Traveling to the past by being fast

According to special relativity [1,2], if you can travel faster than light, then you can travel through time. We can see how this would be possible using spacetime diagrams.

Traveling faster than light

Let’s say that it is possible to travel ten times faster than the speed of light. The worldline would look like the following. There is nothing surprising here.

Traveling to someone else’s past

Now let’s see what this worldline looks like in another reference frame. Specifically, let’s see what it looks like in a reference frame moving at $$0.9c$$ compared to the original reference frame.

Things look different now. The worldline ends up in the past in the other reference frame. But this is in the past in a place far away, so maybe you try telling yourself that it’s not really traveling to the past. Maybe you try to argue that no matter what you do, you will not be able to go to your own past, so it would not count as time travel to the past, and that traveling faster than light does not mean you could travel to the past.

If you think that, you would be wrong.

Now let us say that you slow down to a stop in this other reference frame. Since the same laws of physics must hold in all inertial frames, if you can travel faster than light in the original reference frame, you can travel faster than light the same way in this other reference frame. So let’s travel ten times the speed of light again, except in the opposite direction. The worldline would then look like the following.

Note that we are traveling ten times the speed of light in the $$other$$ reference frame which is moving at $$0.9c$$ relative to the original reference frame, and $$not$$ ten times the speed of light in the original reference frame, when we are traveling in the opposite direction. Now let us see what this looks like in the original reference frame.

Note that the wordline passes through the past of the origin. In other words, it passes through your own past. You could send messages to your past self as you pass by, or you could even interact with yourself if you stop at where you started from. We just found out that being able to travel faster than light means you could travel to your own past.

Traveling to the future

What about traveling to the future? This is easy; we already travel to the future at one second per second. And if you want to travel faster into the future, it’s a “simple” matter of taking advantage of time dilation; you “just” need to figure out the engineering challenges to travel close to the speed of light.