关于什么是爱因斯坦的等效原理 [12]
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关键词:general theoryimportanceEinstein’s equivalence principlechallengedunderstanding
(10a)
where
Gmab = , (10b)
is the Christoffel symbols, and ds2 = gmndxmdxn . Thus, the gravitational field is zero if = 0.
Currently, some [9,22] have mistaken the geodesic representing a motion or the existence of local Minkowski spaces as Einstein's equivalence principle. Such misunderstandings are related to two mathematical theorems [10] as follows:
Theorem 1. Given any point P in any Lorentz manifold (whose metric signature is the same as a Minkowski space) there always exist coordinate systems (x m) in which ¶gmn/¶xa = 0 at P.
Theorem 2. Given any time-like geodesic curve G there always exist a coordinate system (so-called Fermi coordinates) (xm) in which ¶gmn/¶xa = 0 along G.
From these theorems, it is possible to establish further by simple algebra that a local Minkowski metric exists at any given point and that along any time-like geodesic curve G, a moving local constant metric exists [10].
However, there is nothing relating these two theorems to an existence of acceleration to a static particle or other physical situations. Also, there is no physical specification to be the cause of the local coordinate transformation,
(10c)
such that (10c) transforms the Lorentz metric gmn to a local Minkowski metric along a time-like geodesic curve. Pauli’s version of the equivalence principle is essentially a simplified rephrasing of these theorems. Einstein [28] pointed out, "As far as the prepositions of mathematics refers to reality, they are not certain; and as far as they are certain, they do not refer to reality." An application of a theorem should be examined for its relevance although "one cannot really argue with a mathematical theorem [25]". The physical validity of a geodesic depends of whether transformation (10c), which transforms from an Einstein space to the local Minkowski space, is valid in physics. To this end, we can examine either the cause of or the consequence of (10c).
It will be shown that transformation (10c) can be invalid in physics. Consider a manifold K and its orthogonal metric, whose spatial unit is a centimeter and the time unit is a second, as follows:
ds2 = 4c2dt2 - dx2 - dy2 - dz2. (11a)
K is obviously a Lorentz manifold with a Euclidean structure and therefore is an Einstein space. Consider a particle P resting at a point (x0, y0, z0) in the frame of reference K at time t0. Since Gmab = 0, P stays at the same point (x0, y0, z0) forever. Thus, the coordinates of P are (x0, y0, z0, t) at time t. Then, the local coordinate transformation to a local Minkowski metric is
dX = dx, dY = dy, dZ = dz , but dT = 2 dt (11b)
The local coordinate transformation (11b), which is not a rescaling of units, is invalid in physics. Since there is no gravity or relative velocity between the frame of its tetrad and the frame K, there is no physical cause that makes a clock rate changes. Thus, the Einstein space (11a) is not a physical space that models reality. Otherwise, there were two standard clocks having different rates, though resting at the same point of a frame of reference. Nevertheless, Pauli’s equivalence principle is satisfied.
Also, a non-constant metric may not have acceleration on a static observer, although some of its Christo
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