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TheBrownMamba
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In general terms, but not too general.
russ_watters said:If the universe were of infinite age and size, every line of sight would end on the surface of a star and it would be very bright:
http://en.wikipedia.org/wiki/Olbers'_paradox
skeptic2 said:Notwithstanding the post from Eachus with which I agree, I have always questioned the this explanation. It seems to me that although at twice the distance there would be 4 times as many stars, each star would have 1/4 the angular area. Also there would always be some stars hidden by stars in front of them and the farther they are, the more often that would occur. It seems more likely then that with an infinitely large and old universe the sky would not necessarily be very bright but have an intermediate brightness determined by how sparse the stars are.
Olber's paradox also doesn't address the issue of the age of the stars which is not infinite despite the infinite age of the universe. At some point all the hydrogen in a region would be depleted and no new stars could form. In fact if the universe were infinitely old, would that not mean that there could be no shining stars at all - a truly dark sky.
LeonhardEuler said:Suppose the density of stars is roughly constant in the universe and they are randomly distributed. If you take a ray extending from the earth, then over a sufficient distance, the probability that the ray touches the surface of a star over a constant distance, call it "D", is constant.
So the probability of not hitting a star in the first D light years could be (1-p). Not hitting a star in a distance of 2D would have probability (1-p)2. Not hitting a star ever would have probability
[tex]\lim_{n\to\infty}(1-p)^{n} = 0 \ \forall p>0[/tex]
This assumes the universe has some regular structure for a big enough scale of distance. There are big fluctuations in density over even the scale of light years, because of galaxies compared to intergalactic space, but if there is ever a scale over which the distribution of stars is well approximated as homogeneous and isotropic, then this logic would hold.
Of course, there are some assumptions in this argument. If the stars preferentially aligned themselves behind one another from the Earth's perspective, this would not work. But that would make the Earth a very special place in the universe. The universe could be infinite, but with the density of stars diminishing towards 0 quickly as you head outward. This is why you need the assumption of homogeneity.
Well, in order for there to be enough stars visible at once for a significant number to block some behind them, the sky would already need to be extremely bright.skeptic2 said:The discrepancy is that p is not constant with regards to D because some stars will be blocked by other stars in front of them.
True.russ_watters said:Well, in order for there to be enough stars visible at once for a significant number to block some behind them, the sky would already need to be extremely bright.
russ_watters said:In any case, you're still not thinking about it properly. This is isn't like a lottery where once a number (printed on a ball) is used, it can't be used again. Any individual vector has the same finite odds of hitting a star by a particular distance and the fact that some vectors hit more than one star (and some certainly will!) doesn't change that.
No one is suggesting that each vector would hit only one star!
Olbers' paradox is a paradox in astronomy that questions why the night sky is dark if the universe is infinite and filled with an infinite number of stars.
Olbers' paradox is often used as evidence for the Big Bang theory, as the theory suggests that the universe is expanding and therefore the number of observable stars is limited.
There are several proposed solutions to Olbers' paradox, including the idea that light from distant stars gets absorbed by interstellar dust, and the concept of a finite age of the universe.
Olbers' paradox is considered a paradox because it presents a logical contradiction between the observable universe and the proposed properties of an infinite universe.
Olbers' paradox challenges our understanding of the universe by highlighting the limitations of our current theories and the need for further exploration and research in order to fully understand the universe and its properties.