Shearing Off the Tree: Emerging Branch Structure and Born's Rule in the Multiverse

Decoherence theory has shown that, after a unitary system-detector interaction, the components of the wave function belonging to different measurement outcomes behave classical for all practical purposes. So, the story continues, after a second measurement each previous component produces a further set of classically behaving components, and so on and so forth, eventually generating a set of exponentially many decohered branches in which ``everything happens''. By way of example, using exact numerical diagonalization of the Schr\"odinger equation, we show that this picture is wrong. A significant fraction (often even the vast majority) of branches shows the strongest possible interference effects if the above reasoning is repeated many times. This implies that both proponents and opponents of the many worlds interpretation need to revise their argumentation. Moreover, within our toy model we also observe that the remaining classically behaving (i.e., decohering) branches sample frequencies in accordance with Born's rule. We speculate what this could imply for the quantum measurement problem if it turns out to be true in general.