chapter 20

 The Equality of Inertial and Gravitational Mass as an Argument for the General Postulate¹ of Relativity

 

We imagine a large portion of empty space, so far removed from stars and other appreciable² masses, that we have before us approximately the conditions required by the fundamental law of Galilei. It is then possible to choose a Galileian reference-body for this part of space (world), relative to which points at rest remain at rest and points in motion continue permanently³ in uniform rectilinear motion. As reference-body let us imagine a spacious⁴ chest resembling a room with an observer inside who is equipped with apparatus⁵. Gravitation naturally does not exist for this observer. He must fasten himself with strings⁶ to the floor, otherwise the slightest impact against the floor will cause him to rise slowly towards the ceiling of the room.

 

To the middle of the lid of the chest is fixed⁷ externally a hook with rope attached, and now a “being” (what kind of a being is immaterial to us) begins pulling at this with a constant force. The chest together with the observer then begin to move “upwards” with a uniformly accelerated motion. In course of time their velocity⁸ will reach unheard-of values—provided that we are viewing all this from another reference-body which is not being pulled with a rope.

 

But how does the man in the chest regard the Process? The acceleration⁹ of the chest will be transmitted to him by the reaction of the floor of the chest. He must therefore take up this pressure by means of his legs if he does not wish to be laid out full length on the floor. He is then standing¹⁰ in the chest in exactly the same way as anyone stands in a room of a home on our earth. If he releases a body which he previously¹¹ had in his land, the acceleration of the chest will no longer be transmitted to this body, and for this reason the body will approach the floor of the chest with an accelerated relative motion. The observer will further convince himself that the acceleration of the body towards the floor of the chest is always of the same magnitude, whatever kind of body he may happen to use for the experiment.

 

Relying on his knowledge of the gravitational field (as it was discussed in the preceding section), the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time. Of course he will be puzzled for a moment as to why the chest does not fall in this gravitational field. just then, however, he discovers the hook in the middle of the lid of the chest and the rope which is attached to it, and he consequently comes to the conclusion that the chest is suspended at rest in the gravitational field.

 

Ought we to smile at the man and say that he errs¹² in his conclusion? I do not believe we ought to if we wish to remain consistent; we must rather admit that his mode of grasping the situation violates neither reason nor known mechanical laws. Even though it is being accelerated with respect to the “Galileian space” first considered, we can nevertheless regard the chest as being at rest. We have thus good grounds for extending the principle of relativity to include bodies of reference which are accelerated with respect to each other, and as a result we have gained a powerful argument for a generalised postulate of relativity.

 

We must note carefully that the possibility of this mode of interpretation¹³ rests on the fundamental property of the gravitational field of giving all bodies the same acceleration, or, what comes to the same thing, on the law of the equality of inertial and gravitational mass. If this natural law did not exist, the man in the accelerated chest would not be able to interpret the behaviour of the bodies around him on the supposition of a gravitational field, and he would not be justified¹⁴ on the grounds of experience in supposing his reference-body to be “at rest.”

 

Suppose that the man in the chest fixes a rope to the inner side of the lid, and that he attaches a body to the free end of the rope. The result of this will be to stretch the rope so that it will hang “vertically” downwards¹⁵. If we ask for an opinion of the cause of tension in the rope, the man in the chest will say: “The suspended body experiences a downward force in the gravitational field, and this is neutralised by the tension of the rope; what determines the magnitude of the tension of the rope is the gravitational mass of the suspended body.” On the other hand, an observer who is poised¹⁶ freely in space will interpret the condition of things thus: “The rope must perforce take part in the accelerated motion of the chest, and it transmits this motion to the body attached to it. The tension of the rope is just large enough to effect the acceleration of the body. That which determines the magnitude of the tension of the rope is the inertial mass of the body.” Guided by this example, we see that our extension of the principle of relativity implies the necessity of the law of the equality of inertial and gravitational mass. Thus we have obtained a physical interpretation of this law.

 

From our consideration of the accelerated chest we see that a general theory of relativity must yield important results on the laws of gravitation. In point of fact, the systematic¹⁷ pursuit of the general idea of relativity has supplied the laws satisfied by the gravitational field. Before proceeding¹⁸ farther, however, I must warn the reader against a misconception suggested by these considerations. A gravitational field exists for the man in the chest, despite the fact that there was no such field for the co-ordinate system first chosen. Now we might easily suppose that the existence of a gravitational field is always only an apparent one. We might also think that, regardless of the kind of gravitational field which may be present, we could always choose another reference-body such that no gravitational field exists with reference to it. This is by no means true for all gravitational fields, but only for those of quite special form. It is, for instance, impossible to choose a body of reference such that, as judged from it, the gravitational field of the earth (in its entirety) vanishes.

 

We can now appreciate why that argument is not convincing, which we brought forward against the general principle of relativity at the end of Section XVIII. It is certainly true that the observer in the railway carriage experiences a jerk forwards as a result of the application of the brake, and that he recognises, in this the non-uniformity of motion (retardation) of the carriage. But he is compelled by nobody to refer this jerk to a “real “acceleration (retardation) of the carriage. He might also interpret his experience thus: “My body of reference (the carriage) remains¹⁹ permanently at rest. With reference to it, however, there exists (during the period of application of the brakes) a gravitational field which is directed forwards and which is variable with respect to time. Under the influence of this field, the embankment together with the earth moves non-uniformly in such a manner that their original velocity in the backwards²⁰ direction is continuously reduced.”

1 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。

2 appreciable   

adj.明显的，可见的，可估量的，可觉察的

参考例句：

• There is no appreciable distinction between the twins.在这对孪生子之间看不出有什么明显的差别。
• We bought an appreciable piece of property.我们买下的资产有增值的潜力。

3 permanently   

adv.永恒地，永久地，固定不变地

参考例句：

• The accident left him permanently scarred.那次事故给他留下了永久的伤疤。
• The ship is now permanently moored on the Thames in London.该船现在永久地停泊在伦敦泰晤士河边。

4 spacious   

adj.广阔的，宽敞的

参考例句：

• Our yard is spacious enough for a swimming pool.我们的院子很宽敞，足够建一座游泳池。
• The room is bright and spacious.这房间很豁亮。

5 apparatus   

n.装置，器械；器具，设备

参考例句：

• The school's audio apparatus includes films and records.学校的视听设备包括放映机和录音机。
• They had a very refined apparatus.他们有一套非常精良的设备。

6 strings   

n.弦

参考例句：

• He sat on the bed,idly plucking the strings of his guitar.他坐在床上，随意地拨着吉他的弦。
• She swept her fingers over the strings of the harp.她用手指划过竖琴的琴弦。

7 fixed   

adj.固定的，不变的，准备好的；(计算机)固定的

参考例句：

• Have you two fixed on a date for the wedding yet?你们俩选定婚期了吗？
• Once the aim is fixed,we should not change it arbitrarily.目标一旦确定，我们就不应该随意改变。

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 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。

10 standing   

n.持续，地位；adj.永久的，不动的，直立的，不流动的

参考例句：

• After the earthquake only a few houses were left standing.地震过后只有几幢房屋还立着。
• They're standing out against any change in the law.他们坚决反对对法律做任何修改。

11 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。

12 errs   

犯错误，做错事( err的第三人称单数 )

参考例句：

• Man errs so long as he strives. 人只要奋斗就会犯错误。 来自每日一句
• He that talks much errs much. [谚]言多必有失。

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 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。

15 downwards   

adj./adv.向下的（地），下行的（地）

参考例句：

• He lay face downwards on his bed.他脸向下伏在床上。
• As the river flows downwards,it widens.这条河愈到下游愈宽。

16 poised   

a.摆好姿势不动的

参考例句：

• The hawk poised in mid-air ready to swoop. 老鹰在半空中盘旋，准备俯冲。
• Tina was tense, her hand poised over the telephone. 蒂娜心情紧张，手悬在电话机上。

17 systematic   

adj.有系统的，有计划的，有方法的

参考例句：

• The way he works isn't very systematic.他的工作不是很有条理。
• The teacher made a systematic work of teaching.这个教师进行系统的教学工作。

18 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。

19 remains   

n.剩余物，残留物；遗体，遗迹

参考例句：

• He ate the remains of food hungrily.他狼吞虎咽地吃剩余的食物。
• The remains of the meal were fed to the dog.残羹剩饭喂狗了。

20 backwards   

adv.往回地，向原处，倒，相反，前后倒置地

参考例句：

• He turned on the light and began to pace backwards and forwards.他打开电灯并开始走来走去。
• All the girls fell over backwards to get the party ready.姑娘们迫不及待地为聚会做准备。