Non-Probabilistic Decoherent Histories and Causal Histories in Everettian Quantum Mechanics
André L. G. Mandolesi
D. Wallace has combined the Decoherent Histories formalism and Everettian Quantum Mechanics, in an attempt to solve the preferred basis problem. This in turn serves as a foundation for his proof of the Born rule. But approximations used in decoherence depend on the probabilistic interpretation of Born weights, resulting in a circular reasoning. We contest his arguments that the approximations are valid even without probabilities, and show that, without them, the combination of those theories leads to unacceptable results. There is a proliferation of ill behaved histories, compromising his proof of the Born rule. We propose the development of a new causal histories formalism, which might improve the situation. Histories of small amplitude are discarded, not on probability grounds, but for suffering too much interference, which blurs causal relations. The remaining histories might still suffer small amounts of interference, leaving open the possibility of experimental verification.
•Apr 4, 2017•0 citations