"In the delayed choice experiment, the decision whether or not to quantum erase 
the "which way" information can be made long after the original photons hit the 
screen and make their marks there. So decoherence has set in, and any parallel 
universes have necessarily become different in some ways. According to your 
interpretation, therefore, there can then be no interference, because the 
worlds cannot come back together. But we can restore the interference pattern 
by quantum erasing the which way information (e.g., by measuring in an 
orthogonal basis). So it is not a matter of whether there are differences 
between parallel universes -- it is whether or not the which way information 
still exists in some form or the other. Deutsch simply got the explanation of 
interference in terms of interactions between parallel universes wrong.
Bruce"

Zeilinger et al. wrote: 
"It is a general feature of delayed-choice experiments
that quantum effects can mimic an influence of future
actions on past events. However, there never emerges
any paradox if the quantum state is viewed only as `catalogue
of our knowledge' (Schroedinger, 1935) without any
underlying hidden variable description. Then the state is
a probability list for all possible measurement outcomes
and not a real physical object. The relative temporal order
of measurement events is not relevant, and no physical
interactions or signals, let alone into the past, are necessary
to explain the experimental results. To interpret
quantum experiments, any attempt in explaining what
happens in an individual observation of one system has
to include the whole experimental configuration and also
the complete quantum state, potentially describing joint
properties with other systems. According to Bohr and
Wheeler, no elementary phenomenon is a phenomenon
until it is a registered phenomenon (Bohr, 1949; Wheeler,
1984). In light of quantum erasure and entanglement
swapping, one might like to even say that some registered
phenomena do not have a meaning unless they are
put in relationship with other registered phenomena (Ma
et al., 2012)." https://arxiv.org/abs/1407.2930

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