 Let's wrap things up with something which maybe some of you have noticed. We said that if Bob is standing on the platform, watching Alice go past in the train, from Bob's point of view, Alice will be living in slow motion. But we've also been saying all this time, velocity is relative. Bob can't say everyone must agree that I'm stationary. Alice is just as well within her rights to say I'm stationary, and Bob is moving past in that direction. But then in that case, shouldn't Alice see Bob living in slow motion? And the answer is that yes, she will. If Alice and Bob are both waving at each other as the train goes past, Alice will see Bob waving in slow motion, whereas Bob will see Alice waving in slow motion. Okay, but we have these two relations, right? T A equals gamma T B, and T B equals gamma T A. Then both of these equations can't be true at the same time. So whenever there's a paradox in special relativity, try and be as concrete as you can. So when we're talking about time dilation, we're talking about the time between two events. And these events are the clock starting to tick and the clock stopping tick. Start, stop, and T A and T B are the times between those two events in two different frames. So let's look at things from Alice's point of view. Alice is like, I have my light clock like this. The photon starts here, that's where the tick starts. That's my first event. Comes out there and bounces back. And this is the second event, the photon returning to here, finishing the tick. So from Alice's point of view, both of the two events, the start and the stop of the tick, happen in the same place here. Now what about from Bob's point of view? So Bob's on the platform, the clock starts here, and the first tick happens here. But then the clock's moving on the train, and the second tick will happen over here. So from Bob's point of view, the two events we're talking about happened in different places. So that fixes which way around the equation should be. If Alice says the two events happened in the same place, whereas Bob says no, the two events happened in different places, then we use the result T B equals gamma T A. If it's the other way around, then gamma goes on the other side.