Quantum Reality: Theory and Philosophy

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Forward
Preface
About the Author
Introduction
I.1 Physics
I.2 Philosophy
Realists
Instrumentalists
Part 1
Chapter 1 Our First Encounter with the Quantum World: Light
1.1 Some Opening Thoughts
1.2 A Little Light Reading
1.3 Lasers and Video Cameras
1.4 Photons
1.5 An Interference Experiment
1.5.1 Interference as a Wave Effect
1.5.2 Mach–Zehnder with Photons
1.5.3 Delayed Choice
1.6 Summary
Notes
Chapter 2 Particles
2.1 Particles and Waves
2.1.1 Electrons and Electron Guns
2.2 The Stern-Gerlach Experiment
2.2.1 Turning Things Around
2.2.2 Things Get More Puzzling
2.2.3 So, Where Did It Go?
2.2.4 What Does It All Mean?
2.3 Summary
Notes
Chapter 3 Quantum States
3.1 Where Are We Now?
3.2 Describing Classical Systems
3.2.1 Chaos
3.3 Describing Quantum Systems
3.3.1 Specific Example: Mach–Zehnder Again
3.3.2 Probability Amplitudes
3.3.3 Relating Amplitudes to Probabilities
3.3.4 Amplitudes, Complex Numbers and Phase
3.3.5 States in Stern–Gerlach Experiment
3.3.6 General Stern–Gerlach States
3.3.7 Some Further Thoughts
3.4 What Are Quantum States?
Notes
Chapter 4 Amplitudes
4.1 More on Amplitudes
4.1.1 Change of Basis
4.2 Dirac Notation
4.2.1 Orthonormal Bases
4.2.2 New Light Through…
4.2.3 Going the Other Way
Notes
Chapter 5 Measurement
5.1 Embracing Change
5.2 Types of States
5.2.1 Eigenstates
5.2.2 Mixed States
5.3 Expectation Values
5.4 Operators
5.4.1 Operators and Physical Quantities
5.4.2 Classical and Quantum
5.5 How States Evolve
5.5.1 Why Is State Collapse Necessary?
5.5.2 Behind the Veil
5.5.3 Determinism and Free Will
Notes
Chapter 6 Interference
6.1 How Science Works?
6.2 The Double-Slit Experiment
6.2.1 The Double Slit with Electrons
6.2.2 Wave/Particle Duality
6.2.3 Wave Nature of Electrons
6.3 Double-Slit Amplitudes
6.3.1 Phase and Physics
6.3.2 An Experiment with Phase
6.3.3 The Interference Term
6.3.4 Amplitudes and Electron Strikes
6.4 Last Thoughts
Notes
Chapter 7 Free Particles
7.1 The Position Basis
7.2 The Amplitude for a Free Particle
7.2.1 Classical Waves
7.2.2 The Complex Wave of the Amplitude
7.2.3 Frequency
7.2.4 What Does the Amplitude Tell Us About the Motion of a Free Particle?
7.2.5 Amplitudes, Energy, and Momentum
7.3 Where Next?
Notes
Chapter 8 Identical Particles
8.1 Some Opening Thoughts
8.2 Particle Dodgems
8.2.1 Scattering Amplitudes
8.2.2 The Moral of the Story
8.3 States of More Than One Particle
8.3.1 Identical Particles
8.3.2 States in Real World
8.3.3 Overall States
8.3.4 More Than Two Particles
8.3.5 More General States
8.3.6 A More Elegant Approach
8.4 Final Thoughts
Notes
Chapter 9 Scattering Identical Bosons
9.1 Scattering
9.2 The Same, but Different: Identical Particles
9.2.1 Using the Whole Detector
9.2.2 And Another Way
9.3 Transitions Away from States
9.3.1 Spontaneous vs Stimulated
9.3.2 Lasers
9.4 Bose–Einstein Condensates
9.4.1 Einstein's Argument
Notes
Chapter 10 Spin
10.1 Fermions, Bosons, and Stern–Gerlach Magnets
10.2 Angular Momentum
10.2.1 Angular Momentum in Quantum Theory
10.2.2 Eigenstates of Angular Momentum
10.2.3 Magnetic Moments
10.2.4 The Magnetic Moment of an Electron
10.2.5 Intrinsic Angular Momentum
10.3 Spin Operators
10.3.1 Spin Matrices
10.3.2 Fermions and Bosons
10.4 Quantum Scale, Spin, Spinors and Twistors
Notes
Chapter 11 Fermion States
11.1 States, Normalization, and Phase
11.2 Exchange and Rotation
11.3 Rotational Symmetry of States
11.3.1 Reversing the Polarity of the Neutron Flow
11.3.2 Coffee Mugs and Quantum States
11.3.3 Spin, Symmetry, and Exchanges
11.4 Time
11.4.1 Spinning Things Round
11.4.2 Rotation for More Fun and Profit
11.4.3 So Spin Is?
11.5 Boson Spin States
11.5.1 More on Time Reversal
11.5.2 Time-Reversed Boson States
11.6 Deep Waters
Notes
Chapter 12 Continuous Bases
12.1 Representations
12.2 Two Issues
12.2.1 Probability Density
12.2.2 Infinite State Expansions
12.2.3 The Identity Operator
12.2.4 A Short Aside: Projection Operators
12.3 State Functions and Wave Functions
12.4 Observables
12.4.1 The Problem of Momentum
12.4.2 Momentum in Quantum Theory
12.4.3 Operators and Representations
12.4.4 Expectation Values Again
12.4.5 Operators and Variables
Notes
Chapter 13 Uncertainty
13.1 Expectation Is Not Enough
13.1.1 Developing Uncertainty
13.2 Heisenberg's Principle
13.2.1 So What?
13.2.2 I'm Not Sure What You Mean by Uncertainty…
13.3 Yet More Uncertainty
13.3.1 The Generalized Uncertainty Principle
Notes
Chapter 14 The Equations of Quantum Theory
14.1 The Schrödinger Equations
14.1.1 Ê and Ĥ
14.1.2 Stationary States
14.2 Ehrenfest's Theorem
14.2.1 The Classical Limit
14.2.2 Constants of Motion
14.3 The Energy-Time Inequality
14.3.1 I Really Don't Have the Time…
14.3.2 Energy/Time Uncertainty
14.4 Time Evolution
14.5 Conclusions
Notes
Chapter 15 Constrained Particles
15.1 A Particle in a Box
15.1.1 Another Brick in the Wall...
15.1.2 Normalization
15.1.3 Energy within the Box
15.1.4 Momentum in the Box
15.1.5 Spatial Distribution
15.1.6 Wave Packets
15.1.7 Two-Dimensional and Three-Dimensional Boxes
15.2 The Hydrogen Atom
15.2.1 Quantum Numbers for Hydrogen
15.2.2 Visualising Hydrogen State Functions
15.3 A Box Containing More Than One Electron
15.3.1 Temperature and the Fermi Gas
15.3.2 White Dwarf Stars
Notes
Part 2
Chapter 16 Genealogy
16.1 The Scientific Community
16.2 "It Was the Best of Times, It Was the Worst of Times"
Notes
Chapter 17 Planck and Einstein
17.1 Where to Start?
17.2 Planck's Life
17.3 Planck Enters Research
17.3.1 Planck's Formula for Black Body Spectra
17.4 Einstein
17.4.1 Quantization of Light
17.4.2 The Photoelectric Effect
17.4.3 Enter the Photon
17.4.4 Bosons
17.5 Final Thoughts
Notes
Chapter 18 Bohr
18.1 The Godfather
18.2 Early Life
18.3 Atomic Theory
18.3.1 Atomic Spectra
18.3.2 Bohr's Atom
18.3.3 Developments
18.4 Complementarity
18.4.1 Extensions
18.5 Later Life
Notes
Chapter 19 Heisenberg
19.1 Early Days
19.2 The Development of Quantum Theory
19.2.1 Cloud Chamber Tracks
19.2.2 The Uncertainty Principle
19.2.3 Quantum Concepts
19.3 Later Life
Notes
Chapter 20 De Broglie & Schrödinger
20.1 Beginnings
20.1.1 Electron Diffraction
20.2 Enter the Wave Equation
20.2.1 Matter Waves
20.2.2 So What Is ψ?
20.2.3 Nobel Prizes
20.3 Schrödinger's Philosophy
Notes
Chapter 21 Dirac
21.1 Dirac's Influence on Quantum Physics
21.2 Dirac, the Person
21.3 Dirac's Views on the Meaning of Quantum Theory
Notes
Chapter 22 Conclusions
Notes
Part 3
Chapter 23 Quantum Correlations
23.1 Two Threads
23.2 Is Quantum Theory Complete?
23.2.1 The EPR Argument
23.2.2 Follow-Up by David Bohm
23.2.3 Bohr's Reply to the EPR Argument
23.2.4 Einstein and Bohr
23.3 Schrödinger Introduces Entanglement
23.3.1 Entanglement and Measurement
23.3.2 The Sorry Tail of Schrödinger's Cat
23.4 John Bell and Bohm's EPR
23.4.1 Bell's Argument
23.4.2 A Toy Model
23.4.3 Bell's Formula
Experimental Correlations, S[sub(e)]
Local Hidden Variable Correlations, S[sub(H)]
Quantum Mechanical Correlations, S[sub(q)]
23.4.4 Aspect's Experiment
23.5 Implications
Notes
Chapter 24 Quantum Computing
24.1 Historical Perspective
24.2 The Fundamentals of Digital Computing
24.2.1 A Bit More Information
24.2.2 Logic Gates
24.3 Quantum Analogues
24.3.1 Qubits
24.3.2 Quantum Gates
24.3.3 The No-Cloning Theorem
24.3.4 What Makes a Quantum Computer Quantum?
24.4 Quantum Teleportation
24.4.1 Experimental Implementation
24.5 Practical Quantum Computers
Notes
Chapter 25 Density Operators
25.1 Great Expectations
25.2 Why Bother?
25.3 The Density Operator and EPR/Bohm-Type Experiments
25.3.1 Representing a State
25.3.2 The Density Operator and Entangled States
25.4 The Density Matrix and the Measurement Problem
Notes
Chapter 26 Interpretations
26.1 What is An Interpretation?
26.2 A Collection of Problems
26.2.1 The Nature of Probability
26.2.2 Reduction of the State Vector
26.2.3 Entanglement
26.2.4 Measurement
26.3 Important Theorems
26.3.1 Bell's Inequality
26.3.2 The Kochen-Specker Theorem
26.3.3 Proving the Kochen-Specker Theorem
Opening Moves
Development
Endgame
26.3.4 Consequences
26.4 Carnegie Hall
Notes
Chapter 27 The Copenhagen Interpretation
27.1 Bohr's Influence
27.2 Bohr's View of Quantum Theory
27.2.1 Classical Concepts Must Be Used to Describe the Results of Any Experiment
27.2.2 During a Measurement It Is Impossible to Separate a Quantum Object from the Apparatus
27.2.3 The Results of One Experimental Arrangement Cannot Necessarily Be Related to Another
27.2.4 Classical Explanations
27.2.5 Drawing the Threads Together
27.3 Heisenberg and Potentia
27.4 Von Neumann and Measurement
27.4.1 The Mind of an Observer
27.5 The Deep End…
27.6 Criticisms of the Copenhagen View
27.6.1 The Problem of the Cut
27.6.2 Problem of Collapse
Notes
Chapter 28 The Many Worlds Interpretation
28.1 Everett, Wheeler, Bohr & DeWitt
28.2 The Relative State Formulation
28.3 Measurement Records
28.3.1 And the Next One…
28.4 The Ontological Step
28.5 Many Worlds Arrives
28.6 Many Worlds Matures
28.6.1 The Nature of Probability
Everett's Solution
Other Approaches
Decision Theory Enters the Argument
28.6.2 State Reduction
28.6.3 Entanglement
28.6.4 Measurement
28.6.5 Bell's Inequality and the K-S Theorem
28.7 Criticisms of the Many Worlds View
28.8 Time Thoughts
Notes
Chapter 29 Assorted Alternatives
29.1 Being in Two Minds About Something…
29.1.1 Mindless Hulks
29.1.2 The Advantages of Having More Than One Mind
29.2 Objective Collapse
29.2.1 The Penrose Interpretation
Notes
Chapter 30 Consistent Histories
30.1 Frameworks
30.2 Quantum Reasoning
30.2.1 Moggies and Sample Spaces
30.2.2 Meaningless Statements
30.2.3 Contextuality
30.2.4 Non-Locality
30.3 Histories
30.3.1 Combining Histories
30.3.2 Probabilities
30.3.3 Consistent Histories
30.3.4 Histories and Mach-Zehnder
30.3.5 Measurement
30.3.6 Decoherence and the Classical World
30.3.7 Histories in Cosmology
30.4 Ontology
30.4.1 Pre-Probabilities
30.4.2 Unicity
30.4.3 Probability (Again…)
30.4.4 Other Issues
Notes
Chapter 31 The Ontological Interpretation
31.1 Physics and Philosophy
31.2 Wave and Particle
31.2.1 Bohm's Version of the Schrödinger Equation
31.2.2 The Quantum Potential Energy
31.3 Probability
31.4 Quantum Potential Energy in Action
31.4.1 Quantum Potential Energy and the Double Slit Experiment
31.4.2 Quantum Potential Energy and the Particle in a Box
31.4.3 Spin
31.4.4 Entanglement
31.5 Information and Wave Function Collapse
31.6 Deeper Waters
31.7 Reactions to Bohm's Theory
Notes
Chapter 32 Quantum Field Theory
32.1 Why Are We Doing This?
32.2 Taking Identical Particles Seriously
32.2.1 Particle Labels
32.2.2 Substance Abuse
32.3 States in Quantum Field Theory
32.3.1 Fock States
32.3.2 The Vacuum
32.3.3 Up and Down We Go…
32.3.4 Change of Basis
32.3.5 Orderly Matters
32.3.6 Fermions and Bosons
32.3.7 The Number Is Up
32.3.8 Normalization
32.3.9 Round and Round We Go…
32.3.10 Multiparticle Operators Representing Observables
32.4 Basis for Progress
32.4.1 So Why Is It Called Quantum Field Theory?
32.4.2 Wave-Particle Duality
32.5 Interactions in Quantum Field Theory
32.5.1 Interaction Operators
32.5.2 Interaction Potentials
32.6 Vacuum Fluctuations
32.6.1 Fields and Numbers
32.7 Quantum Gravity
32.7.1 Loop Quantum Gravity (LQG)
32.7.2 String Theory
32.7.3 Prospects
Notes
Chapter 33 Personal Conclusions
33.1 Popular Opinion
33.2 Quantum Reality
33.2.1 Critical Realism
33.2.2 Copenhagenism & Consistent Histories
33.2.3 Many Worlds and Many Minds
33.2.4 The Ontological Interpretation
33.2.5 Objective Collapse
33.3 Conclusions
Notes
Appendix List of Important Rules
Index