Talk:Olbers' paradox

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On 21 August 2014, Olbers' paradox was linked from xkcd, a high-traffic website. (See visitor traffic)

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A Thought Experiment[edit]

Let's perform a thought experiment. Assumed is the cosmological principle, that states the spatial distribution of matter in the universe is homogeneous and isotropic when viewed on a sufficiently large scale. We start to assume it is the light from stars that determine the brightness of the sky at night. We neglect e.g. the 2.7 K background radiation that did not origin in stars. Imagine you had a magic button that speeds up star evolution. With this button all molecular clouds in the universe immediately convert into stars and all stars (old ones and the newly formed) immediately convert entirely into radiation, according to E=mc2. The situation cannot become worse. The resulting radiation bath or photon gas as it sometimes is called, when considered at scales large enough for the cosmological principle to become apparent, is uniform and thus in equilibrium with respect to the amount of photons per area. An area can only gain more radiation at the cost of nearby areas and that on the average will counteract statistics. Normally an area will radiate out to nearby areas the same amount as it receives from that areas. Mind the light of stars IS the radiation bath. The amount of radiation that enters a steradian in one second then is the brightness of the sky at night, that is, its upper limit. This is a finite amount and so this suffices as a solution of the Paradox of Olbers.

Mind this solution does not depend on the size of the universe, nor on its age, nor on whether the universe is expanding or not. That is, the considered areas must be large enough for the cosmological principle to become apparent. And the age must be sufficient long for light to have crossed that areas, allowing the photon bath in a single area to become uniform. But it is not important whether the size or age is finite or infinite. It only depends on the density of the universe. The solution works also for the Steady State cosmological model.

Of course expansion of the universe dilutes the radiation bath and lowers its average brightness. In the course of time from the Big Bang up to now the universe passes all densities from, well let's start at 10^17 kg/m3 (neutron star density) down to 10^-26 kg/m3 (critical density of the universe, that it is now, nearly). It depends on the precise moment in this elapse of time where you perform this thought experiment, what precisely is the value of the upper limit of the brightness of the sky at night.

Nowadays most molecular clouds have not yet contracted to stars, and not all star matter will finally convert to radiation. So, what is the actual radiation bath right now? The density of the universe as it is now consists of 73% Dark Energy, 23 % Dark Matter (WIMPs, neutrinos), 4 % ordinary matter (protons, neutrons, electrons) and only 0.005 % consists of photons (starlight and Background radiation).[1] --87.210.223.62 (talk) 11:05, 31 August 2017 (UTC)

References

Temp lock this article[edit]

You might want to temporarily lock this article. In a xkcd "What If?", Randall Munroe casually jokes that he'd been tempted to vandalize this article by placing {{citation needed}} every time the article said the sky was dark (I suppose how dark it is depends on where you live?). It was a joke, but I see we've already had one vandalation, and the xkcd page in question just went up. What does everyone else think? Is a temp protect needed? — Gopher65talk 14:17, 21 August 2014 (UTC)

Two instances, actually, but nothing in several hours. I don't see an issue here yet. Powers T 14:21, 21 August 2014 (UTC)
Ok:). Just wanted to let people know what the source was, so they aren't left wondering what's going on if it gets worse. — Gopher65talk 14:26, 21 August 2014 (UTC)
Yeah, there'll probably be a few more, but it's ultimately a harmless joke and it'll die down. I honestly came here hoping to see a [citation needed] that hadn't been reverted yet. SSSheridan (talk) 15:04, 21 August 2014 (UTC)

The XKCD joke is not immediately obvious: it's buried in a Reference 5 (you have to click on the 5 to see it), in a what-if article. Hopefully that cuts down on the number of pranksters who'd see it. 128.232.254.133 (talk) 18:44, 21 August 2014 (UTC)

You might want to consider that it's a well-known fact among xkcd fans that the comics always have witty alt text, a tradition that was carried along into what-if's "references". It is not unlikely that the majority of readers will open all those references just to have an extra laugh. While the amount of pranksters that actually read what-ifs might be indeed low, I'm seeing [citation needed] marks even in this article's references themselves, and there's been more edits today than in two months. Good luck :) --186.136.111.144 (talk) 20:36, 21 August 2014 (UTC)

Technical note: Randall should really pre-notify Wikipedia if he intends to mention Wikipedia article in his work.

(On the other hand, this can be ended creatively, by actually providing a very scientific source for the fact, that the night sky is dark. Come on, there MUST be some!) — Preceding unsigned comment added by 82.99.189.14 (talk) 22:36, 21 August 2014 (UTC)

The purported need to cite the dark night sky brings to mind User:Jnc/Astronomer vs Amateur. But perhaps Munroe missed the fact that, for nearly a year, one of the references of this article has included the statement that "the night sky is dark" in a direct quote from the reference? —David Eppstein (talk) 03:33, 25 August 2014 (UTC)

I think some of us will just come to see if someone else messed with it. A few of us will come here to see if it's been an issue and to have a laugh. A virtually insignificant number of us will comment here. Even fewer still vandalize your precious post... but I feel it's obligatory at this point to at least make[citation needed] a[citation needed] mockery[citation needed] of[citation needed] the[citation needed] whole[citation needed] thing[citation needed]. -Signed an XKCD fan and wiki lover. 76.113.75.7 (talk) 22:42, 22 August 2014 (UTC)

I'm actually impressed with the small number of vandalism attempts before the article was temp protected for a week against anon edits and edits by newly created accounts (last 3 days I think it is?). Apparently xkcd's (it's all lowercase!) community is more mature than I imagined. — Gopher65talk 02:05, 23 August 2014 (UTC)

I hate to point out the obvious, but... why is the night sky dark? It is obviously easy to criticise a (very bright) writer of web comics, but none of the comments here consider the point he made! Yes, the article itself addresses why the night sky is not 'shining with the brightness of infinite suns', but there does not appear to be any Wikipedia article addressing the direct question of why the sky is dark. Google's first answer to the question is a link to this article. It also sends me off to NASA and then to Scientific American, both of which focus on Olbers' Paradox. There are plenty of other answers that Google wants me to read, but all of them appear to focus only on this sub-set of the question Mr Munroe raised.

So - we have an answer to "Why is the night sky not covered in light from an infinite number of stars?", but that is not the same as answering "Why is the night sky dark?" They are different questions, and this article - as Mr Munroe quite correctly points out - only answers a sub-set of the latter. Is there any chance that we might one day see a Wikipedia article that addresses the full question?

As a side note, are poets considered to be authoritative sources for articles on astronomy? That is, plenty of 'famous people' have made crazy statements about fields in which they have no knowledge, that later turn out to be at least partly true. Does Wikipedia accept such statements as valid sources? Ambiguosity (talk) 08:25, 28 February 2016 (UTC)

This seems weird, but Wikipedia needs as many citations as possible. We should put a "citation needed" after every claim that the night sky is dark because on Wikipedia, every arbritary claim has to be backed up with a citation. However, if you do not like this idea, please just delete my post on here. I agree, we don't want pranksters getting any ideas and vandalizing this article.TheGoldenParadox (talk) 14:47, 17 February 2017 (UTC)

Reference to CMB Dipole Moment[edit]

Regarding the last sentence of the article and the discussion about a 'fractal star distribution' I see no reason to cite G. F. Smoot's paper and the dipole moment of the CMB. This paper is now 40 years old but it gives the cause for the observed dipole moment right in the abstract: the motion of the observer with respect to the CMB restframe. This effect is expected and has to be there. Observing a vanishing dipole moment would instead be worrying. Anyway, the cosine anisotropy has nothing to do with the large scale structure but is interpreted best as a completely local phenomenon attributed to the observer alone. In contrary, Smoot constrain the remaining anisotropy to be smaller than 1/3000. Therefore, the last sentence in the article is nonsense should be removed. The only reason I have not done it myself is that, for totally different reasons, really like that paper. --2.246.187.19 (talk) 19:33, 6 April 2016 (UTC)

Really? The brightness gives an argument?[edit]

"Suppose that the universe were not expanding, and always had the same stellar density; then the temperature of the universe would continually increase as the stars put out more radiation."


"Suppose that the EARTH were not expanding, and always had the same MATTER density; then the temperature of the EARTH would continually increase as the EARTH gathers more radiation."

(1) Where is the radiation from? => There, where it comes from, there isn't it anymore!

Infinite directions?[edit]

Not sure I understand the initial paradox correctly. It assumes that if there were an infinite number of static stars, then a line from the observer in any direction in the night sky should end on the surface of a star, right? But does that mean that that star has been sending out photons along the same line back to the observer? An active star glows, but not in an infinite number of directions, it does not send out an infinite number of photons every second, or am I wrong? Iago212 15:47, 23 November 2016 (UTC)

The brightness per unit of solid angle covered is constant regardless of distance, assuming the standard inverse-square laws. —David Eppstein (talk) 16:43, 23 November 2016 (UTC)
What does that have to do with my question? Iago212 21:37, 23 November 2016 (UTC)
It means that it looks the same brightness no matter how far from it you are; your distance controls how small it looks but not how bright it looks. If you insist on trying to understand it in terms of photons: the photons should not be interpreted as being emitted periodically, but rather randomly, at a given rate. Similarly, it does not emit photons along some fixed finite set of rays, but in all directions, randomly. Given this random process, the number of photons per second that reach your eye from any star (given a fixed value of its surface brightness) is proportional to the area of the sky that it covers from your viewpoint, but does not otherwise depend on the distance to the star. So if you see a star in every direction you look (far enough away in that direction), you would see the whole sky at the surface brightness of a star (the same brightness that we see the surface of the sun). —David Eppstein (talk) 21:47, 23 November 2016 (UTC)
OK, so would not in all directions, randomly man that it has to emit an infinite number of photons to be seen from an infinite number of directions? Iago212 22:17, 23 November 2016 (UTC)
No. Because your eye is not a mathematical point. If it emits a single photon per second, in a uniformly random direction, that still gives it a nonzero brightness in all directions. —David Eppstein (talk) 00:17, 24 November 2016 (UTC)
How does a random distribution of a finite number of photons give you all directions? Iago212 09:33, 24 November 2016 (UTC)

Paradox explanation[edit]

From the article:

To show this, we divide the universe into a series of concentric shells, 1 light year thick. A certain number of stars will be in the shell 1,000,000,000 to 1,000,000,001 light years away. If the universe is homogeneous at a large scale, then there would be four times as many stars in a second shell, which is between 2,000,000,000 and 2,000,000,001 light years away. However, the second shell is twice as far away, so each star in it would appear one quarter as bright as the stars in the first shell. Thus the total light received from the second shell is the same as the total light received from the first shell.
Thus each shell of a given thickness will produce the same net amount of light regardless of how far away it is. That is, the light of each shell adds to the total amount. Thus the more shells, the more light; and with infinitely many shells, there would be a bright night sky.

This doesn't seem to take occlusion from stars in the inner shells into account. That is, the light emission from a layer should be discounted by the fraction of the sky already lit up by layers inside it. In particular, it is incorrect that “the total light received from the second shell is the same as the total light received from the first shell”.

I realize the end result is the same, but this makes several sentences technically incorrect. Also, this passage is unsourced. MattF (talk) 02:59, 22 March 2017 (UTC)

Dust, revisited[edit]

"Dust" may be defined as any substance that absorbs light. This means that impinging photons collide with the substance, effectively transferring some or all of their momentum and energy to the dust, which emits photons of that same or lower energy in a random direction. Photons not colliding with dust, of course, travel on unimpeded, with their full energy intact.

We can see "dust lanes" clearly in magnified views of relatively nearby galaxies, so we know that dust can and does hide stars within observed galaxies.

Intergalactic dust is less obvious, and almost certainly not of high atomic number. There is probably no carbon or gold in intergalactic space, for example. However, there may also not be a complete vacuum there, either. From radio-astronomic evidence we may conclude that hydrogen atoms exist there, far away from any galaxies or stars.

Would a photon from a distant star, several billion light-years away, collide with hydrogen atoms on its way toward Earth? I don't know, but given that enormous distance, it may be possible that photons from this star might have a significant chance of collision along the path to a person's eye on Earth, on average.

This means that fewer of these photons travel unimpeded to our eyes, resulting in less light from a star the farther away the star is from Earth. The rest of the photons are scattered at random angles and possibly at lower energies/frequencies, so they are not seen by human eyes.

This is my favorite answer to Olbers' Paradox; I like it because it does not require space to expand over time or any other difficult-to-prove concepts. It should be possible to calculate the probabilities involved, so it is falsifiable.

Sorry, I forget who developed this answer, and cannot now find a reliable source reference for it. David Spector (talk) 23:06, 18 May 2017 (UTC)

Is this even seriously considered by the scientific community?[edit]

According to the inverse-square law, light dissipates with distance. The so called "perceived darkess of the night sky" is just that: PERCEIVED darkness. That is, the blackness of the night sky is just a problem with our eyes, not the universe lacking something to be seen in every point in the sky. This so called theory seems to have as much grounding as flat earth theories. Am I missing something here? --uKER (talk) 15:00, 1 June 2017 (UTC)

I think you are missing something. Light (considered as a parallel stream of photons) does not dissipate in any way with distance through a vacuum. The only way that a light beam or ray can attenuate is for some of the photons of which it is composed to be absorbed (converted to heat)(or reflected or refracted which mean absorbed and re-emitted in different directions) along the way. This "dust attenuation" should be governed by a linear law, since each unit distance from the point along a line is assumed to contain the same amount of dust.
You may be thinking of the amount of light emitted from a point source, which like gravity has an inverse-square law due to the fact that the photons are emitted equiangularly around the volume of space surrounding the point. Then the number of photons that pass through a square is twice the number that pass through a square twice as far away from the source point, due to similar triangles (elementary geometry).
The blackness of the night sky is a true blackness. In fact, our eyes see much better at night than during the day, not worse. David Spector (talk) 17:29, 9 December 2017 (UTC)

Alternative explanations[edit]

I always thought this paradox was explained by the fact that the universe has been expanding for a very long time, or at least in a very big way such that light will never be able to catch up before expansion equilibrium comes along, the big rip occurs or the big crunch makes it a moot point

In the event of expansion equilibrium, should it ever come to pass, light dissipation, black holes and gravity will all have their effects. The maths are very neat, but I have to figure it's unlikely that universal expansion will perfectly stop on a dime.

In the event of the big rip, the notion that light won't be able to keep up with the expanding rate of the universe makes better sense as time goes on.

The big crunch scenario is a bit more interesting. Black holes will mop up a lot of light over such a long timeframe and this event is going to happen for sure after heat death of all the stars happens. Mind you brings up another point. Are we looking back in spacetime to a point when all the stars have gone out or is it just our faulty human eyes? Shtanto (talk) 20:30, 4 July 2017 (UTC)

The apparent expansion of the universe causes a red-shift, which at extreme distances causes galaxies to become invisible. But I believe that effect is clearly not sufficient to explain why the sky is not ablaze with stars at night. David Spector (talk) 17:33, 9 December 2017 (UTC)

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"Explanations" Suggestion[edit]

How are any of the "alternative explanations" actually explanations if they don't include the Big Bang or expansion? At best these are *previous* or *historical* explanations (though some aren't even that). This section should at least be retiled, and possibly deleted. AldaronT/C 13:43, 30 August 2017 (UTC)

There are believable explanations that don't refer to the apparent expansion of the universe, such as the dust argument I presented above. David Spector (talk) 17:34, 9 December 2017 (UTC)
That doesn't really address the question. These are all bad explanations, and should be characterized as such. AldaronT/C 20:58, 9 December 2017 (UTC)