This synchronisation method was used by telegraphers in the middle 19th century,[citation needed] but was popularized by Henri Poincaré and Albert Einstein, who applied it to light signals and recognized its fundamental role in relativity theory.
The literature discusses many other thought experiments for clock synchronisation giving the same result.
The problem is whether this synchronisation does really succeed in assigning a time label to any event in a consistent way.
To that end one should find conditions under which: If point (a) holds then it makes sense to say that clocks are synchronised.
Given (a), if (b1)–(b3) hold then the synchronisation allows us to build a global time function t. The slices t = const.
Einstein (1905) did not recognize the possibility of reducing (a) and (b1)–(b3) to easily verifiable physical properties of light propagation (see below).
Instead he just wrote "We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following (that is b2–b3) relations are universally valid."
Max von Laue was the first to study the problem of the consistency of Einstein's synchronisation.
[2] Ludwik Silberstein presented a similar study although he left most of his claims as an exercise for the readers of his textbook on relativity.
[3] Max von Laue's arguments were taken up again by Hans Reichenbach,[4] and found a final shape in a work by Alan Macdonald.
However, the previous conditions that guarantee the applicability of Einstein's synchronisation do not imply that the one-way light speed turns out to be the same all over the frame.
Consider A theorem[6] (whose origin can be traced back to von Laue and Hermann Weyl)[7] states that Laue–Weyl's round trip condition holds if and only if the Einstein synchronisation can be applied consistently (i.e. (a) and (b1)–(b3) hold) and the one-way speed of light with respect to the so synchronised clocks is a constant all over the frame.
Indeed, it has been experimentally verified that the Laue–Weyl round-trip condition holds throughout an inertial frame.
Since it is meaningless to measure a one-way velocity prior to the synchronisation of distant clocks, experiments claiming a measure of the one-way speed of light can often be reinterpreted as verifying the Laue–Weyl's round-trip condition.
In rotating frames, even in special relativity, the non-transitivity of Einstein synchronisation diminishes its usefulness.
Synchronisation around the circumference of a rotating disk gives a non-vanishing time difference that depends on the direction used.
A substantive discussion of Einstein synchronisation's conventionalism is due to Hans Reichenbach.
[8][9] In 1898 (in a philosophical paper) he argued that the assumption of light's uniform speed in all directions is useful to formulate physical laws in a simple way.
[10] Based on those conventions, but within the framework of the now superseded aether theory, Poincaré in 1900 proposed the following convention for defining clock synchronisation: 2 observers A and B, which are moving in the aether, synchronise their clocks by means of optical signals.
Because of the relativity principle they believe themselves to be at rest in the aether and assume that the speed of light is constant in all directions.
Therefore, they have to consider only the transmission time of the signals and then crossing their observations to examine whether their clocks are synchronous.
Let us suppose that there are some observers placed at various points, and they synchronize their clocks using light signals.
And in fact they mark the same hour at the same physical instant, but on the one condition, that the two stations are fixed.