The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics: Modern Research on the Foundations of Quantum Mechanics

by George Greenstein, Arthur G. Zajonc

Overview

The Quantum Challenge, Second Edition is an engaging and thorough treatment of the extraordinary phenomena of quantum mechanics, and of the enormous challenge they present to our conception of the physical world. Traditionally, the thrill of grappling with such issues is reserved for practicing scientists, while physical science, mathematics, and engineering students are often isolated from these inspiring questions. This book was written to remove this isolation. Greenstein and Zajonc present the puzzles of quantum mechanics using vivid references to contemporary experiments. The authors focus on the most striking and conceptually significant quantum phenomena, together with a clear theoretical treatment of each. The depth and extent of the challenge of quantum mechanics becomes increasingly compelling as they move from the simplest experiments involving single photons or particles, to the famous Einstein-Podolsky-Rosen and Bell's Theorem, and then to macroscopic quantum phenomena. This text was designed for advanced undergraduate science, mathematics, and engineering students. Possible course titles include: Quantum Physics and Quantum Mechanics. © 2006 | 296 pages

Product Details

ISBN-13:	9780763724702
Publisher:	Jones & Bartlett Learning
Publication date:	08/11/2005
Series:	Physics and Astronomy (Hardcover)
Edition description:	2E
Pages:	296
Product dimensions:	0.67(w) x 7.50(h) x 9.25(d)

About the Author

George Greenstein is the Sidney Dillon professor of astronomy at Amherst College. His research has centered on relativistic astrophysics, and he is currently interested in non-traditional approaches to science education.

Arthur G. Zajonc is professor of physics at Amherst College. His research has focused on laser and atomic physics, the foundations of quantum mechanics, and the relationship between science and the humanities.

Table of Contents

	Preface	xi
	Prologue	xiii
1	Matter Waves	1
1.1	An Experiment	1
1.2	A Second Experiment	5
1.3	Locality	7
1.4	Beyond the Electron	8
	Neutrons	8
	Atoms	9
	Bose-Einstein Condensates	9
	The Experiment	12
1.5	Quantum Theory of Two-Slit Interference	13
1.6	Critique of the Quantum-Mechanical Account	18
2	Photons	23
2.1	Do Photons Exist?	24
	Detection and the Quantum of Light	24
	Photoelectric Effect	24
	Anticoincidences	28
	The Hanbury-Brown and Twiss Experiment	30
	Photons at Last	34
	Remarks	36
2.2	Wave-Particle Duality for Single Photons	37
	The Mystery of Wave-Particle Duality	38
	Delayed Choice	39
	Comments	43
3	The Uncertainty Principle	45
3.1	The Pfleegor-Mandel Experiment	45
	Two Lasers, One Photon	45
	The Heisenberg Uncertainty Principle	47
	Uncertainty in the Pfleegor-Mandel Experiment	50
3.2	Reflections on the Uncertainty Principle	52
	Quantum Uncertainty versus Classical Ignorance	52
	Interpretation of the Uncertainty Principle	53
	The Uncertainty Principle and Causality	53
	The Uncertainty Principle and Descriptions of Natural Phenomena	55
3.3	Some Consequences of the Uncertainty Principle	56
	Atoms	57
	Nuclei	58
	Trajectories	58
3.4	The Energy-Time Uncertainty Relation	59
	Average Properties of Systems	59
	Lifetimes and Line Widths	61
	Time and Frequency Standards	62
	More on Causality: The Uncertainty Principle and an Ambiguity in Time	63
	Origin of the Energy-Time Uncertainty Relation	67
	Comment	71
3.5	Squeezed Light and the Detection of Gravitational Radiation	72
	Gravitational Radiation	72
	Squeezed States of the Simple Harmonic Oscillator	73
	Squeezed States of Light	79
3.6	Quantum Non-Demolition Measurements	83
	Back Action and the Detection of Gravitational Radiation	83
	Seeing a Single Photon Without Destroying It	86
4	Complementarity	91
4.1	Bohr's Discovery of Complementarity	92
	Como, 1927	94
4.2	Einstein's Attack on Complementarity	95
	The Solvay Meetings: Complementarity between Which-Path Information and Interference	96
	Complementarity in the Energy-Time Uncertainty Relation	99
4.3	The New Paradigm: Information	102
	Quantum Beats	102
	Theory of Quantum Beats: Complementarity	105
	Orthogonality and the Role of Information in Quantum Beats	108
	Partial Information	110
4.4	Is Complementarity Enforced by the Uncertainty Principle?	113
	An Experiment	113
	The Aharonov-Bohm Effect	117
	Momentum Kicks in Interference Experiments	120
	Quantum Momentum Transfer	120
4.5	Concluding Remarks	121
5	The EPR Paradox and Bell's Theorem	123
5.1	The EPR Argument	125
	The Argument	127
	Locality	130
	Reality and Hidden Variables	130
5.2	The BKS Theorem and Contextuality	133
	Sketch of the BKS Proof	133
5.3	Hidden-Variable Theories	135
	Elementary Example of a Hidden-Variable Theory	137
5.4	Bell's Theorem	139
	Proof of Bell's Theorem	140
	Mermin's "Local Reality Machine"	142
	Discussion	146
6	Testing Bell's Inequalities: Entangled States	149
6.1	Tests of Bell's Inequalities	150
	Early Work	150
	Two-Photon Entangled States	151
	Linear Polarization	153
	The Aspect Experiments	157
	Comments	161
6.2	Bohm's Nonlocal Hidden-Variable Theory	162
6.3	The Mystery of the EPR Correlations	166
6.4	Does Quantum Nonlocality Violate the Principle of Relativity?	167
6.5	Quantum Nonlocality: A New Source and a New Experiment	169
6.6	The Greenberger-Horne-Zeilinger Theorem	173
	Quantum-Mechanical Analysis	174
	Local Realism Analysis	176
	Experimental Test	177
	Comments	180
6.7	Comments on Quantum Nonlocality	183
7	Schrodinger's Cat	185
7.1	What Is the Cat Paradox?	186
7.2	Superpositions and Mixtures: A More Technical Statement of the Cat Paradox	187
7.3	Further Discussion of the Difference Between Superpositions and Mixtures: Spin	188
7.4	Why Is Quantum Behavior Not Observed in the Large-Scale World?	189
	Interference	190
	Uncertainty Principle	190
	Quantum Tunneling	190
7.5	Decoherence	193
7.6	Watching Decoherence	199
7.7	Laboratory Realizations of Macroscopic Quantum Behavior	202
	Conditions for the Existence of Macroscopic Quantum Behavior	203
	Macroscopic Quantum Tunneling: SQUIDS	205
	Macroscopic Quantum Coherence	207
	A Microscopic Analog	209
8	Measurement	215
8.1	The Measurement Problem	215
	The Collapse of the Wave Function	215
	Is the Collapse of the Wave Function Described by the Schrodinger Equation?	219
	Quantum Theory of Measurement: The Infinite Regress	222
	Termination of the Infinite Regress: The Projection Postulate	224
8.2	The Active Nature of Measurement in Quantum Mechanics	227
	Mixtures and Superpositions	227
	What Is the State of the Photon a Decaying Atom Emits?	229
	The Quantum Zeno Effect	231
8.3	Attempts to Solve the Measurement Problem	237
	Small Detectors and Big Detectors: Decoherence	237
	Does Decoherence Solve the Measurement Problem?	239
	Decoherence Can Be Undone	239
	Coherence Can Be Moved Around: The Quantum Eraser	240
	Comments	243
9	Quantum Information and Computation	245
9.1	Bits and Qubits	246
9.2	Quantum Cryptography	247
	Quantum Key Distribution Via Single-Particle Superposition	248
	Quantum Key Distribution Via Entanglement	251
9.3	Quantum Teleportation	252
	Quantum Information Cannot Be Read	253
	Quantum Teleportation	254
	Experimental Realization of Quantum Teleportation	257
	Comments	258
9.4	Quantum Computation: The Deutsch-Jozsa Algorithm	259
	An Analogy	260
	The Deutsch-Jozsa Problem	262
	Logical Operations on Quantum Registers	262
	The Deutsch-Jozsa Algorithm	264
	Logical Operations and U[subscript f]	267
	A Toy Quantum Computer	268
	A Real Quantum Computer	271
9.5	Comments on Quantum Machines	277
	Epilogue	279
Appendix	A Bibliography of Experiments for the Undergraduate Laboratory	281
	Chapter 1: Matter Waves	281
	Chapter 2: Photons	282
	Chapter 3: The Uncertainty Principle	282
	Chapter 4: Complementarity	283
	Chapter 6: Testing Bell's Inequalities: Entangled States	283
	Chapter 8: Measurement	284
	References	285
	Index	293