chapter 19

 The Gravitational Field

 

“If we pick up a stone and then let it go, why does it fall to the ground?” The usual answer to this question is: “Because it is attracted by the earth.” Modern physics formulates¹ the answer rather differently for the following reason. As a result of the more careful study of electromagnetic phenomena², we have come to regard action at a distance as a process impossible without the intervention³ of some intermediary medium. If, for instance, a magnet attracts a piece of iron, we cannot be content to regard this as meaning that the magnet acts directly on the iron through the intermediate empty space, but we are constrained⁴ to imagine—after the manner of Faraday—that the magnet always calls into being something physically⁵ real in the space around it, that something being what we call a “magnetic field.” In its turn this magnetic field operates on the piece of iron, so that the latter strives to move towards the magnet. We shall not discuss here the justification⁶ for this incidental conception, which is indeed a somewhat arbitrary one. We shall only mention that with its aid electromagnetic phenomena can be theoretically represented much more satisfactorily than without it, and this applies particularly to the transmission of electromagnetic waves. The effects of gravitation also are regarded in an analogous⁷ manner.

 

The action of the earth on the stone takes place indirectly⁸. The earth produces in its surrounding a gravitational field, which acts on the stone and produces its motion of fall. As we know from experience, the intensity⁹ of the action on a body diminishes according to a quite definite law, as we proceed farther and farther away from the earth. From our point of view this means: The law governing the properties of the gravitational field in space must be a perfectly¹⁰ definite one, in order correctly to represent the diminution¹¹ of gravitational action with the distance from operative bodies. It is something like this: The body (e.g. the earth) produces a field in its immediate¹² neighbourhood directly; the intensity and direction of the field at points farther removed from the body are thence determined¹³ by the law which governs the properties in space of the gravitational fields themselves.

 

In contrast to electric and magnetic fields, the gravitational field exhibits a most remarkable¹⁴ property, which is of fundamental importance for what follows. Bodies which are moving under the sole influence of a gravitational field receive an acceleration¹⁵, which does not in the least depend either on the material or on the physical state of the body. For instance, a piece of lead and a piece of wood fall in exactly the same manner in a gravitational field (in vacuo), when they start off from rest or with the same initial velocity¹⁶. This law, which holds most accurately¹⁷, can be expressed in a different form in the light of the following consideration.

 

According to Newton’s law of motion, we have

 

(Force) = (inertial mass) times (acceleration),

 

where the “inertial mass” is a characteristic constant of the accelerated body. If now gravitation is the cause of the acceleration, we then have

 

(Force) = (gravitational mass) times (intensity of the gravitational field),

 

where the “gravitational mass” is likewise a characteristic constant for the body. From these two relations follows:

left-parenthesis acceleration right-parenthesis equals StartFraction gravitational mass Over inertial mass EndFraction times intensity of the gravitational field period

If now, as we find from experience, the acceleration is to be independent of the nature and the condition of the body and always the same for a given gravitational field, then the ratio of the gravitational to the inertial mass must likewise be the same for all bodies. By a suitable choice of units we can thus make this ratio equal to unity¹⁸. We then have the following law: The gravitational mass of a body is equal to its inertial mass.

 

It is true that this important law had hitherto been recorded in mechanics, but it had not been interpreted. A satisfactory interpretation¹⁹ can be obtained only if we recognise the following fact: The same quality of a body manifests itself according to circumstances as “inertia” or as “weight” (lit. “heaviness”). In the following section we shall show to what extent this is actually the case, and how this question is connected with the general postulate²⁰ of relativity.

1 formulates   

v.构想出( formulate的第三人称单数 )；规划；确切地阐述；用公式表示

参考例句：

• Article Eleven SEPA formulates the overall plans of the training. 第十一条环保总局统筹规划培训工作。 来自互联网
• This paper carries on the experimental analysis and formulates some anti-disturbance measures. 文章对电磁干扰进行了实验分析，并有针对性地制定一些抗干扰措施。 来自互联网

2 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。

3 intervention   

n.介入，干涉，干预

参考例句：

• The government's intervention in this dispute will not help.政府对这场争论的干预不会起作用。
• Many people felt he would be hostile to the idea of foreign intervention.许多人觉得他会反对外来干预。

4 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。

5 physically   

adj.物质上，体格上，身体上，按自然规律

参考例句：

• He was out of sorts physically,as well as disordered mentally.他浑身不舒服，心绪也很乱。
• Every time I think about it I feel physically sick.一想起那件事我就感到极恶心。

6 justification   

n.正当的理由；辩解的理由

参考例句：

• There's no justification for dividing the company into smaller units. 没有理由把公司划分成小单位。
• In the young there is a justification for this feeling. 在年轻人中有这种感觉是有理由的。

7 analogous   

adj.相似的；类似的

参考例句：

• The two situations are roughly analogous.两种情況大致相似。
• The company is in a position closely analogous to that of its main rival.该公司与主要竞争对手的处境极为相似。

8 indirectly   

adv.间接地，不直接了当地

参考例句：

• I heard the news indirectly.这消息我是间接听来的。
• They were approached indirectly through an intermediary.通过一位中间人，他们进行了间接接触。

9 intensity   

n.强烈，剧烈；强度；烈度

参考例句：

• I didn't realize the intensity of people's feelings on this issue.我没有意识到这一问题能引起群情激奋。
• The strike is growing in intensity.罢工日益加剧。

10 perfectly   

adv.完美地，无可非议地，彻底地

参考例句：

• The witnesses were each perfectly certain of what they said.证人们个个对自己所说的话十分肯定。
• Everything that we're doing is all perfectly above board.我们做的每件事情都是光明正大的。

11 diminution   

n.减少；变小

参考例句：

• They hope for a small diminution in taxes.他们希望捐税能稍有减少。
• He experienced no diminution of his physical strength.他并未感觉体力衰落。

12 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。

13 determined   

adj.坚定的；有决心的

参考例句：

• I have determined on going to Tibet after graduation.我已决定毕业后去西藏。
• He determined to view the rooms behind the office.他决定查看一下办公室后面的房间。

14 remarkable   

adj.显著的，异常的，非凡的，值得注意的

参考例句：

• She has made remarkable headway in her writing skills.她在写作技巧方面有了长足进步。
• These cars are remarkable for the quietness of their engines.这些汽车因发动机没有噪音而不同凡响。

15 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。

16 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。

17 accurately   

adv.准确地，精确地

参考例句：

• It is hard to hit the ball accurately.准确地击中球很难。
• Now scientists can forecast the weather accurately.现在科学家们能准确地预报天气。

18 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。

19 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。

20 postulate   

n.假定，基本条件；vt.要求，假定

参考例句：

• Let's postulate that she is a cook.我们假定她是一位厨师。
• Freud postulated that we all have a death instinct as well as a life instinct.弗洛伊德曾假定我们所有人都有生存本能和死亡本能。