Action at a Distance and Quantum Gravity
Action at a Distance
Two entangled particles may be separated and then observed by two scientists. When the first measures a property of their quantum particle, QA, they realise which world they are in and know that the second observer's results will be correlated with theirs. But QA does not need to send a signal to QB in order to 'tell' it the results. This is because all results are actualised and so QB only needs to 'know' that it is in a world which is correlated with QA. This information was exchanged when the two quantum states became entangled in the first place.
Quantum Gravity
The Everett approach does not provide a quantum theory of gravity, but it does predict that one exists. If gravity did not obey the laws of quantum mechanics then there would be no reason why the force from one world would not be felt by another. This means that the gravitational force in this universe would include forces from all possible worlds. Even if this effect was not noticeable on Earth, we would notice it on a galactic scale because the distribution of galaxy clusters depended upon the expansion of quantum fluctuations during the inflationary epoch of the early universe (Mukhanov and Chibisov, pp.549-553). If gravity was shared between all possible worlds then stars would be attracted to galaxies that we do not observe as well as those that we do.
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