You may have heard that the universe is not endless, ending at a brick wall, perhaps, some 15 billion light years out. But what you may not know is that there is a classic proof, going back to the middle ages to show that the universe is not an endless expanse of stars.

Consider an endless universe with a uniform distribution of stars. We would expect that, in any large-enough space of this universe there would have to be many stars, e.g. between 100 and 101 trillion miles from earth. At this distance, each of these stars is close enough to see, and the combination of them (the sum in this volumetric shell) will shed a small amount of heat on the earth. Now consider another shell, the same thickness but twice as far from us; if the universe is uniform, there will be 4 times as many stars, but since these stars will be at twice the distance; that is between 200 and 201 trillion miles from earth, each star will present us with ¼ as much heat as the stars in the first shell. Now, since there are 4 times more stars, the total effect is to radiate as much heat to us as from the first shell.

The same argument goes for each shell of 1 trillion miles thick: each one presents us with the same amount of heat. If the universe is infinite and uniform, we find there will be an infinite number of shells radiating this amount of heat, and therefore an infinite amount of heat bathing us. We should expect to roast from all of it. Since we have not roasted, we conclude that the universe is not an endless, uniform expanse.

The universe could still be uniform and not endless (ending with a brick wall, as in the Hitch-hikers guide), or it could be expanding from a big bang 15 Billion years ago. This latter is suggested by the red shift, but not a favored solution of creationists for some reason. Or it could be a closed, oscillating (or not) 4 dimensional hypersphere (Einstein). That is, it could be a non Euclidean, black hole. Or it could be fractal (Mandelbrot). Or it could be a combination of all of the above.

For a thought about galactic arms see here. October 22, 2012.

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