 So a question we might have is, so now we can transform from Alice's frame to Bob's frame. What about the other way, from Bob's frame to Alice's frame? So the way Alice sees the situation is she's not moving forwards. No, she is stationary, while Bob is moving backwards at speed V. So in other words, to transform the other way, we go through the exact same derivation and so end up with the exact same equations, just with V swapped with minus V, or in this case, beta swapped with minus beta. And again, if we look at the low velocity limit, we get the Galilean transformations, this time going in the other direction. So if you're ever trying to transform between two frames, and you can't remember if it's a plus or a minus, which way around the transformation goes, one way to think about it is to imagine in the low velocity limit when you have the Galilean transformations, try and think which way around the sign should be.