Every high school student can easily recall the formula for kinetic energy: K=m*V^2/2. Nevertheless I assert that hardly anyone understands what that formula really means, and very few care.
What is velocity? Can velocity be defined in the universe comprised of a single point-like body? Apparently that cannot be done operationally (i.e. without resorting to the elusive notion of absolute space of Newton). Indeed, it does not make sense to speak of motion in the universe that contains only one object to begin with. Then how many point-like bodies do we need in our universe in order to make introduction of the notion of velocity possible? We need at least three point objects. Can you see why two is not enough?
Let us put aside for the moment the difficult question of what inertial mass is. In order to quantify the intuitive notion of kinetic energy we need at least three point masses in our universe. We take any two of them with inertial masses m and M. Let these two point objects approach each other with a relative (to each other) constant velocity V. Now, it seems reasonable to assert that:
1. Body m has a relative kinetic energy m*V^2/2 with respect to the body M.
2. Body M has a relative kinetic energy M*V^2/2 with respect to the body m.
3. The combined kinetic energy of the two bodies is equal to (m+M)*V^2/2. This total energy can be said now to be absolute because the speed V at which they approach each other does not depend on any particular reference frame.
I am asking you now:
1. What is the correct way to define the notion of kinetic energy: as a relative value, or as an absolute value?
2. If the notion of kinetic energy is to be defined as relative value, it does not seem reasonable to speak of conservation of energy. Wouldn't you agree?
3. If the notion of kinetic energy is to be defined as absolute value, i.e. as a measure of some kind of relationship between two bodies (very much like the notion of potential energy), then where does kinetic energy reside exactly? In the body M? In the body m? In both? Or, perhaps, somewhere in between? Does it make sense at all to ask: where does kinetic energy reside exactly?
4. If the notion of kinetic energy is to be defined as relationship thing, can we rely on the formula (m+M)*V^2/2? If we cannot, then what is the correct formula for kinetic energy?