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Equivalence Principle and the Principle of Local Lorentz Invariance

W. A. Rodrigues Jr.·M. Sharif
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Abstract

In this paper we scrutinize the so called Principle of Local Lorentz Invariance (\emph{PLLI}) that many authors claim to follow from the Equivalence Principle. Using rigourous mathematics we introduce in the General Theory of Relativity two classes of reference frames (\emph{PIRFs} and \emph{LLRF}$γ$\emph{s}) which natural generalizations of the concept of the inertial reference frames of the Special Relativity Theroy. We show that it is the class of the \emph{LLRF}$γ$\emph{s} that is associated with the \emph{PLLI.} Next we give a defintion of physically equivalent referefrence frames. Then, we prove that there are models of General Relativity Theory (in particular on a Friedmann universe) where the \emph{PLLI}is false. However our find is not in contradiction with the many experimental claims vindicating the \emph{PLLI}, because theses experiments do not have enough accuracy to detect the effect we found. We prove moreover that \emph{PIRFs}are not physically equivalent.

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W. A. Rodrigues Jr., M. Sharif. 2003-02-04. Equivalence Principle and the Principle of Local Lorentz Invariance. https://arxiv.org/abs/math-ph/0302009

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