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The quantum-mechanical " Schrödinger's cat " theorem according to the many-worlds interpretation (MWI). In this interpretation, every event is a branch point; the cat is both alive and dead, even before the box is opened, but the "alive" and "dead" cats are in different branches of the universe, both of which are equally real, but which do not interact with each other...etc

Why parallel worlds do not interact with each other? Is it possible (at least theoretically) for parallel worlds to interfere with each other?

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    $\begingroup$ As far as I understand, the many worlds are just a device to convey the idea that quantum mechanics allows different realizations of a measurement (worlds), and we just happen to live in one of these worlds. In my opinion, this is just a nice story to deal psychologically with the fact that quantum mechanics tells us only about probabilities and not about facts, so that there's no physical content behind the interpretation and, in particular, no interaction beetween the different worlds (which are just possibilities). $\endgroup$ – pppqqq Nov 20 '16 at 10:27
  • $\begingroup$ Side note: I am becoming convinced that my extradimensional-self persistently hides my keys $\endgroup$ – user136649 Nov 20 '16 at 10:27
  • $\begingroup$ Basically decoherence. A "world" is defined as a region of the Hilbert space which has become effectively independent due to the effects of decoherence. $\endgroup$ – Bruce Greetham Nov 22 '16 at 7:20
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In the many worlds interpretation, the universe you see around you is part of a larger and more complex structure called the multiverse. To some approximation, on some scales, under some circumstances, the multiverse acts like a collection of parallel non-interacting universes. This approximation breaks down in single particle interference experiments, the EPR experiment and other quantum mechanical experiments. For example, in single particle interference, two or more different versions of a particle interfere to produce the outcome. For a detailed explanation of a single particle interference experiment, see 'The Fabric of Reality' by David Deutsch, Chapter 2. For more explanation of the multiverse, see 'The Fabric of Reality' and 'The Beginning of Infinity' by David Deutsch and

https://arxiv.org/abs/quant-ph/0104033

The answer to why you don't see quantum interference effects in everyday life is that when you copy information from a system undergoing interference you prevent the interference. An object like you or your desk or whatever is having lots of information copied from it on a very short timescale, e.g. the shape of my chair is changed by the pressure my body puts on it and this is a record of my position, light scattering off me records my position and so on. For more on how copying prevents interference see

https://arxiv.org/abs/1212.3245

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