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Local or even non-local hidden variables doesn't actually improve how much you can predict systems, meaning that you'd have a more complex theory that gives the same results, in which case the extra complexity isn't doing anything. Therefore the theory underlying quantum mechanics is called "complete": it describes nature just as well as any more complicated extension of it, so you can get rid of the extensions and just use quantum mechanics as is. The hypothesis that it's a few photons going in different directions, is not able to explain the results of experiment, the photon traveling in all directions as a wave is able to explain such results. A relativel.
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