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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, and Y. Z. Zhang. This work is supported in part by Innotec Design, Inc., U.S.A.
ENDNOTES
1) In general relativity, Einstein [2,3] considers the four-dimensional space-time reality as a physical space-time modeled as a Riemannian space-time (M, g). The Riemannian space M is characterized by a space-time metric gik that can be determined by physical considerations such as the distribution of matter. In elativity and the problem of space", Einstein [27] wrote,
or the functions gik describe not only the field, but at the same time also the topological and metrical structural properties of the manifold. ... There is no such thing as an empty space, i.e., a space without field. Space-time does not claim existence on its own, but only as a structural quality of the field."
Moreover, since such a Riemannian space-time models reality, all the physical requirements must be sufficiently satisfied.
2) A local Minkowskian space is a short hand to express that special relativity is locally valid, except for phenomena involving the space-time curvature.
3) For example, the Wheeler-Hawking School [13,18,40] follows Pauli misinterpretation, and thus, their theories are different from general relativity. They, different from Einstein [2,3], believe that space-time coordinates have no physical meaning. Hawking [18] makes no secret of his disagreements with Einstein [2,3]. More recently, based on misinterpretations of Fock [39], Ohanian, Ruffini, and Wheeler [22] openly criticized Einstein theory as confusing and his principles invalid.
4) Some theorists believe that the solution of gravity for a weak source need not be bounded [38]. However, it has been shown that the equivalent principle implies compatibility with Einstein notion of weak gravity [46]. |
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