The Quantum Mechanics Conundrum - Gennaro Auletta

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The Quantum Mechanics Conundrum (eBook)

Interpretation and Foundations

Gennaro Auletta (Autor)

eBook Download: PDF

2019 | 1st ed. 2019
XXVI, 863 Seiten
Springer International Publishing (Verlag)
978-3-030-16649-6 (ISBN)

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This comprehensive volume gives a balanced and systematic treatment of both the interpretation and the mathematical-conceptual foundations of quantum mechanics. It is written in a pedagogical style and addresses many thorny problems of fundamental physics.

The first aspect concerns Interpretation. The author raises the central problems: formalism, measurement, non-locality, and causality. The main positions on these subjects are presented and critically analysed. The aim is to show that the main schools can converge on a core interpretation.

The second aspect concerns Foundations. Here it is shown that the whole theory can be grounded on information theory. The distinction between information and signal leads us to integrating quantum mechanics and relativity. Category theory is presented and its significance for quantum information shown; the logic and epistemological bases of the theory are assessed.

Of relevance to all physicists and philosophers with an interest in quantum theory and its foundations, this book is destined to become a classic work.

Gennaro Auletta is a researcher at the University of Cassino and Aggregate Professor at the Pontifical Gregorian University. His fields of interest are Foundations and Interpretation of Quantum Mechanics, Quantum Information, System Biology, Cognitive Biology, Philosophy of Nature, Logic. Auletta is author and editor of 17 books and more than 100 papers. His books include: Foundations and Interpretation of Quantum Mechanics: A Critical-Historical Analysis of the Problems and a Synthesis of the Results, World Scientific, 2000, a very complete historical and critical assessment of the field; Quantum Mechanics, Cambridge, University Press, 2009 (with M. Fortunato and G. Parisi), an advanced textbook; and Quantum Mechanics for Thinkers (with Shang-Yung Wang), Singapore, Pan Stanford Publications, 2014, a textbook addressed to people who are beginners or lack formal mathematical knowledge (the necessary math is explained step by step starting form high-school notion).

Preface 5
Introduction 6
Contents 9
Abbreviations 14
List of Figures 15
List of Tables 20
1 Summary of the Basic Elements of the Theory 22
1.1 The Beginning of Quantum Mechanics 22
1.1.1 From the Classical to the Quantum World 22
1.1.2 The Quantum Postulate and Matter's Discontinuity 26
1.1.3 The Road to the Schrödinger Equation 30
1.2 The Basic Principles of Quantum Mechanics 45
1.2.1 The Superposition Principle 45
1.2.2 The Quantisation Principle 51
1.2.3 Physical Observables and Different Representations 65
1.2.4 Commutativity and Uncertainty Relations 82
1.2.5 Unitary Transformations and Symmetries 109
1.3 Some Further Principles 116
1.3.1 Pauli's Exclusion Principle and Spin 116
1.3.2 The Correspondence Principle 126
1.3.3 The Complementarity Principle 129
1.4 Density Operator and Compound Systems 131
1.4.1 Pure and Mixed States 131
1.4.2 Entangled and Product States 137
1.4.3 Total and Marginal States 141
1.5 Summary 145
References 145
2 The Main Problems 150
2.1 Quantum-Mechanical Formalism 150
2.1.1 Two Pictures of Quantum Dynamics 150
2.1.2 Probability and Interference 160
2.1.3 What Does the Quantum-Mechanical Formalism Tell Us? 171
2.2 The Measurement Problem 171
2.2.1 It is Not a Problem for Classical Physics 171
2.2.2 It is a Double Problem for Quantum Mechanics 173
2.2.3 von Neumann's Problem 177
2.2.4 What Are the Consequences? 182
2.2.5 Schrödinger Cat 183
2.3 The Problem of Non-locality 185
2.3.1 The Paradox Proposed by Einstein–Podolsky–Rosen 185
2.3.2 Classical Physics and Locality 192
2.3.3 Reality and Correlations 208
2.3.4 Possible Replies to EPR 212
2.4 The Problem of Causality 212
2.4.1 Classically 212
2.4.2 Quantum-Mechanically 216
2.4.3 Delayed Choice 222
2.5 Summary of the Chapter 227
References 228
3 The Main Interpretations 235
3.1 Solutions to the Measurement Problem 236
3.1.1 Subjectivist Interpretation 236
3.1.2 Objectivist Interpretation 246
3.1.3 Role of the Environment 255
3.1.4 Solution of the Cat's Paradox 264
3.1.5 Summarising 267
3.2 Formalism and Reality: Information 267
3.2.1 Objectivism 267
3.2.2 A Formalism That Denotes a Reality? 268
3.2.3 Dealing with Information 281
3.2.4 Two Points of View on Entropy and Information 291
3.3 Hidden Variables and Non-locality 295
3.3.1 Logical Restatement of the EPR Argument 295
3.3.2 Bohr's Reply to EPR 297
3.3.3 Schrödinger's Reply to EPR 302
3.3.4 Hidden Variables 305
3.3.5 Bell Inequalities for Testing EPR 320
3.3.6 Entanglement Swapping, Teleportation, Quantum Cryptography 328
3.3.7 What Is Non-separability 340
3.4 Back to the Problem of Causality 353
3.4.1 Form, Structure and Information 353
3.4.2 Correlations and Causal Constraints 359
3.4.3 Potentiality 366
3.5 Summary 372
References 373
4 Quantum Computation 384
4.1 A Reversible Multipath Computation 384
4.2 Quantum Gates 391
4.2.1 The Basic Gates 391
4.2.2 Generation of States 395
4.2.3 Relations Among Gates 398
4.3 Quantum Algorithms for Computing 403
4.3.1 Deutsch's Algorithm 403
4.3.2 Shor's Theorem 406
4.3.3 Grover's Algorithm 408
4.4 Heisenberg Picture and Teleportations 411
4.4.1 Heisenberg Picture for Computation 411
4.4.2 Generalised Teleportation 414
4.4.3 Logic Gate Teleportation 416
4.5 Energy and Time in Quantum Computation 420
4.6 Summary 421
References 422
5 Ontological Ascription and Operations 424
5.1 Quantum Events and Features 424
5.1.1 Quantum Events 424
5.1.2 Quantum Features 432
5.1.3 Quantum Features and Discord 448
5.1.4 Again on Complementarity 454
5.1.5 A Participatory Universe: Relativity and Quantum Mechanics 459
5.2 Three Subsequent Steps in the Measurement Process 464
5.2.1 General Considerations 464
5.2.2 Preparation 465
5.2.3 Premeasurement and Reversibility 469
5.2.4 Detection 479
5.2.5 Generalised Operations 500
5.2.6 Some Lessons 505
5.3 Four Convergent Interpretations 508
5.4 Summary 510
References 511
6 Information and Signal Exchanging in Universal Network 516
6.1 A Quantum Theory of Information 517
6.1.1 Information is Conserved in Our Universe 517
6.1.2 No-programming Theorem 523
6.1.3 No-Bit Commitment 526
6.1.4 Information Accessibility 529
6.1.5 Final Considerations 531
6.2 Signal Exchanging 535
6.2.1 Channels for Exchanging Information 536
6.2.2 No Information Acquisition Without Disturbance 539
6.2.3 Informational Completeness and Tomography 545
6.2.4 Green's Functions, Path Integrals, Quantum Trajectories 556
6.2.5 Information Sources, Causality, Reversibility 566
6.3 Networks 577
6.3.1 D-Shaped Circuits 577
6.3.2 Error Correction 579
6.3.3 Teleportation and Entanglement Swapping as Example of POVM Networks 586
6.3.4 Information Selection, Information Sharing, Information Acquiring 593
6.4 Quantum Mechanics Out of Six Informational Principles 600
6.4.1 Principle of Causality 601
6.4.2 Atomicity of the Composition 605
6.4.3 Perfect Discriminability 606
6.4.4 Local Discriminability 606
6.4.5 Ideal Compression 607
6.4.6 Purification 609
6.5 Summary 612
References 613
7 Quantum Mechanics, Fields and Geometry 617
7.1 Fields, Matters, Geometry 618
7.1.1 Classical Electromagnetic Field 618
7.1.2 Second Quantisation 624
7.1.3 Quantum-Field Theory 630
7.1.4 Matters 645
7.1.5 A Basic Exploration of General Relativity 652
7.2 Space-time, Gravity, Signals 668
7.2.1 Quantum and Space-time 668
7.2.2 Loop Quantum Gravity and Entropic Gravity 677
7.2.3 A Dynamical View 688
7.3 Emerging World 692
7.3.1 The Hydrogen Atom 693
7.3.2 Approximation Methods 708
7.3.3 The Emergence of the Molecular World 713
7.4 Summary of the Chapter 729
References 730
8 Category Theory and Quantum Mechanics 735
8.1 Category Theory 735
8.1.1 Introduction 735
8.1.2 Preliminary Notions: Sets and Maps 737
8.1.3 Categories and Functors 745
8.1.4 Universal Constructions 757
8.1.5 Natural Transformations 763
8.1.6 Category Theory and Quantum Information 769
8.2 Logic Assessment: Boolean Algebra and Quantum Mechanics 775
8.2.1 Basic Notions 775
8.2.2 Combinatorial Approach 780
8.2.3 Building Logical Spaces 789
8.2.4 Is Quantum Logic Non-classical? 800
8.3 Epistemological–Gnoseological Assessment 804
8.3.1 Physical (and Operational) Connection 805
8.3.2 Inferential Connection 817
8.3.3 Interpreted and Uninterpreted Ontology 837
8.4 Summary 846
References 847
Bibliography 854
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0File size: 13477399 bytesOptimized: noPDF version: 1.4 854
Author Index 856
Subject Index 865

Erscheint lt. Verlag	17.8.2019
Zusatzinfo	XXVI, 863 p. 218 illus., 43 illus. in color.
Sprache	englisch
Themenwelt	Geisteswissenschaften ► Philosophie ► Erkenntnistheorie / Wissenschaftstheorie
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Boolean algebra • entanglement swapping • entropic quantum gravity • EPR states • error correction • interpretation and philosophy of quantum mechanics • Loop Quantum Gravity • Quantum information • Quantum Measurement • quantum teleportation • randomness of quantum events
ISBN-10	3-030-16649-X / 303016649X
ISBN-13	978-3-030-16649-6 / 9783030166496

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