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Open Quantum Systems Decoherence Entanglement Theory Quantum Correlations Quantum Foundations

Two Forms of Inconsistency in Quantum Foundations

arXiv
Authors: Jeremy Steeger, Nicholas Teh

Year

2017

Paper ID

24698

Status

Preprint

Abstract Read

~2 min

Abstract Words

106

Citations

N/A

Abstract

Recently, there has been some discussion of how Dutch Book arguments might be used to demonstrate the rational incoherence of certain hidden variable models of quantum theory (Feintzeig and Fletcher 2017). In this paper, we argue that the 'form of inconsistency' underlying this alleged irrationality is deeply and comprehensively related to the more familiar 'inconsistency' phenomenon of contextuality. Our main result is that the hierarchy of contextuality due to Abramsky and Brandenburger (2011) corresponds to a hierarchy of additivity/convexity-violations which yields formal Dutch Books of different strengths. We then use this result to provide a partial assessment of whether these formal Dutch Books can be interpreted normatively.

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  • Recently, there has been some discussion of how Dutch Book arguments might be used to demonstrate the rational incoherence of certain hidden variable models of quantum theory...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1712.01614 [2] arXiv https://arxiv.org/abs/1712.01614 [3] Publisher https://arxiv.org/abs/1712.01614

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