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Special Relativity Down to Earth

© Wesley Colley

Relativity is one of those terms invoked in science fiction and lay science writing circles to evoke a sense of mystery, and is often abused to permit time travel and the like. Most people, therefore, have a certain awe for the subject and regard it to be completely inaccessible. I hope to motivate the basic need for special relativity and to make it seem a little less "out there."

Einstein's main idea with special relativity was that the speed of light is the same in all inertial reference frames. Okay, so what is an inertial reference frame? An inertial reference frame is a region of space that is travelling at a constant, unaccelerated velocity. You would be in a very nearly inertial frame if you were somewhere between the galaxies, say half-way between the Milky Way and the Andromeda Galaxy in a spaceship, which was not firing any thrusters, just floating along at a constant velocity. Sitting on the earth, we are not in such a frame, because the earth is rotating, and gravity is pulling on us (among other things), so we are feeling accelerations. However, because those accelerations are small, our reference frame approximates an inertial frame most of the time.

Okay, so what's so grand about this idea. It sounds almost obvious, that any unaccelerated observer finds the speed of light to be the same as would any other unaccelerated observer. As easy as the idea sounds, it has bizarre consequences. Here is the most basic problem. Imagine you're observing a train passing by. On the train there is a clock which works by bouncing light pulses up and down between two mirrors. Let's imagine that the clock is three meters tall, so the light (travelling at 300,000,000 meters per second) strikes a mirror 100,000,000 times per second. So every 100,000,000 reflections is one second, and the clock merrily measures time in that very simple way. So, here comes the train toward you clicking off the seconds precisely. The problem is that because the train is travelling by you, you see the light bouncing along diagonal paths between the mirrors, not vertical paths as an observer on the train would see. If you were to diagram the path of the light, you would see something of a crown-shaped path, as this figure) illustrates. Up and down, but moving horizontally at the same time, the light ray would obviously move faster according to you, than according to someone on the train.

There are one of two possibilities then:

1. We've just established the the total speed of the light ray would have to