# Special Relativity/Lorentz Transformation Derived in two minutes

It's the other way around. We don't know there was a max speed. So the starting point was just an extension of the Galiliean transformation. Then as I showed, we actually have two choices. In one choice, the space-time transformation is symmetric. In such a universe, we find there is a max speed, as shown by the velocity addition formula derived from the transformations. With the other choice, one would have no such properties. The speed can be infinite.
But you confirm that you are using some sort of relativity principle/postulate when you say that a factor is the only possible solution for this extension of the Galilean transfomation, don't you?

DaTario

It's the other way around. We don't know there was a max speed. So the starting point was just an extension of the Galiliean transformation. Then as I showed, we actually have two choices. In one choice, the space-time transformation is symmetric. In such a universe, we find there is a max speed, as shown by the velocity addition formula derived from the transformations. With the other choice, one would have no such properties. The speed can be infinite.
As Dadario has pointed out, by introducing the lorentz contraction factor in equation (4), you have made the maximum speed finite. You state that the coefficient of XA in (6) can be expanded as a Taylor series, without mentioning the interval over which it converges. You then decide to eliminate terms of order 2 and above because the theory is "linear" which looks to me wrong because the transformation is still linear in x and t as long as their coefficients are constant.