Local Inertial Coordinate System and The Principle of Equivalence

TL;DR

This paper explores the calculation of local inertial coordinate systems via transformations from laboratory coordinates, deriving free-fall equations similar to General Relativity but with different covariant derivatives, challenging traditional views of the equivalence principle.

Contribution

It introduces a novel method for defining local inertial frames and proposes a different interpretation of the principle of equivalence using coordinate transformations.

Findings

Derived free-fall equations match those in General Relativity.

Revealed differences in covariant derivatives from classic definitions.

Suggested all gravitational laws can be obtained through coordinate transformations.

Abstract

In this paper, the local inertial coordinate system is calculated through coordinate transformations from laboratory coordinate system. We derived the same free falling equations as those in General Relativity. However, the definitions of second and higher order covariant derivatives are different. Our results 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 by doing coordinate transformations from local inertial coordinate system to lab coordinate system.