Editing Olbers's paradox (section)

==The paradox and resolution==
{{See also|Redshift|expansion of the universe}}
The paradox is that a static, infinitely old universe with an infinite number of stars distributed in an infinitely large space would be bright rather than dark.<ref name="NYT-20150803" />
The paradox comes in two forms: flux within the universe and the brightness along any line of sight. The two forms have different resolutions.<ref name=Peacock-1998>{{Cite book |last=Peacock |first=J. A. |url=https://www.cambridge.org/core/product/identifier/9780511804533/type/book |title=Cosmological Physics |date=1998-12-28 |publisher=Cambridge University Press |isbn=978-0-521-41072-4 |edition=1 |doi=10.1017/cbo9780511804533}}</ref>{{rp|354}} 

[[File:Olbers' Paradox.svg|thumb|A view of a square section of four concentric shells]]
The flux form can be shown by dividing the universe into a series of concentric shells, 1 light year thick. A certain number of stars will be in the shell, say, 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 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 an infinitely bright night sky.<ref name=Byrd-2012>{{cite book |last1=Byrd |first1=Gene |last2=Chernin |first2=Arthur |last3=Teerikorpi |first3=Pekka |last4=Valtonen |first4=Mauri |title=Paths to dark energy: theory and observation |date=2012 |publisher=de Gruyter |location=Berlin |isbn=978-3110258783 |pages=49–50}}</ref>

If intervening gas is added to this infinite model, the light from distant stars will be absorbed. However, that absorption will heat the gas, and over time the gas itself will begin to radiate. With this added feature, the sky would not be infinitely bright, but every point in the sky would still be like the surface of a star.<ref>{{cite book |last=D'Inverno |first=Ray |title=Introducing Einstein's Relativity |publisher=Oxford University Press |year=1992 |url=https://profmcruz.files.wordpress.com/2018/02/livro-introducing-einsteins-relativity-dinverno.pdf |isbn=9780198596868 }}</ref> 

The flux form is resolved by the finite age of the universe: the number of concentric shells in the model above is finite, limiting the total energy arriving on Earth.<ref name=Peacock-1998/>{{rp|355}}

Another way to describe the flux version is to 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. After something like 10<sup>23</sup> years, the universe would reach the average surface temperature of a star. However, the universe is only 13.8 billion (10<sup>12</sup>) years old, eliminating the paradox.<ref name="new cosmos"/>{{rp|486}} 

The line-of-sight version of the paradox starts by imagining a line in any direction in an infinite Euclidean universe. In such universe, the line would terminate on a star, and thus all of the night sky should be filled with light. This version is known to be correct, but the result is different in our expanding universe governed by general relativity. The termination point is on the [[surface of last scattering]] where light from the Big Bang first emerged. This light is dramatically redshifted from the energy similar to star surfaces down to 2.73&nbsp;K. Such light is invisible to human observers on Earth.<ref name=Peacock-1998/>{{rp|355}}

Recent observations suggesting that the estimated number of galaxies based on direct observations is too low by a factor of ten do not materially alter the resolution but rather suggest that the full explanation involves a combination of finite age, redshifts, and UV absorption by hydrogen followed reemission in near-IR wavelengths also plays a role.<ref>{{cite journal |last1=Conselice |first1=Christopher |last2=Wilkinson |first2=Aaron |last3=Duncan |first3=Kenneth |last4=Mortlock |first4=Alice |title=The Evolution of Galaxy Number Density at ''z'' < 8 and its Implications |journal=[[The Astrophysical Journal]] |date=20 October 2016 |volume=830 |issue=3 |page=83 |doi=10.3847/0004-637X/830/2/83 |arxiv=1607.03909 |bibcode=2016ApJ...830...83C |s2cid=17424588 |doi-access=free }}</ref>