The Development of Relativity and Einstein

There are errors in general relativity that must be rectified. As Zhou pointed out, Einstein’s covariance principle is proven to be invalid by explicit examples. Linearization is conditionally valid. Pauli's version of the equivalence principle is impossible in mathematics. Einstein's adaptation of the distance in Riemannian geometry is invalid in physics as pointed out by Whitehead. Moreover, it is inconsistent with the calculation on the bending of light, for which a Euclidean-like framework is necessary. Thus, the interpretation of the Hubble redshifts as due to receding velocities of stars is invalid. The Einstein equation has no dynamic solutions just as Gullstrand suspected. All claims on the existence of dynamic solutions for the Einstein equation are due to mistakes in non-linear mathematics. For the existence of a dynamic solution, the Einstein equation must be modified to the Lorentz-Levy-Einstein equation that have additionally a gravitational energy-stress tensor with an anti-gravity coupling. The existence of photons is a consequence of general relativity. Thus, the space-time singularity theorems of Hawking and Penrose are actually irrelevant to physics because their energy conditions cannot be satisfied. The positive mass theorem of Schoen and Yau is misleading because invalid implicit assumptions are used as Hawking and Penrose did. There are three experiments that show formula E = mc2 is invalid, and a piece of heated-up metal has reduced weight just as a charged capacitor. Thus, the weight is temperature dependent. It is found, due to the repulsive charge-mass interaction, gravity is not always attractive to mass. Since the assumption that gravity is always attractive to mass is not valid, the existence of black holes are questionable. Because of the repulsive charge-mass interaction, the theoretical framework of general relativity must be extended to a five-dimensional relativity of Lo, Goldstein & Napier. Thus Einstein's conjecture of unification is valid. Moreover, the repulsive gravitational force from a charged capacitor is incompatible with the notion of a four-dimensional space. In Quantum theory, currently the charge-mass interaction is neglected. Thus, quantum theory is not a final theory as Einstein claims.