PART II The General Theory of Relativity chapter 18

 Special and General Principle of Relativity

 

The basal principle, which was the pivot¹ of all our previous considerations, was the special principle of relativity, i.e. the principle of the physical relativity of all uniform motion. Let as once more analyse its meaning carefully.

 

It was at all times clear that, from the point of view of the idea it conveys to us, every motion must be considered only as a relative motion. Returning to the illustration we have frequently used of the embankment and the railway carriage, we can express the fact of the motion here taking place in the following two forms, both of which are equally justifiable²:

 

(a) The carriage is in motion relative to the embankment,

(b) The embankment is in motion relative to the carriage.

In (a) the embankment, in (b) the carriage, serves as the body of reference in our statement of the motion taking place. If it is simply a question of detecting or of describing the motion involved, it is in principle immaterial to what reference-body we refer the motion. As already mentioned, this is self-evident, but it must not be confused with the much more comprehensive statement called “the principle of relativity,” which we have taken as the basis of our investigations³.

 

The principle we have made use of not only maintains that we may equally well choose the carriage or the embankment as our reference-body for the description of any event (for this, too, is self-evident). Our principle rather asserts what follows: If we formulate⁴ the general laws of nature as they are obtained from experience, by making use of

 

(a) the embankment as reference-body,

(b) the railway carriage as reference-body,

then these general laws of nature (e.g. the laws of mechanics or the law of the propagation of light in vacuo) have exactly the same form in both cases. This can also be expressed as follows: For the physical description of natural processes, neither of the reference bodies K, K′ is unique (lit. “specially marked out”) as compared with the other. Unlike the first, this latter statement need not of necessity hold a priori; it is not contained in the conceptions of “motion” and “reference-body” and derivable⁵ from them; only experience can decide as to its correctness or incorrectness.

 

Up to the present, however, we have by no means maintained the equivalence of all bodies of reference K in connection with the formulation of natural laws. Our course was more on the following lines. In the first place, we started out from the assumption that there exists a reference-body K, whose condition of motion is such that the Galileian law holds with respect to it: A particle left to itself and sufficiently⁶ far removed from all other particles moves uniformly in a straight line. With reference to K (Galileian reference-body) the laws of nature were to be as simple as possible. But in addition to K, all bodies of reference K′ should be given preference in this sense, and they should be exactly equivalent to K for the formulation of natural laws, provided that they are in a state of uniform rectilinear and non-rotary motion with respect to K; all these bodies of reference are to be regarded as Galileian reference-bodies. The validity of the principle of relativity was assumed only for these reference-bodies, but not for others (e.g. those possessing motion of a different kind). In this sense we speak of the special principle of relativity, or special theory of relativity.

 

In contrast to this we wish to understand by the “general principle of relativity” the following statement: All bodies of reference K, K′, etc., are equivalent for the description of natural phenomena⁷ (formulation of the general laws of nature), whatever may be their state of motion. But before proceeding⁸ farther, it ought to be pointed⁹ out that this formulation must be replaced later by a more abstract one, for reasons which will become evident at a later stage.

 

Since the introduction of the special principle of relativity has been justified¹⁰, every intellect which strives after generalisation must feel the temptation to venture the step towards the general principle of relativity. But a simple and apparently¹¹ quite reliable consideration seems to suggest that, for the present at any rate, there is little hope of success in such an attempt; Let us imagine ourselves transferred to our old friend the railway carriage, which is travelling at a uniform rate. As long as it is moving uniformly, the occupant of the carriage is not sensible of its motion, and it is for this reason that he can without reluctance¹² interpret the facts of the case as indicating that the carriage is at rest, but the embankment in motion. Moreover, according to the special principle of relativity, this interpretation¹³ is quite justified also from a physical point of view.

 

If the motion of the carriage is now changed into a non-uniform motion, as for instance by a powerful application of the brakes, then the occupant of the carriage experiences a correspondingly powerful jerk forwards. The retarded¹⁴ motion is manifested in the mechanical behaviour of bodies relative to the person in the railway carriage. The mechanical behaviour is different from that of the case previously¹⁵ considered, and for this reason it would appear to be impossible that the same mechanical laws hold relatively¹⁶ to the non-uniformly moving carriage, as hold with reference to the carriage when at rest or in uniform motion. At all events it is clear that the Galileian law does not hold with respect to the non-uniformly moving carriage. Because of this, we feel compelled at the present juncture¹⁷ to grant a kind of absolute physical reality to non-uniform motion, in opposition¹⁸ to the general principle of relativity. But in what follows we shall soon see that this conclusion cannot be maintained.

1 pivot   

v.在枢轴上转动；装枢轴，枢轴；adj.枢轴的

参考例句：

• She is the central pivot of creation and represents the feminine aspect in all things.她是创造的中心枢轴，表现出万物的女性面貌。
• If a spring is present,the hand wheel will pivot on the spring.如果有弹簧，手轮的枢轴会装在弹簧上。

2 justifiable   

adj.有理由的，无可非议的

参考例句：

• What he has done is hardly justifiable.他的所作所为说不过去。
• Justifiable defense is the act being exempted from crimes.正当防卫不属于犯罪行为。

3 investigations   

（正式的）调查( investigation的名词复数 )； 侦查； 科学研究； 学术研究

参考例句：

• His investigations were intensive and thorough but revealed nothing. 他进行了深入彻底的调查，但没有发现什么。
• He often sent them out to make investigations. 他常常派他们出去作调查。

4 formulate   

v.用公式表示；规划；设计；系统地阐述

参考例句：

• He took care to formulate his reply very clearly.他字斟句酌，清楚地做了回答。
• I was impressed by the way he could formulate his ideas.他陈述观点的方式让我印象深刻。

5 derivable   

adj.可引出的，可推论的，可诱导的

参考例句：

• These results are derivable from the theory of quantum mechanics. 这些结果是根据量子力学理论推导出来的。 来自辞典例句

6 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。

7 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。

8 proceeding   

n.行动，进行，(pl.)会议录，学报

参考例句：

• This train is now proceeding from Paris to London.这次列车从巴黎开往伦敦。
• The work is proceeding briskly.工作很有生气地进展着。

9 pointed   

adj.尖的，直截了当的

参考例句：

• He gave me a very sharp pointed pencil.他给我一支削得非常尖的铅笔。
• She wished to show Mrs.John Dashwood by this pointed invitation to her brother.她想通过对达茨伍德夫人提出直截了当的邀请向她的哥哥表示出来。

10 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。

11 apparently   

adv.显然地；表面上，似乎

参考例句：

• An apparently blind alley leads suddenly into an open space.山穷水尽，豁然开朗。
• He was apparently much surprised at the news.他对那个消息显然感到十分惊异。

12 reluctance   

n.厌恶，讨厌，勉强，不情愿

参考例句：

• The police released Andrew with reluctance.警方勉强把安德鲁放走了。
• He showed the greatest reluctance to make a reply.他表示很不愿意答复。

13 interpretation   

n.解释，说明，描述；艺术处理

参考例句：

• His statement admits of one interpretation only.他的话只有一种解释。
• Analysis and interpretation is a very personal thing.分析与说明是个很主观的事情。

14 retarded   

a.智力迟钝的，智力发育迟缓的

参考例句：

• The progression of the disease can be retarded by early surgery. 早期手术可以抑制病情的发展。
• He was so slow that many thought him mentally retarded. 他迟钝得很，许多人以为他智力低下。

15 previously   

adv.以前，先前（地）

参考例句：

• The bicycle tyre blew out at a previously damaged point.自行车胎在以前损坏过的地方又爆开了。
• Let me digress for a moment and explain what had happened previously.让我岔开一会儿，解释原先发生了什么。

16 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。

17 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。

18 opposition   

n.反对，敌对

参考例句：

• The party leader is facing opposition in his own backyard.该党领袖在自己的党內遇到了反对。
• The police tried to break down the prisoner's opposition.警察设法制住了那个囚犯的反抗。