Space and Time

`c' in relativity is not only a limiting speed. That arises almost as a byproduct of its much more fundamental role. Most people hear the word `relativity' and think "E=mc2" and "Nothing can go faster than light". Both are partially correct, and partially wrong.

(E=mc2 holds only for an object at rest. The real equation is E2 = p2 c2 + m2 c4, where `p' is the momentum. In terms of speed, p = mv/√(1-v2/c2). I'll give you one guess why the incomplete formula caught on.)

I'll go into the second part a little more deeply. The principle of relativity implies that the no matter how fast you yourself are moving, the speed of light (in vacuum) that you measure will be the same. This is not true of sound. One consequence of this is that a massive object (in the sense that it has mass) accelerating to the speed of light increases in energy without bound. Another is that any massless object has zero energy except at the speed of light. So, objects with mass can't pass the speed of light, objects without can't change speed. But what about objects that might always be moving faster than light? Their rest mass would be a complex number (hence escaping both categories above), which is reasonable since they're never at rest.

Now, back to the original point. Causality.

Another consequence of relativity is that events that look simultaneous to one observer, may not look simultaneous to another. In general, any events that cannot be connected by something travelling slower than light, are ambiguous to the question "which came first?". So, if something travels FTL from Earth to some other star, it will look like it arrived before it left, to someone on a spaceship travelling at a high enough speed (in the right direction) relative to Earth. This may not seem so bad.

After all, it's just another point of view; surely nothing real.

Now, suppose that this other spacecraft is hanging around the far star. And, that it also has FTL equipment. As soon as the first FTL thing arrives, the spaceship uses its FTL equipment to send something back to Earth. Now, by the symmetry of the situation, an observer on Earth will also measure the time of arrival to be earlier than the departure time of the fast-moving spaceship's FTL signal. Fitting these two observations together, the second signal arrived at Earth before the original one left.

It's very difficult to explain in ASCII without diagrams and formulas, but if anyone wants a more technical explanation, try reading some articles from `rec.arts.sf.science'. It comes up in that group rather frequently.

In short: `c' is more than just a speed. It is a conversion between space and time.