對MIT號召基礎研究的回應--魯重賢

Dr. L. Rafael Reif

President of MIT

Dear President Reif:

I feel deeply honored since you are so interested in my basic research and asked me to report more details to you.

As you pointed out that MIT is an institution strengthened throughout its history by the highest standards of excellence, integrity and service, and by its openness to people from around the world who share MIT’s remarkable culture of learning, discovery and innovation. Toward this, there are risk and opportunity. You summed up: “The MIT I know loves challenges. The MIT I know solves the unsolvable, shapes the future, and serves our nation and the world. The MIT I know and love does not stand on the sidelines.”

I am very impressed by your five points, especially your first proclaim that we must all be champions of basic research. In deed, “If a society gives up on basic research, it is giving up on its future. So it will be my job — and our shared responsibility — to argue forcefully, effectively and publicly for retaining robust investment in fundamental research, and to remind ourselves, and our nation, of its importance and value.”

Fifth, you will lead MIT to continue to make significant contributions in the area of race and diversity, equity and inclusion. Your final point is well understood because it is a reason that I came to MIT to study in the first place. As to the other four points, you will find that my basic research would contribute also to all these points.

Indeed, the technological transformation has already reshaped the education landscape. MIT plays a leadership role in affordable and accessible online education for hundreds of thousands of students, or more. I would like to add that another advantage of the online education is that the merits and errors of the educators can be seen clearly and timely. It is through the online education system that I discovered the serious errors of the open courses, Phys. 8.033 and Phys. 8. 962. They include even some well-known mathematical errors at the undergraduate level.¹⁾ I hope the instructors also take advantage of this and would correct the errors as soon as possible.

My interest in general relativity was further intensified from investigations on the unification of all forces which was the major endeavor in the 70’s of the last century. In 1981, to deal with the electromagnetic radiation reaction force, my colleagues at Tufts University, Prof. Goldstein, Prof. Napier, and I developed a five-dimensional theory of five-variables to unify gravitation and electromagnetism. In this paper, we claimed that, as Maxwell showed, unification means that theories to be unified are necessarily inadequate. This is the major difference from the approach of Einstein. This paper was eventually published in 1987, and thus encouraged further investigation on the inadequacy of general relativity.

In 1990, I turned to full time investigation of general relativity in connection with unification. To start with, I investigated the problem of plane-waves of gravitation and electromagnetism. To my surprise, detailed calculations show that there is no bounded plane-wave of gravitation. I reported this in a conference in Kyoto, Japan. Further investigation shows that there is no gravitational wave solution either. This result was reported in a 1993 conference in Hong Kong. This result together with the non-existence of dynamic solution was published in the Astrophysics Journal in 1995.

These findings greatly interested Prof. P. Morrison because it was a conjecture by Gullstrand, Chairman of the Nobel Prize Committee for physics. Moreover, Hilbert approved Einstein’s calculation on the perihelion of Mercury, only before he realized that a perturbation approach must be included. Nevertheless, the 1993 Nobel Committee for Physics abandoned Gullstrand’s conjecture because Christodoulou and Klainerman of Princeton University claimed that they have constructed dynamic solutions for the Einstein equation. I read their book and find that their proof is invalid in mathematics. Moreover, there is a book review in 1996 that finds their book to be incomprehensible.  

Prof. Morrison discussed with me on these issues for about one-month, and then went to Princeton to discuss with Prof. J. A. Taylor for several times. Subsequently, Prof. Morrison suggested that I should write a book on these problems together with related issues. This leads to another 17 years of investigation that results in the discovery (1997) and subsequent verification of a new force, the charge-mass interaction. Thus, Einstein’s conjecture of unification is proven correct.

In 2003, Nobel Laureate G. ‘t Hooft came to MIT to talk about general relativity. This led to our communication that he defended the existence of a wave solution with a bounded solution. However, his example is also invalid because it has no valid source. It turns out that ‘t Hooft also fails to understand the principle of causality adequately just as the Physical Review did.  

In 2009, President Hockfield invited me to participate in a conference on gravitation in Beijing. I informed her about the non-existence of the dynamic solution, and this conference was postponed. In 2011, I informed the audience of a MIT symposium on women scientists that there are many mistakes in current theories of gravitation. Subsequently, President Hockfield encouraged my honesty to sciences, and I wrote two letters to her and also for other MIT VIPs to report further on details. A main point of the letters is that the non-existence of dynamic solution can be illustrated with mathematics at the undergraduate level. Thus, there is no longer any doubt that Christodoulou and Klainerman of Princeton University are wrong in their claim that they have constructed dynamic solutions for the Einstein equation.

On the other hand, the Shaw Prize led by Prof. C. N. Yang and Prof. Peter C. Sarnak of Princeton University decided to give Christodoulou a half 2011 Shaw Prize. (This does not diminish my respect to this University. My respected teachers such as Prof. A. J. Coleman and Prof. I. Halperin, who was my advisor for my degrees (M.Sc. & Ph.D.) in mathematics, were graduated from Princeton.) However, this only leads to a loss of their reputation as serious scholars, instead of affirming the errors of Christodoulou. Subsequent to this award, all the members of the Selection Committee for Mathematical Sciences resigned. Nevertheless, Christodoulou was elected as a member of U.S. National Academy of Sciences (2012). To expose and to rectify this problem and related errors, I have published five papers [1-5] since I wrote to former President Hockfield.

Another significant development is that Dr. Daniel Kulp, Editorial Director of the American Physical Society (official email communication, July 2012) has recently discontinued the current practices of authority worship. Thus, although the current position of the Physical Review is that they are not yet convinced of the recent theoretical developments, but no longer object to the criticisms toward the Physical Review D, and other journals such as General Relativity and Gravitation, Classical and Quantum Gravity, Foundation of Physics and Journal of Mathematical Physics.

Although it is clear now that the mathematical errors can be illustrated at the undergraduate level, it may still be difficult to understand why so many physicists could make errors without discovering it for a long time. There are deep-rooted reasons because of errors in mathematics and physics due to historical immature understanding and misconceptions as follows:

1)        The confusion between mathematics and physics and causality.

An intrinsic difference between mathematics and physics is that physics is related to measurements and there is causality between some physical quantities. On the other hand, mathematics is simply the relation between quantities. Due to the principle of causality, physics requires that a weak source will produce a weak field. However, this may not be satisfied by a mathematical field equation. For the dynamic case, Einstein’s field equation is an example. Although one can always produce a linearized equation, the non-linear equation may not have a bounded solution at all. Thus, the linearization approach may not be valid in mathematics. Due to the principle of causality, a field must have an appropriate source(s). Many theorists consider causality in terms of the light speed in vacuum as a limitation. However, this limitation is only a restriction to the propagation of causality of a physical phenomenon.  

2)        Inadequate background in pure mathematics.

Although many physicists have learned mathematical analysis, most of them do not understand it adequately. This is why Pauli, the Wheeler School, and etc. misinterpreted Einstein’s equivalence principle, but most theoretical physicists did not find their errors even though Einstein has provided an example to illustrate their errors.

3)        Non-linear equation is new to many physicists.

Before general relativity, most theoretical physicists dealt with only linear equations, and the perturbation approach always seemed to work. However, this approach does not work for the dynamic case of the non-linear equation of Einstein. This is the main reason that Einstein’s calculation of the perihelion of Mercury is invalid as Gullstrand suspected. They even mistook Einstein’s invalid 1911 assumption as Einstein’s equivalence principle.

4)        Misconceptions were developed due to misunderstanding of special relativity.

The special relativity is known to have some counter intuitive results. This has led some theorists to look for and advocate abnormal results. The well-known space-time singularity theorems of Hawking and Penrose are good examples. While these theorems are mathematically valid, they are irrelevant to physics because they are based on an invalid implicit assumption that all the couplings have the same sign.

5)        Historically accumulated errors of Einstein in physics.

Einstein was the major architect or foundation builder of three great theories of modern physics, namely: special relativity, quantum mechanics and general relativity. However, he was also a source of oversight in each theory. In special relativity, he failed to see that E = mc² is only conditionally valid. In quantum theory, he failed to recognize that photons must include non-electromagnetic energy. In general relativity, the lack of examples to illustrate his equivalence principle, in fact, helps popular misinterpretations and confusions in physics. His principle of covariance and theory of measurement are invalid, but related criticisms of Whitehead and Zhou were ignored. This issue is settled because Einstein’s justifications for his theory of measurement were actually based on invalid applications of special relativity, in addition leading to disagreements with observations. Thus, it is also difficult to regard any of the current theorists as an expert in general relativity.

Einstein was universally recognized as a genius. However, it was a puzzle that he did not make much progress in gravitation after he came to the U.S. The above issues probably explain how he was restricted by his own limitations. In fact, the over extended formula E= mc² leads to misinterpretations in physics, and thus is also the main obstacle to establish the validity of his conjecture on unification of gravitation and electromagnetism.

Now, it is clear that problems of errors in general relativity have misled generations of physicists. To stop this from continuing, a well-published open conference ²⁾ may be needed as a first step to solve the issues. Also, a well-written textbook on general relativity is needed to rectify the errors and to separate the unverified speculation from the proven facts. Moreover, additional new findings should be added to the new text. Then, new research can be continued and developed in the U.S. and all over the world. In addition, I suggest that the education of pure mathematics for theoretical physicists needs to be strengthened.

Thank you for your kind attention. I shall be glad to answer any question that you and your advisors may have. I am looking forward to hearing from you.

Sincerely yours,

C. Y. Lo

D. Sc. 77

Attachments:

Letter to President Hockfield I; Letter to President Hockfield II; Letter to Prof. Bertschinger.

Endnotes:

1)     The textbook and reference books of phy.8.962 are: Carroll, Sean. An Introduction to General Relativity: Spacetime and Geometry. 2003; Misner, Charles W., Kip S. Thorne, and John Archibald Wheeler. Gravitation,1973; Schutz, Bernard. A First Course in General Relativity,1985; Hartle, James. Gravity: An introduction to Einstein's general relativity, 2002; Weinberg, Steven. Gravitation and Cosmology, 1972; Wald, Robert. General relativity, 1984.

2)     Due to the fact that some errors in general relativity were still regarded by the majority of relativists as if valid, some theorists still pretend that no valid objections have ever existed as Hawking did. As a result, the conventional publication of pointing out errors in journals would have very little effects for a long time.

References:

1.         C. Y. Lo, Comments on the 2011 Shaw Prize in Mathematical Sciences, -- an analysis of collectively formed errors in physics, GJSFR Vol. 12 Issue 4 (Ver. 1.0) (June 2012).

2.         C. Y. Lo, On the Weight Reduction of Metals due to Temperature Increments, GJSFR Vol. 12 Issue 7 (Ver. 1.0) (Sept. 2012).

3.         C. Y. Lo, Rectification of General Relativity, Experimental Verifications, and Error of the Wheeler School, VIGIER VIII - BCS Joint Meeting, The Physics of Reality: Space, Time, Matter, Cosmos, London, 15-18 August 2012.

4.         C. Y. Lo, Gravitation, Physics, and Technology, Physics Essays, 25 (4) – (2012).

5.         C. Y. Lo, Local Lorentz Invariance and the Distortion of Einstein’s Equivalence Principle, GJSFR Volume 12-A Issue 8 Version 1.0 November 2012