A moment’s reflection convinces one that as a result of this alternate
Ansatz, ‘simultaneous’ events in any frame must be those on a worldline parallel to the pure space-like axis.
I had to draw a picture in my head, in that non-euclidean Minkowski geometry, to realize this was saying simply that time and simultaneity work exactly the way we commonly imagine them to work. :) (Actually the non-euclideanness is irrelevant in this case.)
