Entanglement, Information, and the Interpretation of Quantum Mechanics (eBook)

Gregg Jaeger (Autor)

eBook Download: PDF

2009 | 2009
XIV, 307 Seiten
Springer Berlin (Verlag)
978-3-540-92128-8 (ISBN)

Infos

Entanglement was initially thought by some to be an oddity restricted to the realm of thought experiments. However, Bell's inequality delimiting local - havior and the experimental demonstration of its violation more than 25 years ago made it entirely clear that non-local properties of pure quantum states are more than an intellectual curiosity. Entanglement and non-locality are now understood to ?gure prominently in the microphysical world, a realm into which technology is rapidly hurtling. Information theory is also increasingly recognized by physicists and philosophers as intimately related to the foun- tions of mechanics. The clearest indicator of this relationship is that between quantum information and entanglement. To some degree, a deep relationship between information and mechanics in the quantum context was already there to be seen upon the introduction by Max Born and Wolfgang Pauli of the idea that the essence of pure quantum states lies in their provision of probabilities regarding the behavior of quantum systems, via what has come to be known as the Born rule. The signi?cance of the relationship between mechanics and information became even clearer with Leo Szilard's analysis of James Clerk Maxwell's infamous demon thought experiment. Here, in addition to examining both entanglement and quantum infor- tion and their relationship, I endeavor to critically assess the in?uence of the study of these subjects on the interpretation of quantum theory.

After graduating in mathematics, philosophy, and physics at the University of Wisconsin-Madison, Gregg Jaeger undertook his doctoral work in physics at Boston University under Abner Shimony, with whom he discovered new complementarity relations in quantum interferometry. He currently holds a professorship at Boston University, where he has offered courses in the mathematics, natural science, and philosophy departments. His recent research has focused on decoherence, entanglement theory, quantum computing, and quantum cryptography.

Inhalt

Preface 7
Acknowledgments 11
Contents 12
1 Superposition, Entanglement, and Limits of Local Causality 14
Quantum Interference 15
Quantum Indeterminacy and Uncertainty 19
Quantum States and Entanglement 25
Quantum Entanglement Measures 37
Surprising Implications of Entanglement 40
The EPR Program and Absence of Local Causality 45
Problems with Hidden-Variables Models 50
Bell's Theorem and Independence Conditions 53
Conditions Contradicted by Quantum Mechanics 57
Operations, Communication, and Entanglement 60
2 Quantum Measurement, Probability, and Logic 67
Logic and Mechanics 73
Probability and Quantum Mechanics 80
The Completeness of Quantum Mechanics 83
Problems with Measurement in Quantum Mechanics 86
Elements of Quantum Measurement Theory 90
Advances in Quantum Measurement Theory 98
Schrödinger's Cat and Wigner's Friend 101
3 Interpretations of Quantum Mechanics 107
Interpretation and Metaphysics 116
The Basic Interpretation 129
The Copenhagen Interpretation 136
Orthodoxy and Explanation in Quantum Physics 148
The Collapse-Free Approach 151
The Naive Interpretation 177
The Radical Bayesian Interpretation 182
The Process interpretation 191
Interpretational Underdetermination 197
4 Information and Quantum Mechanics 201
The Theory of Information 206
The Quantum Theory of Information 212
Entropy in Quantum Measurement Theory 221
Quantum Communication and Its Limitations 223
Quantum Information Processing and Speedup 227
Protocols and the Nature of Quantum Information 236
Informational Interpretations of Quantum Mechanics 244
Entanglement `Thermodynamics' 257
Information and Entanglement 260
The Great Arc 267
A Appendix 270
Mathematical Elements 270
The Standard Postulates 273
The Dirac Notation 274
The Classification of Entangled States 275
Elements of Traditional and Quantum Logic 278
C*-Algebras 280
References 281
Index 304

Produkt-Details

• Erscheint lt. Verlag: 12.6.2009
• Reihe/Serie: The Frontiers Collection
• Reihe/Serie: The Frontiers Collection
• Zusatzinfo: XIV, 307 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Geisteswissenschaften ► Philosophie ► Erkenntnistheorie / Wissenschaftstheorie
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
• Themenwelt: Technik
• Schlagworte: Applications of quantum phenomena • Entanglement and non-locality • Philosophy of quantum mechanics • Probability • quantum entanglement explained • Quantum information • Quantum information processing • quantum mechanics • Quantum paradoxes • Technology and quantum physics
• ISBN-10: 3-540-92128-1 / 3540921281
• ISBN-13: 978-3-540-92128-8 / 9783540921288