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爱因斯坦同步（庞加莱–爱因斯坦同步）是约定上以讯号交换来同步位于不同地点时钟的方法。早在19世纪中，这种方法就已经为电报员所用，而儒勒·昂利·庞加莱和阿尔伯特·爱因斯坦则进一步的将其用于相对论中，作为同时性的基础定义。同步约定只在单一惯性座标系下有其价值。

爱因斯坦(需检查部分以(?)标记)

若一束光讯号由时钟A的时间$\tau _{1}$开始，从时钟A送至时钟B再反射回来，并在时间$\tau _{2}$时回到时钟A。那么根据爱因斯坦的规定，若时钟B收到讯号时所显示的时间为$\tau _{3}$时，时钟B与时钟A同步的定义则为：

$\tau _{3}=\tau _{1}+{\tfrac {1}{2}}(\tau _{2}-\tau _{1})={\tfrac {1}{2}}(\tau _{1}+\tau _{2}).$

为了使两个时钟同步，可以使用第三个时钟以趋近无限小的速度从时钟A送至时钟B来进行对时调校。另外，爱因斯坦也在文献(?)中提及了许多其他的思想实验来进行时钟调校。

有个问题是，这些同步的机制是否能在所有状况下都可成功的为其他时钟提供同步时间。为了达成此目的，同步必须满足以下条件：

(a) 校准后的时钟必须能一直保持同步。

(b1) 同步必须满足自反关系－任何时钟均需要与自己同步。

(b2) 同步必须满足对称关系－若时钟A与时钟B同步，则时钟B也与时钟A同步。

(b3) 同步必须满足传递关系－若时钟A与时钟B同步、且时钟B与时钟C同步，则时钟A也与时钟C同步。

如果(a)成立，则很合理的－所有的时钟均同步。(?)给定(a)成立，则条件(b1)–(b3)可以得出一个全域性的时间函数t。t=常数的切面则被称为等时面(?)。

事实上，条件(a)及(b1)–(b3)可以从光传播的物理性质推得。不过爱因斯坦当时(1905)却没进一步提出简化上述条件的可能性，而只是写道：“我们假设关于同时性的定义并无矛盾；并且以下的关系（指(a)及(b1)–(b3)）在普遍状况下成立。”

马克斯·冯·劳厄第一个考察了爱因斯坦同步的自洽性（当时的纪录请参考Minguzzi, E. (2011)）。 卢迪威格·席柏斯坦在他所著的教科书中也提供了类似的论述，只不过大部分的证明被他留给了读者作为练习。 汉斯·赖欣巴哈重新讨论了马克斯·冯·劳厄的论证，而最终阿瑟·麦克唐纳在他的著作中得到了结论。结果表明，爱因斯坦同步符合前述条件若且唯若以下条件成立：

• （无红移）若两道光讯号从时钟A，以时钟Ａ纪录的时间间隔Δt分别射向时钟B，则时钟B分别收到两讯号的时间间隔Δt不变。
• （赖欣巴哈往返条件）若ABC构成一三角形，光束由A点出发经由B点反射至C点再反射回A点所花的时间，应该与反向从Ｃ点至Ｂ点回来的时间相同（时钟A纪录）。

一但时钟同步了，单程的光速即可被量测。然而，上面的条件虽然保证了爱因斯坦同步的可行性，却并没有带著光速恒定的假设。考虑：

• （劳厄-魏尔往返条件）若一束光环绕长度为L之闭路径行进，其所需的时间即为L/c。其中，ｃ为一个独立于任意路径的常数。

A theorem (whose origin can be traced back to von Laue and Weyl) 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. The importance of Laue-Weyl's condition stands on the fact that the time there mentioned can be measured with only one clock thus this condition does not rely on synchronisation conventions and can be experimentally checked. Indeed, it is 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.

The Einstein synchronisation looks this natural only in inertial frames. One can easily forget that it is only a convention. In rotating frames, even in special relativity, 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.

A 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.

History: Poincaré

主条目：History of special relativity

Some features of the conventionality of synchronization were discussed by Henri Poincaré. In 1898 (in a philosophical paper) he argued that the postulate of light speed constancy in all directions is useful to formulate physical laws in a simple way. He also showed that the definition of simultaneity of events at different places is only a convention. 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. They attempt to adjust the measured transmission time of the signals, but they are not aware of their common motion, and consequently believe that the signals travel equally fast in both directions. They perform observations of crossing signals, one traveling from A to B, followed by another traveling from B to A. The local time $t'$ is the time indicated by the clocks which are so adjusted. If $V={\tfrac {1}{\sqrt {K_{0}}}}$ is the speed of light, and $v$ is the speed of the Earth which we suppose is parallel to the $x$ axis, and in the positive direction, then we have: $t'=t-{\tfrac {vx}{V^{2}}}$.

In 1904 Poincaré illustrated the same procedure in the following way:

Imagine two observers who wish to adjust their timepieces by optical signals; they exchange signals, but as they know that the transmission of light is not instantaneous, they are careful to cross them. When station B perceives the signal from station A, its clock should not mark the same hour as that of station A at the moment of sending the signal, but this hour augmented by a constant representing the duration of the transmission. Suppose, for example, that station A sends its signal when its clock marks the hour 0, and that station B perceives it when its clock marks the hour $t$. The clocks are adjusted if the slowness equal to t represents the duration of the transmission, and to verify it, station B sends in its turn a signal when its clock marks 0; then station A should perceive it when its clock marks $t$. The timepieces are then adjusted. And in fact they mark the same hour at the same physical instant, but on the one condition, that the two stations are fixed. Otherwise the duration of the transmission will not be the same in the two senses, since the station A, for example, moves forward to meet the optical perturbation emanating from B, whereas the station B flees before the perturbation emanating from A. The watches adjusted in that way will not mark, therefore, the true time; they will mark what may be called the local time, so that one of them will be slow of the other.

See also

• Relativity of simultaneity
• One-way speed of light

Literature

• Darrigol, Olivier, The Genesis of the theory of relativity (PDF), Séminaire Poincaré, 2005, 1: 1–22, Bibcode:2006eins.book....1D, ISBN 978-3-7643-7435-8, doi:10.1007/3-7643-7436-5_1 
• D. Dieks, Becoming, relativity and locality, in The Ontology of Spacetime, online
• D. Dieks (ed.), The Ontology of Spacetime, Elsevier 2006, ISBN 0-444-52768-0
• D. Malament, 1977. "Causal Theories of Time and the Conventionality of Simultaniety," Noûs 11, 293–300.
• Galison, P. (2003), Einstein's Clocks, Poincaré's Maps: Empires of Time, New York: W.W. Norton, ISBN 0-393-32604-7
• 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
• 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
• 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

External links

• Stanford Encyclopedia of Philosophy, Conventionality of Simultaneity [1] (contains extensive bibliography)
• Neil Ashby, Relativity in the Global Positioning System, Living Rev. Relativ. 6, (2003), [2]
• How to Calibrate a Perfect Clock from John de Pillis: An interactive Flash animation showing how a clock with uniform ticking rate can precisely define a one-second time interval.
• Synchronizing Five Clocks from John de Pillis. An interactive Flash animation showing how five clocks are synchronised within a single inertial frame.