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Epistemic horizons and the foundations of quantum mechanics. (English) Zbl 1414.81035

Summary: In-principle restrictions on the amount of information that can be gathered about a system have been proposed as a foundational principle in several recent reconstructions of the formalism of quantum mechanics. However, it seems unclear precisely why one should be thus restricted. We investigate the notion of paradoxical self-reference as a possible origin of such epistemic horizons by means of a fixed-point theorem in Cartesian closed categories due to Lawvere that illuminates and unifies the different perspectives on self-reference.

MSC:

81P05 General and philosophical questions in quantum theory
81P15 Quantum measurement theory, state operations, state preparations
81S05 Commutation relations and statistics as related to quantum mechanics (general)
62J10 Analysis of variance and covariance (ANOVA)
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