Well saying the math 'works' is not quite right. If anything the math doesn't work out because there is no way to transform a normal trajectory into a superlumi

Well saying the math 'works' is not quite right. If anything the math doesn't work out because there is no way to transform a normal trajectory into a superluminal one. Sure you can just define a line through space-time that is superluminal. That's basically equivalent to just defining a singular moment in time, the same way that an (inertial) trajectory defines a constant position.