> But there are such experiments. String theory says that the result of such experiment is: Lorentz invariance not violated.

This is not a new prediction... String theory makes no new predictions, I hear. I don't understand why you need to be told this.

To your point, there exist various reformulations of physics theories, like Lagrangian mechanics and Hamiltonian mechanics, which are both reformulations of Newtonian mechanics. But these don't make new predictions. They're just better for calculating or understanding certain things. That's quite different from proposing special relativity for the first time, or thermodynamics for the first time, which do make novel predictions compared to Newton.

> there exist various reformulations of physics theories, like Lagrangian mechanics and Hamiltonian mechanics, which are both reformulations of Newtonian mechanics

You have no clue what you're talking about. Did you hear this in some youtube video and have been looking to try it on someone?