 One more issue we should talk about is the idea of sight. Throughout this, I've been saying things like Bob sees Alice's clock tick. But normally when someone says sees, they mean light from the event hits your eyes. But if I look at, say, the sun, it's eight light minutes away. So I'm not seeing the sun as it is now in my reference frame. I'm seeing it as it was eight minutes ago. Now throughout what we've done, and in the future, we are going to ignore this effect. When I say Bob sees the clock tick, what I mean is the clock ticks in Bob's reference frame. The field that actually studies what you would see if an object was moving very fast is called relativistic optics, and it's full of lots of interesting results. Because normally, if you look at, say, a train or something in everyday life, you're seeing the back of the train and the front of the train at pretty much the same point in time. If, however, that train is moving close to the speed of light, in the time it takes the light to reach your eyes, the train has moved an appreciable distance. And this changes all the angles and things. This means you see different parts of the train from different angles and at different points in time. And it turns out things like length contraction are never actually visible to you. They happen physically, but you can't see them. And if you were to look at an object traveling close to the speed of light, it wouldn't look shorter to you, but it would actually look rotated. But as you've seen, for example, through things like the neutrino question, Lawrence contraction is a real physical effect which makes real results that we can predict and measure.