- #1
snoopies622
- 840
- 28
I've finally worked out a derivation of the Lorentz transformation that doesn't use the now out of favor [itex]i^2=-1[/itex], but it still has one weak spot: it assumes that the transformation is linear. It seems quite reasonable to me that it would be linear since it has to graph straight lines on to straight lines (since the laws of mechanics should be the same in both reference frames) but how can I go from that fact to
x' = Ax + Bt
t' = Dx + Et
where A,B,D and E are constants without any doubt? Is it mathematically possible for a transformation that requires any straight line in one coordinate system to become a straight line in the other coordinate system to assume some other, non-linear form?
x' = Ax + Bt
t' = Dx + Et
where A,B,D and E are constants without any doubt? Is it mathematically possible for a transformation that requires any straight line in one coordinate system to become a straight line in the other coordinate system to assume some other, non-linear form?