Momentum Conservation in a Charged Retarded Field Engine for Space and General Purpose Vehicles

Addressing the potential conflicts between momentum conservation laws and retardation requires a comprehensive understanding of both principles within the context of specific physical systems and theoretical frameworks. Indeed it was claimed that a retarded engine is impossible due to the lack of linear momentum conservation. The purpose of this work is to settle this issue by demonstrating that linear momentum is indeed conserved for a charged retarded field engine. Earlier research has already introduced the concept of a charged retarded engine. The system gains mechanical momentum and energy when it is subjected to a total force for a certain amount of time. If retardation is taken into account a total force is present even if no external force affects the system, thus momentum seems to appear from nowhere violating the law of momentum conservation. However, momentum is indeed conserved as the present work demonstrates. We present a mathematical proof that the momentum is conserved in a time dependent electromagnetic retarded motor. The expression of field momentum comes out to be equal and opposite to the mechanical momentum gained by the material system as obtained in [1]. This calculation of charged retarded engine is an extension work of papers published earlier [2,3] which explored a non-charged retarded engine. We prove that the total momentum in a retarded motor including both material and electromagnetic linear momentum is indeed conserved as dictated by Noether’s theorem. This is a consequence of the non linearity of the electromagnetic linear momentum which is proportional to the integral of the vector multiplication of the electric and magnetic fields. The problem solved is relevant because it demonstrates that the charged retarded f ield engine does not violate any known physical laws and thus can serve for (space) transportation. The scientific novelty of the solution obtained is in demonstrating that a charged retarded field engine conserves linear momentum. Thus the momentum obtained by the field is equal and opposite to the linear mechanical momentum obtained by the engine.