chapter 9

 The Relativity of Simultaneity

 

Up to now our considerations have been referred to a particular body of reference, which we have styled a “railway embankment.” We suppose a very long train travelling along the rails with the constant velocity¹ v and in the direction indicated in Fig². 1. People travelling in this train will with a vantage view the train as a rigid³ reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. As a natural consequence, however, the following question arises:

 

Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively⁴ to the train? We shall show directly that the answer must be in the negative.

 

When we say that the lightning strokes A and B are simultaneous with respect to be embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length upper A long right-arrow upper B of the embankment. But the events A and B also correspond to positions A and B on the train. Let M′ be the mid-point of the distance upper A long right-arrow upper B on the travelling train. Just when the flashes1 of lightning occur, this point M′ naturally coincides with the point M but it moves towards the right in the diagram with the velocity v of the train. If an observer sitting in the position M′ in the train did not possess this velocity, then he would remain permanently⁵ at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously⁶, i.e. they would meet just where he is situated⁷. Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A. We thus arrive at the important result:

 

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice⁸ versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.

 

Now before the advent⁹ of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, i.e. that it is independent of the state of motion of the body of reference. But we have just seen that this assumption is incompatible¹⁰ with the most natural definition of simultaneity; if we discard this assumption, then the conflict between the law of the propagation of light in vacuo and the principle of relativity (developed in Section VII) disappears.

 

We were led to that conflict by the considerations of Section VI, which are now no longer tenable. In that section we concluded that the man in the carriage, who traverses the distance w per second relative to the carriage, traverses the same distance also with respect to the embankment in each second of time. But, according to the foregoing considerations, the time required by a particular occurrence with respect to the carriage must not be considered equal to the duration of the same occurrence as judged from the embankment (as reference-body). Hence it cannot be contended that the man in walking travels the distance w relative to the railway line in a time which is equal to one second as judged from the embankment.

 

Moreover, the considerations of Section VI are based on yet a second assumption, which, in the light of a strict consideration, appears to be arbitrary, although it was always tacitly made even before the introduction of the theory of relativity.

 

1 As judged from the embankment. 

1 velocity   

n.速度，速率

参考例句：

• Einstein's theory links energy with mass and velocity of light.爱因斯坦的理论把能量同质量和光速联系起来。
• The velocity of light is about 300000 kilometres per second.光速约为每秒300000公里。

2 fig   

n.无花果(树)

参考例句：

• The doctor finished the fig he had been eating and selected another.这位医生吃完了嘴里的无花果，又挑了一个。
• You can't find a person who doesn't know fig in the United States.你找不到任何一个在美国的人不知道无花果的。

3 rigid   

adj.严格的，死板的；刚硬的，僵硬的

参考例句：

• She became as rigid as adamant.她变得如顽石般的固执。
• The examination was so rigid that nearly all aspirants were ruled out.考试很严，几乎所有的考生都被淘汰了。

4 relatively   

adv.比较...地，相对地

参考例句：

• The rabbit is a relatively recent introduction in Australia.兔子是相对较新引入澳大利亚的物种。
• The operation was relatively painless.手术相对来说不痛。

5 permanently   

adv.永恒地，永久地，固定不变地

参考例句：

• The accident left him permanently scarred.那次事故给他留下了永久的伤疤。
• The ship is now permanently moored on the Thames in London.该船现在永久地停泊在伦敦泰晤士河边。

6 simultaneously   

adv.同时发生地，同时进行地

参考例句：

• The radar beam can track a number of targets almost simultaneously.雷达波几乎可以同时追着多个目标。
• The Windows allow a computer user to execute multiple programs simultaneously.Windows允许计算机用户同时运行多个程序。

7 situated   

adj.坐落在...的，处于某种境地的

参考例句：

• The village is situated at the margin of a forest.村子位于森林的边缘。
• She is awkwardly situated.她的处境困难。

8 vice   

n.坏事；恶习；[pl.]台钳，老虎钳；adj.副的

参考例句：

• He guarded himself against vice.他避免染上坏习惯。
• They are sunk in the depth of vice.他们堕入了罪恶的深渊。

9 advent   

n.(重要事件等的)到来，来临

参考例句：

• Swallows come by groups at the advent of spring. 春天来临时燕子成群飞来。
• The advent of the Euro will redefine Europe.欧元的出现将重新定义欧洲。

10 incompatible   

adj.不相容的，不协调的，不相配的

参考例句：

• His plan is incompatible with my intent.他的计划与我的意图不相符。
• Speed and safety are not necessarily incompatible.速度和安全未必不相容。