The corruption of physics began in 1686, when Gottfried Leibniz published the claim that force times distance is the basis of kinetic energy. Prior to that time the relationships between force and motion were on track and provided the basis for Newton's laws. At that time, there was a recognition of two types of force: dead force and living force. Living force is the force which Newton's laws are based on. It accelerates mass. Dead force is stress. It does not accelerate a mass.
Living force is a repelling force, which pushes mass. Dead force is an attracting force, which pulls on mass and holds matter together. Living force is involved in transformations of energy, where energy is said to be conserved. Conserved means that the quantities of energy stay the same after an interaction as before. Dead force does not conserve energy. It includes gravity and stress, which can create and destroy energy. (So-called potential energy is energy which is created and destroyed by gravity.) And it includes levers, which amplify force.
The result is that there are two alternatives for the definition of energy. There are contradictions between the two alternatives, and they cannot be resolved with existing knowledge. If energy is defined in terms of living force, transformations of energy conserve energy, but the dead force of levers amplify energy. If energy is defined in terms of dead force, levers conserve energy, but transformations based on living force do not, as shown with rockets in the mathematical proof.
Should energy be defined in terms of dead force found in levers or living force found in transformations? Since conservation through transformation is considered to be the defining property of energy, transformations through living force should provide the basis for defining energy. In this case, my proof with rockets apply. But physicists based their definition of energy on the dead force of levers and contradict transformations based on living force such as heat produces in a rocket engine.
There is no resolving the contradictions. Dead force and living force contradict each other. Picking one as the basis for defining energy is going to contradict the other. The proper alternative for defining energy is the living force which Newton's laws are based upon and which transformations of energy include, not the dead force which levers amplify. But physicists base their definition of energy on the dead force of levers.
