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,
“主要從事物理學的基礎理論中難度最大的兩個方面即愛因斯坦廣義相對論引力論和流體力學中的湍流理論的研究與教 學並取得出色成果。”
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中國科學技術協會, Zhou’s contribution with details (see attached) has the following errors and/or in accuracy:

1) Zhou is not a “坐標有關論者”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).

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　廣義相對論在物理上取得了許多輝煌成就，但從一開始就存在着一個困難，這就是，表達引力場的方程是一個包含10個二階非線性偏微分方程的方程 組，而這10個方程之間又存在着4個獨立的非線性偏微分方程組所組成的恆等式，也稱為比安基(Bianchi)恆等式，這就使得只用引力方程得不到10個 引力函數的確定解。周培源一進入相對論領域便抓住這個難題，主張引進另外的物理條件才能求解出引力函數的確定解。沿循這個思路，周培源在20世紀20年代 用引入新物理條件的辦法獲得了軸對稱靜態引力場的若干解，以後又於20世紀30年代在引入各向同性條件下，又求得了與靜止場不同類型的嚴格解。
　　與此同時，國際上的同行學者為了克服上述困難，採用坐標變換的方法來減少引力函數的數目。但這種方法只能求出一種常微分方程的特殊引力場——球 對稱靜態引力場的嚴格解，例如史瓦西(Schwazchild)解，而對眾多的其他物理問題仍然束手無策。沿着這條思路求解引力場方程的相對論研究者，在 國際上稱為“坐標無關論者”。他們主張坐標在引力論中無關緊要。與此相反，周培源從一開始進行引力論研究時，就認為坐標是有物理意義的，因此他是一位“坐 標有關論者”。“坐標有關論者”在一些特殊問題上，引進諧和條件以求解引力場方程的做法，可以追溯到1919年愛因斯坦本人。他引進諧和條件的近似式來求 解線性化了的引力場方程，從而獲得了引力波解，預言了引力波的存在。後來，德•東德(de Donder)將諧和條件嚴格化。1923年，郎曲斯(Lanzos)曾用這一條件得到了球對稱靜態引力場的解。
　　沿着這條思路，1979年，周培源把嚴格的諧和條件作為一個物理條件添加進引力場方程中，和他在北京大學的同事以及他在高能物理所的學生一起， 發表了多篇論文，其中包括無限平面、無限長杆、圍繞無限長杆作心速轉動的穩態解和嚴格的平面波解。面對當前存在的兩個解，即坐標無關論者的史瓦西解和坐標 有關論者的郎曲斯解，從20世紀70年代開始，周培源和他的學生李永貴開始從事測量與地面垂直和與地面平行的兩種光速的比較實驗，希望回答兩種解中哪一種 更符合實際。理論上，史瓦西解得到的兩種光速的一級近似之差與光速之比為7×10︰10，而郎曲斯解的這一比值為零。目前，李永貴所獲得的這個比值在準確 到10︰9時表明：兩種光速是相等的。這項實驗仍在進行中，以期取得更高一級的近似。這是“坐標有關論者”同“坐標無關論者”兩種理論較量中的關鍵性實 驗。它的進一步結果，將是整個物理界所關心的。
在廣義相對論方面，周培源一直致力於求解引力場方程的確定解，並應用於宇宙論的研究。早在二三十年代，他就求得了軸對稱靜態引力場的若干解，與靜止場不同 類型的嚴格解，並於1939年證實，在球對稱膨脹宇宙中，若物質和輻射處於熱平衡態，則宇宙必為弗里德曼宇宙。70年代末，他又把嚴格的諧和條件作為一個 物理條件添加進引力場方程，求得一系列靜態解、穩態解及宇宙解。還指導研究生進行了與地面平行和垂直的光速比較實驗，以探求史瓦西解和郎曲斯解哪一個更符 合靜態球對稱引力場的客觀實際。初步結果已顯示出，郎曲斯解與實際相符。80年代，周培源致力於廣義相對論的基本問題，即經過坐標變換聯繫起來的幾個解， 究竟應該是一個解還是幾個解。他對照流體力學中保角變換，認為這種情形應該是幾個解而不是一個解。產生這種不確定的原因在於愛因斯坦方程缺少必要的坐標條 件。