 Okay, so when deriving the Lorentz transformations, we're going to make some assumptions. The first of these is that Alice's and Bob's coordinates start off on top of each other. So at time ta equals tb equals zero, the origins coincided. Zero, zero, zero in Alice's coordinates is the same point that Bob calls zero, zero, zero. Now, this is not the same as saying that at time ta equals tb equals zero, Alice's and Bob's axis are the same. The reason for this is, even though they lie on top of each other, because of length contraction, the scale of Alice's axis could be different to Bob's axis. So all we can say is that time ta equals tb equals zero, the origins were on top of each other. The second assumption we're going to make is that the transformations are what we call linear. That is, xb depends on xa and ta, but not xa squared or xa times ta or anything else like that. So in that case, what is the most general linear transformation between these friends?