6. C. Y. Lo, The Existence of Local Minkowski Spaces Is Insufficient for Einstein's Equivalence Principl

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Volume 15: Pages 303-321, 2002

The Existence of Local Minkowski Spaces Is Insufficient for Einstein's Equivalence Principle

C. Y. Lo

Applied and Pure Research Institute, 17 Newcastle Drive, Nashua, New Hampshire 03060 U.S.A.

Einstein's equivalence principle, which states the local equivalence between acceleration and gravity in the physical space, requires a freefall result in a comoving local Minkowski space. Thus, if acceleration of a static particle did not exist, a nonconstant Lorentzian metric would imply inconsistency in physics. Moreover, if a physical requirement that is independent of coordinates (e.g., the principle of causality) is violated, a Lorentz manifold cannot be diffeomorphic to a physical space. Observation, including confirmation of Einstein's three tests, supports the conclusion that spacetime coordinates (and thus covariance) are restricted by physical requirements such as Einstein's equivalence principle. A socalled coordinatefree derivation is actually logically selfdefeating if a physical formula involves nonscalars. It is pointed out also that Einstein's equivalence principle, different from the inadequate Pauli version, requires a physical meaning of spacetime coordinates, although this was ambiguous in Einstein's theory. Concurrently, the meaning of spacetime coordinates in a physical space and the coordinate relativistic causality are clarified in terms of the Euclideanlike structure, which is actually included in the theoretical framework of general relativity. Then it is clear that the Schwarzschild solution and the isotropic solution are physically different, although they are diffeomorphic manifolds. Thus it is necessary to make measurements related to local terrestrial space contractions to discern the more realistic model for the gravity of Earth.

Keywords: Einstein's equivalence principle, frame of reference, Euclideanlike structure, local light speed, physical space

Received: July 5, 2001; Published online: December 15, 2008