When a system gets entangled to the environment or to the observer and the world (or observer) is duplicated. What happens to the potential and Hamiltonian, does it gets duplicated or entangled too. I'd like an actual example of a system with a potential or Hamiltonian where I can analyze this. Most examples of MWI ignore the potential or Hamiltonian part so I can't see even one example to think of. Thank you.