Einstein synchronisation

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Einstein synchronisation is a convention in relativity for synchronizing clocks at different places.

According to Einstein's prescription from 1905, a light signal is sent at time τ1 from clock 1 to clock 2 and immediately back, e.g. by means of a mirror. Its arrival time back at clock 1 is τ2. The Einstein synchronisation convention sets clock 2 so, that the time of signal reflection is (τ1 + τ2) / 2. Whereas the constant two-way speed of light is included in the axioms of special relativity, the Einstein synchronisation convention also sets the one-way speed of light to c.

The same synchronisation is achieved by "slowly" transporting a third clock from clock 1 to clock 2, in the limit of vanishing transport velocity. The literature discusses many other thought experiments for clock synchronisation giving the same result.

The Einstein synchronisation looks this natural only in inertial frames. One can easily forget that it is only a convention (see relativity of simultaneity). In general relativity frames, most importantly in rotating ones, the non-transitivity of Einstein synchronisation diminishes its usefulness. If clock 1 and clock 2 are not synchronised directly, but by using a chain of intermediate clocks, the synchronisation depends on the path chosen. Synchronisation around the circumference of a rotating disk gives a non vanishing time difference that depends on the direction used. This is important in the Sagnac effect and the Ehrenfest paradox. The Global Positioning System accounts for this effect.

The first substantive discussion of Einstein synchronisation's conventionalism is due to Reichenbach. Most attempts to negate the conventionality of the Einstein synchronisation are considered refuted, with the notable exception of Malament's argument, that it can be derived from demanding a symmetrical relation of causal connectibility. Whether this settles the issue is disputed.

In a popularisation from 1917 however, Einstein presented a definition for deciding which, if any, states of two observers were simultaneous to each other, which is overtly independent of any particular monotonous real-valued parametrization "τ", and without requiring a notion of velocity (much less, whether it were sufficiently "slow" or not). According to this definition, a pair of clocks had been synchronous if for each state of the one there was found a simultaneous state of the other (which, of course, is not guaranteed but may be found as result of measurement) by Einstein simultaneity, and if the simultaneous pairs of states were labelled similarly (although not necessarily by real numbers "τ").

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