关于什么是爱因斯坦的等效原理 [14]
论文作者:佚名论文属性:短文 essay登出时间:2009-04-20编辑:黄丽樱点击率:40037
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关键词:general theoryimportanceEinstein’s equivalence principlechallengedunderstanding
lies on showing that the Euclid-Riemannian manifold under consideration is a physical space. This is another difference from Pauli’s misinterpretation. Also, the claim of John L. Friedman [29], “The existence of local Minkowski space has replaced the equivalence principle that initially motivated it,” is incorrect, and apparently due to inadequate understanding of Einstein’s theory.
Since the physical validity of a g eodesic cannot be determined at one point, it is meaningless to talk about a local solution as physically valid. A physical solution must be established in a finite region of the physical space-time. In other words, when applied to a curved space, Einstein’s principle is necessarily considered as non-local. The crucial point of Einstein’s principle is whether the transformation (12d) that leads to local Minkowski space (12b), has a valid physical cause, and this can be found out by examining the physical validity of its consequences. To this end, Einstein [1] has shown an agreement with the Mercury perihelion, and compared his earlier formula for gravitational red shifts, before deriving his formula for the light bending.
Note that for a given metric gmn, a spatial acceleration may not necessarily exist for a static observer. For instance, when Gmtt = 0 (m ¹ t), there is no Newtonian acceleration for a resting particle. But, the metric may still be non-constant. Einstein’s equivalence principle would imply that such a Lorentz manifold is not a physical space. One might argue that “gravity” would be detected by non-static particles. However, since there is neither acceleration nor motion for an initially static particle, it remains forever in the same position with the same frame of reference. This would mean that the same unit clock and/or the same unit measuring-rod would have two different readings. This non-uniqueness of measurement is not acceptable in physics. In other words, Einstein's equivalence principle removes the possibility of gravity without the static acceleration.
To illustrate this, let us consider a Lorentz manifold KT with the non-constant metric,
ds2 = c2ch2(T/C)dT2 - dx2 - dy2 - dz2, (13)
where ch(T/C) = [exp(T/C) + exp(-T/C)]/2, and C (> 0) is a constant. Metric (13) can be considered as including a Euclidean structure and metric (13) becomes a flat metric when C = ¥. From metric (13), the Christoffel symbols are zeros except Gt,tt = ¶tgtt/2, and thus no static acceleration. The equation of motion for an observer P at (x0, y0, z0, T0) would be
= 0, where ln{ch(T/C)}. (14a)
and
, (14b)
Eq. (14) implies that there is no spatial acceleration to cause a local transformation. Then, it follows eq. (14) that
k{exp(T/C) + exp(-T/C)}-1 and constant, xm (= x, y, z) (15a)
for some constant k. Now, consider the observer P in the state
dx/dT = dy/dT = dz/dT = 0; and thus dx/ds = dy/ds = dz/ds = 0. (15b)
Thus, the geodesic of P is (x0, y0, z0, T), and P would have the same frame of reference whether at "free fall" or not.
Consider the local Minkowski space of P at (x0, y0, z0, T0)
ds2 = c2dT’2 - dx’2 - dy’2 - dz’2
nbsp; (16a)
and
dx' = dx, dy' = dy, dz'
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