Lorentz Transformation
& Particle/Wave Duality
Length Contraction &
Relative Simultaneity
Absolute Simultaneity
& Invarant Lengths
Reciprocity Principle
The Reciprocity Principle
We noted here that John Field came to the conclusion that the Reciprocity Principle did not apply to Special Relativity. Instead, he replaced the Reciprocity Principle:
"If the velocity of an inertial frame S' relative to another such frame S is v, then the velocity of S relative to S' is -v."
With a "Kinematical Reciprocity Principle":
The velocity of an inertial frame S' relative to an inertial frame S in primary space-time experiment is equal and opposite to the velocity of S relative to S' in the reciprocal experiment.
This uses the concept of primary and reciprocal scenarios, instead of reciprocal views of the same scenario. Unlike the Reciprocity Principle, this Kinematical Reciprocity Principle applies to both Galilean and Special Relativity.
From this he derives the "Measurement Reciprocity Principle":
Reciprocal space-time measurements of similar rulers and clocks at rest in two different inertial frames S, S', by observers at rest in S', S respectively, yield identical results.
We can paraphrase the Measurement Reciprocity Principle as "space-time measurements by two different inertial observers will be the same", which is the first postulate Field uses to derive the Lorentz Transformation, as noted here.
John Field's paper "Primary and reciprocal space-time experiments, relativistic reciprocity relations and Einstein's train-embankment thought experiment" may be downloaded here.