Quantum Reality and Measurement: A Quantum Logical Approach

TL;DR

This paper proposes a quantum logical framework to reconcile the universal uncertainty principle with the notion of quantum reality, allowing simultaneous measurement of incompatible observables in different contexts.

Contribution

It introduces a quantum logical language to define observable values independently of measurement, clarifying the relation between quantum reality and measurement.

Findings

Defines joint determinateness and value identity within quantum logic.

Provides a contextual interpretation of simultaneous measurements.

Reconciles measurement of incompatible observables with quantum reality.

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.