>>13816737>you find a way to look at the old in such a way the jump is absolutely minimal to the new things.As far as examples:
https://en.wikipedia.org/wiki/Lagrangian_mechanicsLed to quantum mechanics and the ability to do relativistic physics.
https://en.wikipedia.org/wiki/Newton%E2%80%93Cartan_theoryIs a way to generalize newtonian gravity in a way leading to GR(and useful for obtaining corrections from GR for newtonian gravity.
Physics makes progress by conservative applications of fundamental principles and reformulations of them in productive ways and not by throwing in more and more complicated bullshit by hand.
I need not mention mathematics, where principal ways in which new mathematics was obtained was via introduction of conservative new ways to look at the same things(say in how you can get to general riemannian geometry by just formulating ways to calculate intrinsically things like volumes and lengths and angles and curvatures for (hyper) surfaces and then just forgetting you were in R^n and using same things word for word to do shit with hyperbolic spaces, grassmanians, lie groups and other exotic things which arent practical to think of as surfaces in some ambient space)