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 distortion of Einstein’s equivalence principle by the Wheeler School because they do not understand the essence of its physics and its mathematical foundation adequately. To clarify this, Einstein’s equivalence principle, quoted from Eins-tein, is compared with related theorems. A crucial point is that the Einstein-Minkowski condition is satisfied naturally as part of the physical process. 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 interpreta-tion of Misner, Thorne, & Wheeler, in fact, disagrees with Einstein’s equivalence principle; 3) mathematical analysis shows that their interpretation is a misleading distortion since it is valid only for the case of special relativity.