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Quantum Paradoxes: Quantum Theory for the Perplexed

Quantum Paradoxes: Quantum Theory for the Perplexed

Yakir Aharonov, Daniel Rohrlich

ISBN: 978-3-527-69541-6

Sep 2019

432 pages

$88.99

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Description

Yakir Aharonov and Daniel Rohrlich set the scene by defining the term "quantum paradoxes" and pointing out the value of taking these apparent paradoxes seriously in order to obtain a deeper understanding of the subtleties of quantum mechanics. In the following chapters the authors discuss and explain puzzling quantum-mechanical effects that cannot be understood classically such as the Heisenberg uncertainty principle, the Aharonov-Bohm effect, the quantized Hall effect and the quantized nature of light. A major focus of the book is on the measurement process in quantum mechanics which poses tremendous theoretical and experimental difficulties as each measurement disturbs, and possibly destroys, the quantum-mechanical system in question. Here the authors introduce the readers to the recent advances regarding both the theoretical understanding as well as the experimental instrumentation. The authors finish with an outlook on new interpretations of quantum mechanics.

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THE USES OF PARADOX
Paradox in Physics
Errors
Gaps
Contradictions
Overview of the Book

HOW TO WEIGH A QUANTUM
Why does the Color of the Light Change?
Quanta
Uncertainty Relations
The Clock-in-the-Box Paradox
From Inconsistency to Incompleteness

IS QUANTUM THEORY COMPLETE?
The Einstein-Podolsky-Rosen Paradox
Polarized Photons
Quantum States and Observables
Bell's Inequality
Paradox and Beyond

PHASES AND GAUGES
Two Paradoxical Procedures
Classical and Quantum Phases
Phase Meets Gauge
The Aharonov-Bohm Effect
Quantum Consistency and the Aharonov-Bohm Effect
Flux Quantization
Magnetoresistance
Non-Abelian Phases

MODULAR VARIABLES
A Lattice of Solenoids
Non-overlapping Wave Packets
Modular Momentum
The xmod, pmod Representation
Intimations of Nonlocality

NONLOCALITY AND CAUSALITY
Causality and a Piston
Quantum Effects Without Classical Analogues
Modular Energy
Reconciling the Irreconcilable

QUANTUM MEASUREMENTS
The Velocity Paradox
A Quantum Measurement Paradigm
Quantum Measurements and Uncertainty Relations
Paradox Lost

MEASUREMENT AND COMPENSATION
Paradox Regained
Compensating Forces
Quantum Measurements of Noncanonical Observables
Measuring the Electric Field
Energy and Time

QUANTUM CATS
Schrodinger's Cat
A Quantum Catalyst
Quantum Concatenations
A Quantum Catalog

A QUANTUM ARROW OF TIME?
A Quantum Card Trick
Time Reversal
The Aharonov-Bergmann-Lebowitz Formula
The Arrow of Time Revisited
Boundary Conditions on the Universe

SUPERSELECTION RULES
Superselection Rule for Angular Momentum?
T and Spin
The Wick-Wightman-Wigner Argument
Everything is Relative
Superposing Charge States

QUANTUM SLOW DANCE
A Watched Pot Never Boils
The Adiabatic Approximation
Feynman Paths
Classical Analogues

CHARGES AND FLUXONS
Hidden Momentum?
Duality of the Aharonov-Bohm Effect
The Aharonov-Bohm Effect and Berry's Phase
The Aharonov-Casher Effect

QUANTUM MEASUREMENTS AND RELATIVITY
Collapse and Relativity
Relativistic Constraints on Measurements
Nonlocal Measurements
Which Nonlocal Operators are Measurable?
Measuring a Nonlocal Operator
Collapse and Relativity Revisited

HOW TO OBSERVE A QUANTUM WAVE
Dipole Paradox
How not to Observe a Quantum Wave
Protective Measurements
Galilean Dialogue
Protective Measurements and Causality
Towards Quantum Field Theory

WEAK VALUES
A Weak Measurement
A Paradox of Errors
Pre- and Postselected Ensembles
Weak Measurements and Weak Values
A Quantum Shell Game
The Quantum Walk
Faster than Light
Galilean Dialogue

WEAK VALUE MEASUREMENTS IN EXPERIMENTS

WEAK VALUES AND ENTANGLEMENT
Interaction-free Paradox
A Grin Without a Cat
Alice and Bob in Wonderland
Galilean Dialogue
Complex Weak Values

THE QUANTUM WORLD
Weak Measurements and Interference
From Amplitudes to Probabilities
The Fate of the Universe
The Role of h/2Pi
Causality and Nonlocality as Axioms
Causality, Nonlocality and Scaling
What is the Quantum World?

NEW APPROACHES TO QUANTUM MECHANICS