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= dz, and dT' = ch(T/C)dT. (16b) is the local transformation to the local Minkowski space if Einstein’s equivalence principle were applicable. Thus, KT is not a physical space since (16b) implies that two standard clocks have different rates, resting at the same point of a frame. Although KT is diffeomorphic to the Minkowski space K by the transformation t = C{exp(T/C) - exp(-T/C)}/2 and have the same Euclidean structure, T in metric (13) is not the local time for a physical space-time coordinate system (see also section 7). Also, Eddington [2] observed that special relativity should apply only to phenomena unrelated to the second order derivatives of the metric. Einstein [30] accepted this criticism and added the crucial phrase, "at least to a first approximation" on the indistinguishability between gravity and acceleration. 7. Misunderstandings and Misleading Calculations of Tolman and Fock. To apply Einstein’s equivalence principle, it is crucial that the space-time under consideration must be a physical space where all physical requirements are satisfied adequately. Many theorists, both for and against general relativity have made mistakes by ignoring this. For example, Logunov and Mestvirshvili [12] showed that inconsistent results would be obtained through a coordinate transformation. On the other hand, in an attempt to justify the validity of Einstein’s equivalence principle, Tolman [14] also ignored this problem. Consequently, what he has done, though inadvertently, was justifying a physical principle mathematically in terms of an unphysical space. Thus, instead of validity of Einstein’s theory, Tolman seemed to show its opposite, i.e., arbitrariness and invalidity just as Logunov et al. claimed. Tolman claimed that his treatment [14; p.175] is based the principle of equivalence to the fundamental idea of the relativity of all kind of motion. To illustrate the equivalence principle, Tolman started with system K0 with the flat metric, ds2 = c2dt2 – dx2 - dy2 - dz2, (17) for the first observer. Consider a second observer in a system K’, which can be taken as moving relative to the first with the acceleration a in the x-direction, uses the coordinates x’, y’, z’, and t’ as given by x’ = x – at2 y’ = y z’ = z t’ = t (18) according to the usual transformation to accelerated axes, which Tolman regards as a reasonable change at least at low velocities. Substituting from (18) into (17), Tolman thought that he obtained the formula for interval for the second observer as ds2 = (c2 - a2t’2) dt’2 – 2at’dx’dt’ – dx’2 – dy’2 – dz’2. (19) Then, according to the geodesic equation, from metric (17) Tolman obtained ; (20) and , 21a) (21b) are approximately the equations of motion for the case of particles having negligible velocity. Thus, in spite of that (18) is essentially a Galilean transformation, Tolman claimed that the equivalence principle was illustrated by (21). On the other hand, consider a particle P in K’ at the beginning of a free fall. Since the velocity of K’ relative to K0 is v = at, for the local Minkowski space (X, Y, Z, T) of P, w