Topics in Physics: 'c' THE constant of Relativity

I know that in the comment for my next to last blog I said that the next blog would be about Snell's Law, but I guess I'm not quite ready to get to that. Maybe it wasn't as big of a deal as I was first thinking. Anyway, back to the topic at hand.

In the colloquial domain, I think physics' Theory of Relativity is often confused with Relativism. Whenever I mentioned relativity to a former math classmate of mine, he would always laugh and say "Everything is relative!" But this of course begs the question (not in the sense of a logical fallacy, but in the sense of crying out to be questioned) "Relative to what!?" If EVERYTHING is relative, then nothing means anything. Fortunately, in The Theory of Relativity, c is the absolute which holds everything together. That said, c may not actually be as absolute as we would have liked.

For starters, I can see at least two ways of interpreting the statement that "the speed of light is an absolute". First, it could mean that light always travels at 299,792,458 m/s. It could also mean that absolutely nothing ever travels faster than the speed of light.

In the first case, light that we see almost always travels at less than c, because it is not in a vaccuum. Every medium: air, glass, water, etc has it’s own index of refraction. The speed of light in air (@STP) is actually c/1.00029 = 299,705,543 m/s. That’s a difference of 86,915 m/s. Since everyday air probably varies slightly from Standard Temperature and Pressure, light in our everyday experience probably travels at an exactly constant speed only very rarely. By using Bose-Einstein Condensates, some physicists have even managed to slow light down to about 38 mph! There are even some who think that c has been slowing down over time.

Secondly, some waves can travel faster than the speed of light, in the case of phase velocities. Basically, when you have multiple waves of close frequency traveling together, you get what is called a beat frequency. There is an outer wave, the ‘envelope’ that travels at the group velocity. Inside are waves that travel at individual phase velocities. These phase velocities may be faster than light (or even vice versa), but it doesn’t matter since they are contained by the slower-traveling envelope. Effectively, this means that information cannot travel faster than the speed of light.

So, now I’ve just shown you how c may not be constant at 299,792,458 m/s, light doesn’t consistently travel at c, and somethings can even go faster than c! So much for constancy.

One more thing, if something ever did travel faster than light (and I don’t mean phase velocities), according to spacetime diagrams, that might be the equivalent of going backwards in time. In the somewhat similar Feynman diagrams, a positron might as well be an electron going back in time. That is not to say that a positron actually is an electron going backwards in time, but according to the descriptions that physicists have been able to develop for quantum phenomena, they are identical. Things at the quantum level behave so weirdly anyway, that it just might be possible for things beneath the Plank dimensions to actually go backwards in time.