Your "cut and go physics" produces any amount of word salad you want, but has no connection to reality.
You can't take solutions out of context and use them as you like.
Many solutions are only valid in their niche and not general solutions like a mathematic method.
You can use calculus for many problems, but not the solution of a differential equation for another problem. The analogy has to be proven to be valid otherwise - word salad with mathematic dressing.