Why Is the Night Sky Dark If the Universe Is Infinite?

[vincentm]

I'm having trouble wrapping my head around this, can someone explain this to me?

Thank you,

Vincent

 

[DaveC426913]

I'm having trouble wrapping my head around this, can someone explain this to me?
Thank you,
Vincent

Read a book.

(What? You wanted a better answer? How about asking a better question. )

 

[Garth]

Read a book.

A little brusque maybe?

Vincent - Olber's paradox arose in the Newtonian universe, and still can be used to provide a constraint on speculative 'toy' cosmological models.

"Why is the sky dark at night?"

A seemingly naive question that has a profound answer.

If the universe were :
1. Infinite and
2. Infinitely old i.e. eternal and
3. Static (all three being true together) then the night sky should be burning bright!

The surface brightness of a star does not depend on distance, unless there is ISM absorption, the luminosity and the angular surface area both depend on $\frac{1}{r^2}$ so the surface brightness: luminosity/angular-surface-area is constant. Therefore wherever you look, if the three above conditions all hold, you will see the surface of a star, and that surface brightness will be that of the average star in the sky, similar to but a little less than that of our own Sun, so the whole sky would be almost as bright as the surface of the Sun! If you take the absorption of distant star light by ISM gas and dust into account that ISM will also eventually heat up to the average star surface temperature as the universe is infinitely old.

Before the expansion of the universe was discovered it was generally thought by astronomers, back to the ancient Greeks, that the universe was eternal.

Newton realized that in such a universe all the stars (galaxies today) would after some interval all coalesce together under their mutual gravitational attraction. As this had not happened the universe had to be inifinte as well, then any gravitational force would be canceled out by an opposite force.

Why then was the night sky dark?

The answer of course is although the universe may be infinite it is not infinitely old and so we cannot see further than our particle horizon, and the universe is not static, it is expanding thus red shifting the majority of the starlight.

I hope this helps, you can take the paradox further in curved space-time and closed universes when it provides a constraint on more modern models of the universe.

Garth

 

[DaveC426913]

A little brusque maybe?

It wasn't an admonishment, it was responding in kind to his query.

I hoped to elicit from him what he *did* know, and what was troubling him - to have him put some effort into learning, rather than being hand-fed the answers.

How you you know he even knows what Olber's Paradox is??

 

[vincentm]

Read a book.
(What? You wanted a better answer? How about asking a better question. )

Wow, thanks for being rude. For your information the book's section on this is a little hard to grasp, i was hoping for an explanation from here, if everyone was to follow this advice of yours then why would this site continue to exist? Remind me never to ask for your help, by the way thanks Garth!

 

[DaveC426913]

OK, I guess it came across as a little harsh. It wasn't intended to be harsh, so much as it was intended to be tutorial. My curt response was a not-so-subtle way of saying "I'll put as much effort into this as you do."

See, this forum has a policy of encouraging guidance - helping people through things, rather than doing the work for them. A very common phrase on this board is: "Show your work!"

If your question explained what you DO know about Olber's paradox and where it goes wrong for you, it would be far more likely to elicit all sorts of helpful responses.

Anyway, since Garth covered it fairly well, there's nothing for me to add.

 

[vincentm]

OK, I guess it came across as a little harsh. It wasn't intended to be harsh, so much as it was intended to be tutorial. My curt response was a not-so-subtle way of saying "I'll put as much effort into this as you do."
See, this forum has a policy of encouraging guidance - helping people through things, rather than doing the work for them. A very common phrase on this board is: "Show your work!"
If your question explained what you DO know about Olber's paradox and where it goes wrong for you, it would be far more likely to elicit all sorts of helpful responses.
Anyway, since Garth covered it fairly well, there's nothing for me to add.

Touche' i could have formulated my question better, my apologies as well.

Anyways the way its explained to me in the book I'm reading is an example of a spherical shell surrounding the earth, and as this shell grew in radius then the total luminosity of the stars would increase because more stars are incased in the "shell, but this isn't exactly true, right?

 

[Garth]

Anyways the way its explained to me in the book I'm reading is an example of a spherical shell surrounding the earth, and as this shell grew in radius then the total luminosity of the stars would increase because more stars are incased in the "shell, but this isn't exactly true, right?

That argument is just as valid and approaches the geometry from a different direction. Take any thin shell around the Earth containing typical stars. The luminosity of each star L ~ $\frac{1}{r^2}$ but the surface area of the shell, and hence the typical number of stars within it, A ~ $r^2$ so the total luminosity from each shell, of whatever radius r is the same. Now add each shell out to inifinity and no matter how small the luminosity from each shell is, the total diverges to infinity. It isn't exactly true because what hasn't been taken into account is the light that is blocked by stars in the foreground, which is why it is easier to do the calculation my first way round.

Garth

 

[Chronos]

I think it's a fair question, DaveC. Had you posed the question... we would have jumped all over you because you DO know better. But I think it's a very honest question coming from vincentm; and deserves a friendly answer. Dave is very knowledgeable about this stuff, so don't be too hard on him, vincentm. Less than honest questions appear here too often, and sometimes it is difficult to resist getting impatient. You are asking all the right questions vincentm.

 

[turbo]

Even in an infinite (spacially and temporally) universe, Olber's paradox is mooted by redshift. The more distant an object is, the more redshifted its light. Light from objects sufficiently distant from us will be redshifted into undetectibility.

 

[DaveC426913]

Even in an infinite (spacially and temporally) universe, Olber's paradox is mooted by redshift. The more distant an object is, the more redshifted its light. Light from objects sufficiently distant from us will be redshifted into undetectibility.

Good point, though I would replace the word 'mooted' with the word 'mitigated'. A starscape lit so would still be nigh-infinitely bright.

 

[matt.o]

Even in an infinite (spacially and temporally) universe, Olber's paradox is mooted by redshift. The more distant an object is, the more redshifted its light. Light from objects sufficiently distant from us will be redshifted into undetectibility.

That is why Garth specified a static universe.

 

[vincentm]

That is why Garth specified a static universe.

But doesn't a static universe say that it is not expanding?

 

[Garth]

But doesn't a static universe say that it is not expanding?

Yes -that is why it was a paradox to Olbers and the others back then, today with an expanding universe there is no paradox - the sky is dark at night!

garth

 

[vincentm]

Yes -that is why it was a paradox to Olbers and the others back then, today with an expanding universe there is no paradox - the sky is dark at night!
garth

Ok, stupid question time:

How does Olber's Paradox play into supporting evidence for the big bang?

 

[Garth]

Ok, stupid question time:
How does Olber's Paradox play into supporting evidence for the big bang?

Only in that as a Big Bang universe is not infinite AND eternal AND static it is not surprising that in such the sky is dark at night.

Note: This isn't very strong evidence for the BB, it would only be strong evidence for the opposite, i.e. If the sky was burning bright at night then we would know we were not in a BB universe. Of course in that case we wouldn't be here at all as it would be too hot!

Garth

 

[turbo]

Good point, though I would replace the word 'mooted' with the word 'mitigated'. A starscape lit so would still be nigh-infinitely bright.

Well, we already need to start delving into the infrared regions to see much of anything beyond what Hubble has shown us, and more distant objects will be redshifted still more.

 

[turbo]

That is why Garth specified a static universe.

True, but that's because most of us are under the assumption that redshift is caused by cosmological expansion. When Hubble and his team established the relationship between redshift and distance, he did not embrace this view. He was working within the confines of a steady-state model. Even in Hubble's steady-state model, Olbers paradox would be laid low by the distance/redshift relationship, even for a temporally and spacially infinite universe.

 

[Chronos]

True, but that's because most of us are under the assumption that redshift is caused by cosmological expansion. When Hubble and his team established the relationship between redshift and distance, he did not embrace this view. He was working within the confines of a steady-state model. Even in Hubble's steady-state model, Olbers paradox would be laid low by the distance/redshift relationship, even for a temporally and spacially infinite universe.

What metric do you have in mind that is more predictive than the FRW model?

 

[turbo]

What metric do you have in mind that is more predictive than the FRW model?

I am proposing no metric in that post, merely pointing out that if distant objects are more redshifted than closer objects, sufficiently distant objects will be redshifted out of obvservability, regardless of the mechanism responsible for the redshift, mooting Olber's Paradox.

 

[Chronos]

Agreed, you are not proposing a metric. But, it seems internally inconsistent to use the redshift <> distance without a metric.

 

[Chronos]

Not a stupid question

Ok, stupid question time:
How does Olber's Paradox play into supporting evidence for the big bang?

That is not a stupid question . . . . In fact it is one of the best questions you can ask. What it means, logically, is the universe cannot be both infinitely old and spacious at the same time.

 

[kmarinas86]

That is not a stupid question . . . . In fact it is one of the best questions you can ask. What it means, logically, is the universe cannot be both infinitely old and spacious at the same time.

(addendum) ...when the universe is homogenous and isotropic at the large scales.

If the universe is heterogenous at the large scales, then the basic appearance of 13 billion light years away might still exist today, just far away. Such a perspective might exist for a few Hundred Mpc around us, so it wouldn't defy the Copernican Principle completely - not any more than living somewhere else in Earth would affect the sunspots. But of course, we won't know until 13 billion years from now (if we stick with most recent paradigm that has lasted over half a century). Remember that many cosmological ideas are theories: the idea of a finite universe in time or space could be a very accurate fiction, so could the idea of a infinite universe/multiverse.

 

[Chronos]

I disagree that the universe need be static to validate Olber's paradox. In an infinitely old [and spacious] universe that contains an infinite number of stars, we should see an infinite number of photons bombarding us from every direction. Expansion is irrelevant since the photons have an infinite amount of time to reach us [btw, how does an infinite property of anything 'expand'?] Of course, if distant photons are somehow redshifted out of existence [violating the ever-popular laws of thermodynamics], new physics are required. Otherwise, the night sky should as bright as the surface of the sun.

 

[Garth]

I contest the claim the universe need be static. In an infinitely spacious, infinitely old universe that contains an infinite number of stars, we should see an infinite number of photons bombarding us from every direction. Unless those photons are somehow redshifted out of existence by new physics [i.e., replacing the ever popular laws of thermodynamics], The night sky should as bright as the surface of the sun.

But the sky would only be 'burning bright at night' if the universe were infinite & eternal & static.

If it were not static but expanding then the temperature of the sky would be attentuated by the red shift,

[itex]F \propto \frac{1}{(1 + z)^2}[/tex]<br /> <br /> there would be similar attentuations for a finite size, depending on the circumference, or a finite age, depending on the distance 'out' to either event horizon, or back to the epoch of 'first light'.<br /> <br /> As the universe is both cosmologically red shifted (however that is interpreted), and limited in both age, and (as it is thought) distance out to the particle horizon, the combined attentuations result in the very faint sky background luminosity (down to about mag 29 I believe). <br /> <br /> The CMB provides an example of one form of radiation (the whole sky) that was not covered by Olber's paradox, which has been attenuated from ~ 3000⁰K to ~ 3⁰K.<br /> <br /> Garth[/itex]

 

[sunblock]

Wouldn't it be more logical to say that the sky isn't dark at night. It looks dark to us because person nature evolved us with eyes that detected the highest level possible without looking directly at the sun and our eyes just arn't sensitive enough to see the avaliable light at night. If they were we would be blind in the daytime unless we had really thick sunglasses.

 

[Garth]

Wouldn't it be more logical to say that the sky isn't dark at night. It looks dark to us because person nature evolved us with eyes that detected the highest level possible without looking directly at the sun and our eyes just arn't sensitive enough to see the avaliable light at night. If they were we would be blind in the daytime unless we had really thick sunglasses.

You would need pretty big eyes to see mag 29!

Garth

 

[sunblock]

Miniature hubbles.

 

[Chronos]

But the sky would only be 'burning bright at night' if the universe were infinite & eternal & static.

If it were not static but expanding then the temperature of the sky would be attentuated by the red shift,

[itex]F \propto \frac{1}{(1 + z)^2}[/tex]<br /> <br /> there would be similar attentuations for a finite size, depending on the circumference, or a finite age, depending on the distance 'out' to either event horizon, or back to the epoch of 'first light'.<br /> <br /> As the universe is both cosmologically red shifted (however that is interpreted), and limited in both age, and (as it is thought) distance out to the particle horizon, the combined attentuations result in the very faint sky background luminosity (down to about mag 29 I believe). <br /> <br /> The CMB provides an example of one form of radiation (the whole sky) that was not covered by Olber's paradox, which has been attenuated from ~ 3000⁰K to ~ 3⁰K.<br /> <br /> Garth[/itex]

$I don't entirely disagree, just wonder what number you derive assuming an upper limit of z = 1100?$

 

[Garth]

I don't entirely disagree, just wonder what number you derive assuming an upper limit of z = 1100?

Try 2.76⁰K .

Garth