Contrary quantum histories and contrary inferences

Marcelo Losada, Roberto Laura

Marcelo Losada, Roberto Laura

G. Nisticò

To perform a more transparent analysis of the problems raised by contrary inferences within Consistent History approach to Quantum Theory, we extend the formalism of the conceptual basis. According to our analysis, the conceptual difficulties arising from contrary inferences are ruled out.

Adrian Kent

It was pointed out recently [A. Kent, Phys. Rev. Lett. 78 (1997) 2874] that the consistent histories approach allows contrary inferences to be made from the same data. These inferences correspond to projections $P$ and $Q$, belonging to different consistent sets, with the properties that $PQ = QP = 0$ and $P \neq 1 -Q$. To many, this seems undesirable in a theory of physical inferences. It also raises a specific problem for the consistent histories formalism, since that formalism is set up so as to eliminate contradictory inferences, i.e. inferences $P$ and $Q$ where $P = 1 - Q$. Yet there seems to be no sensible physical distinction between contradictory and contrary inferences. It seems particularly hard to defend the asymmetry, since (i) there is a well-defined quantum histories formalisms which admits both contradictory and contrary inferences, and (ii) there is also a well-defined formalism, based on ordered consistent sets of histories, which excludes both. In a recent comment, Griffiths and Hartle, while accepting the validity of the examples given in the above paper, restate their own preference for the consistent histories formalism. As this brief reply explains, in so doing, they fail to address the arguments made against their approach to quantum theory.

Adrian Kent

D. Sokolovski, Y. Liu