Constancy of the speed of light and the unit matching problem

Space-time symmetries and the principle of relativity alone suffice to obtain Lorentz-like coordinate transformations, in which a free parameter, k, plays the part of $c^{-2}$ in special relativity. Several authors have concluded that special relativity does not need the postulate of the constancy of the speed of light (the “second postulate”). I oppose this claim and argue that the transformations have no physical content unless different observers can ensure that they use the same units. The relativity of lengths and durations makes this non-trivial. One usually assumes boostability to solve this problem. I analyze this concept and show it is also non-trivial and cannot be assumed in general. The second postulate offers a way around this, as well as an economical method to match both time and length units. Without it, additional postulates are necessary to ground the physical meaning of the transformations.