Is Space-Time Curved or Not?
Thinking more about the basket ball example, one might think that there is an easy way out. After all, the basket ball is curved, the floor is not, so maybe there was nothing really deep there.
First of all, as we all know, the earth is round, so the floor is only approximately flat. It’s only a matter of scale. The two cases we were considering were more similar than it first appears.
But there is something more. Remember how we did prove that the ball was flat? Well, if we were to prove that space-time is flat or curved, wouldn’t any similar experiment require that you control your displacement through time? Since you can’t, we have instead to rely on the fact that a tick of a clock “here” is the same as a tick of a clock “there”. But then, did we prove that space-time is curved and the clocks behave the same, or that space-time is flat and the clocks behave differently?
Maybe the problem of finding if something is flat is too complicated. What if we began with something simpler? What if we started by agreeing on what a straight line is? But the closest we have to a physical straight line, like a ray of light, bends under a variety of conditions. We observe that with a simple lens, but even in the vacuum, gravity can bend light, a phenomenon known as “gravitational lensing”.
How do we know that light bends? Because we see multiple light rays starting from the same point (a start) and ending at the same point (our eye). Like the four steps dance describe earlier, this test can be used to determine if space-time is curved (two lines can start and end at the same point) or not (there is exactly one line between two points). But have we proved that space-time is curved, or that light bends under the influence of gravity?
Well, to prove the latter, we would have to find something “straighter” than a light ray. And that’s the whole problem. Not that there aren’t things that are sometimes straighter than rays of light, as anybody who ever put a pencil in water and saw it bend would know: the light bends at the interface between air and water. If we see the pencil make an angle, it must be because the pencil itself does not bend at the same location. So the light ray bends, but not the pencil.
So it seems like the most fundamental measurement of all, the measurement of space and time, obeys markedly different laws depending on how we measure it.
Straight? What Does That Mean?
Sunday, November 19, 2006
