A friend sent me this email regarding her son:
This was my reply. I'll point her here if you'd like to chime in with supplements.
Hi there. I need help with a question that Max just asked.
If someone is traveling at the speed of light, could they see themselves in a mirror?
Well, that's very similar to the question that Einstein asked -- what happens if you run as fast as a beam of light -- and to answer it, you have to change the way you think about the world. Fundamentally.
The speed of light isn't a speed you can go. It's just the end of what 'fast' is. A fuel tank has a gauge, it reads 'empty' to 'full.' For speed, 'Empty' is analogous to not moving. 'Full' is the speed of light. It doesn't make sense to talk about speeds past that any more than it would make sense to add gas to a full tank.
So, OK. The speed of light is the end of acceleration. You can't go the speed of light, because if you could, you could just juice it a little more and go faster, which wouldn't make any sense. You can only approach the speed of light. Acceleration gets harder and harder the closer you get.
Now, what does speed mean? If I leave my house, and trot along at 3 MPH, I'm moving at 3 MPH relative to my house. But, what about when I can't see my house? How would I know how fast I was moving? There's a bunch of other stuff in my neighborhood that moves at the same speed as my house, and I can choose one of those things to measure myself against. But, I have to choose something. And, as I measure it, I'm really measuring how fast that thing is moving relative to me. I really never move, from my perspective, right? We're all the center of our worlds, just like it feels.
Those are two points.
(1) I don't ever actually move. Things move relative to me.
(2) Those things never go as fast as the speed of light.
I forget how old Max is. Ah... you got married in, what, 1993? So, he was born in 1994? He's 14? Einstein was 16, you know. Anyway, I'm not going to muddy the waters with quantum dynamics. I'm not super sure I resolve them off the top of my head, anyway -- I think there's some outstanding paradox; I believe there was some news in recent years, but I didn't follow.
Clearly, there are some implications for time, here, and resolving that has some implication for linear distance. But, I'll let Max work those out for himself.