Hattix

Been a while since I covered some nice hard science in the blog, so here’s some. Caution: May contain traces of Special Relativity, including but not limited to lightcones and worldlines.

The usual uneducated answer is just “Oh that’s just hubris. We’ll learn some new physics that let it happen. It’s just a breakthrough away” so I’m about to show why it can’t happen, no matter what breakthroughs may be made.

For simplicity, we’ll use a hypothetical superluminal signal. It could be anything from a radio transmission to a rocket. We have Earth and a distance spacecraft and we communicate that signal. According to controllers on Earth, the signal is obviously received after it was sent. Our spacecraft is going very fast, however, so is undergoing time dialation. The spacecraft then sends the same signal back, using the same superluminal method, to acknowledge that it arrived correctly.

That all seems well and good, right? It isn’t, we get a VERY big problem. Let’s work out why.

We cannot influence (in any way at all) anything that’s, say, a light year away for at least another year. Nothing we can do can propogate faster than light, but our signal above can. We’ll do this visually.

Let’s plot space against time with our trusty MSPaint.

In our example, Earth is at the origin. We send a message faster than light to our spaceship. As we have both axes as the same unit (spacetime), then a photon’s path would be at 45 degrees from bottom left to top right. Going faster than light, our signal gets there before the photon does, so has a gradient below one. The photon would arrive later. The next diagram shows a photon and our signal getting to the spaceship’s location in space. First, however, we need to plot space and time on the same graph for the spaceship - As it’s moving, it’ll be tilted relative to the one for Earth, this means we have to transform the axes a little bit. Black is Earth, blue is the spaceship. Yellow is a beam of light, the thin black is when Earth sees it arrive at the spaceship, the thin blue is it the spaceship seeing it arrive at itself. You’ll notice these lines are parallel in space and time to the major axes of both observers - This is simultaneity at work, if we had only one axis (as above) then the lines would be vertical and horizontal but being parallel is what counts.

So let’s get on with it and send a signal faster than light already. It’ll be yellow again. Note that we have to draw the line below the blue axis for space for the spaceship. If we didn’t, then it wouldn’t actually be faster than light, we could just shift the axes of course.

The signal is yellow, going faster than light, so it’s going along the space axis more per unit of time than the light would, or going through time less per unit of space than the light would. As far as Earth is concerned, it arrived at the spaceship in the future (the black time marker is positive, it’s in the future) but look where it is for the spaceship. The blue line of simultaniety for the spaceship is in the past, but this has no meaning as the spaceship doesn’t know when it was sent.

What happens when the roles are reversed and the spaceship echoes the message back? The reply arrives back at Earth before the original signal was sent from Earth! Effect has just come before cause. If that signal was a messenger, then that messenger would arrive home before he left, which just doesn’t make any sense.

That, hopefully not too scary, is why we’ll never be able to go faster than light.