On the Contribution of Zhou Pei-Yuan to General Relativity

Dear Professor Cao and Professor Liu:

I have been wondering why the out-standing contribution of Professor Zhou Pei-Yuan of Peking University was not properly recognized even in China. Recently, I have my answer from the announcements in the Internet from different academic organizations in China. From these announcements, I conclude that Zhou’s work was still not well understood at least to those organizations in China. Thus, these would add tremendous difficulties to expect that Zhou’s contribution could be recognized worldwide. The purpose of writing this letter is let you know the facts that you would help improving such a situation.

From the announcements, the contributions of Zhou on general relativity are either without the necessary details or with some details of invalid attributions. In short, none of the announcements indicate an accurate over all understanding of Zhou’s work. These inevitably allow some theorists to belittle or even sneeze at Zhou’s contributions on general relativity and the academic achievements of China. Naturally, this would also add strength to those, who believe in “authorities” in this field, instead of the principle that practice (or experiments) is the only criterion for a theory.

For example, in the announcement of Chinese Academy, Zhou’s contribution is simply,
“主要从事物理学的基础理论中难度最大的两个方面即爱因斯坦广义相对论引力论和流体力学中的湍流理论的研究与教 学并取得出色成果。”
I did not find any other announcement xxxx the Chinese Academy. However, since Professor Peng [1, 2], a student of Zhou and out standing theoretical physicist in China, also did not know the significant of Zhou’s work, I concluded that they probably did not know. In the announcement of中国科学技术协会, Zhou’s contribution with details (see attached) has the following errors and/or in accuracy:

1) Zhou is not a “坐标有关论者”1), which is known to all physicists to be incorrect. What he pointed out is that the physi-cal meaning of coordinates depends on the gauge chosen. Moreover, this gauge dependence can be derived from Ein-stein’s equivalence principle [3, 4]. From Zhou’s experiment [5, 6], it is clear that Zhou is probably the first theorist who understands that Einstein’s equivalence principle implies invalidity of the gauge invariance and the “covariance princi-ple”2). Such an inconsistency is overlooked by Einstein and other theorists until recently. For this reason alone, Zhou is the greatest theorist on general relativity of his time after Einstein.
2) From Zhou’s papers [5], it is clear that the difference between the vertical and horizontal light speeds is not zero for the Lanzos solution although it is zero for the isotropic solution. Moreover, according to the editorial of the Chinese Physics, the experimental result is unclear in favor of the Schwarzschild solution or the isotropic and Lanzos solutions. I check with the original paper [6], and the editorial of Chinese Physics is correct.
3) However, there are existing experiments that is clearly in favor of the isotropic and Lanzos solutions [7, 8]. They are the experiments on gravitational radiation of binary pulsars, and the first experiment of this kind, the Hulse-Taylor experi-ment has won a Nobel Prize. In the explanation of these experiments, the Maxwell-Newton Approximation must be used [7] and this approximation rejects the Schwarzschild solution.
4) Zhou proposed the harmonic gauge only for the case of asymptotically flat metrics [2]. Fock [9], however, advocated the harmonic gauge unconditionally; and Fock’s proposal has been proven incorrect [10].

These are the errors and inaccuracy that I have found and this is probably not a complete list. However, I hope these comments would be useful for you to rectify the situation. Any questions and comments you may have will be appreciated. Please note that it is based on the work of Zhou that the knowledge of the current Royal Society is judged as about 25 years out-dated. However, if one counted from the date of Eddington [11], the current situation is about 85 years out dated!

Sincerely yours,

C. Y. Lo

Endnotes

1) Recently, a board member of the Royal Society comments [12], “The outcome off a real experiment cannot depend on a choice of coordinates. This is true for Newtonian theory as much as general relativity.”
2) The “covariance principle” leads to the notion of Lorentz manifolds [13] that cannot be one-one corresponding to a four-dimensional Minkowski space, and this is the theoretical basis for the paper of Bondi et al [14].

References:

1. Peng Huanwu, & Xu Xiseng, The Fundamentals of Theoretical Physics (Peking University Press, Beijing, 2000).
2. Peng Huangwu, Commun. Theor. Phys. (Beijing, China), 31, 13-20 (1999).
3. An Existence of Local Minkowski Spaces is Insufficient for Einstein's Equivalence Principle, Phys. Essays, 15 (3), 303-321 (September, 2002).
4. Space Contractions, Local Light Speeds, and the Question of Gauge in General Relativity, Chinese J. of Phys. (Taipei), 41 (4), 233-343 (August 2003).
5. Zhou Pei-yuan, “Further Experiments to Test Einstein’s Theory of Gravitation”, International Symposium on Experimental Gravitational Physics (Guangzhou, 3-8 August 1987), edited by Peter F. Michelson, 110-116 (World Sci., Singapore).
6. Measurement of the Relative Difference of the light Velocity in the Horizontal and vertical Directions on the Earth Surface Proceedings of the Fourth Asia Pacific Physics Conference, Seoul, Korea, August 13-17, 1990, 2: 1155-1159.
7. Einstein's Radiation xxxxula and Modifications to the Einstein Equation, Astrophysical Journal 455, 421-428 (1995).
8. On Incompatibility of Gravitational Radiation with the 1915 Einstein Equation, Phys. Essays 13 (4), 527-539 (2000).
9. V. A. Fock, The Theory of Space Time and Gravitation, translated by N. Kemmer (Pergamon Press, 1964).
10. Misunderstandings Related to Einstein’s Principle of Equivalence, and Einstein’s Theoretical Errors on Measurements, Phys. Essays 18 (4), 547-560 (December, 2005).
11. A.S. Eddington, The Mathematical Theory of Relativity (Chelsea, New York, 1975), p. 10.
12. Louise Le Bas, Publishing Editor, the Royal Society, A Board Member’s Comments (July 24, 2007).
13. R. M. Wald, General Relativity (The Univ. of Chicago Press, Chicago, 1984).
14. H. Bondi, F. A. E. Pirani, & I. Robinson, Proc. R. Soc. London A 251, 519-533 (1959).

Attachment:
　广义相对论在物理上取得了许多辉煌成就，但从一开始就存在着一个困难，这就是，表达引力场的方程是一个包含10个二阶非线性偏微分方程的方程 组，而这10个方程之间又存在着4个独立的非线性偏微分方程组所组成的恒等式，也称为比安基(Bianchi)恒等式，这就使得只用引力方程得不到10个 引力函数的确定解。周培源一进入相对论领域便抓住这个难题，主张引进另外的物理条件才能求解出引力函数的确定解。沿循这个思路，周培源在20世纪20年代 用引入新物理条件的办法获得了轴对称静态引力场的若干解，以后又于20世纪30年代在引入各向同性条件下，又求得了与静止场不同类型的严格解。
　　与此同时，国际上的同行学者为了克服上述困难，采用坐标变换的方法来减少引力函数的数目。但这种方法只能求出一种常微分方程的特殊引力场——球 对称静态引力场的严格解，例如史瓦西(Schwazchild)解，而对众多的其他物理问题仍然束手无策。沿着这条思路求解引力场方程的相对论研究者，在 国际上称为“坐标无关论者”。他们主张坐标在引力论中无关紧要。与此相反，周培源从一开始进行引力论研究时，就认为坐标是有物理意义的，因此他是一位“坐 标有关论者”。“坐标有关论者”在一些特殊问题上，引进谐和条件以求解引力场方程的做法，可以追溯到1919年爱因斯坦本人。他引进谐和条件的近似式来求 解线性化了的引力场方程，从而获得了引力波解，预言了引力波的存在。后来，德•东德(de Donder)将谐和条件严格化。1923年，郎曲斯(Lanzos)曾用这一条件得到了球对称静态引力场的解。
　　沿着这条思路，1979年，周培源把严格的谐和条件作为一个物理条件添加进引力场方程中，和他在北京大学的同事以及他在高能物理所的学生一起， 发表了多篇论文，其中包括无限平面、无限长杆、围绕无限长杆作心速转动的稳态解和严格的平面波解。面对当前存在的两个解，即坐标无关论者的史瓦西解和坐标 有关论者的郎曲斯解，从20世纪70年代开始，周培源和他的学生李永贵开始从事测量与地面垂直和与地面平行的两种光速的比较实验，希望回答两种解中哪一种 更符合实际。理论上，史瓦西解得到的两种光速的一级近似之差与光速之比为7×10︰10，而郎曲斯解的这一比值为零。目前，李永贵所获得的这个比值在准确 到10︰9时表明：两种光速是相等的。这项实验仍在进行中，以期取得更高一级的近似。这是“坐标有关论者”同“坐标无关论者”两种理论较量中的关键性实 验。它的进一步结果，将是整个物理界所关心的。
在广义相对论方面，周培源一直致力于求解引力场方程的确定解，并应用于宇宙论的研究。早在二三十年代，他就求得了轴对称静态引力场的若干解，与静止场不同 类型的严格解，并于1939年证实，在球对称膨胀宇宙中，若物质和辐射处于热平衡态，则宇宙必为弗里德曼宇宙。70年代末，他又把严格的谐和条件作为一个 物理条件添加进引力场方程，求得一系列静态解、稳态解及宇宙解。还指导研究生进行了与地面平行和垂直的光速比较实验，以探求史瓦西解和郎曲斯解哪一个更符 合静态球对称引力场的客观实际。初步结果已显示出，郎曲斯解与实际相符。80年代，周培源致力于广义相对论的基本问题，即经过坐标变换联系起来的几个解， 究竟应该是一个解还是几个解。他对照流体力学中保角变换，认为这种情形应该是几个解而不是一个解。产生这种不确定的原因在于爱因斯坦方程缺少必要的坐标条 件。