I am trying to understand Lorentz Transformations in SR. I have some doubts.
1) In the derivation for Lorentz Transformations, why do we assume that Galilean Transformations hold true when an observer isn't in motion?
i.e. when you say $x'=\gamma (x-ut)$. You assume that an observer at rest, measures $x'=(x-ht)$.
2) Why do we think of multiplying only by a factor $\gamma$ and not adding or differentiating or some other linear operator to act on the measurements ?
3) Does the Second Postulate of SR, ultimately comes from the first one only i.e. all inertial observers are equal, hence there is no special inertial ether frame, thus speed of light must be same for all inertial observers. ( We already know the laws of electrodynamics are true)