Probing the Structure of Quantum Mechanics : Nonlinearity, Nonlocality, Computation and Axiomatics.
Title:
Probing the Structure of Quantum Mechanics : Nonlinearity, Nonlocality, Computation and Axiomatics.
Author:
Aerts, Diederik.
ISBN:
9789812778024
Personal Author:
Physical Description:
1 online resource (401 pages)
Contents:
CONTENTS -- Probing the Structure of Quantum Mechanics -- References -- The Linearity of Quantum Mechanics at Stake: The Description of Separated Quantum Entities -- 1 Introduction -- 2 Quantum Axiomatics -- 3 The Representation Theorem -- 4 The Two Failing Axioms of Standard Quantum Mechanics -- 5 Attempts and Perspectives for Solutions -- References -- Linearity and Compound Physical Systems: The Case of Two Separated Spin 1/2 Entities -- 1 Introduction -- 2 A Single Spin 1/2 System -- 3 The Separated Product of Two Spin 1/2 Systems -- 4 The Orthogonality Relation -- 5 Sasaki Regularity -- 6 Discussion -- References -- Being and Change: Foundations of a Realistic Operational Formalism -- 1 Introduction -- 2 Foundations of the Formalism -- 3 Classical and Quantum Entities -- 4 Pre-Order Structures -- 5 Experiments And Preparations -- 6 Meet Properties and Join States -- 7 Operationality -- 8 Conclusion -- References -- The Classical Limit of the Lattice-Theoretical Orthocomplementation in the Framework of the Hidden-Measurement Approach -- 1 Introduction -- 2 The e-Model -- 3 Structures on the Set of Properties -- 4 Physically Denned Orthogonality Relations -- 5 The N-Model: A Model with Vanishing State Transitions in the Classical Limit -- 6 The G-Z Orthogonality Relation for a General Physical System -- References -- State Property Systems and Closure Spaces: Extracting the Classical en Non-Classical Parts -- 1 State Property Systems and Closure Spaces -- 2 Super Selection Rules -- 3 D-classical Properties -- 4 Decomposition Theorem -- 5 Closed Subspaces and ap-Subsystems -- 6 The D-classical Part of a State Property System -- References -- Hidden Measurements from Contextual Axiomatics -- 1 Introduction -- 2 Prerequisites from Convex Geometry -- 3 Basic Assumptions.
4 Axioms for Contextual Interactions -- 5 Conclusion -- References -- Memory Effects in Atomic Interferometry: A Negative Result -- 1 Introduction -- 2 Previous Attempts -- 3 A New Hidden Variable Model -- 4 Experimental Measurement of Temporal Correlations -- 5 Conclusion. -- 6 Appendix -- References -- Reality and Probability: Introducing a New Type of Probability Calculus -- 1 Introducing the Problem -- 2 Subset Probability -- 3 Reality as a Special Case of Probability -- 4 SEP: The Category of State Experiment Probability Systems -- 5 The Categories SEP and SP -- References -- Quantum Computation: Towards the Construction of a 'Between Quantum and Classical' Computer -- 1 Introduction -- 2 Quantum Computation: Main Concepts -- 3 Intermediate Models Between Quantum and Classical -- 4 Computers 'Between Quantum and Classical' -- 5 Conclusions -- 6 Acknowledgments -- References -- Buckley-Siler Connectives for Quantum Logics of Fuzzy Sets -- 1 Introduction -- 2 Buckley-Siler connectives for classical observables -- 3 Generalization of Buckley-Siler approach to the case of fuzzy sets with no underlying sample space -- 4 Buckley-Siler connectives for spin-1/2 observables -- References -- Some Notes on Aerts' Interpretation of the EPR-Paradox and the Violation of Bell-Inequalities -- 1 Introduction -- 2 The EPR-Situation -- 3 Some Causal Influences Do Not Propagate -- 4 Non-Separable Physical Entities Not Situated in Space -- 5 The Creation-Discovery View -- 6 Are Quantum Entities Individuals? -- 7 Is The Creation-Discovery View a Scientific Realism? -- References -- Quantum Cryptographic Encryption in Three Complementary Bases Through a Mach-Zehnder Set Up -- 1 Introduction -- 2 The Mach-Zehnder interferometer considered as a unitary transformation -- 3 Encoding protocol -- 4 Decoding protocol.
5 A realistic variant of the technique -- References -- Quantum Cryptography Without Quantum Uncertainties -- 1 Introduction -- 2 Quantum Cryptography -- 3 Some Technological Limitations of the Quantum Technique -- 4 A Semi-Classical Technique -- 5 Comparison of the Quantum and Semi-Classical Protocols -- 6 Generalisations of the Protocol -- References -- How to Construct Darboux-Invariant Equations of von Neumann Type -- 1 Introduction -- 2 A Systematic Method to Generate Darboux-Invariant Lax Pairs -- 3 Examples of Darboux-Invariant Equations -- 4 A Nonisospectral Case -- 5 The Darboux-Backlund Transformation -- 6 Conclusions -- References -- Darboux-Integrable Equations with Non-Abelian Nonlinearities -- 1 Introduction -- 2 Darboux-Integrable Equations -- 3 Examples -- 4 Binary Darboux Transformation -- 5 The Main Theorem -- 6 Conclusions -- References -- Dressing Chain Equations Associated with Difference Soliton Systems -- 1 Introduction -- 2 Darboux Transformations in Associative Ring with Automorphism -- 3 Stationary Equations as Eigenvalue Problems and Chains -- 4 Joint Covariance of Equations and Nonlinear Problems -- 5 Non-Abelian Hirota System -- 6 Nahm Equations -- 7 Conclusions -- References -- Covariance Approach to the Free Photon Field -- 1 Introduction -- 2 Classical Electromagnetism -- 3 Quantum Description -- 4 Fock Representation -- 5 Poincare Invariance -- 6 Conclusions -- Appendix A: Covariance Systems -- Appendix B: Smeared-out Field Operators -- Appendix D: Existence of the Vacuum State -- Appendix E: Unitary Representation of the Group of Shifts -- References.
Abstract:
During the last decade, scientists working in quantum theory have been engaging in promising new fields such as quantum computation and quantum information processing, and have also been reflecting on the possibilities of nonlinear behavior on the quantum level. These are challenging undertakings because (1) they will result in new solutions to important technical and practical problems that were unsolvable by the classical approaches (for example, quantum computers can calculate problems that are intractable if one uses classical computers); and (2) they open up new 'hard' problems of a fundamental nature that touch the foundation of quantum theory itself (for example, the contradiction between locality and nonlinearity and the interpretation of quantum computing as a universal process). In this book, one can distinguish two main streams of research to approach the just-mentioned problem field: (1) a theoretical structural part, which concentrates on the elaboration of a nonlinear quantum mechanics and the fundamentals of quantum computation; and (2) a theoretical experimental part, which focuses on the theoretical aspects of applications that arise from new technology and novel research perspectives such as quantum optics and quantum cryptography. Particular attention is also paid to the measurement problem, the classical limit and alternative interpretations (such as the hidden measurement approach). Contents: Probing the Structure of Quantum Mechanics (D Aerts et al.); The Linearity of Quantum Mechanics at Stake: The Description of Separated Quantum Entities (D Aerts & F Valckenborgh); Linearity and Compound Physical Systems: The Case of Two Separated Spin 1/2 Entities (D Aerts & F Valckenborgh); Being and Change: Foundations of a Realistic Operational Formalism (D Aerts); The Classical Limit of the Lattice-Theoretical Orthocomplementation in
the Framework of the Hidden-Measurement Approach (T Durt & B D'Hooghe); State Property Systems and Closure Spaces: Extracting the Classical en Non-Classical Parts (D Aerts & D Deses); Hidden Measurements from Contextual Axiomatics (S Aerts); High Energy Approaches to Low Energy Phenomena in Astrophysics (S M Austin); Memory Effects in Atomic Interferometry: A Negative Result (T Durt et al.); Reality and Probability: Introducing a New Type of Probability Calculus (D Aerts); Quantum Computation: Towards the Construction of a 'Between Quantum and Classical Computer' (D Aerts & B D'Hooghe); Buckley-Siler Connectives for Quantum Logics of Fuzzy Sets (J Pykacz & B D'Hooghe); Some Notes on Aerts' Interpretation of the EPR-Paradox and the Violation of Bell-Inequalities (W Christiaens); Quantum Cryptographic Encryption in Three Complementary Bases Through a Mach-Zehnder Set Up (T Durt & B Nagler); Quantum Cryptography Without Quantum Uncertainties (T Durt); How to Construct Darboux-Invariant Equations of von Neumann Type (J L Cie(li(ski); Darboux-Integrable Equations with Non-Abelian Nonlinearities (N V Ustinov & M Czachor); Dressing Chain Equations Associated with Difference Soliton Systems (S Leble); Covariance Approach to the Free Photon Field (M Kuna & J Naudts). Readership: Graduate students, researchers and academics in quantum physics.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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