Wednesday, June 29, 2011

How fat am I?

Suppose I think of myself as shaped like a four-dimensional spacetime worm. We draw diagrams of such things for students—a wide line moving up the board. It is amusing to note that such diagrams are not at all to scale. In a natural unit system, the speed of light will be taken to be c=1. For instance, one might measure time in seconds and distance in in light-seconds. A light second is 299792458 meters long. An average human earthly lifespan is of the order of magnitude of 109 seconds. My largest spatial dimension is about two meters, i.e., about 10−8 light-seconds. That means that my earthly temporal dimension is of the order of magnitude 1017 times longer than my largest spatial dimension. This means that I thought of as a spacetime worm, I am an exceedingly thin worm. If this worm were rotated, projected and scaled so as to be a meter long and maximally thick, a hydrogen atom would be ten million times thicker than the worm.

Moreover, this worm is quite straight. The main variation in its shape seems to be a cork-screw shape induced by the earth's orbit around the sun. But the diameter of the spiral is about a thousand light-seconds, which is a millionth of its length.

So a scale drawing of me in my earthly career as a space-time worm would have me be 1017 times thinner than I am long, and despite a subtle cork-screw, straight to within about one part per million.

No comments: