关于什么是爱因斯坦的等效原理 [18]
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关键词:general theoryimportanceEinstein’s equivalence principlechallengedunderstanding
Newtonian theory of gravity due to a source. Thus, Einstein’s principle of equivalence is really the equivalence of the effects of an accelerated frame to a related uniform gravity whereas others incorrectly perceived that any gravity is equivalent to a uniformly accelerated frame. This is evident if one considers also the case of uniform rotation. Nevertheless, Bergmann [31] “illustrated” the initial version of Einstein’s principle with Einstein’s elevator under the gravity of the globe, and thus inadvertently supported misleading criticisms. For instance, Zel’dovich and Novikov [22] still, in disagreement with Einstein, talked about a “true” gravitational field. A possible problem was that the initial form of Einstein’s equivalence principle was presented only as an idealization of the realistic situation without further elaborations for clarification.
For the second question, however, Norton did no find Einstein’s version of infinitesimal equivalence principle. As expected, this is incorrect. Einstein put his version only as if consequences of his earlier version without the expected further labeling. (A reason would probably be that Einstein did not feel the need of such a labeling. It simply did not seem to serve any useful purpose.) There are two differences from Pauli’s version: 1) As Einstein observed, according to the mathematical theorems, gravity cannot be transformed away for some cases; 2) The manifold under consideration must be a physical space, which is very clear for the cases of uniform acceleration and uniform rotation. This is also clearly implies by specifying that a local Minkowski space is obtained by choosing the appropriate acceleration. Einstein demonstrated the need of verifying a physical space by checking the perihelion of Mercury with his space-time metric. Since it is meaningless to consider the physical validity of a geodesic locally at one point, a physical solution of gravity must involve at least a finite region.
Apparently, Norton [9] believed in the general covariance without understanding clearly what that actually means. Consequently, he did not pay much attention to the physical implication of acceleration to the equivalence principle. The failure of Norton in identifying Einstein’s version testifies how a bias of opinion can affect a theorist.
Another confusing point is that Einstein predicted definitive time dilation and space contraction measurements with a coordinate system of a physical space while claiming general covariance with respect to arbitrary coordinate systems. As shown in the case of uniform rotation, any arbitrary coordinate system can be used for calculations because of general covariance of Riemannian geometry while a space-time coordinate system (of the physical space) that can be used for physical interpretation, is restricted by his equivalence principle. Related to this is the question of criterion for a physical space. For a given Lorentz metric, it would be non-trivial to determine that such a m anifold is a physical space. For instance, before the calculation of light bending, Einstein calculated the perihelion of Mercury to verify a physical space. It seems further work on this area is needed.
A central issue for the applicability of Einstein’s equivalence principle is whether the Lorentz manifold under consideration is a physical space (time), to which the notion of a local time is crucial. However, both Tolman [14] and Fock [11] and more recently Ohanian and Ruff
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