Consistent Sets Yield Contrary Inferences in Quantum Theory

TL;DR

This paper demonstrates that the consistent histories approach to quantum theory can lead to contradictory inferences, including contrary propositions with probability one, highlighting fundamental issues in the interpretation.

Contribution

It reveals that the consistent histories formalism allows for contrary inferences with probability one, challenging its interpretational consistency.

Findings

Contrary propositions with probability one can be derived from the same data.

The formalism produces contrary predictions in generalized time-neutral quantum mechanics.

Contradictions arise from the choice of consistent sets in the framework.

Abstract

In the consistent histories formulation of quantum theory, the probabilistic predictions and retrodictions made from observed data depend on the choice of a consistent set. We show that this freedom allows the formalism to retrodict contrary propositions which correspond to orthogonal commuting projections and which each have probability one. We also show that the formalism makes contrary probability one predictions when applied to Gell-Mann and Hartle's generalised time-neutral quantum mechanics.