The Question of Lorentz Invariance and Einstein’s Equivalence principle in General Relativity -- C. Y. Lo Abstract The local Lorentz symmetry says that the laws of physics are the same for all (local) inertial observers moving through space, regardless of their velocity and orientation. However, this notion of symmetry actually comes from the misinterpretation of Einstein’s equivalence principle by the Wheeler School. To clarify this, Einstein’s equivalence principle is quoted directly form Einstein. It is pointed out also that Einstein’s equivalence principle is supported by experiments. It is shown: 1) based on general relativity, a violation of the local Lorentz invariance is generally expected; 2) the interpretation of Misner et al., in fact, disagrees with Einstein’s equivalence principle; 3) mathematical analysis shows that the interpretation of Misner et al. is misleading in physics since it is valid only for special relativity. Key Words: Lorentz symmetry, Einstein’s equivalence principle, Pauli’s version, Wheeler’s misinterpretation, mathematical analysis; finite open covering theorem. 04.20.-q, 04.20.Cv “Science sets itself apart from other paths to truth by recognizing that even its greatest practitioners sometimes err. …” -- S. Weinberg, Physics Today, November 2005.