I am reading David Deutsch's The Beginning of Infinity. In chapter 11, he explains the basics of quantum theory and gives evidence for the many worlds (Everett) interpretation.
The argument uses a Mach-Zehnder interferometer:
It is explained that if a photon is introduced between the beam splitter and either of the mirrors, it will be detected at one of the two detectors at random. However, if it is introduced before the beam splitter, it will always appear at the same detector. From this follows that the (unobservable) split histories of the photon influence where it will be detected, so an explanation like splitting and interference of universes is necessary.
The question Deutsch doesn't answer is: Why does the photon always appear at the same detector?
(I have a strong mathematical background, but am not familiar at all with the notation used in quantum physics.)