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In this paper, the local inertial coordinate system is calculated throughcoordinate transformations from laboratory coordinate system. We derived thesame free falling equations as those in General Relativity. However, thedefinitions of second and higher order covariant derivatives are different. Ourresults are different from the classic view of the principle of equivalence,and suggest that all the laws of physics in gravitational field can be given bydoing coordinate transformations from local inertial coordinate system to labcoordinate system.

Local Inertial Coordinate System and The Principle of Equivalence