查看“︁愛因斯坦同步法”︁的源代码

{{NoteTA|G1=Physics}}

'''愛因斯坦同步'''（'''龐加萊&ndash;愛因斯坦同步'''）是以訊號交換來同步位於不同地點時鐘的約定方法。早在19世紀中葉該方法已經為電報員所用，而[[儒勒·昂利·庞加莱|儒勒·昂利·龐加萊]]和[[阿尔伯特·爱因斯坦|阿爾伯特·愛因斯坦]]則進一步的將其用於[[相对论|相對論]]中，作為同時性的基礎定義。同步約定主要是指慣性座標系下時鐘的同步。
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'''Einstein synchronisation''' (or '''Poincaré&ndash;Einstein synchronisation''') is a [[風俗|convention]]  for synchronising clocks at different places by means of signal exchanges.
This synchronisation method was used by telegraphers in the middle 19th century, but was popularized by [[儒勒·昂利·庞加莱|Henri Poincaré]] and [[阿尔伯特·爱因斯坦|Albert Einstein]] who applied it to light signals and recognized its fundamental role in [[相对论|relativity theory]].  Its principal value is for clocks within a single inertial frame.
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==愛因斯坦==
若一束光訊號由時鐘 A 的時間<math>\tau_1</math>開始，從時鐘 A 送至時鐘 B 再反射回來，並在時間 <math>\tau_2</math> 時回到時鐘 A。那麼根據愛因斯坦約定，若時鐘 B 收到訊號時所顯示的時間為 <math>\tau_3</math> 時，時鐘 B 與時鐘 A 同步即定義為：

: <math>\tau_3 = \tau_1 + \tfrac{1}{2}(\tau_2 - \tau_1) = \tfrac{1}{2}(\tau_1 + \tau_2)</math><ref>{{Citation | author=Einstein, A. | year=1905 | title=Zur Elektrodynamik bewegter Körper | journal=Annalen der Physik | volume=17 | pages=891–921 | bibcode=1905AnP...322..891E | doi=10.1002/andp.19053221004 | issue=10 | url=http://www.pro-physik.de/Phy/pdfs/ger_890_921.pdf | url-status=dead | archiveurl=https://web.archive.org/web/20091229162203/http://www.pro-physik.de/Phy/pdfs/ger_890_921.pdf | archivedate=2009-12-29 }}.

See also [http://www.fourmilab.ch/etexts/einstein/specrel/ English translation] {{Wayback|url=http://www.fourmilab.ch/etexts/einstein/specrel/ |date=20051125150029 }}</ref>

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，愛因斯坦也在他的文獻中提及了許多其他關於時鐘調校的思想實驗。
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According to [[阿尔伯特·爱因斯坦|Albert Einstein]]'s prescription from 1905, a light signal is sent at time <math>\tau_1</math> from clock 1 to clock 2 and immediately back, e.g. by means of a mirror. Its arrival time back at clock 1 is <math>\tau_2</math>. This synchronisation convention sets clock 2 so that the time <math>\tau_3</math> of signal reflection is defined to be

: <math>\tau_3 = \tau_1 + \tfrac{1}{2}(\tau_2 - \tau_1) = \tfrac{1}{2}(\tau_1 + \tau_2).</math><ref>{{Citation | author=Einstein, A. | year=1905 | title=Zur Elektrodynamik bewegter Körper | journal=Annalen der Physik | volume=17 | pages=891–921 | bibcode=1905AnP...322..891E | doi=10.1002/andp.19053221004 | issue=10 | url=http://www.pro-physik.de/Phy/pdfs/ger_890_921.pdf | url-status=dead | archiveurl=https://web.archive.org/web/20091229162203/http://www.pro-physik.de/Phy/pdfs/ger_890_921.pdf | archivedate=2009-12-29 }}.

See also [http://www.fourmilab.ch/etexts/einstein/specrel/ English translation]</ref>

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.
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主要的問題是，同步的時鐘均須要對所有的事件作符合自洽性的時間測量。為了達成此目的，同步必須滿足以下條件：

: (a) 同步後的時鐘必須一直保持同步。
: (b1) 同步必須滿足[[自反关系|自反關係]]－任何時鐘均需要與自己同步。
: (b2) 同步必須滿足[[对称关系|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[[传递关系|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。

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The problem is whether this synchronisation does really succeed in assigning a time label to any event in a consistent way. To that end one should find conditions under which:

: (a) clocks once synchronised remain synchronised,
: (b1) the synchronisation is [[自反关系|reflexive]], that is any clock is synchronised with itself (automatically satisfied),
: (b2) the synchronisation is [[对称关系|symmetric]], that is if clock A is synchronised with clock B then clock B is synchronised with clock A,
: (b3) the synchronisation is [[传递关系|transitive]], that is if clock A is synchronised with clock B and clock B is synchronised with clock C then clock A is synchronised with clock C.
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如果 (a) 成立，則當然所有時鐘都是同步的。給定 (a) ，則條件 (b1)&ndash;(b3) 的成立使得同步法允許我們建立一個全域性的時間函數 t。t 為常數的切面則被稱為等時面。

事實上，條件 (a) 及 (b1)&ndash;(b3) 可以由光傳播的物理性質來驗證。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)&ndash;(b3)) ''在普遍狀況下成立。''」

馬克斯·馮·勞厄<ref>{{Citation | author=Laue, M. | year=1911 | title=Das Relativitätsprinzip | publisher=Friedr. Vieweg & Sohn | place=Braunschweig }}.</ref>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)<ref>{{Citation | author=Minguzzi, E. | year=2011 | title=The Poincaré-Einstein synchronization: historical aspects and new developments | journal= J. Phys.: Conf. Ser.  | volume =306 | issue=1 | pages =012059 | doi=10.1088/1742-6596/306/1/012059 |bibcode = 2011JPhCS.306a2059M }}</ref>)。
盧迪威格·席柏斯坦<ref>{{Citation | author=Silberstein, L. | year=1914 | title=The theory of relativity | publisher=Macmillan | place=London }}.</ref>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<ref>{{Citation | author=Reichenbach, H. | year=1969 | title=Axiomatization of the Theory of Relativity | publisher=University of California Press | place=Berkeley }}.</ref>，而最終阿瑟·麥克唐納在他的著作中得到了結論<ref>{{Citation | author=Macdonald, A. | year=1983 | title=Clock synchronization, a universal light speed, and the terrestrial red-shift experiment | journal=American Journal of Physics | volume =51 | pages =795–797 | doi=10.1119/1.13500|bibcode = 1983AmJPh..51..795M | issue=9 | citeseerx=10.1.1.698.3727 }}</ref>。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：

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If point (a) holds then it makes sense to say that clocks are synchronised. Given (a), if (b1)&ndash;(b3) hold then the synchronisation allows us to build a global time function t. The slices t=const. are called "simultaneity slices".

Einstein (1905) did not recognize the possibility of reducing (a) and (b1)&ndash;(b3) to easily verifiable physical properties of light propagation (see below). Instead he just wrote "''We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following'' (that is b2&ndash;b3) ''relations are universally valid''."

Max Von Laue<ref>{{Citation | author=Laue, M. | year=1911 | title=Das Relativitätsprinzip | publisher=Friedr. Vieweg & Sohn | place=Braunschweig }}.</ref> was the first to study the problem of the consistency of Einstein's synchronisation (for an account of the early history see Minguzzi, 2011<ref>{{Citation | author=Minguzzi, E. | year=2011 | title=The Poincaré-Einstein synchronization: historical aspects and new developments | journal= J. Phys.: Conf. Ser.  | volume =306 | issue=1 | pages =012059 | doi=10.1088/1742-6596/306/1/012059 |bibcode = 2011JPhCS.306a2059M }}</ref>).  
L. Silberstein<ref>{{Citation | author=Silberstein, L. | year=1914 | title=The theory of relativity | publisher=Macmillan | place=London }}.</ref> presented a similar study although he left most of his claims as an exercise for the readers of his textbook on relativity. 
Max von Laue's arguments were taken up again by H. Reichenbach,<ref>{{Citation | author=Reichenbach, H. | year=1969 | title=Axiomatization of the Theory of Relativity | publisher=University of California Press | place=Berkeley }}.</ref> and found a final shape in a work by A. Macdonald.<ref>{{Citation | author=Macdonald, A. | year=1983 | title=Clock synchronization, a universal light speed, and the terrestrial red-shift experiment | journal=American Journal of Physics | volume =51 | pages =795–797 | doi=10.1119/1.13500|bibcode = 1983AmJPh..51..795M | issue=9 | citeseerx=10.1.1.698.3727 }}</ref> The solution is that the Einstein synchronisation satisfies the previous requirements if and only if the following two conditions hold:
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* (''無紅移'') 若兩道光訊號從時鐘 A，以時鐘 A 紀錄的時間間隔 <math>\Delta t</math> 分別射向時鐘 B，則時鐘 B 分別收到兩訊號的時間間隔 <math>\Delta t</math> 不變。
* (''[[赖欣巴哈|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。

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，卻並沒有帶有光速恆定的假設。我們考慮：

*(''[[马克斯·冯·劳厄|勞厄]]-[[赫尔曼·魏尔|魏爾]]往返條件'') 若一束光環繞長度為 <math>L</math> 之閉路徑行進，其所需的時間即為 <math>L / c</math>。其中，<math>c</math> 為一個獨立於任意路徑的常數。
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* (''No redshift'') If from point A two flashes are emitted separated by a time interval Δt as recorded by a clock at A, then they reach B separated by the same time interval Δt as recorded by a clock at B.
* (''[[赖欣巴哈|Reichenbach's]] round-trip condition'') If a light beam is sent over the triangle ABC, starting from A and reflected by mirrors at B and C, then its arrival time back to A is independent of the direction followed (ABCA or ACBA).

Once clocks are synchronised one can measure the one-way light speed. However, the previous conditions that guarantee the applicability of Einstein's synchronisation do not imply that the one-way light speed turns out to be the same all over the frame. Consider

* (''[[马克斯·冯·劳厄|Laue]]-[[赫尔曼·魏尔|Weyl's]] round-trip condition'') The time needed by a light beam to traverse a closed path of length L is L/c, where L is the length of the path and c is a constant independent of the path.
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一個源自於勞厄及魏爾的理論<ref>{{Citation |author1=Minguzzi, E.  |author2=Macdonald, A. | year=2003 | title=Universal one-way light speed from a universal light speed over closed paths | journal=Foundations of Physics Letters| volume =16 | pages =593–604 | doi=10.1023/B:FOPL.0000012785.16203.52|arxiv = gr-qc/0211091 |bibcode = 2003FoPhL..16..593M | issue=6 }}</ref><ref>{{Citation | author=Weyl, H. | year=1988 | title=Raum Zeit Materie | publisher=Springer-Verlag | place=New York }}  Seventh edition based on the fifth German edition (1923).</ref>提出－愛因斯坦同步恆可以成立 (即條件 (a)和 (b1)&ndash;(b3)成立) 且根據其定義單向光在全座標軸上等速－這樣的情況事實上等價於勞厄－魏爾往返條件。不過，相較之下勞厄－魏爾條件可以只靠著一個時鐘來量測時間、不須倚靠時鐘的同步約定，因此可以實際利用實驗證明的優勢這個給予了其相當的重要性。實際的實驗也證明了任一慣性坐標系中勞厄－魏爾往返條件的確成立。

因為在兩地時鐘同步前量測單向光光速是沒有意義的，多數嘗試量測單向光速的實驗都可以被用來證明勞厄－魏爾往返條件。

很容易被人忘記的是，愛因斯坦同步只是一個約定法，只有在[[惯性参考系|慣性坐標系]]中才有效。於旋轉坐標系中、甚至於在狹義相對論中，愛因斯坦同步的非遞移性導致其並不再有用。這很明顯可以由以下狀況看出：在旋轉系統中，若時鐘一和時鐘二非直接，而是經過一串中繼的時鐘進行同步，同步的結果將會因中繼時鐘的路徑而有所不同。原因是因為在旋轉的系統中，路徑繞行的不同方向將導致一個一定的同步時間差。此現象可以在{{tsl|en|Sagnac effect||薩尼亞克效應}}及{{tsl|en|Ehrenfest paradox||埃倫費斯特悖論}}中看到，而現代的[[全球定位系统|全球衛星定位系統]]也將此現象納入了考量。

[[赖欣巴哈|賴欣巴哈]]為愛因斯坦同步約定的有效性提供確實的論證。雖然根據{{tsl|en|David B. Malament||大衛·馬拉門}}的論述，愛因斯坦同步約定可以更進一步的由假設因果連結的對稱性而得，不過此論點仍含有爭議性。而此外嘗試取代此約定的論點多數都被認為不再成立。
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A theorem<ref>{{Citation |author1=Minguzzi, E.  |author2=Macdonald, A. | year=2003 | title=Universal one-way light speed from a universal light speed over closed paths | journal=Foundations of Physics Letters| volume =16 | pages =593–604 | doi=10.1023/B:FOPL.0000012785.16203.52|arxiv = gr-qc/0211091 |bibcode = 2003FoPhL..16..593M | issue=6 }}</ref> (whose origin can be traced back to von Laue and Weyl)<ref>{{Citation | author=Weyl, H. | year=1988 | title=Raum Zeit Materie | publisher=Springer-Verlag | place=New York }}  Seventh edition based on the fifth German edition (1923).</ref> 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)&ndash;(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 [[惯性参考系|inertial frame]]s. 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 {{tsl|en|Sagnac effect||Sagnac effect}} and the {{tsl|en|Ehrenfest paradox||Ehrenfest paradox}}. The [[全球定位系统|Global Positioning System]] accounts for this effect.

A substantive discussion of Einstein synchronisation's conventionalism is due to [[赖欣巴哈|Reichenbach]]. Most attempts to negate the conventionality of this synchronisation are considered refuted, with the notable exception of {{tsl|en|David B. Malament||Malament}}'s argument, that it can be derived from demanding a  symmetrical relation of causal connectibility. Whether this settles the issue is disputed.-->

==歷史:龐加萊==
{{Main|狹義相對論發現史}}

[[儒勒·昂利·庞加莱|亨利·龐加萊]]於1898年所撰的一篇哲學論文中<ref>Galison (2002).</ref><ref>Darrigol (2005).</ref>，針對了一些關於愛因斯坦同步的約定特性作了討論。他認為光速在任意方向的恆定性假設有助於簡潔的地解釋物理定律，而對於事件於不同空間位置的同步定義，他亦論證了其最多只具約定性<ref>{{Citation|author=Poincaré, Henri|year=1898-1913|title=The foundations of science|chapter=[[s:The Measure of Time|The Measure of Time]]|place=New York|publisher=Science Press|pages=222&ndash;234}}</ref>。龐加萊在1900年根據了這些約定，在現今已被取代的{{tsl|en|Lorentz ether theory||乙太理論}}框架中提出了以下的約定來定義時鐘的同步：對於乙太具相對速度的 A、B 兩人透過光訊號來同步彼此的時鐘。因為[[相对性原理|相對性原理]]，他們各自認為光速在任意方向恆定、且分別相信自己對於乙太是靜止的。也因此，他們只需要由訊號延遲校準之後的時間來確認彼此時鐘的同步即可。
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{{Main|History of special relativity}}
Some features of the conventionality of synchronization were discussed by [[儒勒·昂利·庞加莱|Henri Poincaré]].<ref>Galison (2002).</ref><ref>Darrigol (2005).</ref> 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.<ref>{{Citation|author=Poincaré, Henri|year=1898-1913|title=The foundations of science|chapter=[[s:The Measure of Time|The Measure of Time]]|place=New York|publisher=Science Press|pages=222&ndash;234}}</ref> Based on those conventions, but within the framework of the now superseded {{tsl|en|Lorentz ether theory||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 [[相对性原理|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.-->
{{Quote|讓我們假設存在不同地點的觀察者們均用光訊號來同步他們的時鐘。當試著調整訊號量測到的時間長時，因為他們都不認為自己具有任何方向的運動，所以都相信自己的光訊號在各方向速度不變。一人自 A 點向 B 運動、另一人則由 B 向 A ，各自量測延遲校準過後的訊號。時鐘在調整過後，顯示的時間 <math>t'</math> 由以下方式決定：如果 <math>V = \frac{1}{\sqrt{K_0}}</math> 為光速，且 <math>v</math> 是地球沿 <math>x</math> 軸正方向遠離的速度，則 <math>t' = t - \frac{v x}{V^2}</math>。<ref>{{Citation|author=Poincaré, Henri|year=1900|title=La théorie de Lorentz et le principe de réaction|journal=Archives Néerlandaises des Sciences Exactes et Naturelles|volume=5|pages=252–278|title-link=s:fr:La théorie de Lorentz et le principe de réaction}}. See also the [http://www.physicsinsights.org/poincare-1900.pdf English translation] {{Wayback|url=http://www.physicsinsights.org/poincare-1900.pdf |date=20080626193037 }}.</ref>}}
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{{Quote|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 <math>t'</math> is the time indicated by the clocks which are so adjusted. If <math>V=\tfrac{1}{\sqrt{K_{0}}}</math> is the speed of light, and <math>v</math> is the speed of the Earth which we suppose is parallel to the <math>x</math> axis, and in the positive direction, then we have: <math>t'=t-\tfrac{vx}{V^{2}}</math>.<ref>{{Citation|author=Poincaré, Henri|year=1900|title=La théorie de Lorentz et le principe de réaction|journal=Archives Néerlandaises des Sciences Exactes et Naturelles|volume=5|pages=252–278|title-link=s:fr:La théorie de Lorentz et le principe de réaction}}. See also the [http://www.physicsinsights.org/poincare-1900.pdf English translation].</ref>}}-->

龐加萊於1904年將同樣的方法描述為：

{{Quote|想像有兩個觀測者藉由光訊號來調正各自的時鐘；他們互相交換訊號，不過因為知道訊號傳遞會有延遲，他們小心地對訊號進行延遲校準。當 B 接收到 A 的訊號，B 的時鐘不應該讀出與 A 送出訊號時相同的時間讀值，而是應該讀出加上了訊號傳遞延遲的時間讀值。舉個例子，假如 A 在時間 0 送出了一個訊號，則如果兩者時鐘同步， B 在收到訊號的時候，其時鐘的讀值<math>t</math>即應為訊號傳遞延遲所花的時間。而同樣為了確認，B 也在時間 0 送出了一個訊號，則 A 同步後的時鐘也應在收到訊號的時候顯示 <math>t</math>。 事實上，如果 A、B 為固定不動的話，兩者的時鐘同樣的時間讀值應代表他們在同一個「瞬間」。不過在其他的情況下，這個「傳遞訊號的延遲」對於兩者會有所不同，例如，A 與 B 同時朝 A 至 B 的方向前進，則 A 隨時都在往前、並早一刻接收 B 所傳遞的訊號，而 B 則在反向逃離 A 、因此都會晚一拍才收到訊號。在這情況下同步的時鐘即不會真的同步，而是同步為各自「區域性的時間」－總是有一個時鐘較另一個慢<ref>{{Citation|author=Poincaré, Henri|year=1904-1906|chapter=[[s:The Principles of Mathematical Physics|The Principles of Mathematical Physics]]|title=Congress of arts and science, universal exposition, St. Louis, 1904|volume=1|pages=604–622|publisher=Houghton, Mifflin and Company|place=Boston and New York}}</ref>。}}
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In 1904 Poincaré illustrated the same procedure in the following way:

{{Quote|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 <math>t</math>. 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 <math>t</math>. 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.<ref>{{Citation|author=Poincaré, Henri|year=1904-1906|chapter=[[s:The Principles of Mathematical Physics|The Principles of Mathematical Physics]]|title=Congress of arts and science, universal exposition, St. Louis, 1904|volume=1|pages=604–622|publisher=Houghton, Mifflin and Company|place=Boston and New York}}</ref>}}-->

==參見==
{{portal box|物理}}
*[[相對同時|相對同時]]
*{{tsl|en|One-way speed of light||單向光速}}

==引用==
{{Reflist}}

== 延伸閱讀 ==
*{{Citation|author=Darrigol, Olivier|title=The Genesis of the theory of relativity|year=2005|journal=Séminaire Poincaré|volume=1|pages=1–22|url=http://www.bourbaphy.fr/darrigol2.pdf|doi=10.1007/3-7643-7436-5_1|bibcode=2006eins.book....1D|isbn=978-3-7643-7435-8|accessdate=2022-03-14|archive-date=2018-11-08|archive-url=https://web.archive.org/web/20181108205041/http://www.bourbaphy.fr/darrigol2.pdf|dead-url=no}}
* {{tsl|en|Dennis Dieks||D. Dieks}}, ''Becoming, relativity and locality'', in ''The Ontology of Spacetime'', [http://philsci-archive.pitt.edu/archive/00002533/ online] {{Wayback|url=http://philsci-archive.pitt.edu/archive/00002533/ |date=20100627160241 }}
* {{tsl|en|Dennis Dieks||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&ndash;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'', [http://philsci-archive.pitt.edu/archive/00000184/ online] {{Wayback|url=http://philsci-archive.pitt.edu/archive/00000184/ |date=20100702170213 }}
* 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, [http://philsci-archive.pitt.edu/archive/00000350/ online] {{Wayback|url=http://philsci-archive.pitt.edu/archive/00000350/ |date=20100629234139 }}
* Hanoch Ben-Yami, ''Causality and Temporal Order in Special Relativity'', British Jnl. for the Philosophy of Sci., Volume 57, Number 3, pp.&nbsp;459&ndash;479, [https://web.archive.org/web/20061003172711/http://bjps.oxfordjournals.org/cgi/content/short/axl019v1 abstract online]

==外部連結==
*Stanford Encyclopedia of Philosophy, ''Conventionality of Simultaneity'' [http://plato.stanford.edu/entries/spacetime-convensimul/] {{Wayback|url=http://plato.stanford.edu/entries/spacetime-convensimul/ |date=20220712064425 }} (contains extensive bibliography)
*Neil Ashby, ''Relativity in the Global Positioning System'', Living Rev. Relativ. 6,  (2003), [http://www.livingreviews.org/lrr-2003-1]
* [http://math.ucr.edu/~jdp/Relativity/Calibration.html How to Calibrate a Perfect Clock] {{Wayback|url=http://math.ucr.edu/~jdp/Relativity/Calibration.html |date=20220624183749 }} ''from John de Pillis'': An interactive Flash animation showing how a clock with uniform ticking rate can precisely define a one-second time interval.
* [http://math.ucr.edu/~jdp/Relativity/Clock_Synch.html Synchronizing Five Clocks] {{Wayback|url=http://math.ucr.edu/~jdp/Relativity/Clock_Synch.html |date=20211028172322 }} ''from John de Pillis.'' An interactive Flash animation showing how five clocks are synchronised within a single inertial frame.

{{阿爾伯特·愛因斯坦}}

{{DEFAULTSORT:Einstein Synchronisation}}
[[Category:相对论|Category:Theory of relativity]]
[[Category:阿尔伯特·爱因斯坦|Category:Albert Einstein]]