Geometric phases, Everett's many-worlds interpretation of quantum mechanics, and wormholes

Abstract

We present how the formalism of geometric phases in adiabatic quantum dynamics provides geometric realisations permitting to ``embody'' the Everett's many-worlds interpretation of quantum mechanics, including interferences between the worlds needed for the probability changes and the decoherence processes needed to solve the preferred basis problem. We show also that this geometric realisation is intimately related to quantum gravity (especially to matrix models), showing that the many-world interpretation can be consistent with quantum gravity. The concept of wormhole borrowed to general relativity is central in this geometric realisation. It appears not only as an image by analogy to help the interpretations, but also as a true physical model of quantum wormhole in quantum gravity, the two ones being consistent which each other.