  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.

Quantum Physics