No mass can move at velocity squared. As a result, the formula for kinetic energy (KE=½mv²) is an abstraction apart from the motion of the mass.
This claim is not obvious to a lot of persons, and it proves nothing in itself. But the mathematical proof of the error shows that this statement is correct. The statement says nothing about mathematics or the use of abstractions in mathematics. It says how kinetic energy can or cannot be represented. Kinetic energy is the energy of motion. Motion cannot be represented as velocity squared, because nothing can move at velocity squared. Anyplace else, velocity can be squared when needed. The distinction here is between a representation and a procedure. Math is a procedure. It can have anything in it which is useful. The formula for kinetic energy can only produce a correct result when it properly represents kinetic energy. A correct procedure must follow a correct representation of kinetic energy. What the formula represents is motion. Motion cannot be represented with velocity squared, because motion is defined as velocity nonsquared. The implication of the erroneous definition of kinetic energy (KE=½mv²) is that energy is not the motion of a mass but an abstraction that goes with it. The logic can be questioned, but my analysis says kinetic energy cannot be an abstraction apart from the motion of the mass, because gallons of fuel are not an abstraction, and fuel has to transform quantitatively into kinetic energy. The two proofs that I use show that there are points of conflict in separating kinetic energy from the motion of the mass. Analogy: An analogy would be to determine how high a door should be to prevent heads from getting bumped. The height of a population can be measured. It cannot be represented as height squared. Height squared will not tell how high the door should be, because height squared is not height.