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We investigatewhether quantum theory can be understood as the continuumlimit of a mechanical theory, in which there is a huge, but finite, number of classical “worlds,” and quantum effects arise solely from a universal interaction between these worlds, without reference to anywave function. Here, a “world” means an entire universe with well-defined properties, determined by the classical configuration of its particles and fields. In our approach, each world evolves deterministically, probabilities arise due to ignorance as to which world a given observer occupies, and we argue that in the limit of infinitely many worlds thewave function can be recovered (as a secondary object) from the motion of these worlds.We introduce a simple model of such a “many interacting worlds” approach and showthat it can reproduce some generic quantum phenomena—such as Ehrenfest’s theorem, wave packet spreading, barrier tunneling, and zero-point energy—as a direct consequence of mutual repulsion between worlds. Finally, we perform numerical simulations using our approach.We demonstrate, first, that it can be used to calculate quantum ground states, and second, that it is capable of reproducing, at least qualitatively, the double-slit interference phenomenon.
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