Special relativity based on 3+3 space-time

Based on the analysis of successive space-time transformation with direction changed, we prove the Galilean transformation can be derived by two postulates, the principle of relativity, and the homogeneous and isotropic of time and space that meets the Euclidean geometry. As the two postulates are also believed to be satisfied by the special relativity, we further demonstrate the successive Lorentz boost with direction changed will lead to paradox. It is discussed the Wigner rotation should not be regarded as the relativistic effect for the composition of two Lorentz boosts, but it will give contradictory events against the Euclidean geometry. We believe seeking new space-time model for the special relativity would be the most feasible approach, and a hypothesis of 3+3 space-time model is proposed to solve the paradox. We also extend the Maxwell equations to the 3+3 space-time and obtain the new electromagnetic field quantities and the corresponding covariant electromagnetic field equations. It is discussed the 3+3 space-time can be approximated to the 3+1 space-time and the new field equations based on the 3+3 space-time can also be approximated to the Maxwell equations.