Thursday, July 15, 2010

Why is the sky dark at night?

Olbers' Paradox
If the universe were infinite and stars were uniformly distributed throughout it there would be an infinite number of stars. If the universe had always existed, the light from every one of those stars would have had time to reach us.

That means that no matter where we looked, our line of sight would end in a star. There would be no space between them. The sky should be a solid white sheet of the faces of stars.

But it isn't. Which means that at least one of those three assumptions (infinite universe, uniform distribution of stars, universe always existed) must be wrong. So far the one which appears not to be true is that the universe has not always existed.

The best estimate is that the Big Bang was 13.7 billion years ago. In that time light can have traveled only 13.7 billion light-years. So the furthest away thing we can see is 13.7 billion light-years away. (It was that far away when it gave off the light we would eventually see. It is further away now because the universe has been expanding rapidly the whole time the light was en route to us.) So though the stars are indeed infinite in number, the stars we can see, even in theory, are not.

Thus our lines of sight in the sky are not infinitely long. They reach out no further than 13.7 billion light-years and thus generally do not end on the surface of a star. Which is why the sky is dark at night.

Which means that cosmology and the Big Bang and the origin of the universe and all that woo-woo stuff that it seems like only astrophysicists understand, is not far away and abstruse and hocus-pocus and remote from your life. You can look up and see it tonight.



  1. One question that always comes up when people think about the Big Bang and the origin of the universe is, "What was here before the universe was here?"

    The answer is that it is a trick question, but it is the asker who is tricking herself in asking it. The beginning of the universe is not just the beginning of the stuff in it, like you and me and your pet hamster Rudolf. It is also the origin of time and space. Before there was time and space there was no "before" and no "here".

    It is analogous to asking, "What is north of the North Pole?" The problem isn't that there is no answer. The problem is that the question violates the definition of the thing it is asking about.

    Just as "north" means "closer to the north pole", so "before" means "earlier in time". Without time, there is no "before", just as without the north pole there is no "north".

    The same applies for the existence of space and "here". Since there was no here here, it follows therefore that before the Big Bang the entire universe was Oakland.

  2. Nick Danger11:29 PM

    The last sentence of the fourth paragraph should start "So if the stars ...", since we don't know if there are an infinite number of stars (though it is unlikely for other reasons). We also now know that there is no uniform distribution of stars, since they mostly reside in galaxies, which are themselves non-uniformly distributed. The dark night sky reveals not only that the Big Bang (or something like it) actually marked the beginning of the universe we know, but that the universe is not infinitely old, that it evolves.
    But, if the entire universe before the Big Bang was Oakland, then God must have been in Berkeley.