Parallel worlds and the concept of causality

Some theoretical physicists and cosmologists believe that our universe and our world may be one of many parallel worlds, each having its own independent existence.

This vision has a basis in the science of physical mathematics, and it follows from the theory of tendons and some interpretations of laws and equations of quantum mechanics.

Although the concept of parallel worlds in string theory may be somewhat different from the same concept derived from quantum mechanics, some scientists have tried to unify the two concepts recently.

But we will not go into this issue, because we would like to talk here about one of the amazing benefits of this vision.
Conventional interpretations of quantum mechanics (especially the Copenhagen interpretation) tell us that the universe (or objects within the universe) may take several parallel states at the same time.
But when someone observes or sees this object, the wave function breaks down into one of these situations.

If we take the Schrodinger as an example, the Copenhagen interpretation tells us that the cat is alive and dead at the same time, but when we monitor the real cat situation, its condition will collapse into one of the two, either alive or dead. Now in the late 1950s, the American physicist Hugh Everett introduces a new and astonishing interpretation of the phenomena of quantum mechanics.

Instead of breaking the wave function into one of the two cases, Everett suggested that the two cases continue to exist, but each is in a parallel world. The observer or viewer sees only one of these two situations (the situation in his world). But what does this interpretation mean to the law or principle of Causality Principle?

The principle of causality states that each result can not precede the cause, events are linked to each other in chronological order. The result does not only occur with the effect of the cause but is imposed by it. In traditional physical interpretations, scientists believe that travel over time is impossible to happen because this will impose many logical contradictions.
One of these contradictions is the grandfather paradox. When a person travels to the past and kills his grandfather, changing his past, he eliminates the possibility of his existence. And here is the paradox, so how does that person (the result) to travel to the past and kill the cause of his existence (grandfather) and the result becomes a precedent for the cause ?! But the theory of parallel worlds makes this act worthless because every world and every event lives in its own being and every change in a world of these worlds does not affect our world. The killing of that person's grandfather may happen in a parallel world, and nothing will change this world, and the future remains the same.