chapter 32

 The Structure of Space According to the General Theory of Relativity

 

According to the general theory of relativity, the geometrical properties of space are not independent, but they are determined¹ by matter. Thus we can draw conclusions about the geometrical structure of the universe only if we base our considerations on the state of the matter as being something that is known. We know from experience that, for a suitably chosen co-ordinate system, the velocities² of the stars are small as compared with the velocity³ of transmission of light. We can thus as a rough approximation arrive at a conclusion as to the nature of the universe as a whole, if we treat the matter as being at rest.

 

We already know from our previous discussion that the behaviour of measuring-rods and clocks is influenced by gravitational fields, i.e. by the distribution of matter. This in itself is sufficient to exclude the possibility of the exact validity of Euclidean geometry in our universe. But it is conceivable that our universe differs only slightly from a Euclidean one, and this notion seems all the more probable, since calculations show that the metrics of surrounding space is influenced only to an exceedingly small extent by masses even of the magnitude of our sun. We might imagine that, as regards geometry, our universe behaves analogously⁴ to a surface which is irregularly curved in its individual parts, but which nowhere departs appreciably⁵ from a plane: something like the rippled⁶ surface of a lake. Such a universe might fittingly be called a quasi-Euclidean universe. As regards its space it would be infinite. But calculation shows that in a quasi-Euclidean universe the average density⁷ of matter would necessarily be nil⁸. Thus such a universe could not be inhabited by matter everywhere; it would present to us that unsatisfactory picture which we portrayed⁹ in Section XXX.

 

If we are to have in the universe an average density of matter which differs from zero, however small may be that difference, then the universe cannot be quasi-Euclidean. On the contrary, the results of calculation indicate that if matter be distributed uniformly, the universe would necessarily be spherical¹⁰ (or elliptical). Since in reality the detailed¹¹ distribution of matter is not uniform, the real universe will deviate¹² in individual parts from the spherical, i.e. the universe will be quasi-spherical. But it will be necessarily finite. In fact, the theory supplies us with a simple connection1 between the space-expanse of the universe and the average density of matter in it.

 

1 For the “radius” R of the universe we obtain the equation

upper R squared equals StartFraction 2 Over kappa rho EndFraction

The use of the C.G.S. system in this equation gives 2 slash¹³ kappa equals 1.08 dot 10 Superscript 27; rho is the average density of the matter and kappa is a constant connected with the Newtonian constant of gravitation.

The End

1 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。

2 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

3 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。

4 analogously   

adv.类似地，近似地

参考例句：

• Analogously, the slowdown in population growth puts pressure on Social Security finances. 以此类推，人口增长率缓慢下来时就会给社会安全基金的财经带来压力。 来自互联网
• The cited experimental curves analogously with simulation appearances found in this study. 所引用的实验曲线也出现雷同的表现。 来自互联网

5 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。

6 rippled   

使泛起涟漪（ripple的过去式与过去分词形式）

参考例句：

• The lake rippled gently. 湖面轻轻地泛起涟漪。
• The wind rippled the surface of the cornfield. 微风吹过麦田，泛起一片麦浪。

7 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。

8 nil   

n.无，全无，零

参考例句：

• My knowledge of the subject is practically nil.我在这方面的知识几乎等于零。
• Their legal rights are virtually nil.他们实际上毫无法律权利。

9 portrayed   

v.画像( portray的过去式和过去分词 )；描述；描绘；描画

参考例句：

• Throughout the trial, he portrayed himself as the victim. 在审讯过程中，他始终把自己说成是受害者。
• The author portrayed his father as a vicious drunkard. 作者把他父亲描绘成一个可恶的酒鬼。 来自《现代汉英综合大词典》

10 spherical   

adj.球形的；球面的

参考例句：

• The Earth is a nearly spherical planet.地球是一个近似球体的行星。
• Many engineers shy away from spherical projection methods.许多工程师对球面投影法有畏难情绪。

11 detailed   

adj.详细的，详尽的，极注意细节的，完全的

参考例句：

• He had made a detailed study of the terrain.他对地形作了缜密的研究。
• A detailed list of our publications is available on request.我们的出版物有一份详细的目录备索。

12 deviate   

v.(from)背离，偏离

参考例句：

• Don't deviate from major issues.不要偏离主要问题。
• I will never deviate from what I believe to be right.我绝不背离我自信正确的道路。

13 slash   

vi.大幅度削减；vt.猛砍，尖锐抨击，大幅减少；n.猛砍，斜线，长切口，衣衩

参考例句：

• The shop plans to slash fur prices after Spring Festival.该店计划在春节之后把皮货降价。
• Don't slash your horse in that cruel way.不要那样残忍地鞭打你的马。