vity should be the Einstein field equation alone. However, experimentally the unrestricted validity of Einstein? equation has not yet been established beyond reasonable doubt [7,25,26,41].
Theoretically there is no satisfactory proof of rigorous validity of Einstein? field equation [42-44] (e.g., the inadequate source term mentioned in §1, is the cause of the unphysical solution (29) [6,8]). In fact, in 1953 Hogarth [36] conjectured that the 1915 Einstein equation is invalid for a dynamic two-body problem; and Einstein himself had pointed out that his equation might not be valid for matter of very high density [3]. Moreover, it has been proven by the binary pulsar experiment that Einstein? equation must be modified [7] and Yilmaz [45] pointed out that Einstein? equation of 1915 is only a test particle theory. Moreover, in terms of physics, a static solution is only an approximation for some dynamical problems. This means that, to support Einstein? illustration of the equivalence principle with calculations on the light bending, it is necessary to show that his linear equation is justifiable for dynamical problems. Thus, it is necessary to derive the Maxwell-Newton Approximation independently from physical principles (§4) since the 1915 Einstein equation is valid for static problems only.


A simple dynamical problem would be the gravity due to the interaction of two massive particles. Then, Einstein? condition of weak gravity, which is also due to the equivalence principle [46], requires such a solution of gravity must be bounded. Thus, satisfying boundedness of gravity due to a weak source is independent of the field equation. But, no such solution has ever been proven to be in existence. Being aware of the unboundedness of cylindrical and spherical ?aves" [47,48], after proving the existence of Cauchy solutions, Bruhat [4] remarked that the physical validity of any Cauchy solution is up to the experiments to decide. While her clarification is reasonable for a mathematician, physicists should have known physics better.
The equivalence principle remains indispensable because of its solid experimental foundation such as gravitational red shifts and the blending of light [7,20]. Theoretically, as illustrated, its failure is always accompanied with a violation of another physical requirement. Thus, as Weinberg [5] points out, ?t is much more useful to regard general relativity above all as a theory of gravitation, whose connection with geometry arises from the peculiar empirical properties of gravitation, properties summarized by Einstein? Principle of the Equivalence of Gravitation and Inertia."
The long-standing errors in general relativity have profound historical reasons. Most physicists are used to linear equations, and unavoidably they would apply techniques, which are valid for linear equations. But, in nonlinear field equation, a second order term from the viewpoint of physics, may be crucial for the existence of a bounded physical solution. In other words, one may not take it for granted (i.e., without a proof) that a physical requirement is compatible with a field equation. Even well known physicists such as Einstein [49] and more recently Feymann [33] made such mistakes in general relativity.
In general relativity, assuming the existence of a bounded dynamics physical solution, has never been proven, but it has been used with blind faith [50-53]. This is essentially where many of the mathematical errors come from. A most telling evidence is that the ?lane-waves" proposed by Bondi et al. [37] are not bounded although they believe that they are. Furthermore, it has been proven that there are no bounded plane-waves [8] for the 1915 Einstein equation. Then, the non-existence of a dynamic solution for massive matter is proven [7] because experiments support the Maxwell-Newton Approximation. This approach of proof has been completed since the Maxwell-Newton Approximation can be derived from physical principles (§4).
Currently, relativists often ignore physical requirements [1,5] because they misunderstood the equivalence principle and accepted the covariance principle, which was rejected by Eddington. Historically, after early observational confirmations of Einstein? predictions, Einstein declared logical completeness of his theory [34] although such confirmations verify only the theoretical framework of general relativity. Subsequently, a blind faith on the theoretical self-consistency of general relativity was developed. Many physicists working on general relativity, in spite of warnings from Gullstrand [25,26], Bohr & Klein [40], and other physicists [10,37], tend to have over confidence on Einstein? equation (except a few such as N. Rosen [35]).


A dynamic physical solution, as pointed out by Low [54], is not just a time-dependent solution, which can be obtained from the Minkowski metric by making a coordinate transformation. In physics, such a dynamic solution must be related to the dynamics of source matter and gravitational radiation. Nevertheless, Christodoulou and Klainerman [55] claimed the existence of dynamical solutions by their construction although such ?olutions" are unrelated to dynamical sources or radiation. It is also surprising that their main mathematical mistakes are actually at the fundamental level [56-58]. As pointed out by Kramer et al. [1], many relativists have a problem in distinguishing a physically valid solution from mathematical solutions. Bonnor et al [5] further confirm this problem by pointing out that it is not possible to have a consistent physical interpretation.
9. Acknowledgments
This paper is dedicated to my grandfather Lu Zhu Qiu. The author gratefully acknowledges stimulating discussions with Professors C. Au, C. L. Cao, S.-J. Chang, A. J. Coleman, Li-Zhi Fang, L. Ford, R. Geroch, J. E. Hogarth, Liu Liao, F. E. Low, P. Morrison, A. Napier, H. C. Ohanian, R. M. Wald, Erick J. Weinberg, J. A. Wheeler, Chuen Wong, H. Yilmaz, Yu Yun-qiang,