28 March 2011

Olbers' Paradox

I just read the wikipedia article on Olbers' Paradox.  What a bunch of nonsense!

The paradox goes like this:   The night sky appears dark.  Yet when we use magnification to look at any dark area of the sky, it's all full of stars, with dark areas between.  When we use even more magnification to look at those dark areas, there are even more stars in there.  The statement is then that if we look at the sky at any angle, we'll eventually run into a star.  So if there are so many stars, why is it that the sky appears dark and not bright?  So then the article goes on to blather about the cosmic background radiation and this being proof for the big bang, and a bunch of other silly explanations.  

Olbers' Paradox is one of those things that is only a paradox if you don't quite get the concepts of infinitesimal and relativeness.  Darkness is a relative thing.  The space between stars is dark because we can't see anything there.  Because our eyes (or whatever tool we're using) aren't capable of getting enough photons to trigger a sensor, we record it as dark.  That's really the end of the necessary explanation.  If we use a more powerful sensor, the threshold changes along with the shrinking field of view, but there's still a minimum.  We would still perceive this as a dark sky even if the universe was actually infinite.  A star that's too far for whatever sensor we're using would be registered as dark, even if it's actually shining bright.

Zeno's Paradox is another of the same sort of thing.  In it, in order to get from A to B, you must first travel halfway.  In order to get from A to halfway, you must first get to half halfway.  And so on.  So if there's an infinite regression of these halfways, then how can we ever get anywhere?  Again, the answer is simply that when you split the distance, you also split the time it takes to get there.  You can always split time and distance farther.  As long as you split them at the same rate, there is no paradox.

(Actually, there is a limit to this sort of splitting, caused by quantum effects.  This impacts our sensors at a much larger scale than it impacts reality.  It's interesting, but not in any way relevant to either paradox)

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