Einstein synchronisation

Einstein synchronisation (or Poincaré–Einstein synchronisation) is a convention for synchronising clocks at different places by means of signal exchanges. This synchronisation method was used by telegraphers in the middle 19th century, but was popularized by Henri Poincaré and Albert Einstein, who applied it to light signals and recognized its fundamental role in relativity theory. Its principal value is for clocks within a single inertial frame. According to Albert Einstein's prescription from 1905, a light signal is sent at time from clock 1 to clock 2 and immediately back, e.g. by means of a mirror. Its arrival time back at clock 1 is . This synchronisation convention sets clock 2 so that the time of signal reflection is defined to be The same synchronisation is achieved by transporting a third clock from clock 1 to clock 2 "slowly" (that is, considering the limit as the transport velocity goes to zero). 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. are called "simultaneity slices". 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. Ludwik Silberstein presented a similar study although he left most of his claims as an exercise for the readers of his textbook on relativity.