Olbers' paradox and infinite number of stars

[brianhurren]

Olbers' paradox reckons that the sky should be blazing bright if there is an infinite number of evenly distributed stars (galaxies). the argument is something like in every direction that you look there would be a star. so the sky would be blazing bright. but even if there were an infinite number of starts in an infinite space. wouldn't the foreground stars be blocking the light from the infinite starts behind them? so for example if I looked at Sirius, I would only see Sirius and not the infinite stars behind Sirius, so that point in the sky would only be as bright as Sirius.
so another way to put it is, wouldn't an infinite number of stars cast an infinite number of shadows? and would there be more shadows than stars ( so there would be aleph 0 stars and aleph 1 shadows)?
and how seriously can we take Olbers' paradox?

 

[mfb]

wouldn't the foreground stars be blocking the light from the infinite starts behind them?

Sure, but they would be stars as well, so you would still see a star in every direction - just not an infinite number of them.
"As bright as Sirius" is much brighter than the sun (per solid angle).

and how seriously can we take Olbers' paradox?

We know it relies on a static universe where stars live forever, and we know those conditions are not true, so it has no relevance to cosmology any more. If the condition for the paradox would be satisfied then it would apply.

 

[rootone]

A lot of stars which could be visible can't in fact be seen anyway because of shadows caused by interstellar dust.
I suppose it could be argued though that in an infinite universe the dust would become infinitely heated and itself become blazing bright.
Still again, this could only apply to static universe

 

[Chronos]

Olber paradox requires a spatially and temporally infinite universe. While spatial infinity remains an open question, we are reasonably sure the universe is not infinitely old - thus no paradox.

 

[Ken G]

In fact, the paradox says the sky would have to be infinitely bright, if there were an infinitude of static evenly spaced stars that have been shining for an infinite time. It doesn't matter if dust or stars is blocking the light, as light that is absorbed must eventually be emitted, given conservation of energy. So like most "paradoxes" in physics, it's not really a paradox at all, it is a proof by contradiction that something cannot be the case-- in this case, the non-infinite brightness of the night sky implies that we do not have a spatially infinite static universe that has been evenly populated with stars for all time.

That might sound like a straw man to begin with, given our current understanding of a universe with a finite age, but we don't have to go that far back in time before this was a very important constraint indeed. In fact, it often makes me wonder why Einstein incorporated his cosmological constant in the first place. Remember, he did this originally to allow the universe to be static (never mind instability problems) and infinite. But why would Einstein, and Newton before him, have wanted a static infinite universe, given Olbers' paradox? It doesn't make sense, I don't understand why they would make a model like that.

 

[Chronos]

Just as an aside, I believe Olber's paradox leads to the conclusion the night sky should be as bright as the surface of an average star, given every line of sight falls on a star. Interestingly enough, Einstein favored a finite universe based on Mach's principle, as did Mach himself - see http://mathpages.com/rr/s7-01/7-01.htm and page 518 of https://books.google.com/books?id=R...hat the universe is closed and finite&f=false for discussion. This is curious in that it seems to contradict his belief in an eternal universe. Unless he was a steady state kind of guy, an eternal finite universe would appear to run out of gas - literally and figuratively - on thermodynamic grounds.

 

[Ken G]

Just as an aside, I believe Olber's paradox leads to the conclusion the night sky should be as bright as the surface of an average star, given every line of sight falls on a star.

It's often framed that way, but that's wrong, for the reasons I gave. It is easy to see-- if the night sky was as bright as a star, the stellar surfaces would be bathed in light as bright as a star, so would need to get hotter as the radiation piled up. Of course, if all stars are doing that, then the night sky is getting brighter... etc. There is no point of convergence, if stars emit energy and you have an infinitude of them for all time, which is the assumptions of Olbers, you get an infinitely bright sky.

Interestingly enough, Einstein favored a finite universe based on Mach's principle, as did Mach himself - see http://mathpages.com/rr/s7-01/7-01.htm and page 518 of https://books.google.com/books?id=RaRB8OKLlJ0C&pg=PA547&lpg=PA547&dq=einstein's+conviction+that+the+universe+is+closed+and+finite&source=bl&ots=1R_JdPNCzm&sig=bYRRiRQwhXUsocc3zENvPhEc5K4&hl=en&sa=X&ei=ABEbVZv_HJTtoATq0ICQDw&ved=0CCsQ6AEwAg#v=onepage&q=einstein's conviction that the universe is closed and finite&f=false for discussion. This is curious in that it seems to contradict his belief in an eternal universe. Unless he was a steady state kind of guy, an eternal finite universe would appear to run out of gas - literally and figuratively - on thermodynamic grounds.

I'll look at that, I've always wondered about the apparent contradictions in Einstein's cosmology, and Newton's also for that matter. Remember that neither knew what allowed stars to shine, they might have thought they had some kind of rejuvenating mechanism.

 

[mfb]

if the night sky was as bright as a star, the stellar surfaces would be bathed in light as bright as a star, so would need to get hotter as the radiation piled up.

We are assuming that stars shine forever, I don't see the point of trying to add realism exactly at the surface of stars.

 

[Ken G]

Why not? The question is a scientific one: could the stars have shone forever in an infinite universe? To address that question, we should apply the full power of science, all the laws we have that could be relevant. If we leave some out, how do we know we are drawing the correct conclusions?

 

[brianhurren]

what if there is more than one level of infinity? what if every star mapped onto an infinite amount of space. so, even though there is an infinite amount of stars there is even more infinite amount of space so stars are aleph 0 and the space is aleph 1 a mapping of 1 to infinity, the space would almost be at zero degrees as it sucks away the energy from every star, since every stars has an infinity large heat sink. even though there is an infinite number of them. I don't see anything that suggest only one level of infinity, or that there can only be one level of infinity?

 

[Ken G]

The assumption in Olbers' paradox is that the distribution of stars is uniform, not just infinite in extent. So that means a fixed density, so that means the same infinity. I think what you are getting at is that if the stars are not uniformly distributed, they could have a fractal distribution or something like that, and that could get around the paradox. But they needed a uniform distribution to think that the gravity would cancel out. They were wrong about that, the gravity wouldn't have canceled out, but even Einstein tried to rectify that problem in an unstable way.

 

[brianhurren]

there seams to be a lot off assumptions? I am really just playing devils advocate here

 

[Drakkith]

there seams to be a lot off assumptions? I am really just playing devils advocate here

It's not that they are assumptions so much as requirements. If we existed in a static, eternal universe, then Olber's paradox tells us the things we should see and the conditions the universe must be in. Because we don't live in an eternal, static universe, we don't see these things. Uniformity is required because otherwise gravity would pull everything together (in the absence of something like a cosmological constant to keep them from collapsing under gravity).

what if there is more than one level of infinity? what if every star mapped onto an infinite amount of space. so, even though there is an infinite amount of stars there is even more infinite amount of space so stars are aleph 0 and the space is aleph 1 a mapping of 1 to infinity, the space would almost be at zero degrees as it sucks away the energy from every star, since every stars has an infinity large heat sink. even though there is an infinite number of them. I don't see anything that suggest only one level of infinity, or that there can only be one level of infinity?

Don't think of space as a 'heat sink'. It's only like that in real life because the universe is neither static nor eternal and most of your lines of sight will not end on a stars surface. In effect, objects are able to radiate energy away along those lines of sight without receiving anything back in return. That's why space acts like a heat sink. In an eternal, static universe, this is no longer the case. There are no directions in which an object can radiate energy without receiving some in return.

 

[Armonicus]

Generally speaking, the paradox is biased on some certain premises; it's an affirmation which contradicts the premises. But the same premises could lead (until the moment when the paradox was formulated) to different "true" affirmations. Now, once that certain paradox appear, endanger the "true" values of all affirmations which was formulated, deduced, inferred until that particular moment when the paradox was discovered. This is not good cause threate to ruin a lot of intellectual investment, which sometimes is painful. In order to save that particular investment we need to solve that paradox.
To solve a paradox, you have two options:
1. To modify the premises, without altered the "true" value of all affirmations deduced a priori, by accepting the old premises but transforming the paradox in a "true" or "false" sentence.
2. To expand the premises, in order to accept all a priori true sentences inferred from them and to transform the paradox in a proof which maintain the expanded premises by "reductio ad absurdum".
In our case we excluded from our premises that stars are dying... They have a limited lifetime... The second thing which was ignored is the limited speed of light, doesn't matter how much is it and that, the energy decay which hit our eye from a source is proportionally with 1/(d*d), d being the distance between source and our eyes. In this case if the rate of dying stars is a little bigger than the rate of new born stars (let's say 50.000...1%) on a radius let say of 5 times bigger than our observable universe, then the fact that we have black sky have perfect sense and yet we can accept that the universe is infinite... So we can have an infinite universe and yet having a black sky being a "local" accident in which we leave today . Yet, you may argue that cannot be an infinite universe as long as there are more dying stars than alive... Ok, here in our local area this is the case but the even distribution of dying-alive stars is maintained by compensating in another area with more alive stars than dying stars. If that is the case in that particular observation point the people there will have a nice and shining bright sky ... :)

 

[Drakkith]

Generally speaking, the paradox is biased on some certain premises; it's an affirmation which contradicts the premises. But the same premises could lead (until the moment when the paradox was formulated) to different "true" affirmations. Now, once that certain paradox appear, endanger the "true" values of all affirmations which was formulated, deduced, inferred until that particular moment when the paradox was discovered. This is not good cause threate to ruin a lot of intellectual investment, which sometimes is painful. In order to save that particular investment we need to solve that paradox.

Forgive me, but I can barely understand what you're getting at. Olber's paradox is an argument against an eternal, static universe, nothing more. It's only a paradox in the sense that if the universe was both eternal and static then the sky should be overwhelmingly bright. The fact that it is not bright, and is in fact very, very dark, is evidence that the model of the universe as both eternal and static is not correct. The current model of the universe as both finite in age and expanding 'solves' the paradox. (Or rather it avoids it completely since the original premise of Olber's paradox is of an eternal, static universe)

The second thing which was ignored is the limited speed of light

The speed of light isn't being ignored, it simply doesn't matter. In an eternal, static universe, light has had plenty of time to arrive from any point in the universe, no matter how fast light actually travels.

Yet, you may argue that cannot be an infinite universe as long as there are more dying stars than alive...

I don't follow you here. What does the ratio of dead stars to living ones have to do with the size of the universe?

 

[Armonicus]

Let's take it cronologically:
1.[In 1584, Giordano Bruno published two important philosophical dialogues in which he argued against the planetary spheres (Christoph Rothmann did the same in 1586 as did Tycho Brahe in 1587). Bruno's infinite universe was filled with a substance—a "pure air," aether, or spiritus (dark matter? :) =my note)—that offered no resistance to the heavenly bodies (stars, galaxies, quasars , etc =my note) which, in Bruno's view, rather than being fixed, moved under their own impetus (momentum). Most dramatically, he completely abandoned the idea of a hierarchical universe.[citation needed]

"The universe is then one, infinite, immobile... It is not capable of comprehension and therefore is endless and limitless, and to that extent infinite and indeterminable, and consequently immobile." (Giordano Bruno)].
Sadly, Giordano was assassinated for this idea (burned alive) by Catholic Inquisition in 1600.2.[Olbers' paradox, described by him in 1823 (and then reformulated in 1826), states that the darkness of the night sky conflicts with the supposition of an infinite and eternal static universe.]

3.[Edward Robert Harrison's Darkness at Night: A Riddle of the Universe (1987) gives an account of the dark night sky paradox, seen as a problem in the history of science. According to Harrison, the first to conceive of anything like the paradox was Thomas Digges, who was also the first to expound the Copernican system in English and also postulated an infinite universe with infinitely many stars.[1]Kepler also posed the problem in 1610, and the paradox took its mature form in the 18th century work of Halley and Cheseaux.[2] The paradox is commonly attributed to the German amateur astronomer Heinrich Wilhelm Olbers, who described it in 1823, but Harrison shows convincingly that Olbers was far from the first to pose the problem, nor was his thinking about it particularly valuable. Harrison argues that the first to set out a satisfactory resolution of the paradox was Lord Kelvin, in a little known 1901 paper,[3] and that Edgar Allan Poe's essay Eureka (1848) curiously anticipated some qualitative aspects of Kelvin's argument].

4.[A different resolution, which does not rely on the Big Bang theory, was first proposed by Carl Charlier in 1908 and later rediscovered by Benoît Mandelbrot in 1974. They both postulated that if the stars in the Universe were distributed in a hierarchical fractal cosmology (e.g., similar to Cantor dust)—the average density of any region diminishes as the region considered increases—it would not be necessary to rely on the Big Bang theory to explain Olbers' paradox. This model would not rule out a Big Bang but would allow for a dark sky even if the Big Bang had not occurred.] (The math behind this assumption is a bit cumbersome, but trust me, has perfect sense = my note).

5.[In contrast to this model, Albert Einstein proposed a temporally infinite but spatially finite model as his preferred cosmology in 1917, in his paper Cosmological Considerations in the General Theory of Relativity.]

6.[After the discovery of the redshift-distance relationship (deduced by the inverse correlation of galactic brightness to redshift) by Vesto Slipher and Edwin Hubble, the Roman Catholic priest Georges LeMaitre interpreted the redshift as proof of universal expansion and thus a Big Bang, whereas Fritz Zwicky proposed that the redshift was caused by the photons losing energy as they passed through the matter and/or forces in intergalactic space. Zwicky's proposal would come to be called 'tired light'- a term coined by the leading Big Bang proponent Richard Tolman.]

Between [ ] there are Infos copied and pasted from Wikipedia (I doubled-crossed often the Infos from wiki with other trusted sources and I can say that wiki generally is a reliable info source).

Now, first, it is very annoying that the Big Bang model was proposed by a catholic priest and not by an astrophysicist, (despite the fact that the IQ of an astrophysicist is at least 2 times bigger than to a priest) just to defend the iudeo-christian religion premises ... (see my first post regarding premises-paradox discussion). And, as I shown in 4., what's wrong with the anisotropic model of the Universe? ... my part in defending Giordano's assumption and at the same time to accept LaMaitre theory ... Is the model of "fireworks" where like fireworks on the sky there are many and infinite big bangs but they are appearing not synchronized and very far away one of another therefore despite the fact that there are infinite big bangs they cannot interfere one with another.
More than that, our universe is as it is because the antimatter at a certain moment was vanished interacting with equal quantity of matter creating in this process the dark matter and the dark energy. (This is my assumption and I am working right now to a math model to sustain that) This evolution is not compulsory for other big bangs, the appearance of our universe being an unique feature of this particular Big Bang due to some statistic energy and entropy distributions in the first 1000 years of our good universe.
To conclude: as you can see the Olber's Paradox (which seems that doesn't belongs to him) doesn't deny the Giordano's assumption, but yet we can accept the Big Bang theory, and the anisotropic distribution could work as well ... Anyway thanks for subject... Was a very interesting one ... :)

 

[Drakkith]

Now, first, it is very annoying that the Big Bang model was proposed by a catholic priest and not by an astrophysicist, (despite the fact that the IQ of an astrophysicist is at least 2 times bigger than to a priest) just to defend the iudeo-christian religion premises ... (see my first post regarding premises-paradox discussion).

I don't know if this a joke or not. Georges LeMaitre was a trained astronomer, so I don't see how your criticism applies. And I still have little idea what your previous post even says thanks to an overuse of fancy language and several apparent grammatical errors.

And, as I shown in 4., what's wrong with the anisotropic model of the Universe?

It doesn't match observations.

Is the model of "fireworks" where like fireworks on the sky there are many and infinite big bangs but they are appearing not synchronized and very far away one of another therefore despite the fact that there are infinite big bangs they cannot interfere one with another.

This makes absolutely no sense. The Big Bang was not an explosion in space and is nothing like a firework. There are plenty of threads around here explaining that.

More than that, our universe is as it is because the antimatter at a certain moment was vanished interacting with equal quantity of matter creating in this process the dark matter and the dark energy. (This is my assumption and I am working right now to a math model to sustain that)

The imbalance between matter and antimatter is a known issue and is being actively investigated on several fronts. Please be aware that we do not accept personal theories here on PF.