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Quantum Paradoxes: Quantum Theory for the Perplexed

ISBN: 978-3-527-40391-2
299 pages
April 2005
Quantum Paradoxes: Quantum Theory for the Perplexed (3527403914) cover image
A Guide through the Mysteries of Quantum Physics!
Yakir Aharonov is one of the pioneers in measuring theory, the nature of quantum correlations, superselection rules, and geometric phases and has been awarded numerous scientific honors. The author has contributed monumental concepts to theoretical physics, especially the Aharonov-Bohm effect and the Aharonov-Casher effect.
Together with Daniel Rohrlich, Israel, he has written a pioneering work on the remaining mysteries of quantum mechanics. From the perspective of a preeminent researcher in the fundamental aspects of quantum mechanics, the text combines mathematical rigor with penetrating and concise language. More than 200 exercises introduce readers to the concepts and implications of quantum mechanics that have arisen from the experimental results of the recent two decades.
With students as well as researchers in mind, the authors give an insight into that part of the field, which led Feynman to declare that "nobody understands quantum mechanics".

* Free solutions manual available for lecturers at www.wiley-vch.de/supplements/
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1 The Uses of Paradox.

1.1 Paradox in Physics.

1.2 Errors.

1.3 Gaps.

1.4 Contradictions.

1.5 Overview of the Book.


2 How to Weigh a Quantum.

2.1 Why does the Color of the Light Change?

2.2 Quanta.

2.3 Uncertainty Relations.

2.4 The Clock-in-the-Box Paradox.

2.5 From Inconsistency to Incompleteness.


3 Is Quantum Theory Complete?

3.1 The Einstein–Podolsky–Rosen Paradox.

3.2 Polarized Photons.

3.3 Quantum States and Observables.

3.4 Bell’s Inequality.

3.5 Paradox and Beyond.


4 Phases and Gauges.

4.1 Two Paradoxical Procedures.

4.2 Classical and Quantum Phases.

4.3 Phase Meets Gauge.

4.4 The Aharonov–Bohm Effect.

4.5 Quantum Consistency and the Aharonov–Bohm Effect.

4.6 Flux Quantization.

4.7 Magnetoresistance.

4.8 Non-Abelian Phases.


5 Modular Variables.

5.1 A Lattice of Solenoids.

5.2 Non-overlapping Wave Packets.

5.3 Modular Momentum.

5.4 The xmod, pmod Representation.

5.5 Intimations of Nonlocality.


6 Nonlocality and Causality.

6.1 Causality and a Piston.

6.2 Quantum Effects Without Classical Analogues.

6.3 Modular Energy.

6.4 Reconciling the Irreconcilable.


7 Quantum Measurements.

7.1 The Velocity Paradox.

7.2 A Quantum Measurement Paradigm.

7.3 Quantum Measurements and Uncertainty Relations.

7.4 Paradox Lost.


8 Measurement and Compensation.

8.1 Paradox Regained.

8.2 Compensating Forces.

8.3 Quantum Measurements of Noncanonical Observables.

8.4 Measuring the Electric Field.

8.5 Energy and Time.


9 Quantum Cats.

9.1 Schr¨odinger’s Cat.

9.2 A Quantum Catalyst.

9.3 Quantum Concatenations.

9.4 A Quantum Catalog.


10 A Quantum Arrow of Time?

10.1 A Quantum Card Trick.

10.2 Time Reversal.

10.3 The Aharonov–Bergmann–Lebowitz Formula.

10.4 The Arrow of Time Revisited.

10.5 Boundary Conditions on the Universe.


11 Superselection Rules.

11.1 Superselection Rule for Angular Momentum?

11.2 T and Spin.

11.3 The Wick–Wightman–Wigner Argument.

11.4 Everything is Relative.

11.5 Superposing Charge States.


12 Quantum Slow Dance.

12.1 A Watched Pot Never Boils.

12.2 The Adiabatic Approximation.

12.3 Feynman Paths.

12.4 Classical Analogues.


13 Charges and Fluxons.

13.1 Hidden Momentum?

13.2 Duality of the Aharonov–Bohm Effect.

13.3 The Aharonov–Bohm Effect and Berry’s Phase.

13.4 The Aharonov–Casher Effect.


14 Quantum Measurements and Relativity.

14.1 Collapse and Relativity.

14.2 Relativistic Constraints on Measurements.

14.3 Nonlocal Measurements.

14.4 Which Nonlocal Operators are Measurable?

14.5 Measuring a Nonlocal Operator.

14.6 Collapse and Relativity Revisited.


15 How to Observe a Quantum Wave.

15.1 Dipole Paradox.

15.2 How not to Observe a Quantum Wave.

15.3 Protective Measurements.

15.4 Galilean Dialogue.

15.5 Protective Measurements and Causality.

15.6 Towards Quantum Field Theory.


16 Weak Values.

16.1 A Weak Measurement.

16.2 A Paradox of Errors.

16.3 Pre- and Postselected Ensembles.

16.4 Weak Measurements and Weak Values.

16.5 A Quantum Shell Game.

16.6 The Quantum Walk.

16.7 Faster than Light.

16.8 Galilean Dialogue.


17 Weak Values and Entanglement.

17.1 Interaction-free Paradox.

17.2 A Grin Without a Cat.

17.3 Alice and Bob in Wonderland.

17.4 Galilean Dialogue.

17.5 Complex Weak Values.


18 The Quantum World.

18.1 Weak Measurements and Interference.

18.2 From Amplitudes to Probabilities.

18.3 The Fate of the Universe.

18.4 The Role of h.

18.5 Causality and Nonlocality as Axioms.

18.6 Causality, Nonlocality and Scaling.

18.7 What is the Quantum World?



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Professor Yakir Aharonov, born in 1932, studied physics at Technion in Haifa, Israel, and Bristol University, England, where he received his PhD in 1960. He currently works as Professor of Physics at the University of Tel Aviv and the University of South Carolina. Professor Aharonov's research interests are nonlocal and topological effects in quantum mechanics, relativistic quantum field theories, and interpretations of quantum mechanics. Professor Aharonov is an elected member of the U.S. National Academy of Sciences.

Dr. Daniel Rohrlich, born in 1954, received his Ph.D. in physics from the State University of New York at Stony Brook in 1986. He currently works as a research scientist at the Weizmann Institute in Rehovot, Israel. His research interests lie in the fields of quantum information, fundamental aspects of quantum mechanics, path integrals, and experimental mesoscopic physics.

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"This is a wonderful book for everyone who wishes to deep the knowledge and understanding of the foundations of quantum mechanics.[...] As a whole, "Quantum Paradoxes. Quantum Theory for the Perplexed" is an exclusively rare and inspirational book on quantum mechanics that explores the never-ending mysterious quantum paradoxes to bring the readers to the QuantumWonderland. This book I do believe should be recommended to everyone."
Zentralblatt MATH
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