Probing The Meaning Of Quantum Mechanics: Physical, Philosophical, And Logical Perspectives

Physical, Philosophical and Logical Perspectives

Diederik Aerts, Sven Aerts, Christian de Ronde

• Publisher: WSPC
• Year: 2014
• eBook ISBN: 9789814596305
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

This book provides a new original perspective on one of the most fascinating and important open questions in science: What is quantum mechanics talking about? Quantum theory is perhaps our best confirmed physical theory. However, in spite of its great empirical effectiveness and the subsequent technological developments that it gave rise to in the 20th century, from the interpretation of the periodic table of elements to CD players, holograms and quantum state teleportation, it stands even today without a universally accepted interpretation. The novelty of the book comes from the multiple viewpoints and the original angles taken by a group of young researchers from Europe and South America who gathered for several years under the auspices of the Center Leo Apostel.Each member of the group presented ideas concerning the interpretation of quantum mechanics. We had discussions ranging from the philosophical underpinnings of local realism and holism, information and decision theoretic approaches to quantum theory all the way to the many worlds interpretation. Strikingly, in much the same way as different — and indeed incompatible observations are needed to fully describe the physical state of affairs in quantum mechanics — the various interpretations of the theory also seem to shed viable, but not necessarily compatible, perspectives on different aspects of the same grand framework. The discussions that followed were both technical and lively, but perhaps their most remarkable quality was the absence of rigid points of view that unfortunately seems to paralyze so much of the discussion in this area. This book is an expression which can be interesting not only to the specialists but also for the general public attempting to get a grasp on one of the still most fundamental questions of present physics. Contents:

• Do Quantum Dice Remember? (T Durt)
• Quantum Ontology in the Light of Gauge Theories (G Catren)
• The Probabilistic Structure of Quantum Theory as Originating from Optimal Observation in the Face of the Observer's Lack of Knowledge of His Own State (S Aerts)
• Quantum Realism, Information, and Epistemological Modesty (A Grinbaum)
• The Problem of Representation and Experience in Quantum Mechanics (C de Ronde)
• Bohrian Complementarity in the Light of Kantian Teleology (H Pringe)
• How Understanding Matters — Or Not (S Le Bihan)
• On the Orthocomplementation of State-Property-Systems of Contextual Systems (B D'Hooghe)
• The Deleuzian Concept of Structure and Quantum Mechanics (W A Christiaens)
• Understanding Probabilities in the Everett Interpretation of Quantum Mechanics (A Barton)
• Metaphysical Underdetermination and Logical Determination: The Case of Quantum Mechanics (J R B Arenhart)
• Neither Name, Nor Number (F Holik)
• EPR Correlations, Bell Inequalities and Common Cause Systems (G Hofer-Szabó)
• A Logic-Algebraic Framework for Contextuality and Modality in Quantum Systems (H Freytes) Student, professional, and the general public interested in the quantum theory. Key Features:
  • The constitution of the group is of mainly PhD students in Europe working in the physics, philosophy and logic of quantum theory. The group, though young, is technically skilled both in the formalism as well as in the traditional and contemporary philosophical discussions regarding the interpretation of quantum mechanics. It is such a constitution which can provide the conditions for a "fresh look" at the field of foundations of quantum mechanics
  • Quantum mechanics is simply fascinating and remains even today an open problem for those who wish to seek for answers
  • The book will be a single unity, as it will be directed by "seeking understanding of quantum mechanics", but it will also be wide and diverse in scope of topics and personal in choice and motivation of the topics handled, which is what makes this enterprise unique

ON THE ORTHOCOMPLEMENTATION OF
STATE-PROPERTY-SYSTEMS OF
CONTEXTUAL SYSTEMS

BART D’HOOGHE

Centrum Leo Apostel for Interdisciplinary Studies
and Foundations of the Exact Sciences
Vrije Universiteit Brussel, Belgium
E-mail: [email protected]

We describe a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter which corresponds with the number N of possible outcomes in an experiment. In the limit N = 2 the system reduces to a model for the spin measurements on a quantum spin-

particle. This model fits in the hidden measurement approach to quantum mechanics in which quantum probabilities are explained as due to an uncontrollable fluctuation in the measurement process. In the limit N → ∞ the system is classical, i.e. the experiments are deterministic and its set of properties is a Boolean lattice. For intermediate situations the change of state due to measurement is neither ‘maximal’ (i.e. quantum) nor ‘zero’ (i.e. classical). We show that two of the axioms used in Piron’s representation theorem for quantum mechanics are violated, namely the covering law and weak modularity. Next, we discuss a modified version of the model for which it is even impossible to define an orthocomplementation on the set of properties. Another interesting feature for the intermediate situations of this model is that the probability of a state transition in general not only depends on the angular distance between the two states but also on the measurement context which induces the state transition. Therefore our models also shed new light on Gleason’s theorem and suggest that transition probability maybe is not a secondary concept which can be derived from the structure on the set of states and properties, but instead should be regarded as a primitive concept by its own right for which the measurement context is crucial.

Keywords: Quantum logic; orthomodular lattices; Piron’s representation theorem.

1. Introduction

In the last century two fundamental new physical theories have been introduced in science, which force us to abandon the age-old classical Newtonian intuition about the nature of reality and how this reality can be represented in a mathematical–physical framework. On the one hand, the theory of general relativity (GR) puts forward a model of a universe populated by material objects moving along world-lines on a 4-dimensional manifold, bending and curving this space–time manifold by their mass. On the other hand, quantum mechanics (QM) describes the reality of microscopic particles on the (sub)atomic level by representing their states and properties in an infinite dimensional complex Hilbert space. ...

Table of contents

• Cover
• HalfTitle
• Title
• Copyright
• DEDICATION
• ACKNOWLEDGMENTS
• PREFACE
• Contents
• Do Quantum Dice Remember?
• Quantum Ontology in the Light of Gauge Theories
• The Probabilistic Structure of Quantum Theory as Originating from Optimal Observation in the Face of the Observer’s Lack of Knowledge of His Own State
• Quantum Realism, Information, and Epistemological Modesty
• The Problem of Representation and Experience in Quantum Mechanics
• Bohrian Complementarity in the Light of Kantian Teleology
• How Understanding Matters — Or Not
• On the Orthocomplementation of State-Property-Systems of Contextual Systems
• The Deleuzian Concept of Structure and Quantum Mechanics
• Understanding Probabilities in the Everett Interpretation of Quantum Mechanics
• Metaphysical Underdetermination and Logical Determination: The Case of Quantum Mechanics
• Neither Name, Nor Number
• EPR Correlations, Bell Inequalities and Common Cause Systems
• A Logic-Algebraic Framework for Contextuality and Modality in Quantum Systems