We shall examine in the following section two reasons for adopting PULC (given PLC), the first based on (a 'weak' version of) the relativity principle, and the second on the outcome of the 1887 Michelson-Morley experiment.
More recently, the notion that PR and PLC jointly imply only PULC (and not light-speed invariance) found support in the 1984 work of Tzanakis and Kyritsis, who claimed that PR 'does not a priori mean that the speed of light (or any other parameter) characterising each of these |inertial~ systems has the same value in all of them' (Tzanakis and Kyritsis |1984~).(12) In analysing the validity of this claim, one is faced with a putative ambiguity inherent in the slippery concent of form invariance of physical laws.
What Robertson did not say explicitly was that PULC is also a consequence of the Michelson-Morley experiment (given the standard Einstein convention for synchronizing clocks, which Robertson explicitly adopted), despite the fact that variations in the speed of the light-source was not a feature of the experiment.
(iii) We have seen, then, that given Einstein's light postulate PLC, the principle PULC can be justified by appeal either to the weak principle of relativity or to the Michelson-Morley experiment.
For it follows directly from Robertson's analysis that PULC and the 'reciprocity' principle, together with the standard symmetries, jointly imply the Lorentz transformations up to a scale factor, as we shall see later.
The question arises whether reciprocity is strictly necessary in the derivation of relativistic kinematics based on PULC. To answer this question, we must first define our terms.
So far we have not used the requirement that c in S and c|prime~ in S|prime~ are independent of the spatial orientation of the light ray, which is a consequence of PULC. Once PULC is adopted, it becomes fairly obvious that reciprocity is equivalent to light-speed invariance.
The use of contrived clocks also allows us to derive in a very simple way the coordinate transformations appropriate to the standard clocks when PULC holds.
which can be checked directly from (11) and (3), showing again that reciprocity is equivalent to light-speed invariance given PULC.
The transformations (11) do not appear in his study, but they follow from the conditions Robertson derived as a result of PLC and the Michelson-Morley experiment,(27) which (as we saw in the last section) jointly imply PULC. Robertson's more lengthy derivation made no use of contrived clocks and the transformations known to hold for them, but was based on first principles.