第十章 黎曼球面泡的惯性质量
Chapter 10 The inertial mass of a Riemann-sphere-bubble
鉴于(8.5-2),一个扭量光影的惯性质量是在该扭量空间里的引力场的惯性质量.
In view of (8.5-2), the inertial mass of a twistor-light-silhouette is the inertial mass of the gravitational field in this twistor space.
彭罗斯指出:
在爱因斯坦理论里,出现在场方程里的张量 T 包含了所有非引力场(和粒子)的能量动量.而引力场本身无论有什么能量都被排除在 T 的任何表示之外.
但是这种"能量动量守恒"只是一种近似,只要存在由引力场的不均匀性引起的相对加速度(潮汐)效应,就必须给予修改.引力对能量动量守恒的贡献应以某种非局域的方式加入进来,作为对于总能量动量计算的修改. (《通向实在之路》第331页.)
Penrose pointed out:
In Einstein's theory, the symmetric tensor T that appears in his field equation is to include the energy-momentum of all non-gravitational fields (and particles). Whatever energy there is in the gravitational field itself is to be excluded from having any representation within T.
This "energy-momentum conservation" is, however, only an approximation, which is expected to need correction as soon as the relative acceleration (tidal) effects due to the non-uniformity of the gravitational field begin to play a role. The contributions of gravity to energy-momentum conservation should somehow enter nonlocally as corrections to the calculation of total energy-momentum. (The Road to Reality. p. 458.)
参考文献
罗杰·彭罗斯.《通向实在之路——宇宙法则的完全指南》.王文浩 译.长沙:湖南科学技术出版社.2013年11月.
Reference
Roger Penrose. The Road to Reality: A Complete Guide to the Laws of the Universe. Copyright 2004. First Vintage Books edition, January 2007.
10.1 胡宁的工作
10.1 Hu Ning's work
胡宁(1916 ~ 1997)是中国科学院前院士.
Hu Ning (Hu, Ning 1916 ~ 1997) was a late academician of the Chinese Academy of Sciences.
胡宁写道,"应该指出,广义相对论是以局域性的场量为基础的."(胡宁.引力场能量密度的恒正性问题. 中国科学, 1977, (3)：210-217.)
Hu Ning (Hu, Ning) wrote, "It should however be pointed out that the general theory of relativity accepts only local field quantities." (Hu N. The positive definite property of the energy density in gravitational fields. Scientia Sinica, 1977, (20): 335.)
胡宁院士在他的遗著《广义相对论和引力场理论》的第1章"引言"里强调了这样一个观点：
| 引力场是一个物质场. (10.1-1) |
In Chapter 1 "Introduction" in his posthumous work The General Theory of Relativity and Theory of the Gravitational Field, HU Ning (Hu, Ning) also written as Ning Hu, N. Hu, or Hu N.) (1916 ~ 1997), a late academician of the Chinese Academy of Sciences, laid emphasis on the viewpoint that
| The gravitational field is a material field. (10.1-1) |
胡宁在他的遗著《广义相对论和引力场理论》[1]的第12章"惯性质量和引力质量"里,在进行了大量计算之后写道:
In Chapter 12 "Inertial Mass and Gravitational Mass" of his posthumous work The General Theory of Relativity and Theory of the Gravitational Field (In Chinese.)[1], after making a great many calculations, Hu Ning wrote
| “比较(12.32)式和(12.43)式,我们看到双星系统的惯性质量不等于它的引力质量,而且这两种质量在空间的分布是完全不同的,引力质量分布只在星体的内部不等于零；而惯性质量密度在星体内部和外部都不等于零,这表示引力场作为物质的一种形式是具有惯性质量的.” (10.1-2) |
| "Comparing Eqs. (12.32) and (12.43), we see that the inertial mass of a double-star system is not equal to the gravitational mass of the system, and the distributions of these two masses are entirely different: the gravitational mass distribution is different from zero only inside the celestial body, while the inertial mass density is different from zero both within and out of the celestial body; this means that as a form of matter, the gravitational field possesses inertial mass." (10.1-2) |
|
“如果在引力场中的物体具有内部的运动，那将存在着使这个物体所受到的引力加速度与质量有关的另外一个原因：引力质量不等于惯性质量。" “最简单的例子是地球和月球在太阳引力场中的运动，我们可以把地球和月球看作是一个有内部运动的体系,……” “严格地讲,所有物体都具有内部运动,例如组成每个物体的分子间的热运动和原子内部的电子运动等都是物体的内部运动,尽管引力作用对这个运动的效应很小,但它使得惯性质量和引力质量的相等只可能是近似地正确.” “上面结果指出引力质量和惯性质量之差,与原质量的比值属于数量级v2/c2 ,……” (10.1-3) |
| "If a body in the
gravitational field has internal motion, then there is
another factor in making the gravitational acceleration
which the body is subject to related to its mass: the
gravitational mass is not equal to the inertial mass." "The simplest example is that the Earth and the Moon moving in the Sun's gravitational field can be considered as a system having the internal motion, ... "Strictly speaking, everything has internal motion; for example, inside a body, thermal motion of molecules and motion of electrons within atoms are both the body's internal motion, on which the action of gravitation has tiny effect, owing to which, nevertheless, it can only be approximately true that the inertial mass and the gravitational mass are equal." "The above result indicates that the ratio of the difference between the gravitational mass and the inertial mass to the original mass is of the order of magnitude v2/c2 , ..." (10.1-3) |
|
“上式给出的总能量正是两个星体的静止能量加上在经典理论里这一对双星的动能和位能,亦即两个星体的静止能量加上经典力学里的总能量.值得注意的是,由非线性近似解所得出的总能量除掉引入两个静质量以外完全和牛顿力学的结果一样.” (10.1-4) |
|
"The total energy given by the above equation is exactly the rest energies of the two stars plus the kinetic energies and the potential energies of the pair of double stars in the classical theory; i.e. the rest energies of the two stars plus the total energies in classical mechanics. It's worth noting that the total energy given by the non-linear approximate solution, except for the introduction of two rest masses, is completely the same as the result from Newtonian mechanics." (10.1-4) |
参考文献
References
[1] 胡宁.广义相对论和引力场理论.北京:科学出版社,2000年1月. ISBN 7- 03 - 007835 - 7. 第84~85页.
[1] Hu Ning. The General Theory of Relativity and the Theory of the Gravitational Field. Beijing: Science Press, January, 2000. Print. ISBN 7- 03 - 007835 - 7. pp. 84~85. (In Chinese.)
10.2 黎曼球面泡的惯性质量
10.2 The inertial mass of a Riemann-sphere-bubble
根据(10.1-3),下式成立:
( m惯 - m引 ) / m原 = (v内部运动)2 / c2, (10.2-1)
According to (10.1-3), the following expression holds:
( minertial - mgravitational ) / moriginal = (vinternal motion)2 / c2, (10.2-1)
式中m惯是一个物体的惯性质量,m引是这个物体的引力质量,m原是这个物体的原质量,v内部运动是这个物体的内部运动的速率.
where minertial is the inertial mass of a body, mgravitational is the gravitational mass of the body, moriginal is the original mass of the body, vinternal motion is the speed of the internal motion of the body.
(见本网站第四章和第七章.)
(See Chapter 4 and Chapter 7 of this website.)
爱因斯坦于1948年6月19日在给Lincoln Barnett的信中写道:
“对于运动物体引入无法给出明确定义的质量概念 M = m / ( 1 - v2 / c2 )1/2 是不好的.建议除了‘静质量’ m 以外不再引入其他质量概念.建议不要引入 M ,而应该通过运动物体的动量和能量的表达式来论述.”[1]
In the letter to Lincoln Barnett, 19, June 1948, Einstein wrote:
"It is not good to introduce the concept of the mass M = m / ( 1 - v2 / c2 )1/2 of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion."[1]
因此(10.2-1)变为
mRSB = m v2 / c2 , (10.2-2)
式中mRSB是黎曼球面泡的惯性质量, m 是物体的原质量, v 是扭量光影的运动速度.
Hence (10.2-1) becomes
mRSB = m v2 / c2. (10.2-2)
where mRSB is the inertial mass of the Riemann-sphere-bubble, m is the original mass of the body, and v is the speed of the motion of the twistor-light-silhouette.
黎曼球面泡的质量是由内部运动导致的.因此基于(10.1-4),也许可以以如下的方式来理解(10.2-2).
设物体的内部动能是 E内部 ,物体的内部势能是 P内部 .于是有下列关系式：
mRSB = ( E内部 + P内部 ) / c2 ~ ( 2 E内部 / c2 ); (机械能守恒定律)
mRSB ~ 2 ( (1/2) m (v内部运动)2 ) / c2 ;
mRSB ~ m (v扭量光影)2 / c2 .
The mass of the Riemann-sphere-bubble is brought by internal motion. Hence, based on (10.1-4), perhaps (10.2-2) can be understood in the following way.
Let Einternal be the internal kinetic energy of the body, and Pinternal be the internal potential energy of the body. Then there are the following relations:
mRSB = ( Einternal + Pinternal ) / c2 ~ ( 2 Einternal / c2 );
mRSB ~ 2 ( (1/2) m (vinternal motion)2 ) / c2 ;
mRSB ~ m (vtwistor-light-silhouette)2 / c2 .
[1] Lev B. Okun. The concept of mass [J]. Physics Today, June 1989: 31 - 36.
http://www.itep.ru/theor/persons/lab180/okun/em_3.pdf
[1] Lev B. Okun. The concept of mass [J]. Physics Today, June 1989: 31 - 36.