@naturallyInconsistent The speech you made is certainly interesting, full of rigour and conceptually very stable. However, I never said I wanted a solution to my problem. My initial challenge was to try to understand if it was possible to preserve the characteristics of Galilean transformations by moving from an inertial frame to a non-inertial frame. We realised that this can be done, although doing it is difficult. @RyderRude proposed his version of a time-dependent transformation and was quite helpful to me, showing me how my problem could be approached. I make no claim to a total resolu…