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by vba616
1539 days ago
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>The paradox itself is that if the universe is both infinite and eternal then we shouldn't have a dark sky I've never really felt like I understood the paradox, since the way people explain it, it sounds to me like they're just denying the idea that an infinite sum can have a finite value. Like, why couldn't the brightness of the sky in an infinite universe be any value at all, depending on the density? The argument against an infinite universe that makes sense to me is that it would collapse on itself. But as a thought experiment, the stars could be massless and/or fixed in place. |
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> 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.
The argument that the universe would collapse in on itself is made using similar math (gravity decreasing with the square of the distance is by no accident the same as brightness) so if you buy one you sorta have to buy the other. Of course, the universe probably is infinite and isn't collapsing in on itself, but that's because of dark energy (OK yes, there are all sorts of universes that obey relativity, and some of them are infinite and not collapsing, but if we live in one of those no one's found the solution that fits our observations. The dominant thinking was that the universe would eventually collapse until we discovered it's actually expanding).