What the paper claims it is saying: you can get the Lorentz transformations without requiring an invariant speed. What the paper is actually saying: assuming t

What the paper claims it is saying: you can get the Lorentz transformations without requiring an invariant speed. What the paper is actually saying: assuming there isn’t a privileged reference frame, you can show that either the Galilean transformations hold (i.e. simultaneity is invariant, suggesting instantaneous propagation of forces, a special case of Lorentz transformations where c is infinity) or Lorentz transformations hold (i.e. a single invariant speed in all reference frames, suggesting propagation of forces at that speed). Empirically, we know from measuring the speed of light that we live in the latter world. But we can’t prove that a priori as the title suggests.