Everettian Decoherent Histories and Causal Histories

Abstract: D. Wallace has tried to use decoherence to solve the preferred basis problem of Everettian Quantum Mechanics, and this solution lays the foundation for his proof of the Born rule. But this is a circular argument, as approximations used in decoherence usually rely on the probabilistic interpretation of the Hilbert space norm. He claims the norm can measure approximations even without probabilities, but this assumption has not been properly justified. Without it, the combination of the Everettian and decoherent histories formalisms leads to strange consequences, such as a proliferation of small amplitude histories with lots of macroscopic quantum jumps. Still, this erratic behavior may provide a way to justify the approximations, in a new histories formalism, in which macroscopic causal relations play a central role. Small histories, suffering too much interference, may lose causality, being thus discarded as invalid. The remaining branches can present some small interference, opening the possibility of experimental verification.