Olbers Paradox

[Astro Imp]

I have recently been reading a thread on SGL that in passing mentions Olbers paradox:- http://stargazerslounge.com/topic/218463-if-the-universe-is-infinite-does-that-mean-there-is-an-infinite-number-of-mes/

As is pointed out in this thread the answer to the paradox is the expansion of the universe.

I have always believed this to be true but have given this topic some thought.

On reflection it seems that the answer is the paradox relies on an incorrect premise. It is assumed that the stars are equally distributed in all directions and that they stretch to infinity.

Unbeknown at the time the stars one sees are members of the Galaxy which is not infinite so there are insufficient of them to lighten the night sky. 

Observing at a dark site and looking along the plain of the Galaxy one sees the Milky Way which is a pale image of what Olbers was describing but look at right angles and you see scattered stars as you look out of the Galaxy into space.

Look forward to your learned comments. 

[Knight of Clear Skies]

This minute physics video does a good job of explaining Olber's Paradox.

[ronin]

Suppose the simple answer is tha there are not infinite stars, assuming the Big Bang to be correct there was a lot of energy but not infinite. I suppose if infinite then it would by that definition be ongoing still. To get infiinite energy into our universe at a finite rate take infinite time.

Olbers knowledge was based on the knowledge during his life time, 1758–1840.

It has changed a little since then, bet Obler didn't go home and discuss the super massive black hole at the centre of the Milky Way, until Edwin Hubble the belief was that the milky way was all of the universe, that was as recent as 1922-1923.

Olbers question/paradox was relevant to early 1800's but not to modern cosmology.

Equally our questions today may be considered irrelevant in 50 or 100 years time.

Really sounds more like the question: If we are at the centre of everything then why is the number of stars high when looking at the Milky Way but empty other directions. Simple answer we are not at the centre of anything, we are stuck 2/3 of the way out of the galaxy so the view one way is different to another.

The other aspect is Wiki says:

In astrophysics and physical cosmology, Olbers' paradox, named after the German astronomer Heinrich Wilhelm Olbers (1758–1840) and also called the "dark night sky paradox", is the argument that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe.

The universe isn't infinite, eternal nor static.

Therefore the assumptions, all 3, for the paradox is therefore wrong,

If you think about it Olber must have known this, or realised at least on part was incorrect.

[acey]

Olbers paradox (in fact first noted by Kepler) rested on the assumption that the universe was infinite, infinitely old, and contained infinitely many stars. We now know that at least one of these assumptions is wrong: the observable universe is not infinitely old, i.e. the Big Bang provides a resolution of the paradox.

Suppose that the universe were infinitely old, infinitely large, but contained finitely many stars. Then these would all have gravitated together. So it was generally assumed there were an infinite number of stars (though in fact, even under that assumption, Newtonian physics still implies that they would gravitate together - but this wasn't realised).

Under the assumptions, any line of sight in the sky will land on a star - the sky should be completely filled with starlight. However this would not be like the Milky Way (where empty space is visible between the stars seen in telescopes). It would be total, unbroken starlight across the sky. Hence, since surface brightness is independent of distance*, the surface brightness of the whole sky should be that of a star, i.e. the night sky should be as bright as the surface of the sun. This was the paradox. The most common answer was there must be a lot of dust etc blocking the light, but when conservation of energy came to be understood it was realised that the dust would re-radiate the light, so that was no answer.

The correct resolution of the paradox is that even if there are infinitely many stars spread over infinite space, the finite age of the universe means there are stars too far away for their light to have reached us yet - we only see the light of finitely many stars. (The argument could be equivalently restated using the word "galaxies" rather than "stars"). The first person to propose this solution was Edgar Allan Poe in his book Eureka, in which he claimed the universe must be expanding (he thought it would collapse and then re-explode, repeating the cycle forever). There was no observational evidence for this speculative theory in 1848, and it was ignored. Arthur Eddington was asked his opinion of Poe's theory and called it a lucky hit. Even crank science is sometimes right.

* Proof that surface brightness is independent of distance. If you double your distance from an object then the light you receive from it is reduced by a factor of 4 (by the inverse square law), and its apparent angular size is also reduced by a factor of 4 (by simple geometry), so the surface brightness is unchanged.

[Astro Imp]

Nothing is ever as easy/obvious as one first thinks.

Thank you all for taking the trouble to reply.