Einstein synchronisation
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Einstein synchronisation is a convention in relativity how to synchronize 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 the mean 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 a lot of other thought experiments for clock synchronisation giving the same result.
The Einstein synchronisation looks so natural in inertial frames only. 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 has a diminished 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 its 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).
Accordingly, 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").
[edit] Literature
- A. Einstein, On the Electrodynamics of Moving Bodies. Translation from the German article: Zur Elektrodynamik bewegter Körper, Annalen der Physik 17:891-921. (June 30, 1905).
- A. Einstein, Relativity. The Special and the General Theory, Sect. 8 On the Idea of Time in Physics, Henry Holt (1920). Translation from the German Über die spezielle and die allgemeine Relativitätstheorie. (Gemeinverständlich), Vieweg & Sohn (1917; submitted Dec. 1916).
- H. Reichenbach, Axiomatization of the theory of relativity, Berkeley University Press, 1969
- H. Reichenbach, The philosophy of space & time, Dover, New York, 1958
- H. P. Robertson, Postulate versus Observation in the Special Theory of Relativity, Reviews of Modern Physics, 1949
- Dennis Dieks (ed.), The Ontology of Spacetime, Elsevier 2006, ISBN 0-444-52768-0
[edit] References
- D. Dieks, Becoming, relativity and locality, in The Ontology of Spacetime, online
- D. Malament, 1977. "Causal Theories of Time and the Conventionality of Simultaniety," Noûs 11, 293-300.
- A. Grünbaum. David Malament and the Conventionality of Simultaneity: A Reply, online
- S. Sarkar, J. Stachel, Did Malament Prove the Non-Conventionality of Simultaneity in the Special Theory of Relativity?, Philosophy of Science, Vol. 66, No. 2
- R. Rynasiewicz, Definition, Convention, and Simultaneity: Malament's Result and Its Alleged Refutation by Sarkar and Stachel, Philosophy of Science, Vol. 68, No. 3, Supplement, online
- Hanoch Ben-Yami, Causality and Temporal Order in Special Relativity, British Jnl. for the Philosophy of Sci., Volume 57, Number 3, Pp. 459-479, abstract online
