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patial contraction. This illustrates that a particle resting at K’, can attached to a local Minkowski space. This probably was a starting point of Einstein’s version of infinitesimal equivalence principle. Also, from metric (6b), a light speed at r’ (¹ 0) observed in system K’ would be smaller than c because of time dilation effect of gravity. But, space contraction is directional. The light speed is even smaller in the j-direction, that is, a light speed can decrease more after a velocity Wr’ is “added to”. However, such relations for the coordinate system K* (x’, y’, z’, t), in spite of rdf’ = [1 – (rW/c)2]1/2 dX, are complicated. Since dt = [1 – (rW/c)2]-1/2 [dT + (rW/c2) dX], a corresponding time dilation for d t in K* is not there. This illustrates also that the Galilean transformation (7) is invalid in general relativity. For the frame K’ (x’, y’, z’), Einstein [15] remarked, “So he will be obliged to define time in such a way that the rate of a clock depends upon where the clock may be.” The time coordinate for K’ (x’, y’, z’), as shown, is severely restricted because the time is related to the local clock rate. Thus, Einstein invented the notion of a space-time coordinate system in physics. On the other hand, Einstein [8] also remarked, “So there is nothing for it but to regards all imaginable systems of coordinates, in principle, as equally suitable for the description of nature.” From the above examples, this description of nature by the coordinate system K* (x’, y’, z’, t) includes certain calculations but not physical interpretations. Thus, although tensor equations may be covariant with respect to any substitutions of whatever (generally covariant), the freedom toward the physical space-time coordinate system, and thus a valid physical interpretation, is severely limited by his equivalence principle. In his book, Einstein [1] remarked, “As in special theory of relativity, we have to discriminate between time-like and space-like line elements in the four-dimensional continuum; owing to the change of sign introduced, time-like line elements have a real, space-like line elements an imaginary ds. The time-like ds can be measured directly by a suitably chosen clock.” Special relativity has already taught us [8] that some mathematical coordinate systems are not physically realizable and therefore cannot be used to describe nature. The same has been illustrated for general relativity3). Moreover, from metric (6b), the metric element (c2 - W2r’2) is zero at a point r’0, which corresponds to the speed of a particle resting at r’0 would reach the light speed. When r’ > r’0 , two metric element change signs. Would this mean that the space coordinate r’df’ becomes time-like and the time coordinate becomes space-like? The answer is obviously no because we have r = r’, and r is still space-like according to metric (6a). The correct answer is that when r’ ³ r’0 , the coordinate system K’ no longer makes sense in physics. The frame of reference K’ cannot go beyond r’0 because c is the upper limit of any speed for moving matter. This illustrates that a formal validity in mathematics could be inadequate in physics, and also that, for a spatial coordinate system to be meaningful in physics, in principle a massive particle must be able to rest on it. The change of sign for very large r manifests such a restriction in physics. Otherwise, it would be impossible that such a coordinate system can be associated with local physical