Foundations of Physics 41 (3):592-607 (2011)

Abstract
The recently established universal uncertainty principle revealed that two nowhere commuting observables can be measured simultaneously in some state, whereas they have no joint probability distribution in any state. Thus, one measuring apparatus can simultaneously measure two observables that have no simultaneous reality. In order to reconcile this discrepancy, an approach based on quantum logic is proposed to establish the relation between quantum reality and measurement. We provide a language speaking of values of observables independent of measurement based on quantum logic and we construct in this language the state-dependent notions of joint determinateness, value identity, and simultaneous measurability. This naturally provides a contextual interpretation, in which we can safely claim such a statement that one measuring apparatus measures one observable in one context and simultaneously it measures another nowhere commuting observable in another incompatible context
Keywords Quantum logic  Quantum set theory  Quantum measurement  Joint determinateness  Simultaneous measurability  Contextual interpretation
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DOI 10.1007/s10701-010-9462-y
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References found in this work BETA

The Problem of Hidden Variables in Quantum Mechanics.Simon Kochen & E. P. Specker - 1967 - Journal of Mathematics and Mechanics 17:59--87.
The Physical Principles of the Quantum Theory.Werner Heisenberg - 1930 - Chicago: Ill., The University of Chicago Press.

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Citations of this work BETA

Theodicy, Supreme Providence, and Semiclassical Theism.James Goetz - 2021 - Theology and Science 19 (1):42-64.
Quantum Set Theory: Transfer Principle and De Morgan's Laws.Masanao Ozawa - 2021 - Annals of Pure and Applied Logic 172 (4):102938.

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