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The Einstein synchronisation looks this natural only in inertial frames.
A substantive discussion of Einstein synchronisation's conventionalism is due to Reichenbach.
In rotating frames, even in special relativity, the non-transitivity of Einstein synchronisation diminishes its usefulness.
Einstein synchronisation (or Poincaré-Einstein synchronisation) is a convention for synchronising clocks at different places by means of signal exchanges.
Other examples concerns all the subtleties involved with synchronisation procedures in special and general relativity (Sagnac effect and Einstein synchronisation)
For this reason, and since more recent developments are not so well known, some physical papers still present the assumption of consistency of Einstein synchronisation among the postulates of relativity theory.
In the question whether simultaneity in STR, the Einstein synchronisation, is conventional, Malament argues against conventionalism and is thought to have refuted Adolf Grünbaum's argument for conventionalism.
However, contrary to Einstein, who later used a similar synchronization procedure which was called Einstein synchronisation, Darrigol says that Poincaré had the opinion that clocks resting in the ether are showing the true time.
It relied on the principle of relativity to derive the Lorentz transformations and used a similar clock synchronisation procedure (Einstein synchronisation) that Poincaré (1900) had described, but was remarkable in that it contained no references at all.