Foundations of Physics

, Volume 41, Issue 3, pp 592–607 | Cite as

Quantum Reality and Measurement: A Quantum Logical Approach

  • Masanao OzawaEmail author


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.


Quantum logic Quantum set theory Quantum measurement Joint determinateness Simultaneous measurability Contextual interpretation 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Graduate School of Information ScienceNagoya UniversityNagoyaJapan

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