Faster Than Light?

And now for something completely different ...

A long time ago, I read a compilation of Fred Saberhagen's Berserker short stories. The first one, I think, was a piece about the final battle between the Berserker fleet, and the humans that had united to resist them. One of the stranger things in the story was a weapon Saberhagen called the "C-Plus Cannon", a gun that launched its projectiles faster than light. There's an unfriendly weapon for you: first you get the kaboom that comes with getting hit, then you see a missile flying backwards to the ship that fired it. Weird.

But would it really work that way? Let's think about that for a moment.

Let's try a thought experiment. We're going to visit our experimental station on Eris, way the heck out in the Kuiper Belt. We're going to watch a demonstration flight of a prototype vessel capable of flying twice the speed of light. (Yes, this "experiment" contains a fatal flaw ... but bear with me, we'll come around to it presently.)

The flight plan is that it'll fly out twelve light-seconds, do a flip-turn, and fly back to base. At T=0, it begins to fly away. The image begins to fly off in the direction of the target, but not as fast as we'd expect. After three seconds, the image has only receded by two light-seconds. Huh? That doesn't seem right ... At six seconds, it's at the four light-second mark. It continues to crawl into the distance, reaching eight light-seconds away at the twelve-second mark. We're about ready to call it a bust, when BLAM! The vehicle suddenly re-appears at the dock! And, its image begins to shoot backwards at what appears to be twice the speed of light. We watch, boggled, as the two images converge on either side of the flip-turn, when they both vanish.

Weird enough for you? Except for one problem ... It could never actually happen that way. We'll show that by doing another thought-experiment. But we're going to lay down a few simple rules first. They're based on some simple principles that describe the way we think the world works.

One: It's a property of photons that they can only travel at one speed in a particular medium. That's to say, light always moves at the speed of light. It can't accelerate or decelerate, it can only gain or lose energy in frequency.

Two: There's no such thing as a universally-preferred frame of reference. Which is to say, there's no such thing as absolute motion. Motion is always relative to something else you can see.

Three: If you're way, way out in deep space, there's no way to tell if you're at rest, or if you're moving at a constant speed, in a straight line. That's a subset of the principle above. Absent a reference to the contrary, you may as well be standing still.

Four: The speed of light is the same in every inertial frame of reference. That means it doesn't matter who's looking at it, they all clock a beam of light at the same speed.

Bearing those four things in mind, let's imagine two ships out in deep space. Both are moving at a constant speed in straight lines. One of them is charged up to several million volts relative to the other, and they're going to pass very close to one another.

Let's look at the encounter from the first ship's point of view. Your instruments can't tell if you're moving or not, so you're perfectly justified in saying that you're sitting still while this other fool zips past you. At closest approach, a spark jumps between the ships, causing a flash. ZAP! You're now at the center of an expanding shell of photons, racing away at the speed of light in all directions.

The interesting thing is that we can make the exact same observation from the point of view of the second ship. You're minding your own business when this other guy flashes past, then ZAP! You're at the center of an expanding shell of photons.

Notice that we haven't said anything about the relative speed of the "moving" ship. It can be arbitrarily large, up to a point ... But do notice that from either point of view, both ships are within the expanding shell of photons!

Therefore, both ships must be traveling slower than the speed of light. However fast we imagine either ship moving, we cannot imagine a situation that places either ship outside of the flash zone, unless one of our four assumptions is incorrect.

Now, if we go back and look at our first experiment, we see that the way it's set up does violate the assumptions. It assumes a preferred, God's eye frame of reference that can't exist. And it ignores the fact that light always moves the same speed in every frame of reference. There are probably other problems too, but those are the major deal-breakers.

The sad and sorry fact is that faster-than-light travel does not appear to be possible within our space-time. There may be ways to cheat, by bending or folding space, but that's a story for another day.