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From Complementarity to Quantum Properties: An Operational Reconstructive Approach

Philip Goyal

Abstract

Quantum theory brings into question the compatibility of the twin desiderata of exact knowability of the present state of the physical world and perfect predictability of its future states. Bohr's coordination-causality complementarity principle transforms this tension into one between properties (as ordinarily understood in classical physics) and deterministic causality. Here, we develop an explicit model of quantum properties which accommodates this essential tension. Our approach integrates operational, reconstructive, and metaphysical standpoints. In particular, we make use of an operational framework employed in a recent operational reconstruction of Feynman's formulation of quantum theory; base our property model on an analysis of property types; and use the notions of actuality and potentiality to frame the model. We show that this quantum property model provides a natural resolution of Zeno's paradox of motion, and provides reliable intuitions about phenomena such as electron diffraction and the non-local behaviour of entangled states of non-identical particles.

From Complementarity to Quantum Properties: An Operational Reconstructive Approach

Abstract

Quantum theory brings into question the compatibility of the twin desiderata of exact knowability of the present state of the physical world and perfect predictability of its future states. Bohr's coordination-causality complementarity principle transforms this tension into one between properties (as ordinarily understood in classical physics) and deterministic causality. Here, we develop an explicit model of quantum properties which accommodates this essential tension. Our approach integrates operational, reconstructive, and metaphysical standpoints. In particular, we make use of an operational framework employed in a recent operational reconstruction of Feynman's formulation of quantum theory; base our property model on an analysis of property types; and use the notions of actuality and potentiality to frame the model. We show that this quantum property model provides a natural resolution of Zeno's paradox of motion, and provides reliable intuitions about phenomena such as electron diffraction and the non-local behaviour of entangled states of non-identical particles.

Paper Structure

This paper contains 50 sections, 11 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Operationality.
  3. Reconstruction.
  4. Metaphysics.
  5. Operational framework
  6. An Ideal Experiment and its Theoretical Modelling
  7. Defining an Experiment via Causal Closure
  8. Closure condition.
  9. Atomic and Non-atomic Measurement Outcomes
  10. Sequence Probabilities and their Interrelations
  11. Properties
  12. Properties in Human Language and their Metaphysical Classification
  13. Properties in Classical Physics
  14. Properties in Quantum Theory
  15. Operationalization of Physical Properties
  16. ...and 35 more sections

Figures (1)

  • Figure 1: Stern-Gerlach experiments on silver atoms. In (a), a silver atom is subject to a sequence of atomic Stern-Gerlach measurement. Each measurement yields one of two atomic outcomes, labelled $1$ or $2$. The sequence of outcomes is denoted $[1,2,1]$. In (b), the intermediate Stern-Gerlach measurement yields non-atomic outcome $\{1,2\}$. The sequence of outcomes is denoted $[1,\{1,2\},1]$. Using Eq. \ref{['eqn:parallel-combination']}, we can regard this sequence as the combination $[1,1,1] \lor [1,2,1]$.

Theorems & Definitions (6)

  • Example 1: Closure for single classical particle
  • Example 2: Closure for classical rotating triad ('spin')
  • Example 3: Evolutive property of a classical particle
  • Example 4: Atomic position measurement establishes closure
  • Example 5: Quantum particle
  • Remark 1: Bohr's Coordination--Causality Complementarity