GR and Curvature
obviously the equations of tidal forces and geodesic deviation are very similar to lead one to motivate yourself to explore gravity as not a field but as a curved geometry, Einstein also said that if each accelerated frame is locally an inertial one the euclidean geometry of Lorentz can not hold, which also motivated him to explore the geometry instead of a field. can some one explain/give me an example of Lorentz geometry not holding in all accelerated frames, basically prove the second statement.
I am trying to understand why Einstein abandons a field for geometry yes the equations are similar very similar still that is not enough to say it is proof that they are the same, E&M and classic gravity have similar mathematical qualities but they are (as far as we know) not the same. please help me out here proof or giving an example of the second statement, thank you.