V The Principle of Relativity in the Restricted Sense

 In order to attain¹ the greatest possible clearness, let us return to our example of the railway carriage supposed to be travelling uniformly. We call its motion a uniform translation (“uniform” because it is of constant velocity² and direction, “translation” because although the carriage changes its position relative to the embankment yet it does not rotate in so doing). Let us imagine a raven³ flying through the air in such a manner that its motion, as observed from the embankment, is uniform and in a straight line. If we were to observe the flying raven from the moving railway carriage. we should find that the motion of the raven would be one of different velocity and direction, but that it would still be uniform and in a straight line. Expressed in an abstract manner we may say: If a mass m is moving uniformly in a straight line with respect to a co-ordinate system K, then it will also be moving uniformly and in a straight line relative to a second co-ordinate system K′ provided that the latter is executing a uniform translatory motion with respect to K. In accordance with the discussion contained in the preceding section, it follows that:

 

If K is a Galileian co-ordinate system. then every other co-ordinate system K′ is a Galileian one, when, in relation to K, it is in a condition of uniform motion of translation. Relative to K′ the mechanical laws of Galilei-Newton hold good exactly as they do with respect to K.

 

We advance a step farther in our generalisation when we express the tenet thus: If, relative to K, K′ is a uniformly moving co-ordinate system devoid⁴ of rotation⁵, then natural phenomena⁶ run their course with respect to K′ according to exactly the same general laws as with respect to K. This statement is called the principle of relativity (in the restricted sense).

 

As long as one was convinced that all natural phenomena were capable of representation with the help of classical mechanics, there was no need to doubt the validity of this principle of relativity. But in view of the more recent development of electrodynamics and optics it became more and more evident that classical mechanics affords an insufficient⁸ foundation for the physical description of all natural phenomena. At this juncture⁹ the question of the validity of the principle of relativity became ripe for discussion, and it did not appear impossible that the answer to this question might be in the negative.

 

Nevertheless, there are two general facts which at the outset speak very much in favour of the validity of the principle of relativity. Even though classical mechanics does not supply us with a sufficiently¹⁰ broad basis for the theoretical presentation of all physical phenomena, still we must grant it a considerable measure of “truth,” since it supplies us with the actual motions of the heavenly bodies with a delicacy¹¹ of detail little short of wonderful. The principle of relativity must therefore apply with great accuracy in the domain¹² of mechanics. But that a principle of such broad generality should hold with such exactness in one domain of phenomena, and yet should be invalid¹³ for another, is a priori not very probable.

 

We now proceed to the second argument, to which, moreover, we shall return later. If the principle of relativity (in the restricted sense) does not hold, then the Galileian co-ordinate systems K, K′, K″, etc., which are moving uniformly relative to each other, will not be equivalent for the description of natural phenomena. In this case we should be constrained¹⁴ to believe that natural laws are capable of being formulated¹⁵ in a particularly simple manner, and of course only on condition that, from amongst all possible Galileian co-ordinate systems, we should have chosen one (upper K 0) of a particular state of motion as our body of reference. We should then be justified¹⁶ (because of its merits for the description of natural phenomena) in calling this system “absolutely at rest,” and all other Galileian systems K “in motion.” If, for instance, our embankment were the system upper K 0 then our railway carriage would be a system K, relative to which less simple laws would hold than with respect to upper K 0. This diminished simplicity¹⁷ would be due to the fact that the carriage K would be in motion (i.e. “really”) with respect to upper K 0. In the general laws of nature which have been formulated with reference to K, the magnitude and direction of the velocity of the carriage would necessarily play a part. We should expect, for instance, that the note emitted by an organpipe placed with its axis¹⁸ parallel to the direction of travel would be different from that emitted if the axis of the pipe were placed perpendicular¹⁹ to this direction.

 

Now in virtue²⁰ of its motion in an orbit round the sun, our earth is comparable with a railway carriage travelling with a velocity of about 30 kilometres per second. If the principle of relativity were not valid⁷ we should therefore expect that the direction of motion of the earth at any moment would enter into the laws of nature, and also that physical systems in their behaviour would be dependent on the orientation²¹ in space with respect to the earth. For owing to the alteration²² in direction of the velocity of revolution of the earth in the course of a year, the earth cannot be at rest relative to the hypothetical system upper K 0 throughout the whole year. However, the most careful observations have never revealed such anisotropic properties in terrestrial physical space, i.e. a physical non-equivalence of different directions. This is very powerful argument in favour of the principle of relativity.

1 attain   

vt.达到，获得，完成

参考例句：

• I used the scientific method to attain this end. 我用科学的方法来达到这一目的。
• His painstaking to attain his goal in life is praiseworthy. 他为实现人生目标所下的苦功是值得称赞的。

2 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。

3 raven   

n.渡鸟，乌鸦；adj.乌亮的

参考例句：

• We know the raven will never leave the man's room.我们知道了乌鸦再也不会离开那个男人的房间。
• Her charming face was framed with raven hair.她迷人的脸上垂落着乌亮的黑发。

4 devoid   

adj.全无的，缺乏的

参考例句：

• He is completely devoid of humour.他十分缺乏幽默。
• The house is totally devoid of furniture.这所房子里什么家具都没有。

5 rotation   

n.旋转；循环，轮流

参考例句：

• Crop rotation helps prevent soil erosion.农作物轮作有助于防止水土流失。
• The workers in this workshop do day and night shifts in weekly rotation.这个车间的工人上白班和上夜班每周轮换一次。

6 phenomena   

n.现象

参考例句：

• Ade couldn't relate the phenomena with any theory he knew.艾德无法用他所知道的任何理论来解释这种现象。
• The object of these experiments was to find the connection,if any,between the two phenomena.这些实验的目的就是探索这两种现象之间的联系，如果存在着任何联系的话。

7 valid   

adj.有确实根据的；有效的；正当的，合法的

参考例句：

• His claim to own the house is valid.他主张对此屋的所有权有效。
• Do you have valid reasons for your absence?你的缺席有正当理由吗？

8 insufficient   

adj.(for，of)不足的，不够的

参考例句：

• There was insufficient evidence to convict him.没有足够证据给他定罪。
• In their day scientific knowledge was insufficient to settle the matter.在他们的时代，科学知识还不能足以解决这些问题。

9 juncture   

n.时刻，关键时刻，紧要关头

参考例句：

• The project is situated at the juncture of the new and old urban districts.该项目位于新老城区交界处。
• It is very difficult at this juncture to predict the company's future.此时很难预料公司的前景。

10 sufficiently   

adv.足够地，充分地

参考例句：

• It turned out he had not insured the house sufficiently.原来他没有给房屋投足保险。
• The new policy was sufficiently elastic to accommodate both views.新政策充分灵活地适用两种观点。

11 delicacy   

n.精致，细微，微妙，精良；美味，佳肴

参考例句：

• We admired the delicacy of the craftsmanship.我们佩服工艺师精巧的手艺。
• He sensed the delicacy of the situation.他感觉到了形势的微妙。

12 domain   

n.(活动等)领域，范围；领地，势力范围

参考例句：

• This information should be in the public domain.这一消息应该为公众所知。
• This question comes into the domain of philosophy.这一问题属于哲学范畴。

13 invalid   

n.病人，伤残人；adj.有病的，伤残的；无效的

参考例句：

• He will visit an invalid.他将要去看望一个病人。
• A passport that is out of date is invalid.护照过期是无效的。

14 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。

15 formulated   

v.构想出( formulate的过去式和过去分词 )；规划；确切地阐述；用公式表示

参考例句：

• He claims that the writer never consciously formulated his own theoretical position. 他声称该作家从未有意识地阐明他自己的理论见解。 来自《简明英汉词典》
• This idea can be formulated in two different ways. 这个意思可以有两种说法。 来自《现代汉英综合大词典》

16 justified   

a.正当的，有理的

参考例句：

• She felt fully justified in asking for her money back. 她认为有充分的理由要求退款。
• The prisoner has certainly justified his claims by his actions. 那个囚犯确实已用自己的行动表明他的要求是正当的。

17 simplicity   

n.简单，简易；朴素；直率，单纯

参考例句：

• She dressed with elegant simplicity.她穿着朴素高雅。
• The beauty of this plan is its simplicity.简明扼要是这个计划的一大特点。

18 axis   

n.轴，轴线，中心线；坐标轴，基准线

参考例句：

• The earth's axis is the line between the North and South Poles.地轴是南北极之间的线。
• The axis of a circle is its diameter.圆的轴线是其直径。

19 perpendicular   

adj.垂直的，直立的；n.垂直线，垂直的位置

参考例句：

• The two lines of bones are set perpendicular to one another.这两排骨头相互垂直。
• The wall is out of the perpendicular.这墙有些倾斜。

20 virtue   

n.德行，美德；贞操；优点；功效，效力

参考例句：

• He was considered to be a paragon of virtue.他被认为是品德尽善尽美的典范。
• You need to decorate your mind with virtue.你应该用德行美化心灵。

21 orientation   

n.方向，目标；熟悉，适应，情况介绍

参考例句：

• Children need some orientation when they go to school.小孩子上学时需要适应。
• The traveller found his orientation with the aid of a good map.旅行者借助一幅好地图得知自己的方向。

22 alteration   

n.变更，改变；蚀变

参考例句：

• The shirt needs alteration.这件衬衣需要改一改。
• He easily perceived there was an alteration in my countenance.他立刻看出我的脸色和往常有些不同。