wavelengths (http://ipac.jpl.nasa.gov/media_images/ssc2004-19a_medium.jpg) (the IR image is at 24 microns) -- total energy is conserved.

But the universe isn't blazingly bright at 100 microns, either.

agingjb
2008-Nov-21, 05:26 PM
I wonder about this solid wall of stars. Roughly, and I'll be corrected, I get that at the distance of the galactic centre the Sun would occupy 1/200,000,000,000,000 of the size it does from Earth. There are a lot of stars in there, but are there enough?

Spaceman Spiff
2008-Nov-21, 09:30 PM
I wonder about this solid wall of stars. Roughly, and I'll be corrected, I get that at the distance of the galactic centre the Sun would occupy 1/200,000,000,000,000 of the size it does from Earth. There are a lot of stars in there, but are there enough?

I think it's more like a factor of 10^-9 (1 AU * 1.496e13 cm per AU / (9.46e17 cm/ly * 27,400 ly), but in any case you should just forget the "solid wall of stars" argument. It's not useful.

agingjb
2008-Nov-21, 09:41 PM
Oh well, I just squared what I thought to be the rough ratio of the differences. (10^9 is rather different fom my 10^14 - ish.)

FWIW, if there were an area in the sky around, let's say, a hundredth of a square degree where the disks of stars as seen from the Earth pretty much overlapped, then I'd guess it would be bright - ish.

doc33
2008-Nov-21, 09:47 PM
To rephrase the question; If the size of the total universe is greater than the observable universe, how is the total universe's size calculated ? And how did it get bigger than the observable universe ?

Spaceman Spiff
2008-Nov-21, 09:50 PM
Oh well, I just squared what I thought to be the rough ratio of the differences. (10^9 is rather different fom my 10^14 - ish.)

FWIW, if there were an area in the sky around, let's say, a hundredth of a square degree where the disks of stars as seen from the Earth pretty much overlapped, then I'd guess it would be bright - ish.

Well, my calculation was one of angular diameter. In terms of ratio of angular areas, then one would square that number: 10^-18.

Spaceman Spiff
2008-Nov-21, 10:07 PM
To rephrase the question; If the size of the total universe is greater than the observable universe, how is the total universe's size calculated ? And how did it get bigger than the observable universe ?

In principle the universe could approach or even be infinite, but the stars contained within have been around for less than 14 billion years. Add to that that the universe is expanding with time. Put 'em together and one can compute the distance to our cosmic horizon.

We cannot at present "calculate" the size of our universe. What we can do is compute the size of the cosmic horizon, some 46 billion light years in "radius" (by the usual definition), given knowledge of its expansion history. I'll link to this article (http://en.wikipedia.org/wiki/Observable_universe), yet again. Try these animations (http://www.phys.ksu.edu/personal/gahs/phys191/horizon.html), as well. And this (http://www.atlasoftheuniverse.com/redshift.html) might be useful, too.

There have been attempts to place a minimum size (http://arxiv.org/abs/astro-ph/0310233) of our universe. But without an understanding of the physics that led to the inflation of our universe we cannot know its actual size. It's just likely to be far larger than our cosmic horizon.

agingjb
2008-Nov-21, 10:07 PM
Well, I'm sure the numbers require refinement, but to estimate whether a random group of stellar disks would more or less cover an area, then I do think the areas rather than the diameters should be used.

Again, FWIW, I used the ratio between 8 minutes and 25,000 years, and squared it - but I could have easily got this very wrong.

Spaceman Spiff
2008-Nov-21, 10:21 PM
Well, I'm sure the numbers require refinement, but to estimate whether a random group of stellar disks would more or less cover an area, then I do think the areas rather than the diameters should be used.

Agreed, but you said:

I get that at the distance of the galactic centre the Sun would occupy 1/200,000,000,000,000 of the size it does from Earth (emphasis mine) which was ambiguous.



Again, FWIW, I used the ratio between 8 minutes and 25,000 years, and squared it - but I could have easily got this very wrong.

(365.25 days/year * 24 hr/day * 60 min/hr * 25,000 yr / 8 mins)^2 = 2.7e18. Same as I got. Your original number is missing some zeros.

agingjb
2008-Nov-21, 10:42 PM
Oh well., I'm sure my ideas are vague, but I was addressing the idea of the "wall of stars" or whatever it was, which I found implausible.

As to Olber's paradox. I'd say that in a non-expanding uniform universe infinite in size and age, then the sky would glow hot. It doesn't, so one or more of the conditions don't obtain.

timb
2008-Nov-22, 03:37 AM
I am not talking about parallel universes or fairies or leprechauns or orbiting teapots, but simply our universe, And if it is part of the same universe we inhabit, then science can address it. The question was:

Our cosmic horizon is not a fixed distance as time progresses. Thus some objects that were once beyond (or "below") that horizon will have come up above it,


That implies that they are not causally disconnected from us, which seems to contradict the implication in the wikipedia article you cite that objects outside the observable universe are causally disconnected from us.


Why would you think that our universe is exactly as large as the cosmic horizon dictated by the speed of light?


I don't know what you mean by "our universe" when it includes unobservables.

Spaceman Spiff
2008-Nov-22, 04:21 AM
Since I don't wish to get into a debate concerning the semantics, I thought I'd quote a couple of the relevant passages from the link (http://en.wikipedia.org/wiki/Observable_universe) I gave (emphases mine):


Both popular and professional research articles in cosmology often use the term "universe" to mean "observable universe". This can be justified on the grounds that we can never know anything by direct experimentation about any part of the universe that is causally disconnected (http://en.wikipedia.org/wiki/Causality_%28physics%29) from us, although many credible theories, such as cosmic inflation (http://en.wikipedia.org/wiki/Cosmic_inflation), require a universe much larger than the observable universe. No evidence exists to suggest that the boundary of the observable universe corresponds precisely to the physical boundary of the universe (if such a boundary exists); this is exceedingly unlikely in that it would imply that Earth is exactly at the center of the universe, in violation of the cosmological principle (http://en.wikipedia.org/wiki/Cosmological_principle). It is likely that the galaxies (http://en.wikipedia.org/wiki/Galaxy) within our visible universe represent only a minuscule fraction of the galaxies in the universe.

It is also possible that the universe is smaller than the observable universe. In this case, what we take to be very distant galaxies may actually be duplicate images of nearby galaxies, formed by light that has circumnavigated the universe. It is difficult to test this hypothesis experimentally because different images of a galaxy would show different eras in its history, and consequently might appear quite different. A 2004 paper [1] (http://en.wikipedia.org/wiki/Observable_universe#cite_note-cornish-0) claims to establish a lower bound of 24 gigaparsecs (http://en.wikipedia.org/wiki/Parsec) (78 billion (http://en.wikipedia.org/wiki/1000000000_%28number%29)light-years (http://en.wikipedia.org/wiki/Light-year)) on the diameter of the whole universe, making it, at most, only slightly smaller than the observable universe. This value is based on matching-circle analysis of the WMAP (http://en.wikipedia.org/wiki/WMAP) data.
and


The comoving distance (http://en.wikipedia.org/wiki/Comoving_distance) from Earth to the edge of the visible universe (also called particle horizon) is about 14 billion parsecs (46.5 billion light-years) in any direction.[2] (http://en.wikipedia.org/wiki/Observable_universe#cite_note-ly93-1) This defines a lower limit on the comoving radius (http://en.wikipedia.org/wiki/Radius) of the observable universe, although as noted in the introduction, it's expected that the visible universe is somewhat smaller than the observable universe since we only see light from the cosmic microwave background radiation (http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation) that was emitted after the time of recombination (http://en.wikipedia.org/wiki/Timeline_of_the_Big_Bang#Recombination:_240.2C000-310.2C000_years), giving us the spherical surface of last scattering (http://en.wikipedia.org/wiki/Cosmic_background_radiation#Features) (gravitational waves could theoretically allow us to observe events that occurred earlier than the time of recombination, from regions of space outside this sphere). The visible universe is thus a sphere with a diameter (http://en.wikipedia.org/wiki/Diameter) of about 28 billion parsecs (about 93 billion light-years).The above statement concerning the CBR isn't quite correct, since the blackbody nature of the CBR was frozen in when the matter-radiation processes that established blackbody radiation became slower than the expansion rate of the universe (at about 1 month old, compared to 389,000 years old for the matter-radiation decoupling event).

Since it is conceivable that a scientific model, such as some version of Inflation or something different altogether (loop quantum gravity), can tell us about the physics of what led to the inflation of the universe we inhabit, then it is perfectly logical to consider stuff that happens to lie beyond our cosmic horizon, but is part of the same space-time structure that underwent inflation, as part of our universe. Have a look at this animation (http://www.astro.ucla.edu/%7Ewright/CMB-MN-03/inflating_bubble.html) (the inflating bubble takes a bit of time to get going, so have patience) and its discussion.

Or we can split hairs over semantics. :)

Jens
2008-Nov-22, 08:17 AM
In case you are unfamiliar with the Milky Way, looking at the core, from an edge on view, (from our planet), there is nothing but stars, there are so many of them, that we can't see what is on the other side.

Somebody please correct me if I'm wrong, but I think this is probably not true. In fact, I assume that given a powerful enough telescope, we would be able to see through the Andromeda Galaxy to what is behind it. I think that we are unable to see through it because of a problem like glare, for the same reason that you can't see a person's face when they are standing in front of the sun. The eyes (or camera) adapt to the strong glare.

Jens
2008-Nov-22, 08:19 AM
As to Olber's paradox. I'd say that in a non-expanding uniform universe infinite in size and age, then the sky would glow hot. It doesn't, so one or more of the conditions don't obtain.

No, you forgot the third condition. Infinite in size, infinite in age, and of uniform density.

agingjb
2008-Nov-22, 09:00 AM
The word "uniform" appears in my post, and in fact, although I did not spell it out, I regarded the word as applying even more generally than to density.

Jens
2008-Nov-22, 09:02 AM
The word "uniform" appears in my post, and in fact, although I did not spell it out, I regarded the word as applying more generally than to density.

Geez, I don't know I missed that. Apologies for the "correction". :doh:

agingjb
2008-Nov-22, 09:15 AM
Cheers and OK, and, as you say, the uniformity condition is worth emphasizing anyway.

Spaceman Spiff
2008-Nov-22, 02:36 PM
No, you forgot the third condition. Infinite in size, infinite in age, and of uniform density.

The uniformity in density need only apply as averaged over great distances. It needn't be imposed strictly.

The fact that stars tend to be found clumped up in galaxies just pushes the required lookout limit (the distance at which the disks of stars overlap over the entire sky), in the language of the "wall of starlight" argument, to greater distances. I've heard arguments either way concerning the effects of fractal distributions of stars on the "wall of starlight" -- don't know if that's been settled.

Spaceman Spiff
2008-Nov-22, 05:26 PM
This does not address the assumption as I quoted it. Using the example of the Milky Way, the matter blocking out the light from the Galactic center is not glowing as bright as the stars. Looking directly at our galaxies center, we would see a solid mass of stars, which according to theory should look as bright as the sun.

It doesn't. The matter blocking out the light also is not glowing as bright as the stars. So the Milky Way looks dark.

The Andromeda galaxy is another example. Looking at the center of that galaxy, we see a solid mass of stars, because of the density there. According to theory, it should look as bright as the sun.

Or, if light is being blocked by matter between us and the galaxy core, it should be glowing as bright as the starlight it is absorbing. It isn't.

Somewhere in all the theory, reality shows up. If a nearby galaxy, or our own galaxy, does not look bright, it is obvious that objects very far away are not going to. No matter how many stars and galaxies there are.

To make it very simple, forget about the entire sky, the entire Universe.

Why doesn't the center of the Milky Way look as bright as the sun? If it is because of matter blocking the light, why doesn't it glow? After billions and billions of years of absorbing radiation?

No matter what the answer is, reality still shows that a solid mass of stars will not appear as bright as the sun. It has nothing to do with an expanding Universe, or redshift, or anything else that cosmic. Because both our galaxy, as well as Andromeda, are not moving away from us. There is no expanding space-time on that relationship.

So why doesn't our galaxy, where the density of stars is great enough to appear as a solid wall of starlight, appear to be bright?

There appear to be two issues of concern here.

1) You have a problem with the oft quoted statement concerning the presence of dusty gas clouds as not being a solution to Olbers' paradox.

I agree that this argument is less than useful, and can be a cause of confusion. You are correct that as long as the energy density of starlight is tiny, dusty gas clouds remain "cold" to the human eye (emit at ~100 microns in the IR). But stars are not completely encased in dusty cocoons emitting at ~100 microns. Most of the luminous energy of a star escapes without warming up some dusty gas cloud. So invoking dust under these conditions just means that the required lookout limit (that distance at which the integrated starlight reaches the conditions stated in the paradox) must be larger than it otherwise would be in the absence of the dusty gas clouds.

But if the phenomenon of stars is old enough and the universe filled with these stars is large enough to include the required lookout limit, the high radiation energy density conditions of Olbers' paradox will be met. In which case the temperatures of these dusty gas clouds would be raised to the temperature of the incident radiation field (the argument put forth). Dust does not exist under those conditions -- and if it did, it would radiate at the temperature of the ambient radiation field. One way or the other, total energy is conserved. That's really all that the dusty gas cloud argument was saying.

The fact that stars and dusty gas clouds exist is an observation that the universe is no longer radiation dominated, with its matter and light in thermodynamic equilibrium. The sky is dark. These were not considerations of those who first pondered Olbers' paradox.

2) You don't seem to understand how the flux of light sources grows without limit for the standard, if over-simplified, case of uniform number density of stars.

The point here is that each volume element 4*pi*r^2*dr contains a greater number of stars that exactly cancels the 1/r^2 dilution of flux. Here is how:

The total power emitted by a shell of stars: L_star * N(stars per shell). Consider all stars have luminosity (or some average luminosity) L_star = L.

dL(r) = L * dN(r); the total luminosity element for the shell located between distances r and r+dr.

dN(r) = 4*pi*r^2*n(r)*dr, the number of stars contained within the shell dr where,

n(r) = the number density of stars (number of stars per unit volume).

The observed flux of luminous energy from shell:
df(r) = dL(r)/(4*pi*r^2); it is diluted with inverse distance squared.

For the simple case of uniform number density of stars, n(r) = n, then the integrated flux is:

f = Integral{df(r)} = n * L * r{evaluated from finite distance to some arbitrary great distance r).

So the integrated flux grows without limit with increasing r. The lookout limit, as mentioned above, can then be shown to be:

r_lookout = (1/n) * 1/(cross sectional area of a star). And at that limit the incident flux is similar to that found at the surface of a typical star.

I am not defending the arguments put forth or underlying assumptions made by those who posited Olbers' paradox, I am just explaining them.

I hope that was helpful.

Gigabyte
2008-Nov-22, 05:33 PM
I'm a practical sort of scientist. It is obvious that dust and gas and who knows what else blocks much of the light from distant stars. And that the starlight doesn't cause the matter blocking the light to shine as bright as the stars.

The Andromeda galaxy is a simple example of an object that should look as bright as the sun, where the center is almost completely glowing stars, and hot gases, which is also blueshifted, moving towards us. (No loss from redshift)

No part of the galaxy appears very bright, much less as bright as the sun. If a nearby (relatively speaking) mass of stars don't appear bright, why would the rest of the very distant objects appear bright?

The center of our own galaxy is even more to the point. The explanation that obscuring gas and dust would soon glow as bright as the stars the block out, is simply not true.

Unless "soon" means after 10 or 12 billion years.

Spaceman Spiff
2008-Nov-22, 05:48 PM
I'm a practical sort of scientist. It is obvious that dust and gas and who knows what else blocks much of the light from distant stars. And that the starlight doesn't cause the matter blocking the light to shine as bright as the stars.

The Andromeda galaxy is a simple example of an object that should look as bright as the sun, where the center is almost completely glowing stars, and hot gases, which is also blueshifted, moving towards us. (No loss from redshift)

No part of the galaxy appears very bright, much less as bright as the sun. If a nearby (relatively speaking) mass of stars don't appear bright, why would the rest of the very distant objects appear bright?

The center of our own galaxy is even more to the point. The explanation that obscuring gas and dust would soon glow as bright as the stars the block out, is simply not true.

Unless "soon" means after 10 or 12 billion years.

There are not enough stars to make the Andromeda galaxy bright or to make the gas clouds glow at the same temperatures and fluxes found at the surfaces of stars. This is the point I've been making and you've been missing. And as I've said, clumping stars into galaxies just pushes the required lookout limit to greater distances. One can then use galaxies as the luminous unit, instead of stars. So whether you knew it or not, your argument is simply that Olbers' paradox does not obtain because the energy density in radiation is FAR too low.

If you're a practical sort of scientist then presumably you can do some simple calculations involving some simple calculus to figure out the required number density of stars (and the required total number of stars out to our cosmic horizon) to bring the universe to the conditions of the paradox. Or since you're stuck on the bit on clumping stars within galaxies, determine the number density of stars within a galaxy necessary to bring the gas clouds to blackbody-like emissivities at temperatures similar to surface temps of stars.

Spaceman Spiff
2008-Nov-22, 05:50 PM
It is obvious that dust and gas and who knows what else blocks much of the light from distant stars.

That's not at all obvious. The Hubble Ultra Deep Field and our observations of quasars and high redshift galaxies are cases in point. Most of the obscuration from our point of view occurs within the disk of the MW.

agingjb
2008-Nov-22, 06:00 PM
I suspect that at the distance of the galactic centre the images of stars in a photograph, even using Hubble, are considerably larger than the actual stellar disks. In any case the stellar disks would not be, in general, contiguous. There just aren't enough stars.

(My estimate of 1014 for the area ratio was far too low; as pointed out, 1018 was much better, and it is of course area that matters for "sky filling".)

Spaceman Spiff
2008-Nov-22, 06:02 PM
I suspect that at the distance of the galactic centre the images of stars in a photograph, even using Hubble, are considerably larger than the actual stellar disks. In any case the stellar disks would not be, in general, contiguous. There just aren't enough stars.

(My estimate of 1014 for the area ratio was far too low; as pointed out, 1018 was much better, and it is of course area that matters for "sky filling".)

Your suspicions are correct.

Gigabyte
2008-Nov-23, 12:01 AM
There are not enough stars to make the Andromeda galaxy bright or to make the gas clouds glow at the same temperatures and fluxes found at the surfaces of stars.

I can't help but think you have never looked through a telescope at the Andromeda galaxy.

Going outside and actually observing the heavens, my point will be obvious. Sitting inside and running it around in your mind, it may never be.

Both our Galaxy, as well as Andromeda, both have a center cluster of stars, packed so tightly it looks almost like a solid ball of stars. We know this from photographs or telescopes, to the naked eye you can hardly tell.

But what is obvious, by simply observation, is that the starlight isn't anywhere close to the brightness of the sun. Nor is the matter obscuring the light glowing brightly. Even though it has been blocking the light for billions of years.

Which is the simple point.

A claim was made, that dust and gas can't be obscuring the light of the stars, or soon the dust and glass would glow as brightly as the stars. This is obviously not true.

There is no way to explain this, it is one of those things you have to actually go and look at to understand. The central core of Andromeda, (which looks like a solid mass of stars and glowing gas when observed through a telescope), is very dim. It is far dimmer than the full moon.

No part of that mass of stars is very bright. You can look at it through a telescope, where you see nothing but stars, and it won't even make you blink. It doesn't hurt the eyes, to stare at billions of stars.

Something is blocking most of the light. And that something isn't glowing as bright as the stars it is blocking.

Gigabyte
2008-Nov-23, 12:04 AM
http://www.astronet.ru/db/xware/msg/1219021

That may help those who can't go and look. See how big the central core of Andromeda is? If you look at that, even with a small scope, you will understand what I am saying.

Or this photo
http://www.astronet.ru/db/xware/msg/1210528/m31_gendler_Nmosaic1.jpg.html

Look at the center of it.

cjameshuff
2008-Nov-23, 12:25 AM
That may help those who can't go and look. See how big the central core of Andromeda is? If you look at that, even with a small scope, you will understand what I am saying.

What you're missing is that every pixel of that image contains many stars and a good deal of black sky behind Andromeda. It looks solid because you can't resolve the stars, not because their discs overlap, and dim because in addition to dust along the line of sight, it isn't entirely stellar disc. And dust and gas between us and that "wall of stars" is not surrounded by that wall of stars, so of course its equilibrium temperature is lower.

In an infinitely old, infinitely large, non-expanding universe, the whole sky would be that wall of stars. Dust and gas would thus be at equilibrium with those stars, there being no areas of sky to radiate to that don't radiate back just as much, and the stars themselves would be hotter.

Spaceman Spiff
2008-Nov-23, 12:50 AM
What you're missing is that every pixel of that image contains many stars and a good deal of black sky behind Andromeda. It looks solid because you can't resolve the stars, not because their discs overlap, and dim because in addition to dust along the line of sight, it isn't entirely stellar disc. And dust and gas between us and that "wall of stars" is not surrounded by that wall of stars, so of course its equilibrium temperature is lower.

In an infinitely old, infinitely large, non-expanding universe, the whole sky would be that wall of stars. Dust and gas would thus be at equilibrium with those stars, there being no areas of sky to radiate to that don't radiate back just as much, and the stars themselves would be hotter.

Well said. Thanks for going to bat!

StupendousMan
2008-Nov-23, 12:50 AM
http://www.astronet.ru/db/xware/msg/1219021

That may help those who can't go and look. See how big the central core of Andromeda is? If you look at that, even with a small scope, you will understand what I am saying.

Or this photo
http://www.astronet.ru/db/xware/msg/1210528/m31_gendler_Nmosaic1.jpg.html

Look at the center of it.

Looking at a picture is one thing. Performing quantitative estimates to back up your statements is another thing. Permit me to use this second method, which is the one preferred by scientists.

You claim that the bulge of M31 presents a solid wall of stars, so that no matter where we look in the direction of the bulge, we ought to strike the photosphere of a star. I disagree.


Let R = 1.0 x 10^(9) m be the radius of a star

Then the cross-section area of that star is



A = pi*R^2 = 3.1 x 10^(18) m^2


Now, move the star so that it is at a distance D from you.
If D >> R, then the solid angle subtended by the star will be
approximately



A pi R^2 pi ( R )2
S = ------- = -------- = ---- (---) steradians
D^2 D^2 1 ( D )


Let's make the distance D = 780 kpc = 2.4 x 10^(22) m,
which is the distance to the Andromeda Galaxy. After a little
computing, we find the solid angle subtended by the star
at that distance is



S(star) = 5.5 x 10^(-27) steradians


Okay. Next, let's ask -- how large is the solid angle
subtended by the Andromeda Galaxy? Let's pick the bulge only,
which has a apparent angular radius of about 7 arcminutes
(I just measured it from the POSS I E plate),
or about 0.0041 radians. That means that the solid angle
subtended by the bulge of the Andromeda Galaxy is about



S(bulge) = pi (0.0041 radians)^2

= 5.3 x 10^(-5) steradians


Right. So, if we took a bunch of stars and placed them carefully
throughout the bulge of the Andromeda Galaxy, so that none of them
overlapped another from our point of view, how many stars would it
take to fill the bulge with stars? In other words, how many stars
would the Andromeda Galaxy's bulge need in order to present the
appearance of a solid wall of stars, with no gaps in between any
of them?



S(bulge) 5.3 x 10^(-5) steradians
N = ------------- = ------------------------
S(star) 5.5 x 10^(-27) steradians

= 9.6 x 10^(21) stars



How many stars does the bulge of the Andromeda Galaxy actually
contain? Well, the mass of the entire Andromeda Galaxy is around
2 x 10^(12) solar masses; see, for example, recent estimates in

http://adsabs.harvard.edu/abs/2008MNRAS.384.1459L
http://adsabs.harvard.edu/abs/2008ApJ...678..187V


If we assume that the typical star is 0.1 solar masses,
and put the entire mass of the Andromeda Galaxy into its bulge,
we end up with an overestimate of



N (actually in bulge of M31) < 2 x 10^(13) stars


The result is that there are too few stars in the bulge of
the Andromeda Galaxy to form a "wall of stars." The great majority
of the lines of sight running from the Earth to the Andromeda
Galaxy will fly right through the bulge without touching the
photosphere of a star. In fact, only about 1 in every billion
lines of sight will touch a star.

Your claims to resolve Olber's Paradox are incorrect. Spaceman Spiff has been trying to explain this to you for quite a while, but you don't seem to be listening to him. Perhaps you'll listen to some numbers.

If you wish to continue with your claims, back them up with some numbers of your own. When you make bold statements about the collective ignorance of generations of astronomers, you really ought to justify them.

George
2008-Nov-23, 01:43 AM
http://www.astronet.ru/db/xware/msg/1219021

That may help those who can't go and look. See how big the central core of Andromeda is? If you look at that, even with a small scope, you will understand what I am saying.

Or this photo
http://www.astronet.ru/db/xware/msg/1210528/m31_gendler_Nmosaic1.jpg.html

Look at the center of it.
Those are time lapse images, right? If the core were solid with stars then it would be like looking at a small area of the Sun's disk. Such a surface brightness would wash-out the rest of the image. The dust will absorb a fair amount of the light but even the dust will glow just as hot if the entire sky was glowing as hot as the Sun.

Spaceman Spiff
2008-Nov-23, 02:41 AM
After my interactions with agingjb, that's (http://www.bautforum.com/astronomy/80909-olbers-paradox-4.html#post1371598) exactly the argument I was going to post next. Stupendous Man beat me to it, and did an excellent job. I'll pile on with the tidbit that M31 probably contains ~10^12 stars (and some fraction of that lies in the bulge), according to some work done by Spitzer.

And for the record, I have looked at M31 through a telescope, binoculars, and with my unaided eye in a dark sky.

And George also makes an important point. For the sake of argument, if the bulge of M31 actually spanned a half a degree in the sky, and if it were the "wall of stars" as claimed, it would be roughly equivalent to our Sun(!) in the night sky. Now paste ~185,000 such sections over the entire sky (around the earth), and we're cooked (equivalently we're sitting at the surface of our Sun).

But the important point I've been trying to get across is that stars and gas clouds do not form or exist under these conditions. So THIS fact and that the cosmic background radiation is the fossil record of such a radiation filled universe of the distant past (now thankfully diluted in energy density by expansion) are the useful contributions of Olbers' paradox.

Most of the rest is noise generated by earlier thinkers who did not have enough data or physical understanding.

Jens
2008-Nov-23, 03:20 AM
There is no way to explain this, it is one of those things you have to actually go and look at to understand. The central core of Andromeda, (which looks like a solid mass of stars and glowing gas when observed through a telescope), is very dim. It is far dimmer than the full moon.


The problem isn't the observation. Many of us have looked at M31 through a telescope. I used to have a poster of it on my ceiling when I was in high school. And there is no doubt that it looks like the core is solid. But it isn't. It just looks that way. As an analogy, you must have had the experience of seeing a fence faraway, and not being able to see through it, but then getting closer and realizing that there are holes in it that you can see through. I have a pair of eyeglasses at home that are made for training, and there are tiny holes in the black lenses. It looks perfectly solid from faraway, but when you put them on you can actually see. So repeating myself, if you had a good enough telescope, you would be able to see through the disk of M31.

Jens
2008-Nov-23, 03:21 AM
In an infinitely old, infinitely large, non-expanding universe, the whole sky would be that wall of stars.

This time, I read it carefully, and can make the correction. You have to add "uniform" universe.

cjameshuff
2008-Nov-23, 03:33 AM
This time, I read it carefully, and can make the correction. You have to add "uniform" universe.

Yes...not all non-uniform universes will be different, but some of them could be. I originally also had something in there about a hypothetical galaxy with enough stars that every light path through it hit one, the "wall of stars" that I mentioned...trimmed the post a little too aggressively.

George
2008-Nov-23, 05:24 AM
It looks perfectly solid from faraway, but when you put them on you can actually see. So repeating myself, if you had a good enough telescope, you would be able to see through the disk of M31. Yes. And if we consider how many stars would have to exist just within the central bulge of about 1250 lyrs. radius, it becomes even more obvious. More than a billion Milky Way galaxies would have to be poured into the central bulge to fill the cross sectional view.

Gigabyte
2008-Nov-23, 04:56 PM
What you're missing is that every pixel of that image contains many stars and a good deal of black sky behind Andromeda. It looks solid because you can't resolve the stars, not because their discs overlap ...

I have considered this (and all the other responses) and did some research, and I think you are correct. In fact I am positive you are correct, based on photos of the galactic center, both Andromeda and our own Galaxy core. With a powerful scope you can zoom in and with high enough resolution there is indeed mostly empty space between the stars.
See this photo (http://www.eso.org/gallery/d/3125-1/phot-23a-02.jpg) of the center of the Milky Way

Even in the very center of the galaxy, it is mostly *empty* space, not a solid mass of stars.

If it wasn't for all the dust and gas we could see through the center of a galaxy. There are a multitude of other issues in that case, but it seems to me (and I could be wrong about this as well), that stars are so far away they just look like a point, no matter how much we zoom in with a telescope, we can't resolve anything more than a point of light.

Another way of understanding this (and correct me if I am wrong), is that if we took all the stars in Andromeda and put them so they all did overlap, making a solid wall of stars, it would look like a point of light, due to the extreme distance.

Same for our Milky Way. If we put all the stars together, overlapping them, it would still look like a point of light, though much brighter than any one star, it would still be just a very small point.

Does that make sense? Is that correct?

StupendousMan
2008-Nov-23, 05:44 PM
I have considered this (and all the other responses) and did some research, and I think you are correct. ...

Thanks for doing the extra research and the considering.



Even in the very center of the galaxy, it is mostly *empty* space, not a solid mass of stars.

...

Another way of understanding this (and correct me if I am wrong), is that if we took all the stars in Andromeda and put them so they all did overlap, making a solid wall of stars, it would look like a point of light, due to the extreme distance.

Same for our Milky Way. If we put all the stars together, overlapping them, it would still look like a point of light, though much brighter than any one star, it would still be just a very small point.

Does that make sense? Is that correct?

Well, if we could arrange all the stars of Andromeda so that they did overlap,
then they could cover a solid angle which is about (using the numbers from
my previous post) very roughly one-billionth of the entire solid angle of the
bulge of Andromeda. Let's see ... the angular radius of the bulge is about
7 arcminutes, so an object which subtended one-billionth of that solid angle
would be about sqrt(one-billionth) of that radius; that's about 0.00022 arcminutes,
or about 0.013 arcseconds. With current optical and IR telescopes, an object
of that size would indeed look like a point source, unresolved. If the stars
emitted significantly in the radio (which ordinary stars do not), then some of
our radio interferometers _could_ resolve such a solid wall.

For the Milky Way, let's just move Andromeda's bulge to the position of
the Milky Way's bulge -- not correct, but close enough for these purposes.
Since M31 is at about 780 kpc, and the MW's center at about 8 kpc,
that means that the angular size of the "wall of stars" would grow by
a factor of (780/8) = 97. Thus, the wall of stars would appear about
(97 * 0.013) = 1.3 arcseconds in radius. This certainly could be resolved
by current ground-based optical and IR telescopes at good sites, though
not with any great detail.

Spaceman Spiff
2008-Nov-23, 07:23 PM
I have considered this (and all the other responses) and did some research, and I think you are correct. In fact I am positive you are correct, based on photos of the galactic center, both Andromeda and our own Galaxy core. With a powerful scope you can zoom in and with high enough resolution there is indeed mostly empty space between the stars.
See this photo (http://www.eso.org/gallery/d/3125-1/phot-23a-02.jpg) of the center of the Milky Way

Even in the very center of the galaxy, it is mostly *empty* space, not a solid mass of stars.

If it wasn't for all the dust and gas we could see through the center of a galaxy. There are a multitude of other issues in that case, but it seems to me (and I could be wrong about this as well), that stars are so far away they just look like a point, no matter how much we zoom in with a telescope, we can't resolve anything more than a point of light.

Another way of understanding this (and correct me if I am wrong), is that if we took all the stars in Andromeda and put them so they all did overlap, making a solid wall of stars, it would look like a point of light, due to the extreme distance.

Same for our Milky Way. If we put all the stars together, overlapping them, it would still look like a point of light, though much brighter than any one star, it would still be just a very small point.

Does that make sense? Is that correct?

Yes, thanks for your efforts to consider the information presented to you and come to a new understanding. Let me provide some visual examples that help to illustrated the vast amounts of empty space within galaxies.

Have a look at these two (1 (http://www.seds.org/MESSIER/Jpg/m104.jpg), 2 (http://antwrp.gsfc.nasa.gov/apod/ap060115.html)) images of the same object, M104 (the 'Sombrero' Galaxy), the first from a ground based telescope of modest angular resolution and recorded photographically, the other from the HST ACS which produced an image near the intrinsic diffraction limited angular resolution of the telescope. Note the appearance of a "wall of stars" within the large central bulge in the first, which disappears in the second (which still does not resolve the disks of individual stars within the bulge -- not even close). An infrared image (http://antwrp.gsfc.nasa.gov/apod/ap070121.html) by the Spitzer Space Telescope and an alternative processing (http://antwrp.gsfc.nasa.gov/apod/ap080308.html) of the HST image also show the transparency of sight lines through the bulge.

Grand_Marquis
2008-Nov-25, 03:01 AM
While this is all very interesting, and indeed some of it is pretty enlightening regarding unrelated topics, I'm confused as to why it's being discussed so heatedly. Regardless of all other considerations and details about the universe and how it works, the simple fact that our universe is expanding should be sufficient to solve the paradox. Why all this other stuff?

Or is this some kind of thought experiment about what if the universe wasn't expanding? In which case, I must've missed the premise while I was reading through..

cjameshuff
2008-Nov-25, 03:21 AM
While this is all very interesting, and indeed some of it is pretty enlightening regarding unrelated topics, I'm confused as to why it's being discussed so heatedly. Regardless of all other considerations and details about the universe and how it works, the simple fact that our universe is expanding should be sufficient to solve the paradox. Why all this other stuff?

I'm scratching my head a bit as well. I've always seen Olber's paradox discussed as an item of evidence for an expanding universe, or at least one of finite age. Going into exhaustive detail about why there's no such paradox in the real world is missing the point...with some assumptions (infinite age and non-expanding universe, tricky fractal geometries aside), the paradox occurs, therefore there's an issue with those assumptions.

Gigabyte
2008-Nov-25, 03:28 AM
Actually, according to what we have been discussing, distance and space alone solves the paradox. There aren't enough stars, and they are too far away.

:D

Jens
2008-Nov-25, 04:11 AM
Or is this some kind of thought experiment about what if the universe wasn't expanding? In which case, I must've missed the premise while I was reading through..

In a sense, yes, at least for me. Or rather, to argue against the notion that Olber's paradox is essentially evidence in favor of a non-infinite universe.


I'm scratching my head a bit as well. I've always seen Olber's paradox discussed as an item of evidence for an expanding universe, or at least one of finite age. Going into exhaustive detail about why there's no such paradox in the real world is missing the point...with some assumptions (infinite age and non-expanding universe, tricky fractal geometries aside), the paradox occurs, therefore there's an issue with those assumptions.

I think the problem I have here is that I don't see fractal geometries as "tricky". My understanding is that we see fractality at lower levels in the universe, so it really isn't a leap to imagine that the fractality goes up to higher levels as well.

Now clearly, there is good evidence in favor of the expanding universe, i.e. the Hubble redshift. So I wouldn't go as far as to argue that the universe is not expanding. But still I like to point out that Olber's paradox is not proof of expansion.

Ivan Viehoff
2008-Nov-25, 04:08 PM
Actually, according to what we have been discussing, distance and space alone solves the paradox. There aren't enough stars, and they are too far away.
I think this is an example of the difficulty we have with mathematical arguments involving the infinite, which often come out rather counter-intuitively.

What initially seemed unlikely to me was "every line of sight ends on a star". But the same argument above about the inverse square law demonstrates that it must.

We look into the sky, and most of the light comes from local stars. As you go further, the density of stars is very low. But of course the local galaxy, indeed the local cluster, is a local increase in density, and we need to ignore that. That makes the sky, aside the local stars, very dark indeed.

We can consider the possible sight-lines from our location as the surface of the unit ball. Consider the subset which are the directions to the stars. The former has the cardinality of the continuum, but the latter is a denumberably infinite set. A denumerably infinite set is null, ie, you can put a disk around each one, add up the area of all the disks, and get as small a number you like. Eg, if you order them (1, 2, 3....) and for star n give it a disk of area a*2^(-n), then if you add them that infinite series to get the total area of all the disks, it comes to a. We can choose a to be as small as we choose. This works even if the stars are uniformly distributed, eg, like the rational numbers distributed in the reals. Even though they are densely distributed int he reals, you can cover them with disks and still have space left over. Very counter-intuitive.

The question is, are the stars, as Robinson suggests, sufficiently lacking in density that their disks do not completely cover the sky. Does the angular area each covers diminish fast enough that their disks cover only a finite amount (less than 100%) of the sky? In principle they could be that lacking in density, but this contradicts the uniformly distributed assumption. The argument relating to consider "shells" of space around us, ie concentric spherical surfaces, each shell actually contains a quantity of stars increasing according to the square of distance. But the angular area taken up by the average star also decreases according to the square of distance. So each shell contains a constant quantity of angular area. So even though the actual density of stars outside our immediate neighbourhood is actually so low that the sky is essentially black to our eyes, even the sum of an infinite quantity of small but equal numbers is infinite.

Thus I convince myself that Olbers has actually proved that we cannot live in a universe of constant density but infinite extent and age.

grav
2008-Nov-25, 07:16 PM
Now clearly, there is good evidence in favor of the expanding universe, i.e. the Hubble redshift. So I wouldn't go as far as to argue that the universe is not expanding. But still I like to point out that Olber's paradox is not proof of expansion.Actually, now that you've mentioned it, it is precisely the redshift itself that solves Olber's paradox. It provides the correct intensity and temperature of the CMB, exactly as we observe it. So the real issue now just becomes "what causes the redshift?" There are only two possibilities that I can think of at the moment; tired light and an expanding universe. So that now eliminates the possibilities of the age and size of the universe alone (without expansion), the burn time of stars, the geometry of a fractal universe (sorry), etc.

Spaceman Spiff
2008-Nov-25, 08:34 PM
I'll quote myself (http://www.bautforum.com/astronomy/80909-olbers-paradox-4.html#post1371694):


But the important point I've been trying to get across is that stars and gas clouds do not form or exist under these conditions. So THIS fact and that the cosmic background radiation is the fossil record of such a radiation filled universe of the distant past (now thankfully diluted in energy density by expansion) are the useful contributions of Olbers' paradox.

Most of the rest is noise generated by earlier thinkers who did not have enough data or physical understanding.

gsgs
2009-Feb-08, 08:55 AM
assuming all stars were as bright as the sun, would a reall "wall of stars" (no gaps) always appear
as bright as {the sun when seen from short distance} ?

the moon appears as big as the sun, still less bright.

gsgs
2009-Feb-08, 12:47 PM
OK, I found:

---------------------------
After all, if you move the Sun twice as far away from us, we will intercept one quarter as many photons, but the Sun will subtend one quarter of the angular area. So the areal intensity remains constant. With infinitely many stars, every angular element of the sky should have a star, and the entire heavens should be as bright as the sun. We should have the impression that we live in the center of a hollow black body whose temperature is about 6000 degrees Celsius.

But the number of stars, finite as it might be, is still large enough to light up the entire sky, i.e., the total amount of luminous matter in the Universe is too large to allow this escape. The number of stars is close enough to infinite for the purpose of lighting up the sky
----------------------------
http://math.ucr.edu/home/baez/physics/Relativity/GR/olbers.html

....

which was a bit surprising to me after reading this thread.



would the light which we receive be sufficient to light up the sky if
the Universe were not expanding, so distant stars were not red-shifted into obscurity ?

If not, how much more density would be needed to fulfil this ?
If yes, what fraction of density would be sufficient to achieve this ?

Spaceman Spiff
2009-Feb-08, 05:12 PM
OK, I found:

---------------------------
After all, if you move the Sun twice as far away from us, we will intercept one quarter as many photons, but the Sun will subtend one quarter of the angular area. So the areal intensity remains constant. With infinitely many stars, every angular element of the sky should have a star, and the entire heavens should be as bright as the sun. We should have the impression that we live in the center of a hollow black body whose temperature is about 6000 degrees Celsius.

But the number of stars, finite as it might be, is still large enough to light up the entire sky, i.e., the total amount of luminous matter in the Universe is too large to allow this escape. The number of stars is close enough to infinite for the purpose of lighting up the sky
----------------------------
http://math.ucr.edu/home/baez/physics/Relativity/GR/olbers.html

....

which was a bit surprising to me after reading this thread.



would the light which we receive be sufficient to light up the sky if
the Universe were not expanding, so distant stars were not red-shifted into obscurity ?

If not, how much more density would be needed to fulfil this ?
If yes, what fraction of density would be sufficient to achieve this ?

What John Baez states above is true (within the context of the paradox as it was posed), and that argument has already been made in this thread (go here (http://www.bautforum.com/astronomy/80909-olbers-paradox-4.html#post1371353) and here (http://www.bautforum.com/astronomy/80909-olbers-paradox-4.html#post1371694), and the posts between). You don't need an infinite universe with infinite stars to meet the conditions of a sky ablaze with the light of a star's surface. However, the above arguments are "true" only if the condition holds that we actually observe stars all the way out to the required lookout limit (or anywhere near it -- since it does not matter much if the sky glows at 1000K or 6000K as far as we're concerned). The required lookout limit is that which results in adding up enough starlight to create a radiation field equivalent to that of a blackbody at some temperature, usually taken to be 6000K (as our Sun's surface).

The point is we don't observe stars out to this required lookout limit -- not even close. This is quite apparently true whether or not stars are clumped into galaxies or galaxies into the large scale structure (which isn't fractal in any case), or whether or not the universe is expanding (which acts to reduce what little energy density there is in starlight). The finite age of the phenomenon known as "stars", the finite speed of light in a universe whose matter density and energy density in radiation are (presently) insignificant together guarantee a dark sky.

If you follow the arguments of the links I gave above, you can compute for yourself that you need something like {10^42 / n^2} stars (with average radii and luminosities matching those of our Sun) in the observable universe, with n = the average number of stars per cubic light year, and a required lookout limit of (6x10^13 / n) ly. If we lived in a static universe in which stars had been around for only 10^10 years, this reduces the required lookout limit to 10^10 ly, which then requires n = 5700 stars per cubic light year (on average), and thus something like 2e34 observable stars out to 10^10 ly. This is too large by a factor of ~10^12 or so.

However, all of these arguments are moot, as far as starlight is concerned. And that's because stars (and dusty gas clouds and astronomers on planets asking questions such as this) thermodynamically cannot exist in a radiation dominated universe -- the one that gives us a sky as bright as the surface of a star (or anywhere near that), as I stated above (http://www.bautforum.com/astronomy/80909-olbers-paradox-4.html#post1373586).

The universe was once in a radiation dominated state, up to some 70,000 years after the big bang, this radiation being left over (in net) from matter-anti-matter annhilation during the first ~1s with a slight imbalance (1 part in 10^8) in favor of matter, and the energy density temperature was about 10,000 K (as that of the surface of the star Sirius) at that time. Expansion has since reduced the energy density of this relic radiation field to a present temperature of 2.725 K, the Planck spectrum of which peaks out near 2mm wavelengths. The sky does glow 'brightly' in all directions from this radiation.

The first stars did not and could not form until the temperature of this radiation field had fallen to some ~100 K and below, FAR below that of the stars' interior and surface temperatures. The universe has been matter dominated since ~70 kyr after the big bang, but the average matter density has been highly diluted (via expansion), just a fraction of this matter has collapsed to form stars, and just ~0.1% of the rest mass of this matter is ever converted into starlight.

gsgs
2009-Feb-08, 06:31 PM
thanks.

> But the number of stars, finite as it might be, is still large enough to light up the entire sky

> ...which then requires n = 5700 stars per cubic light year (on average), and thus something
> like 2e34 observable stars out to 10^10 ly. This is too large by a factor of ~10^12 or so.

> 7e22 stars in the known universe

is usually given. I found no other number.

so the number of stars as referrenced above is >2e34 and somehow means the
calculated number of stars in the "entire" universe as opposed to observable universe ?

Spaceman Spiff
2009-Feb-09, 03:24 AM
You're confused. I suggest reading the preceding posts.

10^22 - 10^23 stars is indeed the estimate of stars in the observable universe. All the rest of the number of stars I quoted above are those required to produce a sky as intense as the surface of the Sun.

This quote from Baez:

But the number of stars, finite as it might be, is still large enough to light up the entire sky...

was simply making the point that an infinite number of stars in an infinite universe is not necessary to produce the paradox (a blazingly bright sky).

ExpErdMann
2009-Feb-10, 04:56 PM
Actually, now that you've mentioned it, it is precisely the redshift itself that solves Olber's paradox. It provides the correct intensity and temperature of the CMB, exactly as we observe it. So the real issue now just becomes "what causes the redshift?" There are only two possibilities that I can think of at the moment; tired light and an expanding universe. So that now eliminates the possibilities of the age and size of the universe alone (without expansion), the burn time of stars, the geometry of a fractal universe (sorry), etc.
Right you are, grav. Tired light does solve Olbers' paradox for the infinite, ageless universe. The math is simple and is shown, for example, in this paper (http://redshift.vif.com/JournalFiles/Pre2001/V00N12PDF/V0N12ASS.pdf) by Andre Assis.

Spaceman Spiff
2009-Feb-10, 07:34 PM
Sorry man, but tired light is a tiresome (http://www.astro.ucla.edu/~wright/tiredlit.htm) subject for discussion in the ATM.:hand:
And no, this forum isn't the place to discuss the fine qualities of one's personal favorite version of tired light.

And yes, this lone genius has at long last (16 years ago) come up with the solution to all questions cosmic. :whistle:

Spaceman Spiff
2009-Feb-10, 07:44 PM
Actually, now that you've mentioned it, it is precisely the redshift itself that solves Olber's paradox. It provides the correct intensity and temperature of the CMB, exactly as we observe it. So the real issue now just becomes "what causes the redshift?" There are only two possibilities that I can think of at the moment; tired light and an expanding universe. So that now eliminates the possibilities of the age and size of the universe alone (without expansion), the burn time of stars, the geometry of a fractal universe (sorry), etc.

This is what I have been emphasizing all along. The sky is "bright" with a uniform glow of radiation. It's just that this light is not starlight (http://www.astro.ucla.edu/~wright/stars_vs_cmb.html), but light that is the echo of the big bang, redshifted in intensity and temperature to a 2.725K blackbody -- a single temperature blackbody to within 1-3 parts in 100,000. Except I would not say that it "solves" Olbers' paradox, but rather shows that there is no paradox, once you realize that the universe was once in a radiation dominated state, that this state no longer holds, and that this (virtually) homogeneous and isotropic radiation field has been redshifted by a factor of ~1000.

ExpErdMann
2009-Feb-10, 08:24 PM
Sorry man, but tired light is a tiresome (http://www.astro.ucla.edu/~wright/tiredlit.htm) subject for discussion in the ATM.:hand:
And no, this forum isn't the place to discuss the fine qualities of one's personal favorite version of tired light.

And yes, this lone genius has at long last (16 years ago) come up with the solution to all questions cosmic. :whistle:

Being rather selective, aren't we? This thread has a lot of discussion about the infinite universe and the ageless universe, but you're going to gripe about tired light? In any event, Ned Wright offers a useful starting point for studying tired light models, but he doesn't have the whole story on this. If we (a) rule out tired light models involving scattering of photons and (b) include time dilation in TL models, as discussed here (http://www.bautforum.com/space-astronomy-questions-answers/83462-tired-light-query.html), Wright is only left with the supposed cooling of the CMBR over time. That is a problem, but not one without possible solutions. And I'll be happy to let a moderator not you determine if this thread is one to discuss a specific TL model if and when I introduce one. Finally, what's with the gratuitous putdown on Assis? Doesn't look good on you.

Nereid
2009-Feb-10, 08:36 PM
Right you are, grav. Tired light does solve Olbers' paradox for the infinite, ageless universe. The math is simple and is shown, for example, in this paper (http://redshift.vif.com/JournalFiles/Pre2001/V00N12PDF/V0N12ASS.pdf) by Andre Assis.
If you'd like to present, and defend, the ATM ideas in this document, please start a new thread in the ATM section.

FWIW, while "the math" may be simple, if what's in that document is supposed to show that "[t]ired light [] solve[s] Olbers' paradox for the infinite, ageless universe", it fails, and I for one would welcome the opportunity to challenge your assertion to the contrary (in an appropriate thread in the ATM section, of course).

ExpErdMann
2009-Feb-10, 09:10 PM
If you'd like to present, and defend, the ATM ideas in this document, please start a new thread in the ATM section.

FWIW, while "the math" may be simple, if what's in that document is supposed to show that "[t]ired light [] solve[s] Olbers' paradox for the infinite, ageless universe", it fails, and I for one would welcome the opportunity to challenge your assertion to the contrary (in an appropriate thread in the ATM section, of course).

Perhaps you are taking issue with Assis' mechanism, whereby light is absorbed and then reemitted at lower energy. I also would not choose this TL mechanism. What I was really drawing attention to was Assis' equations 1-3, which show how the starlight received from the whole universe, even if infinite, attains a finite value with TL.

PetersCreek
2009-Feb-10, 09:11 PM
Being rather selective, aren't we? This thread has a lot of discussion about the infinite universe and the ageless universe, but you're going to gripe about tired light?

We are selective about the fora in which ATM theories are advanced. If you wish to advocate for tired light, do so in the ATM forum, in your own thread.

ExpErdMann
2009-Feb-10, 09:33 PM
As you wish, but at least be aware that tired light is not out of place in any discussion on Olbers' paradox. This is a thread where Edgar Allen Poe and Kelvin have been cited as contributors to the debate. To leave the static universe side out is, at the very least, to downplay its historical significance on this particular topic.

Spaceman Spiff
2009-Feb-10, 11:46 PM
As you wish, but at least be aware that tired light is not out of place in any discussion on Olbers' paradox. This is a thread where Edgar Allen Poe and Kelvin have been cited as contributors to the debate. To leave the static universe side out is, at the very least, to downplay its historical significance on this particular topic.

Their contributions were/are a matter of historical significance. They both shed some useful light on the "paradox" (the finite ages of stars and the finite speed of light from both, and an energy density argument from Lord Kelvin), albeit with missing pieces to the puzzle.

grav
2009-Feb-11, 12:47 AM
Thanks for the links, ExpErdMann and Spaceman Spiff. They should provide some interesting reading.

Spaceman Spiff
2009-Feb-12, 01:16 AM
Thanks for the links, ExpErdMann and Spaceman Spiff. They should provide some interesting reading.

Well, if you think that statements (from the paper (http://redshift.vif.com/JournalFiles/Pre2001/V00N12PDF/V0N12ASS.pdf) linked by ExpErdMann) such as:


In our model we assumed that galaxies are in thermal equilibrium with the 2.7 K cosmic background radiation. Althouth most photons emitted by ordinary galaxies originate at stellar surfaces which are not at 2.7 K, this is a reasonable assumption for two reasons.have any basis in reality (and his "reasons" that follow are groundless), then, yes, you'll enjoy the paper. Or maybe even if you don't think highly of such a statement, you may find that it brings on laughter.

It was not my purpose to introduce a "debate" here about that paper linked above in this thread on Olbers' paradox. However, readers of this thread should understand that making unsubstantiated, unphysical assumptions (and the paper is rife with them) does not a scientific paper make. Science isn't about making stuff up. This paper has never seen the light of day in any peer-reviewed journal, and unless we give up and head back to the dark ages, it never will.

ExpErdMann
2009-Feb-12, 02:50 PM
Since Assis has been slammed again, readers should also be aware of that he has an impressive publication record, in many languages, and in mostly mainstream journals:

http://www.ifi.unicamp.br/~assis/

Apeiron facilitates a wider degree of speculation on many physics and cosmology topics than the mainstream journals, which is why some of Assis' work appears there. As I noted just a few posts ago, I was mainly wanting to draw attention to the first paper of Assis' paper up until Eqn. 3. As far as I can discern there is nothing disputable in this part.

An interesting question is whether the same set of equations, or a slight variation of them, could also be used to describe the BBT scenario. The energy of starlight from distant galaxies is falling off exponentially and we cannot tell, by looking at that starlight alone, what is the cause of the redshift. It could be a Doppler shift, an expansion (scale factor) shift or, according to Assis and others, a tired light effect. Or even something else again. Some BBT theorists, such as Harrison, even hold that the energy lost from photons due to expansion is truly lost from the system, and that this need not pose a conservation of energy problem. In that case, I don't see why we couldn't use the same equations as used in an exponential decay or absorption model in the BBT case. Why should this not work for BBT?

Spaceman Spiff
2009-Feb-12, 04:10 PM
One's publication record does not shield one from making uninformed statements. Frankly, I am surprised at the level of presentation in the above linked paper (and that it is copyrighted by some individual), given the nature of his work in electromagnetism in circuits (btw a significant majority of which appear in conference proceedings, rather than in journals such as J.Phys (A,B,C,D..) or Physical Review).

Regarding energy conservation in general relativity. John Baez has written up a nice page (http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html) discussing this (warning -- some parts introduce some complex mathematics, but the written explanations are still good).

In a nutshell, nature is more subtle than one might think regarding this issue. Although I am not an expert in General Relativity, this is a reasonable summary of Baez' article:

According to General Relativity (GR): most generally the quantity known as the energy-momentum (a 4-vector) is conserved, not energy by itself. Since in GR there are no preferred coordinate frames, and energy is a frame-dependent concept, energy then isn't a well-defined concept in curved space-time, nor is whether it is conserved or not (similar problems arise with the concepts of space and time taken by themselves which make concepts such as "recession velocity" coordinate-dependent). In the limit that space-time becomes flat (at least locally so), then energy becomes a better-defined concept and can then be considered to be a (locally) conserved quantity. This was what Edward Harrison was saying (in simpler language without these details) btw in his book "Cosmology - The Science of the Universe", that ExpErdMann referred to.

Tying this back to the concept of redshift...the cosmological redshift is due to the fact that light was emitted in one space-time frame (there and then) and observed in another (here and now). Read this paper (http://arxiv.org/abs/0707.0380) for more details.

But we're digressing too far afield from the topic of the thread.

ExpErdMann
2009-Feb-12, 07:03 PM
From what I can tell, there are two schools of thought in BBT about this. One is the frame-switch explanation, which you support. The other is the 'stretching' effect. Examples of each type were mentioned in the thread I linked to above, here (http://www.bautforum.com/space-astronomy-questions-answers/83462-tired-light-query.html#post1412143). Nereid gave the opinion that since there is no way of distinguishing between these two possibilities, they were to be regarded as equivalent.

It might seem like a digression. It does lead to a different literature. But I don't see how it could not come into Olbers at some level.

Spaceman Spiff
2009-Feb-12, 07:53 PM
From what I can tell, there are two schools of thought in BBT about this. One is the frame-switch explanation, which you support. The other is the 'stretching' effect. Examples of each type were mentioned in the thread I linked to above, here (http://www.bautforum.com/space-astronomy-questions-answers/83462-tired-light-query.html#post1412143). Nereid gave the opinion that since there is no way of distinguishing between these two possibilities, they were to be regarded as equivalent.

It might seem like a digression. It does lead to a different literature. But I don't see how it could not come into Olbers at some level.

The "stretching" of light is an analogy, a way of communicating the complexities of how GR describes the behavior of nature (expanding space-time). So it depends on what one means by the "stretching of light"; the usual expanding balloon analogy falls on its face, here. It definitely IS NOT another mechanism or school of (informed) thought. This paper (http://arxiv.org/abs/0707.0380) does an excellent job of explaining all of this.

The cosmological redshift DOES affect the energy density of starlight as we measure it in the here and now, but it is not the whole ball of wax as far as Olbers' Paradox is concerned. This has nothing at all to do with the cosmic background radiation (CBR) -- one would never mistake starlight (http://www.astro.ucla.edu/%7Ewright/stars_vs_cmb.html) (or anything else in this anything but isothermal universe we presently live in), in whatever way it might be transformed along the way, for a single temperature blackbody to 1-3 parts per 100,000 in ALL directions. There are measurable distortions at this level (e.g., SZ effect(s) (http://en.wikipedia.org/wiki/Sunyaev-Zel%27dovich_effect), integrated Sachs-Wolfe effect (http://en.wikipedia.org/wiki/Sachs-Wolfe_effect) are the most important) due to "effects" that occurred to the spectrum post-decoupling of matter and light due to its interactions with the hot, low density halos of large galaxy cluster and with the gravitational potential wells of same. Both were theoretical predictions before their confirmations.

As has been said by myself and others here, the whole business of what to do with the starlight is a red herring. Stars and dusty gas clouds do not form and cannot exist (it's thermodynamics) in a universe set ablaze with an energy density of radiation of several 1000 K. Nevertheless, the sky is indeed uniformly 'lit up' by the CBR, but in our "here and now" slice of space-time the energy density of this radiation field has a temperature of just 2.725K due to the expansion of space-time.

If you've ideas deeply at odds with the above, then I suppose you'll need to discuss them over at ATM.

gsgs
2009-Feb-14, 08:46 AM
my conclusion is that probably the sci.phys FAQ is just wrong here
and there are not enough stars+density in our reasonably
assumed universe. (ignoring relativistic aspects).

how many years after the big bang would the sky have become dark
if we ignore relativistic aspects (yet expansion as presumed) ?

well, I could secretly do the math ... but I think it's useful
to be stated here and maybe searchable for later interested people

Nereid
2009-Feb-17, 03:05 PM
Since Assis has been slammed again, readers should also be aware of that he has an impressive publication record, in many languages, and in mostly mainstream journals:

http://www.ifi.unicamp.br/~assis/

Apeiron facilitates a wider degree of speculation on many physics and cosmology topics than the mainstream journals, which is why some of Assis' work appears there. As I noted just a few posts ago, I was mainly wanting to draw attention to the first paper of Assis' paper up until Eqn. 3. As far as I can discern there is nothing disputable in this part.

An interesting question is whether the same set of equations, or a slight variation of them, could also be used to describe the BBT scenario. The energy of starlight from distant galaxies is falling off exponentially and we cannot tell, by looking at that starlight alone, what is the cause of the redshift. It could be a Doppler shift, an expansion (scale factor) shift or, according to Assis and others, a tired light effect. Or even something else again. Some BBT theorists, such as Harrison, even hold that the energy lost from photons due to expansion is truly lost from the system, and that this need not pose a conservation of energy problem. In that case, I don't see why we couldn't use the same equations as used in an exponential decay or absorption model in the BBT case. Why should this not work for BBT?
As you know, I've somewhat of an interest in how the perceptions of what constitutes science - at least as far as astrophysics, astronomy, cosmology, and space science are concerned - differ between everyday scientists and proponents of ATM ideas (at least those who propose them in BAUT's ATM section).

And in another thread I thanked you for your posts (in that thread), as they indeed did help me a lot, in terms of realising that there is a significant difference, and something of its nature.

Your recent posts on Olbers' paradox, in this thread, read in conjunction with your posts in that other thread, have given me some insight into an aspect of this difference, wrt the nature of what constitutes 'ad hoc' explanations, and the role of consistency.

So, thanks again.

ExpErdMann
2009-Feb-17, 05:49 PM
You're welcome. I've sent you a PM on this, so as not to take the thread off topic.

Jens
2009-Feb-20, 09:50 AM
As has been said by myself and others here, the whole business of what to do with the starlight is a red herring.

My impression is this: Olber's paradox is posing certain problems for a non-expanding universe. And I think you're arguing that they are solved by the fact that the universe is expanding. You may just be arguing that Olber's paradox isn't something that we should bother thinking about. Is that true, or am I missing something?