Chapter 8

 On the Idea of Time in Physics

 

Lightning has struck the rails on our railway embankment at two places A and B far distant from each other. I make the additional assertion that these two lightning flashes occurred simultaneously¹. If I ask you whether there is sense in this statement, you will answer my question with a decided² “Yes.” But if I now approach you with the request to explain to me the sense of the statement more precisely³, you find after some consideration that the answer to this question is not so easy as it appears at first sight.

 

After some time perhaps the following answer would occur to you: “The significance of the statement is clear in itself and needs no further explanation; of course it would require some consideration if I were to be commissioned to determine by observations whether in the actual case the two events took place simultaneously or not.” I cannot be satisfied with this answer for the following reason. Supposing that as a result of ingenious considerations an able meteorologist were to discover that the lightning must always strike the places A and B simultaneously, then we should be faced with the task of testing whether or not this theoretical result is in accordance with the reality. We encounter the same difficulty with all physical statements in which the conception “simultaneous” plays a part. The concept does not exist for the physicist⁴ until he has the possibility of discovering whether or not it is fulfilled in an actual case. We thus require a definition of simultaneity such that this definition supplies us with the method by means of which, in the present case, he can decide by experiment whether or not both the lightning strokes occurred simultaneously. As long as this requirement is not satisfied, I allow myself to be deceived as a physicist (and of course the same applies if I am not a physicist), when I imagine that I am able to attach a meaning to the statement of simultaneity. (I would ask the reader not to proceed farther until he is fully⁵ convinced on this point.)

 

After thinking the matter over for some time you then offer the following suggestion with which to test simultaneity. By measuring along the rails, the connecting line AB should be measured up and an observer placed at the mid-point M of the distance AB. This observer should be supplied with an arrangement (e.g. two mirrors inclined at 90 Superscript ring) which allows him visually to observe both places A and B at the same time. If the observer perceives the two flashes of lightning at the same time, then they are simultaneous.

 

I am very pleased with this suggestion, but for all that I cannot regard the matter as quite settled, because I feel constrained⁶ to raise the following objection:

 

“Your definition would certainly be right, if only I knew that the light by means of which the observer at M perceives the lightning flashes travels along the length upper A long right-arrow upper M with the same velocity⁷ as along the length upper B long right-arrow upper M. But an examination of this supposition would only be possible if we already had at our disposal the means of measuring time. It would thus appear as though we were moving here in a logical circle.”

 

After further consideration you cast a somewhat disdainful glance at me—and rightly so—and you declare:

 

“I maintain my previous definition nevertheless, because in reality it assumes absolutely nothing about light. There is only one demand to be made of the definition of simultaneity, namely, that in every real case it must supply us with an empirical decision as to whether or not the conception that has to be defined is fulfilled. That my definition satisfies this demand is indisputable. That light requires the same time to traverse the path upper A long right-arrow upper M as for the path  upper B long right-arrow upper M is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation⁸ which I can make of my own freewill in order to arrive at a definition of simultaneity.”

 

It is clear that this definition can be used to give an exact meaning not only to two events, but to as many events as we care to choose, and independently of the positions of the scenes of the events with respect to the body of reference1 (here the railway embankment). We are thus led also to a definition of “time” in physics. For this purpose we suppose that clocks of identical construction are placed at the points A, B, and C of the railway line (co-ordinate system) and that they are set in such a manner that the positions of their pointers are simultaneously (in the above sense) the same. Under these conditions we understand by the “time” of an event the reading (position of the hands) of that one of these clocks which is in the immediate⁹ vicinity (in space) of the event. In this manner a time-value is associated with every event which is essentially¹⁰ capable of observation.

 

This stipulation contains a further physical hypothesis, the validity of which will hardly be doubted without empirical evidence to the contrary. It has been assumed that all these clocks go at the same rate if they are of identical construction. Stated more exactly: When two clocks arranged at rest in different places of a reference-body are set in such a manner that a particular position of the pointers of the one clock is simultaneous (in the above sense) with the same position, of the pointers of the other clock, then identical “settings” are always simultaneous (in the sense of the above definition).

 

1 We suppose further, that, when three events A, B, and C occur in different places in such a manner that A is simultaneous with B, and B is simultaneous with C (simultaneous in the sense of the above definition), then the criterion for the simultaneity of the pair of events upper A comma upper C is also satisfied. This assumption is a physical hypothesis about the the of propagation of light: it must certainly be fulfilled if we are to maintain the law of the constancy of the velocity of light in vacuo. 

1 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。

2 decided   

adj.决定了的，坚决的；明显的，明确的

参考例句：

• This gave them a decided advantage over their opponents.这使他们比对手具有明显的优势。
• There is a decided difference between British and Chinese way of greeting.英国人和中国人打招呼的方式有很明显的区别。

3 precisely   

adv.恰好，正好，精确地，细致地

参考例句：

• It's precisely that sort of slick sales-talk that I mistrust.我不相信的正是那种油腔滑调的推销宣传。
• The man adjusted very precisely.那个人调得很准。

4 physicist   

n.物理学家，研究物理学的人

参考例句：

• He is a physicist of the first rank.他是一流的物理学家。
• The successful physicist never puts on airs.这位卓有成就的物理学家从不摆架子。

5 fully   

adv.完全地，全部地，彻底地；充分地

参考例句：

• The doctor asked me to breathe in,then to breathe out fully.医生让我先吸气，然后全部呼出。
• They soon became fully integrated into the local community.他们很快就完全融入了当地人的圈子。

6 constrained   

adj.束缚的,节制的

参考例句：

• The evidence was so compelling that he felt constrained to accept it. 证据是那样的令人折服，他觉得不得不接受。
• I feel constrained to write and ask for your forgiveness. 我不得不写信请你原谅。

7 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。

8 stipulation   

n.契约，规定，条文；条款说明

参考例句：

• There's no stipulation as to the amount you can invest. 没有关于投资额的规定。 来自《简明英汉词典》
• The only stipulation the building society makes is that house must be insured. 建屋互助会作出的唯一规定是房屋必须保险。 来自《简明英汉词典》

9 immediate   

adj.立即的；直接的，最接近的；紧靠的

参考例句：

• His immediate neighbours felt it their duty to call.他的近邻认为他们有责任去拜访。
• We declared ourselves for the immediate convocation of the meeting.我们主张立即召开这个会议。

10 essentially   

adv.本质上，实质上，基本上

参考例句：

• Really great men are essentially modest.真正的伟人大都很谦虚。
• She is an essentially selfish person.她本质上是个自私自利的人。