I A new solution to Olbers' Paradox?

[John_RB]

I read in a popular science magazine in the UK that "recent" observations of the universe indicate that the number of galaxies in the the universe is actually so vast that Olbers paradox is still a paradox. The short article postulated that they had solved the paradox by proving that light from distant objects is absorbed by hydrogen gas clouds thus causing it to be dark at night. I thought that Olbers paradox was resolved long ago - is this not so?

 

[phinds]

I read in a popular science magazine in the UK that "recent" observations of the universe indicate that the number of galaxies in the the universe is actually so vast that Olbers paradox is still a paradox. The short article postulated that they had solved the paradox by proving that light from distant objects is absorbed by hydrogen gas clouds thus causing it to be dark at night.

That is NOT a solution, it's nonsense.

I thought that Olbers paradox was resolved long ago - is this not so?

Yes, it is so.

 

[Drakkith]

Olber's paradox has been resolved for a long time.

From wiki: https://en.wikipedia.org/wiki/Olbers's_paradox
Olber's paradox is: "the argument that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe.The darkness of the night sky is one of the pieces of evidence for a dynamic universe, such as the Big Bang model. If the universe is static, homogeneous at a large scale, and populated by an infinite number of stars, any sight line from Earth must end at the (very bright) surface of a star, so the night sky should be completely bright. This contradicts the observed darkness of the night."

Several things immediately solve this paradox.

The first is the known finite age of the universe as we know it. It means the universe is not eternal and light simply hasn't had time to travel from every point in the universe to us.

The second is that the expansion of the universe means that it is not static. Light from galaxies very far away is redshifted so much that we can't see any of it with our eyes. So even an eternal universe would not have a sky as bright as the surface of a star because most of our lines of sight would end on a heavily redshifted star and we wouldn't be able to see it.

In addition, stars themselves are dynamic. They are born, they shine for a while, and then they burn out and eventually stop glowing. I believe this conflicts with the "eternal" assumption since it would mean that even in a static, eternal universe, the universe should consist solely of dead stars and fundamental particles with no available energy for things like light and life. For there to be life and bright stars in such a universe, there would need to be some means of replenishing the energy tied up in these dead stars and preventing them from building up. But no such mechanism has ever been observed and any mechanism would violate a number of fundamental laws of physics.

The short article postulated that they had solved the paradox by proving that light from distant objects is absorbed by hydrogen gas clouds thus causing it to be dark at night.

I believe this would cause the hydrogen to glow, as the temperature eventually reaches a temperature equal to the surface of a star. But this isn't observed.

 

[Chalnoth]

I read in a popular science magazine in the UK that "recent" observations of the universe indicate that the number of galaxies in the the universe is actually so vast that Olbers paradox is still a paradox. The short article postulated that they had solved the paradox by proving that light from distant objects is absorbed by hydrogen gas clouds thus causing it to be dark at night. I thought that Olbers paradox was resolved long ago - is this not so?

Nope. Olber's paradox is solved by the expansion of space.

1. The expansion of space makes it so that the observable universe is finite in extent. Olber's paradox relies upon the number of visible stars being infinite, but if the extent of the observable universe is finite, then it that can't be.
2. The expansion causes far-away objects to be redshifted. If you have a star sitting at $z=1$, then the incoming photons from that star will be at half the temperature they are at the source. Even if the observable universe were infinite (which isn't possible with a finite age of the universe, or in an expanding universe), the far-away stars just wouldn't contribute meaningfully to the temperature at anyone location on the sky, because that temperature would have been reduced so far by the expansion.

 

[Rupert Roy]

This is incorrect: the metric expansion of the universe is only one( relatively minor) contributor to the resolution of Olbers' Paradox. In a static universe the night sky would be brighter by less than two magnitudes according to Wesson Ap. J. 367, 399, 1991). Conselice et al. (Ap. J. 830, 83C, 2016) contend that the finite age and size of
the universe, absorption in and near galaxies at high redshifts , and metric expansion together contribute to the resolution of Olbers' Paradox.

 

[PeterDonis]

Wesson Ap. J. 367, 399, 1991). Conselice et al. (Ap. J. 830, 83C, 2016)

Are you referring to these papers?

https://ui.adsabs.harvard.edu/abs/1991ApJ...367..399W/abstract

https://iopscience.iop.org/article/10.3847/0004-637X/830/2/83

 

[PeterDonis]

the finite age

A static universe would not have a finite age. The reason the universe has a finite age is that it is not static: it began a finite time ago in a Big Bang and has been expanding ever since. So while mathematically it might be true that the finite age has much more of an impact on the observed light intensity of the night sky than expansion, it is still true that the two are connected and it does not make sense to consider a model that has the first but not the second.

and size

While there are of course static models with a finite size, such as the Einstein static universe, in addition to not having a finite age, as above, such models are also unstable. They won't stay static long enough to be reasonable contenders for a model of our universe with its observed age.

absorption in and near galaxies at high redshifts

Absorption won't help with Olbers' paradox because the light that is absorbed just gets re-emitted again. There is no such thing as an object that can absorb light indefinitely and not re-emit anything.

 

[phyzguy]

I read in a popular science magazine in the UK ...

I suggest you stop reading this magazine.

 

[Rupert Roy]

Are you referring to these papers?

https://ui.adsabs.harvard.edu/abs/1991ApJ...367..399W/abstract

https://iopscience.iop.org/article/10.3847/0004-637X/830/2/83

Yes

 

[Rupert Roy]

A static universe would not have a finite age. The reason the universe has a finite age is that it is not static: it began a finite time ago in a Big Bang and has been expanding ever since. So while mathematically it might be true that the finite age has much more of an impact on the observed light intensity of the night sky than expansion, it is still true that the two are connected and it does not make sense to consider a model that has the first but not the second.

Wesson used a de Sitter universe merely to demonstrate the relatively small contribution of redshift compared with the expanding universe's finite size and age. Of course both play a role in the resolution of Olbers Paradox. The post I originally responded to said Olbers' Paradox "...is solved by the expansion of space".

While there are of course static models with a finite size, such as the Einstein static universe, in addition to not having a finite age, as above, such models are also unstable. They won't stay static long enough to be reasonable contenders for a model of our universe with its observed age.

See above - it's not suggested our universe is static.

Absorption won't help with Olbers' paradox because the light that is absorbed just gets re-emitted again. There is no such thing as an object that can absorb light indefinitely and not re-emit anything.

The rest-frame UV continuum of galaxies ionizes the local hydrogen, which re-combines emitting longer wavelength Lyman-alpha and other redder hydrogen emission lines. For z>~5 these lines are in the near-infrared in our reference frame, and so the originating UV continuum photons don't contribute to our visible-light night sky background.

So, the the universe's finite age and size, redshift and absorption all play roles in the resolution of Olbers' Paradox.

 

[Jarvis323]

I suggest you stop reading this magazine.

The magazine was correct in this case though.

 

[Jarvis323]

@phinds read the paper.

https://iopscience.iop.org/article/10.3847/0004-637X/830/2/83

 

[phinds]

@phinds read the paper.

https://iopscience.iop.org/article/10.3847/0004-637X/830/2/83

I was/am going by what the OP said, which has been shown to be incorrect. If he misrepresented the article he was quoting that's a different story.

 

[Jarvis323]

I was/am going by what the OP said, which has been shown to be incorrect. If he misrepresented the article he was quoting that's a different story.

No, what the OP said was correct. Read the paper, which is what the OP's magazine was referring to.

 

[phinds]

No, what the OP said was correct. Read the paper, which is what the OP's magazine was referring to.

This

The short article postulated that they had solved the paradox by proving that light from distant objects is absorbed by hydrogen gas clouds thus causing it to be dark at night.

is not correct

 

[Jarvis323]

This

is not correct

It is not correct only in the use of the word "prove". The authors instead show that the other factors appear to be insufficient and absorption by hydrogen gas appears to also be needed to resolve the paradox.

 

[PeterDonis]

our visible-light night sky background

I don't think Olbers' paradox in its modern form (however Olbers might have originally phrased it) is limited to visible light wavelengths: our night sky is relatively "dark" across the spectrum, not just in visible light, and that fact should have an explanation.

 

[PeterDonis]

Wesson used a de Sitter universe merely to demonstrate the relatively small contribution of redshift compared with the expanding universe's finite size and age.

I don't see where Wesson is using a de Sitter model in his paper. All his "static" case appears to be is setting the scale factor $R(t)$ to be a constant in his equations but changing nothing else. He doesn't even appear to consider the question of whether this "static" case is an actual valid solution of the Einstein Field Equation, or if so, what the resulting metric is. (Perhaps that is done in one of the references he mentions; I have not tried to look at any of those.)

 

[Rupert Roy]

I don't think Olbers' paradox in its modern form (however Olbers might have originally phrased it) is limited to visible light wavelengths: our night sky is relatively "dark" across the spectrum, not just in visible light, and that fact should have an explanation.

Yes, true. In the case of galaxies it's finite age, and in the case of the CMB it's redshift.

 

[Hornbein]

I have long thought that if light had an infinitely large speed -- that is, traveled from point to point in zero time -- then we would see an all-light Olber's sky (disregarding red shift). Turning this around, given we have an infinite Universe, the fact we don't see an Olber's sky shows that the speed of light is finite.

Would zero time light also mean that at every moment our fair Earth would be exposed to infinite energy? No. The number of stars to which the Earth would be exposed, though very large, would be finite. These stars would shield the Earth from infinite amounts of radiation. (The expansion red shift helps too.) All and all the Universe would be a hotter place. All the energy now in transit from matter to matter would be heating up things instead. I wonder how much hotter things would be?

All in all, it seems to me that finite light speed is part of the resolution of the paradox.

 

[LastScattered1090]

The assumption that every sightline should terminate on a luminous object is indeed based on the premise of a static Universe of infinite age, not just infinite spatial extent. With non-static Universe of finite age, two things make this assumption untrue

• Finite age combined with finite speed of light creates a horizon (maximum distance out to which we can see). Just because there may be infinitely-many objects now doesn't mean that light from all of them has had time to reach us.
• Finite age and changing state with time (non-static Universe) means that discrete luminous objects haven't always existed in the first place, so even if you can look outward really far, there may be nothing to see at the time you're looking back to. (But this also depends on what we mean by "luminous": see below).

EDIT: I guess the second bullet point relies on the finiteness of the speed of light as well. If light propagated instantaneously, then this effect of "lookback time" would not be an issue -- we'd always see things as they are now.

Extending to all wavelengths, a facetious resolution to Olbers' Paradox that I sometimes like to trot out is that the sky is indeed bright everywhere, provided you can see microwaves (or far IR, or 21 cm or...) :)

But I think there's a danger in taking this resolution at face value and just concluding that Olbers was right (no paradox -- issue resolved!). Olbers was right that every sightline should terminate on matter that is "luminous" in some band, but he was not right about the reason. The reason is not that there have always been infinitely-many visible-light-emitting objects, and you can see all of them now. Both of those things are untrue. The actual reason is that if you look back far enough, you reach an epoch where there were no discrete objects, and instead all the matter (neutral gas or primordial plasma) was distributed nearly homogeneously (initially down to 1 part in 10^5). I think this explanation falls under the second "state change" bullet point above, and is an example of the continuous state change eventually making the "bright everywhere" assumption true again, albeit in a wavelength-dependent way.