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In this paper, we aim to resolve two fundamental issues in the dynamics ofrelativity: (i) Under what condition, the time-column space integrals of aLorentz four-tensor constitute a Lorentz four-vector, and (ii) under whatcondition, the time-element space integral of a Lorentz four-vector is aLorentz scalar; namely two "conservation laws", which are mispresented intraditional textbooks, and widely used in fundamental research, such asrelativistic analysis of the momentum of light in a medium, and the proofs ofthe positive mass theorem in general relativity. To resolve issue (i), we havedeveloped a generalized Lorentz \emph{four-vector} theorem based on theprinciples of classical mathematical analysis, with a simplified analyticexample given to illustrate how to transform a space integral from one inertialframe to another, and a strict mathematical derivation provided to confirm theeffect of Lorentz contraction. We use this four-vector theorem to verifyM{\o}ller's theorem, and surprisingly find that M{\o}ller's theorem isfundamentally wrong. We provide a corrected version of M{\o}ller's theorem. Wealso use this four-vector theorem to analyze a plane light wave in a movinguniform medium, and find that the momentum and energy of Minkowski quasi-photonconstitute a Lorentz four-vector and Planck constant is a Lorentz invariant. Toresolve issue (ii), we have developed a generalized Lorentz \emph{scalar}theorem. We use this theorem to verify the "invariant conservation law" inrelativistic electrodynamics, and unexpectedly find that it is alsofundamentally wrong. Thus the two "conservation laws" in traditional textbooks,which have magically attracted several generations of most outstandingscientists, turned out to be imaginary, just like the emperor's new clothes;creating a scientific myth in the modern theoretical and mathematical physics:Believing is seeing.

Resolution of two fundamental issues in the dynamics of relativity and exposure of a real version of the emperor's new clothes