chapter 15

 General Results of the Theory

 

It is clear from our previous considerations that the (special) theory of relativity has grown out of electrodynamics and optics. In these fields it has not appreciably¹ altered the predictions of theory, but it has considerably² simplified the theoretical structure, i.e. the derivation of laws, and—what is incomparably more important—it has considerably reduced the number of independent hypothese forming the basis of theory. The special theory of relativity has rendered the Maxwell-Lorentz theory so plausible³, that the latter would have been generally accepted by physicists⁴ even if experiment had decided⁵ less unequivocally in its favour.

 

Classical mechanics required to be modified before it could come into line with the demands of the special theory of relativity. For the main part, however, this modification⁶ affects only the laws for rapid motions, in which the velocities⁷ of matter v are not very small as compared with the velocity⁸ of light. We have experience of such rapid motions only in the case of electrons and ions; for other motions the variations from the laws of classical mechanics are too small to make themselves evident in practice. We shall not consider the motion of stars until we come to speak of the general theory of relativity. In accordance with the theory of relativity the kinetic⁹ energy of a material point of mass m is no longer given by the well-known expression

m StartFraction v squared Over 2 EndFraction

but by the expression

StartFraction m c squared Over StartRoot 1 minus StartFraction v squared Over c squared EndFraction EndRoot EndFraction period

This expression approaches infinity¹⁰ as the velocity v approaches the velocity of light c. The velocity must therefore always remain less than c, however great may be the energies used to produce the acceleration¹¹. If we develop the expression for the kinetic energy in the form of a series, we obtain

m c squared plus m StartFraction v squared Over 2 EndFraction plus three-eighths m StartFraction v Superscript 4 Baseline Over c squared EndFraction plus midline-horizontal-ellipsis

When StartFraction v squared Over c squared EndFraction is small compared with unity¹², the third of these terms is always small in comparison with the second, which last is alone considered in classical mechanics. The first term m c squared does not contain the velocity, and requires no consideration if we are only dealing¹³ with the question as to how the energy of a point-mass; depends on the velocity. We shall speak of its essential significance later.

 

The most important result of a general character to which the special theory of relativity has led is concerned with the conception of mass. Before the advent¹⁴ of relativity, physics recognised two conservation laws of fundamental importance, namely, the law of the conservation of energy and the law of the conservation of mass these two fundamental laws appeared to be quite independent of each other. By means of the theory of relativity they have been united into one law. We shall now briefly¹⁵ consider how this unification came about, and what meaning is to be attached to it.

 

The principle of relativity requires that the law of the conservation of energy should hold not only with reference to a co-ordinate system K, but also with respect to every co-ordinate system K′ which is in a state of uniform motion of translation relative to K, or, briefly, relative to every “Galileian” system of co-ordinates. In contrast to classical mechanics; the Lorentz transformation¹⁶ is the deciding factor in the transition from one such system to another.

 

By means of comparatively simple considerations we are led to draw the following conclusion from these premises¹⁷, in conjunction with the fundamental equations of the electrodynamics of Maxwell: A body moving with the velocity v, which absorbs1 an amount of energy upper E 0 in the form of radiation without suffering an alteration¹⁸ in velocity in the process, has, as a consequence, its energy increased by an amount

StartFraction upper E 0 Over StartRoot 1 minus StartFraction v squared Over c squared EndFraction EndRoot EndFraction

In consideration of the expression given above for the kinetic energy of the body, the required energy of the body comes out to be

StartStartFraction left-parenthesis m plus StartFraction upper E 0 Over c squared EndFraction right-parenthesis c squared OverOver StartRoot 1 minus StartFraction v squared Over c squared EndFraction EndRoot EndEndFraction period

Thus the body has the same energy as a body of mass left-parenthesis m plus StartFraction upper E 0 Over c squared EndFraction right-parenthesis moving with the velocity v. Hence we can say: If a body takes up an amount of energy upper E 0, then its inertial mass increases by an amount StartFraction upper E 0 Over c squared EndFraction; the inertial mass of a body is not a constant but varies according to the change in the energy of the body. The inertial mass of a system of bodies can even be regarded as a measure of its energy. The law of the conservation of the mass of a system becomes identical with the law of the conservation of energy, and is only valid¹⁹ provided that the system neither takes up nor sends out energy. Writing the expression for the energy in the form

StartFraction m c squared plus upper E 0 Over StartRoot 1 minus StartFraction v squared Over c squared EndFraction EndRoot EndFraction comma

we see that the term m c squared, which has hitherto attracted our attention, is nothing else than the energy possessed²⁰ by the body2 before it absorbed the energy upper E 0.

 

A direct comparison of this relation with experiment is not possible at the present time (1920; see3 Note, p. 48), owing to the fact that the changes in energy upper E 0 to which we can Subject a system are not large enough to make themselves perceptible as a change in the inertial mass of the system. StartFraction upper E 0 Over c squared EndFraction is too small in comparison with the mass m, which was present before the alteration of the energy. It is owing to this circumstance that classical mechanics was able to establish successfully the conservation of mass as a law of independent validity.

 

Let me add a final remark of a fundamental nature. The success of the Faraday-Maxwell interpretation²¹ of electromagnetic action at a distance resulted in physicists becoming convinced that there are no such things as instantaneous actions at a distance (not involving an intermediary medium) of the type of Newton’s law of gravitation. According to the theory of relativity, action at a distance with the velocity of light always takes the place of instantaneous action at a distance or of action at a distance with an infinite velocity of transmission. This is connected with the fact that the velocity c plays a fundamental role in this theory. In Part II we shall see in what way this result becomes modified in the general theory of relativity.

 

1upper E 0 is the energy taken up, as judged from a co-ordinate system moving with the body.  

 

2 As judged from a co-ordinate system moving with the body.  

 

3 The equation upper E equals m c squared has been thoroughly²² proved time and again since this time. 

1 appreciably   

adv.相当大地

参考例句：

• The index adds appreciably to the usefulness of the book. 索引明显地增加了这本书的实用价值。
• Otherwise the daily mean is perturbed appreciably by the lunar constituents. 否则，日平均值就会明显地受到太阳分潮的干扰。

2 considerably   

adv.极大地；相当大地；在很大程度上

参考例句：

• The economic situation has changed considerably.经济形势已发生了相当大的变化。
• The gap has narrowed considerably.分歧大大缩小了。

3 plausible   

adj.似真实的，似乎有理的，似乎可信的

参考例句：

• His story sounded plausible.他说的那番话似乎是真实的。
• Her story sounded perfectly plausible.她的说辞听起来言之有理。

4 physicists   

物理学家( physicist的名词复数 )

参考例句：

• For many particle physicists, however, it was a year of frustration. 对于许多粒子物理学家来说，这是受挫折的一年。 来自英汉非文学 - 科技
• Physicists seek rules or patterns to provide a framework. 物理学家寻求用法则或图式来构成一个框架。

5 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。

6 modification   

n.修改，改进，缓和，减轻

参考例句：

• The law,in its present form,is unjust;it needs modification.现行的法律是不公正的，它需要修改。
• The design requires considerable modification.这个设计需要作大的修改。

7 velocities   

n.速度( velocity的名词复数 )；高速，快速

参考例句：

• In experimenting we find out that sound travels with different velocities through different substances. 在实验中，我们发现声音以不同的速度通过不同的物质而传播。 来自《现代汉英综合大词典》
• A gas in thermal equilibrium has particles of all velocities. 处于热平衡的气体，其粒子有一切速度。 来自辞典例句

8 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。

9 kinetic   

adj.运动的；动力学的

参考例句：

• There exist many sources of energy both potential and kinetic.存在着许多势能和动能的能源。
• The kinetic theory of gases is the best known example.气体动力学理论就是最有名的例子。

10 infinity   

n.无限，无穷，大量

参考例句：

• It is impossible to count up to infinity.不可能数到无穷大。
• Theoretically,a line can extend into infinity.从理论上来说直线可以无限地延伸。

11 acceleration   

n.加速，加速度

参考例句：

• All spacemen must be able to bear acceleration.所有太空人都应能承受加速度。
• He has also called for an acceleration of political reforms.他同时呼吁加快政治改革的步伐。

12 unity   

n.团结，联合，统一；和睦，协调

参考例句：

• When we speak of unity,we do not mean unprincipled peace.所谓团结，并非一团和气。
• We must strengthen our unity in the face of powerful enemies.大敌当前，我们必须加强团结。

13 dealing   

n.经商方法，待人态度

参考例句：

• This store has an excellent reputation for fair dealing.该商店因买卖公道而享有极高的声誉。
• His fair dealing earned our confidence.他的诚实的行为获得我们的信任。

14 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。

15 briefly   

adv.简单地，简短地

参考例句：

• I want to touch briefly on another aspect of the problem.我想简单地谈一下这个问题的另一方面。
• He was kidnapped and briefly detained by a terrorist group.他被一个恐怖组织绑架并短暂拘禁。

16 transformation   

n.变化；改造；转变

参考例句：

• Going to college brought about a dramatic transformation in her outlook.上大学使她的观念发生了巨大的变化。
• He was struggling to make the transformation from single man to responsible husband.他正在努力使自己由单身汉变为可靠的丈夫。

17 premises   

n.建筑物，房屋

参考例句：

• According to the rules,no alcohol can be consumed on the premises.按照规定，场内不准饮酒。
• All repairs are done on the premises and not put out.全部修缮都在家里进行，不用送到外面去做。

18 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。

19 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？

20 possessed   

adj.疯狂的；拥有的，占有的

参考例句：

• He flew out of the room like a man possessed.他像着了魔似地猛然冲出房门。
• He behaved like someone possessed.他行为举止像是魔怔了。

21 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。

22 thoroughly   

adv.完全地，彻底地，十足地

参考例句：

• The soil must be thoroughly turned over before planting.一定要先把土地深翻一遍再下种。
• The soldiers have been thoroughly instructed in the care of their weapons.士兵们都系统地接受过保护武器的训练。