As explained in this answer, linearity is a consequence of continuity and homogeneity. In the context of coordinate transformations, homogeneity refers to the equation \begin{equation}\tag{1} T(y+v)-T(x+v)=T(y)-T(x). \end{equation} In other words, if $y'-x'=y-x$, then $$T(y')-T(x')=T(y)-T(x),$$ i.e. if the difference between two pairs of events is equal w.r.t. one initial observer, then this is also the case for any other initial observer.
- Homogeneity doesn't seem like an obvious / intuitive requirement for me, am I missing something? I.e. is there some justification or derivation from other principles?
- At first glance, $(1)$ doesn't have anything to do with the definition of homogeneity given e.g. in the Wikipedia article. Am I missing something?
