chapter 30

 Cosmological Difficulties of Newton’s Theory

 

Part from the difficulty discussed in Section XXI, there is a second fundamental difficulty attending classical celestial¹ mechanics, which, to the best of my knowledge, was first discussed in detail by the astronomer² Seeliger. If we ponder over the question as to how the universe, considered as a whole, is to be regarded, the first answer that suggests itself to us is surely this: As regards space (and time) the universe is infinite. There are stars everywhere, so that the density³ of matter, although very variable in detail, is nevertheless on the average everywhere the same. In other words: However far we might travel through space, we should find everywhere an attenuated⁴ swarm⁵ of fixed⁶ stars of approximately the same kind and density.

 

This view is not in harmony with the theory of Newton. The latter theory rather requires that the universe should have a kind of centre in which the density of the stars is a maximum, and that as we proceed outwards⁷ from this centre the group-density of the stars should diminish, until finally, at great distances, it is succeeded by an infinite region of emptiness. The stellar universe ought to be a finite island in the infinite ocean of space1.

 

This conception is in itself not very satisfactory. It is still less satisfactory because it leads to the result that the light emitted by the stars and also individual stars of the stellar system are perpetually passing out into infinite space, never to return, and without ever again coming into interaction with other objects of nature. Such a finite material universe would be destined⁸ to become gradually but systematically⁹ impoverished¹⁰.

 

In order to escape this dilemma¹¹, Seeliger suggested a modification¹² of Newton’s law, in which he assumes that for great distances the force of attraction between two masses diminishes more rapidly than would result from the inverse¹³ square law. In this way it is possible for the mean density of matter to be constant everywhere, even to infinity¹⁴, without infinitely¹⁵ large gravitational fields being produced. We thus free ourselves from the distasteful conception that the material universe ought to possess something of the nature of a centre. Of course we purchase our emancipation¹⁶ from the fundamental difficulties mentioned, at the cost of a modification and complication of Newton’s law which has neither empirical nor theoretical foundation. We can imagine innumerable laws which would serve the same purpose, without our being able to state a reason why one of them is to be preferred to the others; for any one of these laws would be founded just as little on more general theoretical principles as is the law of Newton.

 

1Proof.—According to the theory of Newton, the number of “lines of force” which come from infinity and terminate in a mass m is proportional to the mass m. If, on the average, the Mass density rho 0 is constant throughout tithe¹⁷ universe, then a sphere of volume V will enclose the average mass rho 0 upper V. Thus the number of lines of force passing through the surface F of the sphere into its interior is proportional to rho 0 upper V. For unit area of the surface of the sphere the number of lines of force which enters the sphere is thus proportional to rho 0 StartFraction v Over upper F EndFraction or to rho 0 upper R. Hence the intensity¹⁸ of the field at the surface would ultimately become infinite with increasing radius¹⁹ R of the sphere, which is impossible.

1 celestial   

adj.天体的；天上的

参考例句：

• The rosy light yet beamed like a celestial dawn.玫瑰色的红光依然象天上的朝霞一样绚丽。
• Gravity governs the motions of celestial bodies.万有引力控制着天体的运动。

2 astronomer   

n.天文学家

参考例句：

• A new star attracted the notice of the astronomer.新发现的一颗星引起了那位天文学家的注意。
• He is reputed to have been a good astronomer.他以一个优秀的天文学者闻名于世。

3 density   

n.密集，密度，浓度

参考例句：

• The population density of that country is 685 per square mile.那个国家的人口密度为每平方英里685人。
• The region has a very high population density.该地区的人口密度很高。

4 attenuated   

v.（使）变细( attenuate的过去式和过去分词 )；（使）变薄；（使）变小；减弱

参考例句：

• an attenuated form of the virus 毒性已衰减的病毒
• You're a seraphic suggestion of attenuated thought . 你的思想是轻灵得如同天使一般的。 来自辞典例句

5 swarm   

n.(昆虫)等一大群；vi.成群飞舞；蜂拥而入

参考例句：

• There is a swarm of bees in the tree.这树上有一窝蜜蜂。
• A swarm of ants are moving busily.一群蚂蚁正在忙碌地搬家。

6 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。

7 outwards   

adj.外面的，公开的，向外的；adv.向外；n.外形

参考例句：

• Does this door open inwards or outwards?这门朝里开还是朝外开？
• In lapping up a fur,they always put the inner side outwards.卷毛皮时，他们总是让内层朝外。

8 destined   

adj.命中注定的；(for)以…为目的地的

参考例句：

• It was destined that they would marry.他们结婚是缘分。
• The shipment is destined for America.这批货物将运往美国。

9 systematically   

adv.有系统地

参考例句：

• This government has systematically run down public services since it took office.这一屆政府自上台以来系统地削减了公共服务。
• The rainforest is being systematically destroyed.雨林正被系统地毀灭。

10 impoverished   

adj.穷困的，无力的，用尽了的v.使（某人）贫穷( impoverish的过去式和过去分词 )；使（某物）贫瘠或恶化

参考例句：

• the impoverished areas of the city 这个城市的贫民区
• They were impoverished by a prolonged spell of unemployment. 他们因长期失业而一贫如洗。 来自《简明英汉词典》

11 dilemma   

n.困境，进退两难的局面

参考例句：

• I am on the horns of a dilemma about the matter.这件事使我进退两难。
• He was thrown into a dilemma.他陷入困境。

12 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。

13 inverse   

adj.相反的，倒转的，反转的；n.相反之物；v.倒转

参考例句：

• Evil is the inverse of good.恶是善的反面。
• When the direct approach failed he tried the inverse.当直接方法失败时，他尝试相反的做法。

14 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。

15 infinitely   

adv.无限地，无穷地

参考例句：

• There is an infinitely bright future ahead of us.我们有无限光明的前途。
• The universe is infinitely large.宇宙是无限大的。

16 emancipation   

n.（从束缚、支配下）解放

参考例句：

• We must arouse them to fight for their own emancipation. 我们必须唤起他们为其自身的解放而斗争。 来自《简明英汉词典》
• They rejoiced over their own emancipation. 他们为自己的解放感到欢欣鼓舞。 来自《简明英汉词典》

17 tithe   

n.十分之一税；v.课什一税，缴什一税

参考例句：

• It's not Christ plus your tithe.这不是基督再加上你的什一税。
• The bible tells us that the tithe is the lords.圣经说十分之一是献给主的。

18 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。

19 radius   

n.半径，半径范围；有效航程，范围，界限

参考例句：

• He has visited every shop within a radius of two miles.周围两英里以内的店铺他都去过。
• We are measuring the radius of the circle.我们正在测量圆的半径。