All of the above problems come from the fact that, even without worrying about gravity, the surface of the Earth is not an inertial frame. An inertial frame is, roughly speaking, one in which Newton's laws do hold. Playing catch on a train is little different from on the ground — at least in principle, and so long as the train is not speeding up or slowing down. Furthermore, an observer on the ground would see nothing out of the ordinary, it merely being necessary to combine the train's velocity with that of the ball.

However, shining a flashlight on a moving train, and especially the description of this from the ground, turns out to be another story, which we will study in more detail below. Light doesn't behave the way balls do, and this difference forces a profound change in our description of the world around us. As we will see, this forces moving objects to change in unexpected ways: their clocks slow down, they change size, and, in a certain sense, they get heavier.

So time is not time.

Of course, these effects are not very noticeable in our daily lives, any more than Coriolis forces affect a game of catch. But some modern conveniences, notably global positioning technology, are affected by relativistic corrections.

The bottom line is that the reality is quite different from what our intuition says it ought to be. The world is neither Euclidean nor Newtonian. Special relativity isn't just some bizarre theory, it is a correct description of nature (ignoring gravity). It is also a beautiful theory, as I hope you will agree. Let's begin.