In classical physics there exists deterministic motion i.e. x and t are coupled as x(t) which allows for quantities such as velocity and acceleration to also be coupled. Measurements to not affect this coupled motion. In quantum mechanics, V(x) we argue is really an average of probabilistic impulse hits. Thus quantum mechanics is already a statistical theory i.e. one has resonance/equilibrium states yet one does want measurements to create new resonances. They can, however, destroy resonances. As a result, we argue there are two sets of probabilities, measurement related ones P(x) and P(p) and resonance creating probabilities P(p/x). The resonance probabilities are based on a kind of invariance/nonlocal periodic probability scheme which must create local quantities such as V(x) or KE(x) (kinetic energy) through interference/superposition. The measurement scheme cannot discern the various P(p/x) because otherwise it would create a new resonance, so it only sees the superposed result. This holds for both bound and free type interactions which we argue are both statistical.