suppose two rockets with a passenger are nearing speed of light velocities and are going opposite directions. Relative to eachother one rocket will seem stationary while the other rocket will look like it’s going almost twice the speed of light. What do both passengers see?

Question

I can’t wrap my head around it. But maybe it might be a very silly question with a simple answer.

In: Physics

Answer 1

Space, time and speed don’t work the way we think they do, or are used them working.

Our intuitive ideas about these things only work for small relative speeds (so tens of thousands of miles per hour). When things get to relative speeds that are a decent factor of the speed of light things work differently. Or rather, the approximations we use normally no longer work.

To use an analogy, we know the Earth is a sphere. But if you only look locally (dozens of miles) it looks flat, and we can treat it as flat. The surface of the Earth isn’t flat, but we can pretend it is. If we look on larger scales (or want really, really precise measurements) we have to add corrections for the Earth being curved.

The key rule in Special Relativity is that the “speed of light” (noting that it is the speed that is special, not the light part – light (sometimes) travels at this speed because the speed is important) is the same for all inertial observers. If something is travelling at *c* relative to you, it is travelling at *c* relative to everyone else, no matter how fast they are moving compared with you. *c* is the ‘hinge’ around which space, time and speed rotate and twist.

As things get faster compared with you, their time and space get twisted together; their time passes slower (from your point of view) and their distances get squished (from your point of view). The result of this is that from your point of view they’re not moving as fast as they “should” be.

So if we are in a rocket that is still, and another rocket that is travelling at 0.9c towards us, its time will be slowed down (and it will be squished) by a factor of about 2 when viewed from our point of view. If we have another rocket travelling in the other direction towards us at the same speed, it will also be squished by that factor (from our point of view).

But the second rocket will see things differently; they will see our rocket coming towards them and 0.9c, and it will be *our* time that is running slow, and us that are squished. And then they’ll see a second rocket travelling towards them at about 0.99c (who will be slowed down by a factor of about 7, and squished by that factor).

Times, distances and speeds all look different from the different perspectives. And each perspective is equally valid.