用戶:Zsdezsc/沙盒

愛因斯坦同步（龐加萊–愛因斯坦同步）是約定上以訊號交換來同步位於不同地點時鐘的方法。早在19世紀中，這種方法就已經為電報員所用，而儒勒·昂利·龐加萊和阿爾伯特·愛因斯坦則進一步的將其用於相對論中，作為同時性的基礎定義。同步約定只在單一慣性座標系下有其價值。

愛因斯坦(需檢查部分以(?)標記)

若一束光訊號由時鐘A的時間$\tau _{1}$開始，從時鐘A送至時鐘B再反射回來，並在時間$\tau _{2}$時回到時鐘A。那麼根據愛因斯坦的規定，若時鐘B收到訊號時所顯示的時間為$\tau _{3}$時，時鐘B與時鐘A同步的定義則為：

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

為了使兩個時鐘同步，可以使用第三個時鐘以趨近無限小的速度從時鐘A送至時鐘B來進行對時調校。另外，愛因斯坦也在文獻(?)中提及了許多其他的思想實驗來進行時鐘調校。

有個問題是，這些同步的機制是否能在所有狀況下都可成功的為其他時鐘提供同步時間。為了達成此目的，同步必須滿足以下條件：

(a) 校準後的時鐘必須能一直保持同步。

(b1) 同步必須滿足自反關係－任何時鐘均需要與自己同步。

(b2) 同步必須滿足對稱關係－若時鐘A與時鐘B同步，則時鐘B也與時鐘A同步。

(b3) 同步必須滿足傳遞關係－若時鐘A與時鐘B同步、且時鐘B與時鐘C同步，則時鐘A也與時鐘C同步。

如果(a)成立，則很合理的－所有的時鐘均同步。(?)給定(a)成立，則條件(b1)–(b3)可以得出一個全域性的時間函數t。t=常數的切面則被稱為等時面(?)。

事實上，條件(a)及(b1)–(b3)可以從光傳播的物理性質推得。不過愛因斯坦當時(1905)卻沒進一步提出簡化上述條件的可能性，而只是寫道：「我們假設關於同時性的定義並無矛盾；並且以下的關係（指(a)及(b1)–(b3)）在普遍狀況下成立。」

馬克斯·馮·勞厄第一個考察了愛因斯坦同步的自洽性（當時的紀錄請參考Minguzzi, E. (2011)）。 盧迪威格·席柏斯坦在他所著的教科書中也提供了類似的論述，只不過大部分的證明被他留給了讀者作為練習。 漢斯·賴欣巴哈重新討論了馬克斯·馮·勞厄的論證，而最終阿瑟·麥克唐納在他的著作中得到了結論。結果表明，愛因斯坦同步符合前述條件若且唯若以下條件成立：

• （無紅移）若兩道光訊號從時鐘A，以時鐘Ａ紀錄的時間間隔Δt分別射向時鐘B，則時鐘B分別收到兩訊號的時間間隔Δt不變。
• （賴欣巴哈往返條件）若ABC構成一三角形，光束由A點出發經由B點反射至C點再反射回A點所花的時間，應該與反向從Ｃ點至Ｂ點回來的時間相同（時鐘A紀錄）。

一但時鐘同步了，單程的光速即可被量測。然而，上面的條件雖然保證了愛因斯坦同步的可行性，卻並沒有帶着光速恆定的假設。考慮：

• （勞厄-魏爾往返條件）若一束光環繞長度為L之閉路徑行進，其所需的時間即為L/c。其中，ｃ為一個獨立於任意路徑的常數。

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

主條目：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.