# The Fun of Going Faster-Than-Light

“There is also an amplitude for light to go faster (or slower) than the conventional speed of light. You found out… that light doesn’t go only in straight lines; now, you find out that it doesn’t go only at the speed of light! It may surprise you that there is an amplitude for a photon to go at speeds faster or slower than the conventional speed, c.” –Richard Feynman

You’ve been around the block a few times, and you know how it goes when you try to go faster and faster. Everything works just like you expect, until you start getting close to the speed of light, c. And then, all sorts of weird things start happening.

Lengths contract, clocks run slow, and the more and more energy you put into the system, the faster it moves!

Only, it can never reach the speed of light. It can approach the speed of light, but it will never reach it. In fact, no matter how fast an object moves, it always sees light moving at c, the Universal speed of light.

But we’re very clever. If we can’t make things with mass even go at the speed of light, much less faster than it, perhaps we can go in the other direction: slow light down.

This is easier than you think; all you need is some sort of non-vacuum to pass light through! (Every Pink Floyd fan should know how to do this.)

After all, even though you can’t go faster than the speed of light in vacuum, there’s no law saying you always need to be in a vacuum. So what can we do? Perhaps we can create a particle (like an electron) in some nuclear reaction that’s moving close to the speed of light in vacuum, and then make it enter a medium, like water, glass, or acrylic!

What happens now, if the particle — moving slower than c — goes faster than light in some medium?

Amazingly enough, the particle freaks out, and starts emitting light. The light is very special, and comes off in a particularly cone-like shape, and is the particle’s way of trying to shed that extra energy until it gets down safely below the speed of light! The light is called Čerenkov radiation (pronounced and sometimes-lazily-spelled Cherenkov), after its Nobel-prize-winning discoverer.

It’s almost always high-energy light, so that if any part of it appears visible, it’s in the blue end of the spectrum. In fact, if you go inside your nearest nuclear reactor, you’re likely to see a bluish glow.

So that’s what happens if you move faster than the speed of light! Some particles, like cosmic rays, move so close to c (we’re talking with millions of times the energy we can create at the LHC), that even the atmosphere, where the speed of light is 99.97% of c, can produce Čerenkov radiation!

Now, for those of you who are science fiction fans, the gears might be turning in your brain. “What about,” you might ask, “a Tachyon?!” What about theoretical particles that move not slower than light, nor at the speed of light, but faster than c?

If such a thing as a tachyon exists, shouldn’t it emit Čerenkov radiation, and therefore be detectable by the Čerenkov light it emits?

It turns out that the answer is no, for some surprising reasons. Let’s think about these three classes of particles: the slower-than-light ones, the at-the-speed-of-light ones, and the tachyons.

• You move slower-than-light if you have a real, positive mass. Nothing with mass can ever reach or exceed the speed of light in vacuum; that would take an infinite amount of energy, and that’s why c is the speed limit of the Universe. If you move faster than light-speed in a medium, you’ll emit Čerenkov radiation until you’re moving slower than light-speed in that medium.
• If you move at the speed of light, that means you have zero mass. Relativity doesn’t really give you much choice; that’s the speed you travel at. This means you move at c in vacuum, you move at whatever the speed-of-light-in-media is when you’re not in vacuum, and that’s it.
• But if you move faster than light, something’s got to be different. Your first guess might be that you have negative mass, but that’s not quite right. Negative mass would still mean that you’re just like normal matter, except you’re not a real particle; you’re a virtual one. If you want to be a tachyon, you need something even more ridiculous seeming:

You need the square of your mass to be less than zero, which means you need an imaginary mass!

And it turns out that a tachyon, with its imaginary mass, moving faster-than-c is just like a normal, massive particle, moving slower-than-c. In other words, a tachyon traveling faster-than-light through a vacuum would be just fine, just like a normal particle would be fine moving slower-than-light. No emitted radiation, no changing of its speed, nothing like that at all.

In other words, a tachyon wouldn’t spontaneously just emit Čerenkov light, or produce a show like the above image.

But let’s say you’re really gung-ho about this, and wanted to know what could cause a tachyon to emit Čerenkov light. Well, learn relativity and quantum field theory, and you can figure it out!

What it takes — assuming your tachyon exists and is electrically charged — is to find a medium where the speed of the tachyon is smaller than the speed of light in that medium! That will force you to emit Čerenkov light, and as you do, your tachyon will gain speed until it goes back to its “normal” state: moving faster than the speed of light!

And that’s all you need! In theory, if there are charged tachyons zipping around through space and we just haven’t seen them, building just the right kind of material with the right index of refraction could allow us to detect them! And now you know a fun result that many theoretical physicists botch: tachyons don’t emit Čerenkov radiation unless they move slower-than-light in a medium!