关于什么是爱因斯坦的等效原理 [13]
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关键词:general theoryimportanceEinstein’s equivalence principlechallengedunderstanding
ffel symbols are non-zero (section 6), and a Lorentz manifold may not be diffeomorphic to any physical space [17,23].
6. Einstein’s Infinitesimal Equivalence Princi ple and Acceleration.
The mathematical theorems are intimately related to Einstein’s Infinitesimal equivalence principle, which is applicable only to a physical space (-time) that models reality such that all physical requirements are sufficiently satisfied. Both of Einstein’s version and Pauli’s version agree on the existence of a local Minkowski space at any point. But, only Einstein specified such a space is obtained through a choice of acceleration. Einstein wrote in the section 4 of his 1916 paper [8,15], “For this purpose we must choose the acceleration of the infinitely small (“local”) system of the coordinates so that no gravitational field occurs; this is possible for an infinitely small region.” Any acceleration to a particle is, of course, relative to a frame of reference. Thus, Einstein’s principle requires that a physical space is a Riemannian space having a Euclidean structure as a frame of reference.
This difference means that Einstein’s equivalence principle is a physical principle, whereas Pauli’s version is only a rephrasing of mathematical theorems. Moreover, Einstein’s equivalence principle explicitly requires the existence of acceleration for a static massive particle (i.e., ¹ 0 for some m ¹ t,), and as shown later, theoretical self-consistency also demands this.
Consider a local space L (X, Y, Z, CT) whose origin is attached to a particle in free fall. The Galilean weak equivalence principle that all massive matter falling with the same acceleration in the physical space implies only that, at the origin, = 0 for m ¹ T, but the local metric need not have
= 0 for any a, b, s. (12a)
But, the mathematical theorems imply that this is always possible. Moreover, the local metric of space L can be chosen as
ds2 = c2dT2 - dX2 - dY2 - dZ2, (12b)
i.e., a local Minkowski metric. Metric (12b) is proposed by Einstein [1] due to, "special theory of relativity applies to the special case of the absence of a gravitational field." This proposal is the essence of Einstein’s infinitesimal equivalence principle that includes its initial form and later version as the special cases. Now, we shall call it simply as Einstein’s equivalence principle.
Einstein [1] clarified, “According to the principle of equivalence, the metric relation of the Euclidean geometry are valid relative to a Cartesian system of reference of infinitely small dimensions and in a suitable state of motion (free falling, and without rotation).” This is the way that Einstein proclaimed the final infinitesimal form of his principle on the local equivalence of gravity and a suitable acceleration in a physical space.
The real world, by definition, is a physical space, where the physical principles are satisfied. The local transformations,
gmn (x, y, z, ct) = gab(X, Y, Z, cT), (12c)
and
, (12d)
by assumption, are due to gravity - the physical cause. Moreover, the results implied by (12d) must be valid in physics. Einstein [1,8] obtained the time dilation and space contraction through (12d). Thus, the application of Einstein’s principle
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