关于什么是爱因斯坦的等效原理 [17]
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关键词:general theoryimportanceEinstein’s equivalence principlechallengedunderstanding
= x’ cosh (at’/c) + (c/a)[cosh (at’/c) - 1] (27a)
y = y’ ; z = z’ (27b)
t = (c/a) sinh (at’/c) + (x’/c) sinh (at’/c) , (27c)
although its physics is not clear. Under the condition at’/c << 1, the above equation can be written approximately as
x = x’ + at’2/2; y = y’; z = z’; t = t’ (28)
Substituting (27) into the flat metric, one obtains exactly
ds2 = (c + ax’/c)2 dt’2 – dx’2 – dy’2 – dz’2 , (29a)
Finally, Fock has obtained a metric whose time dilation seems to be compatible with Einstein’s paper of 1911. An important difference is, however, Einstein’s derivation is based on physical considerations; whereas Fock derivation is only a pure mathematical manipulation to obtain a desired result. The problem of a valid physical space remains.
To determine the validity of a manifold as a physical space, the physics must be considered. Apparently, the mathematical requirement, at’/c << 1, instead of just at’/c < 1, is to make (28) approximately valid, but it does not seem to have a physical basis. Moreover, metric (29), in addition to be incompatible with the observed light bending, does not produce a uniform acceleration as claimed. The equation of motion for dx’/ds = 0, though better than (25a), is not a uniform gravity as follows:
= - a c-2[1 + ax’/c2]-1. (29b)
As expected, Fock cannot find a valid interpretation for (29a). Nevertheless, Fock believed that this is due to an intrinsic deficienc y of Einstein’s equivalence principle. Fock [11] believed that the only correct metric form would approximately be,
ds2 = (c2 – 2U) d t2– (1 + 2U/c2)(dx2 + dy2 + dz2) , (30)
where U = - F. However, metric (30) is not universal because form (30) cannot accommodate the case of a uniform rotation.
Thus, an appropriate metric form for the effects of uniformly accelerated frame remains an interesting question to be solved.
8. Discussions and Conclusions
The “Einstein elevator” thought experiment is commonly used in the formulation of Einstein’ equivalence principle. This is challenged by theorists based on the notion of a “true” gravitational field characterized by the non-vanishing curvature. Since the tidal forces cannot be transformed away by a coordinate transformation, Einstein’s insistence on the fundamental importance of the principle on general relativity was a puzzle to many theorists as well as historians of science. Another related question is that if Einstein strongly objected Pauli’s version of infinitesimal equivalence principle, in view of the importance of the infinitesimal case, should not Einstein have his own version?
For the first question, Norton has essentially the right answer. He found that the major problem is different notions for gravity. Einstein [9] believes, “what characterizes the existence of a gravitational field, from the empirical standpoint, is the non-vanishing of the Glik (field strength), not the non-vanishing of the Riklm” and that no gravity is a kind of gravity. But, the others remain in the area of
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