After googling a lot about Unitarity and understanding Simon formulas. I understood about it more. Unitarity just says that probability equals to 100% meaning when you have 50% in one slit, you have 50% in another slit. And so if you suddenly have 30% in one slit, you have 70% in one slit (or other setups). And overlap has to do with the vectors. But all this is assuming the wave function is a probabilistic medium per Born specification. Is there solid proof at all that this is the case. No. Because one can introduce Many worlds where the wave functions are not wave of probabilities but real. And here how can you say that unitarity is preserved? They now search for Lorentz violations, is there a similar search for unitarity violation? I think the black hole firewall stuff is one of those where they explore the possibility unitarity may not be true. So this means there is no solid proof unitarity is a law in Quantum mechanics, right?Ok. Let's not mention the mind as the group is not equipped to handle it.
Let's just focus on this unitarity conserving information thing. Is it like law of conservation of energy or the law of conservation of information where information cant be created nor destroyed? Then if you introduce new Hamiltonian to the system, then can't you add information to the system that can make you say couple two branches together? Ping expert Simon Phoenix and Vanhees. Need your expertise here and the math. Thanks!