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# Einstein synchronisation

Einstein synchronisation (or Einstein-Poincaré synchronisation) is a convention in relativity for synchronizing clocks at different places.

## Poincaré

In the framework of Lorentz ether theory, it was stated by Henri Poincaré in 1900 that 2 observers A and B which are moving in the luminiferous aether, synchronize their clocks by optical signals. Since they believe to be at rest (because of the relativity principle) they 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. In 1904 Poincaré illustrated the same procedure in the following way: A sends a signal at time 0 to B. B also sends a signal at time 0 to A. If in both cases the signals arrive at the same time t the clocks are synchronous.

## Einstein

According to Albert Einstein's prescription from 1905, a light signal is sent at time $tau_1$ from clock 1 to clock 2 and immediately back, e.g. by means of a mirror. Its arrival time back at clock 1 is $tau_2$. This synchronisation convention sets clock 2 so, that the time of signal reflection is $\left(tau_1 + tau_2\right) / 2$. Whereas the constant two-way speed of light is included in the axioms of special relativity, this 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.

## Convention

This 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 this 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 "$tau$", 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 Definition by ::Einstein:: from ::1917::, and if the simultaneous pairs of states were labelled similarly (although not necessarily by real numbers "$tau$").

## Literature

• . Reprinted in Poincaré, Oeuvres, tome IX, pp. 464-488. See also the English translation
• English translation in Reprinted in "The value of science" (1905a), Ch. 7-9.
• 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
• Galison, P. (2003), Einstein's Clocks, Poincaré's Maps: Empires of Time, New York: W.W. Norton, ISBN 0393326047
• Dennis Dieks (ed.), The Ontology of Spacetime, Elsevier 2006, ISBN 0-444-52768-0

## 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