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