Resolving Olbers' Paradox: Is That Quote Wrong?

[Martin_G]

I understand Olbers' Paradox and its resolution, however such phrases as this - "If the universe extends infinitely, then eventually if we look out into the night sky, we should be able to see a star in any direction, even if the star is really far away" - which can be found http://cmb.physics.wisc.edu/tutorial/olbers.html" and also in at least one textbook, strike me as plain wrong. Even if there are infinitely many stars, there is no reason to expect that any infinite line from a point would hit at least one of them. This seems intuitively obvious. Am I missing something, or is that quote just a bad way of formulating the paradox?

 

[Chronos]

Your interpretation is correct. In an infinitely old universe with an infinite number of stars, the night sky should be about as bright as the sun. That was Olber's point.

 

[russ_watters]

Actually, chronos, the OP said just the opposite...

Martin_G, you can construct a function that calculates the probability of a line of sight landing on a star based on the density of stars in the universe and length of the sight line (age of the universe). As the length of the sight line (age of the universe) grows, the probability rises toward the limit of 1.

 

[Phrak]

Even if there are infinitely many stars, there is no reason to expect that any infinite line from a point would hit at least one of them. This seems intuitively obvious. Am I missing something, or is that quote just a bad way of formulating the paradox?

You may think of it this way.

Assume stars are randomly distributed.

For any given point of observation, construct spherical shells out to infinity. Each spherical shell will block some small ratio of dark area, d along the radial direction to the point of the observer. d parts dark vs. (1-d) parts light.

You have to think in reverse, here, where we are blocking darkness instead of light. Each shell let's through (1-d) parts of the remaining darkness.

N shells let though (1-d)^N parts darkness.

How much darkness gets though as N goes to infinity?

Because the stars are randomly distributed, d is not constant. We may ignore those shells for which d is less than some given value, D. There are M shells for which d is over our critical value, D. But M also goes to infinity. So we get the same answer.

(1-d')^M → 0

d' is a finite random variable less than one and greater than D.

The upper bound of (1-d')^M is (1-D)^M. (1-D)^M = 0.

 

[unerkennbar]

as long as this thread remains polite, objective and focused
on the scientific argument of Olber's paradox, there should be no problems.

 

[navilon]

If the universe is infinite..we may then be able to view point A,,B,,C,,D,,etc,,at any given moment..like a picture that contains everything..it just depends on where we r statnding..

 

[Chronos]

Some papers to consider.

Inferences from the dark sky: Olbers' paradox revisited
http://arxiv.org/abs/astro-ph/0007428
The classical formulation of "Olbers' Paradox" consists in looking for an explanation of the fact that the sky at night is dark. We use the experimental datum of the nocturnal darkness in order to put constraints on a Newtonian cosmological model. We infer then that the Universe, in such a model, should have had an origin at a finite time in the past.

John Baes gives a brief, but, illuminating discussion here
http://math.ucr.edu/home/baez/physics/Relativity/GR/olbers.html

See also
http://cmb.physics.wisc.edu/tutorial/olbers.html
http://hyperphysics.phy-astr.gsu.edu/Hbase/Astro/olbers.html
http://en.wikipedia.org/wiki/Olbers'_paradox

The most important point, IMO, if infinitely old and populated, the universe should be in thermal equilibrium. This is not observed as noted here:

Molecular Hydrogen in a Damped Lyman-alpha System at z_abs=4.224
http://www.arxiv.org/abs/astro-ph/0602212
". . . The high excitation of neutral carbon in one of the components can be explained if the temperature of the Cosmic Microwave Background Radiation has the value expected at the absorber redshift, T=14.2 K. "

- and -

http://babbage.sissa.it/abs/astro-ph/0012222
The microwave background temperature at the redshift of 2.33771
Authors: R. Srianand (IUCAA, Pune), Patrick Petitjean (IAP, Paris), Cedric Ledoux (ESO, Munich)
Comments: 20 pages, 5 figures, accepted for publication in Nature, Press embargo until 1900 hrs London time (GMT) on 20 Dec 2000

The Cosmic Microwave Background radiation is a fundamental prediction of Hot Big Bang cosmology. The temperature of its black-body spectrum has been measured at the present time, $T_{\rm CMBR,0}$ = 2.726$\pm$ 0.010 K, and is predicted to have been higher in the past. At earlier time, the temperature can be measured, in principle, using the excitation of atomic fine structure levels by the radiation field. All previous measurements however give only upper limits as they assume that no other significant source of excitation is present. Here we report the detection of absorption from the first {\sl and} second fine-structure levels of neutral carbon atoms in an isolated remote cloud at a redshift of 2.33771. In addition, the unusual detection of molecular hydrogen in several rotational levels and the presence of ionized carbon in its excited fine structure level make the absorption system unique to constrain, directly from observation, the different excitation processes at play. It is shown for the first time that the cosmic radiation was warmer in the past. We find 6.0 < T_{\rm CMBR} < 14 K at z = 2.33771 when 9.1 K is expected in the Hot Big Bang cosmology.

 

[droogie01]

... back on topic...


what about if there was some sort of massive body like a black hole between you and the closest star in one particular direction... would that black hole " suck up" all the photons not allowing you to detect them? Is it possible that this would create a dark spot in your continuous sphere of light? Also is it possible for stars nearby the star hidden by the black hole to send out light that may get bent around the gravity well of the black hole, creating the illusion that there are stars where the black hole is? (i know that is an observed phenomenon i had an assignment question on it 2 years ago) Would Olbers Paradox consider these "images" of a star to truly fill in the dark spot?


you------empty-space------ black hole----empty-space----- closeststar

 

[DaveC426913]

... back on topic...


what about if there was some sort of massive body like a black hole between you and the closest star in one particular direction... would that black hole " suck up" all the photons not allowing you to detect them? Is it possible that this would create a dark spot in your continuous sphere of light? Also is it possible for stars nearby the star hidden by the black hole to send out light that may get bent around the gravity well of the black hole, creating the illusion that there are stars where the black hole is? (i know that is an observed phenomenon i had an assignment question on it 2 years ago) Would Olbers Paradox consider these "images" of a star to truly fill in the dark spot?


you------empty-space------ black hole----empty-space----- closeststar

They are called Einsteinian Rings.

And, unless you're proposing that black holes are more common than pimples on a teenager, I don't see how it would play into Olber's Paradox in any significant way.

 

[droogie01]

well doesn't olber's suggest that the whole sky would be lit up with stars? how can the whole sky be lit up if there are black spots?.. whether it be one or as many as "pimples on a teenager"

correct me if that's off... I am new to the olbers paradox

 

[ideasrule]

Olber's paradox suggests that IF the universe is static, eternal, AND infinite, the sky would be lit up with stars. The universe is not static or eternal, and it may well be finite.

 

[DaveC426913]

well doesn't olber's suggest that the whole sky would be lit up with stars? how can the whole sky be lit up if there are black spots?.. whether it be one or as many as "pimples on a teenager"

correct me if that's off... I am new to the olbers paradox

You're missing the universe forest for the black hole trees.


Let's suppose a bunch of black holes. Now we should see a "night" sky that's filled with suns in all directions, and homogenously as bright as the sun - with some black spots (be it one or many).

See, adding that detail doesn't change anything. We do not see a sky that is filled with suns in all directions. Even the addition of a bunch of black holes doesn't change the original unavoidable conclusion - that the universe is not infinite in extent and age.

 

[S.Vasojevic]

Even the addition of a bunch of black holes doesn't change the original unavoidable conclusion - that the universe is not infinite in extent and age.

How do you know that universe is not infinite in extent?

 

[DaveC426913]

How do you know that universe is not infinite in extent?

No one said we do.

You've got understand the world in which Olber's Paradox arose. It was thought that the universe was infinite in extent and infinite in age and static and homogenous on large scales.

Olber's Paradox shows that these cannot all be true. It does not show that some of them can't be true.

 

[Vanadium 50]

I've just pruned this thread of all the off-topic posts. I hope only the messages about Olber's paradox remain.

 

[edpell]

If the universe is infinite in size and age then looking in any direction you will be looking at the surface of a star. But this does not tell you how bright it will appear. The sun is very close. If you look away from the sun your sight line will hit a star at various distances depending on where you look. On average the distance will be D which is a function of the density of stars in the universe. The lower the density the farther on average you will need to go to hit a star. The farther you have to go the dimmer it will appear. So when you say the night sky is dark what do you mean? How dark? The minimum measured light (I think intensity is the right word here) from a "dark spot" should give us an upper bound on the density of stars in the universe.

 

[DaveC426913]

The farther you have to go the dimmer it will appear.

Why?

Stars are dim because their disc is small and because of their intrinsic brightness, not because they are far away.

Unless you factor in intervening dust and gas.

But setting aside intervening objects, your above assumption is wrong.

 

[edpell]

You are right. If you want to know the number of photons per second coming from a certain square steradian part of the sky you integrate over the whole area at distance D. As D get bigger the area gets bigger (as D squared) and the contribution from each individual star declines, as D squared, but the number of stars in the field increases as D squared. So the brightness is the same. You are right my bad.

 

[heldervelez]

The full spectrum received is richer than the narrow optical band.
Matter age also limits the dept of view in consideration to the finite speed of light.
We can only observe part of the universe. Infinite in extension or not infinite is a speculation.

 

[edpell]

This is why part of the paradox states "infinite in age" so that light from infinitely far can be observed.

 

[RayTomes]

If the Universe is infinite in size and is uniformly full of galaxies, then it is indeed true that every line of sight will eventually hit a star. However there are more unwritten assumptions here ...

1. The universe needs to be infinite in age also for us to see such far away stars.

2. Individual stars would need to have an infinite life of giving light (which violates known physics laws), or there would need to be some means for recycling dead burned out stars.

This leads to some different conclusions that the standard Olber's paradox. If the Universe is infinitely old and still managing to make new stars, ...

If starlight is absorbed on its journey, as we know it is, then we would expect that starlight to be present as a cosmic microwave background radiation and to have a temperature of about 3 K. Funny that, we do see such a thing. But that in turn would have to be absorbed also and recycled eventually.

Here is the clincher ...

If the Universe were infinitely old and infinite in extent with stars spread uniformly and recycled so that there are always about the same number of stars, THEN, starting from a position in which there is a modest but finite brightness to the sky, how would it ever get to be the case that the sky became almost infinitely bright? Is that not a violation of conservation of energy per unit volume? Think about it. If energy is recycled, as it must be in an infinite aged universe, then the sky cannot ever get so bright.

 

[edpell]

Ray #1 is an explicit part of the statement of the paradox. I agree #2 is an implicit part of the statement of the paradox. I would guess the paradox was stated before the life cycle of stars was known. Does anyone know?

I disagree with the 3 degree K the "background" would be at the temperature of the surface of the stars (or average surface temp) so 6000 degrees K.

Yes where would all that energy come from?

 

[RayTomes]

I disagree with the 3 degree K the "background" would be at the temperature of the surface of the stars (or average surface temp) so 6000 degrees K.

If the line of sight went to stellar surfaces then it would be 6000 K. However to a distance of ~14 billion light years, which is as far as we can see, the scattering of star light produces a 3 K temperature over the whole sky. This was worked out correctly (by Eddington and others) long before the big bang was ever thought of (and the initial big bang estimate was 50 K).

 

[DaveC426913]

If the line of sight went to stellar surfaces then it would be 6000 K. However to a distance of ~14 billion light years, which is as far as we can see, the scattering of star light produces a 3 K temperature over the whole sky. This was worked out correctly (by Eddington and others) long before the big bang was ever thought of (and the initial big bang estimate was 50 K).

I am not sure what you are arguing now.

You're talking about scattering. Olbers' universe has us looking directly at the surface of a star, no matter where we looked.

 

[Chronos]

Eddington was wrong. You are correct in noting the CMB temperature was initially guessed to be much higher than 3K. Errors in estimating the age of the universe [among others] contributed to this inaccuracy.

 

[RayTomes]

Eddington was wrong. You are correct in noting the CMB temperature was initially guessed to be much higher than 3K. Errors in estimating the age of the universe [among others] contributed to this inaccuracy.

But in fact Eddington was right, wasn't he. Maybe you don't know why he was right, but his figure was spot on.

 

[frankinstein]

I understand Olbers' Paradox and its resolution, however such phrases as this - "If the universe extends infinitely, then eventually if we look out into the night sky, we should be able to see a star in any direction, even if the star is really far away" - which can be found http://cmb.physics.wisc.edu/tutorial/olbers.html" and also in at least one textbook, strike me as plain wrong. Even if there are infinitely many stars, there is no reason to expect that any infinite line from a point would hit at least one of them. This seems intuitively obvious. Am I missing something, or is that quote just a bad way of formulating the paradox?

Well the universe is not infinite, but there are enough stars in the universe, for certain animals, to see night as clear as day without a full moon...

Frank

 

[Chronos]

But in fact Eddington was right, wasn't he. Maybe you don't know why he was right, but his figure was spot on.

Explain the physics behind 'Eddington was right'. Being right does not make you right without evidence you are not wrong.

 

[twofish-quant]

Explain the physics behind 'Eddington was right'. Being right does not make you right without evidence you are not wrong.

Also there are numerous cases in which people just *lucked out*. Pluto was discovered as a result of calculations that we now know to be totally wrong.

Then there is America. All of the astronomers in the late 1400's thought that Columbus's plans to sail to Asia were totally insane, because he was completely miscalculating the size of the earth, and he'd never make it. It turns out that there *was* land within sailing distance of Europe.

I think there should be some sort of award like the ignoble prize for this sort of thing.