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Quantum Reality

Theory and Philosophy

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## Book Description

Probably the most successful scientific theory ever created, quantum theory has profoundly changed our view of the world and extended the limits of our knowledge, impacting both the theoretical interpretation of a tremendous range of phenomena and the practical development of a host of technological breakthroughs. Yet for all its success, quantum theory remains utterly baffling.

**Quantum Reality: Theory and Philosophy** cuts through much of the confusion to provide readers with an exploration of quantum theory that is as authoritatively comprehensive as it is intriguingly comprehensible. Requiring no more than school level physics and mathematics background, this volume requires only an interest in understanding how quantum theory came to be and the myriad ways it both explains how our universe functions and extends the reach of human knowledge.

Written by well-known physics author and teacher Dr. Jonathan Allday, this highly engaging work:

- Presents a thorough grounding in the theoretical machinery of quantum physics
- Offers a whistle-stop tour through the early part of the 20
^{th}century when the founding fathers of quantum theory forever altered the frontiers of human thought - Provides an example-filled interpretation of the theory, its applications, and its pinnacle in quantum field theory (QFT), so crucial in shaping ideas about the nature of reality
- Separates fact from speculation regarding quantum physics’ ability to provide a starting point for philosophical queries into ultimate understanding and the limits of science

The world beneath the one that we experience with our senses is profoundly mysterious, and while we may never completely unravel that mystery, quantum theory allows us to come closer than ever to understanding where the science leaves off and the mystery begins. **Quantum Reality: Theory and Philosophy** makes that understanding accessible to anyone possessing a quest for knowledge and a sense of awe.

## Table of Contents

Preface

Introduction

Author

Part I

Our First Quantum Object: Light

Some Opening Thoughts

A Little Light Reading

Lasers and Video Cameras

Photons

An Interference Experiment with Photons

Interference as a Wave Effect

Mach–Zehnder with Photons

Delayed Choice

Summary

Endnotes

Interlude 1: Another Interference Experiment

Particles

Electrons

The Electron Gun

The Stern–Gerlach Experiment

Turning Things Round

Things Get More Puzzling

So, Where Did It Go?

What Does It All Mean?

Some Indications with Other Particles

The Long and the Short of It

Summary

Endnotes

Quantum States

Where Are We Now?

Describing Classical Systems

Chaos

Describing Quantum Systems

Specific Example: Mach–Zehnder Again

What’s in a Number?

Probability Amplitudes

States in Stern–Gerlach Experiment

General Stern–Gerlach States

Some Further Thoughts

What Are Quantum States?

Endnotes

Amplitudes

More on Amplitudes

Change of Basis

Dirac Notation

Orthogonal Bases

New Light Through…

Going the Other Way

Endnotes

Measurement

Embracing Change

Types of States

Eigenstates

Mixed States

Expectation Values

Operators

How States Evolve

Why Is State Reduction Necessary?

Behind the Veil

Determinism and Free Will

Endnotes

Interlude 2: The Complex Plane

Magnitude and Phase

Multiplying Complex Numbers

Next Phase

And Lastly…

Apologies

Endnotes

Interference

How Science Works

The Double-Slit Experiment

The Double Slit with Electrons

Wave/Particle Duality

Wave Nature of Electrons

Double-Slit Amplitudes

Phase and Physics

An Experiment with Phase

The Interference Term

Last Thoughts

Endnotes

The Free Particle

The Position Basis (And a Useful Abbreviation)

Continuous Bases

The Amplitude for a Free Particle

Wavelength

Frequency

What Does the Amplitude Tell Us about the Motion of a Free Particle?

Amplitudes, Energy, and Momentum

Energy and Momentum Eigenstates

Where Next?

Endnotes

Identical Particles

Some Opening Thoughts

Particle Dodgems

Emphasizing the Weird

The Moral of the Story

States of More than One Particle

Identical Particles

States in Real World

Final Thoughts

Endnote

Scattering Identical Bosons

Scattering

The Same, but Different: Identical Particles

Using the Whole Detector

And Another Way…

Transitions Away from States

What Does It All Mean?

Lasers

Bose–Einstein Condensates

Einstein’s Argument

Endnotes

Interlude 3: Matrix Operators

Endnote

Spin

Fermions, Bosons, and Stern–Gerlach Magnets

Angular Momentum

Angular Momentum in Quantum Theory

Magnetic Moments

The Magnetic Moment of an Electron

Intrinsic Angular Momentum

Spin Operators

Fermions and Bosons

In Closing

Endnotes

Fermion States

Exchange and Rotation

Rotational Symmetry of States

Reversing the Polarity of the Neutron Flow

Coffee Mugs and Quantum States

Spin, Symmetry, and Exchanges

Time

Spinning Things Round

Time for Some Bullet Points

Boson Spin States

More on Time Reversal

Time-Reversed Boson States

What Just Happened?

Endnotes

Wave Functions

Representations

Infinite Expansions

Wave Functions and State Functions

Observables

The Problem of Momentum

Obtaining Momentum

Operators and Representations

So What Can We Do with pˆ x?

Position Operator

Energy Operator

The Equations of Quantum Theory

ˆE and ˆH

Stationary States

Conclusions

Endnotes

Uncertainty

Expectation Is Not Enough

Heisenberg’s Principle

So What?

I’m Not Sure What Uncertainty Means…

Yet More Uncertainty

Conjugation

Time, Again…

Energy/Time Uncertainty

Final Musings

Endnotes

Interlude 4: Heisenberg’s Equation

Stationary States

Energy–Time Uncertainty

Endnote

Part II

Genealogy

The Scientific Community

"It Was the Best of Times, It Was the Worst of Times"

Endnote

Planck and Einstein

Where to Start?

Planck’s Life

Planck Enters Research

Planck’s Formula for Black Body Spectra

Einstein

Quantization of Light

Photoelectric Effect

Enter the Photon

Bosons

Final Thoughts

Endnotes

Niels Bohr

The Godfather

Early Life

Atomic Theory

Atomic Spectra

Bohr’s Atom

Developments

Complementarity

Extensions

Later Life

Endnotes

Werner Heisenberg

Early Days

The Development of Quantum Theory

Cloud Chambers

The Uncertainty Principle

Quantum Concepts

Later Life

Endnotes

Erwin Schrödinger

Beginnings

Electron Diffraction

Enter the Wave Equation

Matter Waves

So What Is Ψ?

Nobel Prizes

Schrödinger’s Philosophy

Endnotes

Paul Dirac

Dirac’s Contributions to Quantum Physics

Dirac the Person

Dirac’s Views on the Meaning of Quantum Theory

Endnotes

Conclusions

Endnotes

Part III

Applications of Quantum Theory

A Particle in a Box

Another Brick in the Wall…

Fixing the Momentum

Energy Eigenstates

Time Factor

Normalization

Two-Dimensional and Three-Dimensional Boxes

Hydrogen Atom

A Box Containing More than One Electron

White Dwarf Stars

Wave Packets

That’s All, Folks…

Endnotes

Entanglement

Is Quantum Theory Complete?

The EPR Argument

Follow-Up by David Bohm

Bohr’s Reply to the EPR Argument

Einstein and Bohr

Schrödinger Introduces Entanglement

Entanglement and Measurement

That Damned Cat

John Bell and Bohm’s EPR

Bell’s Formula

Aspect’s Experiment

Implications

Endnotes

Interlude 5: Density Operator

Great Expectations

Why Bother?

Density Operator and EPR/Bohm Experiments

Representing a State

Density Operator and Entangled States

The Density Matrix and the Measurement Problem

Endnotes

Interpretations

What Is an Interpretation?

A Collection of Problems

The Nature of Probability

State Reduction

Entanglement

Measurement

Carnegie Hall

Endnotes

The Copenhagen Interpretation

Bohr’s Influence

Bohr’s View of Quantum Theory

Heisenberg and Potentia

Von Neumann and Measurement

Mind of an Observer

The Deep End…

Conclusions

Endnotes

The Many Worlds Interpretation

Criticisms of the Copenhagen

Interpretation

The Problem of the Cut

Problem of Collapse

The Many Worlds Interpretation

Relative States

Measurement Records

And the Next One…

The Ontological Step

Many Worlds Arrives

Many Worlds Matures

The Nature of Probability

State Reduction

Entanglement

Measurement

Criticisms of the Many Worlds View

Time Thoughts

Endnotes

Other Interpretations

Being in Two Minds about Something…

Mindless Hulks…

The Advantages of Having More than One Mind

The Ideas of David Bohm

Ontological Interpretation

Bohm’s Version of Schrödinger Equation

The Quantum Potential in Action

Probability

Quantum Potential and the Double-Slit

Experiment

Quantum Potential and the Particle in a Box

Wave Function Collapse

Reactions to Bohm’s Theory

Consistent Histories

Projection Operators

Histories

Histories and Double Slits

Environmental Imprint

Histories in Cosmology

What Have We Gained?

Endnotes

Quantum Field Theory

Why Are We Doing This?

Taking Identical Particles Seriously

Particle Labels

Substance Abuse

States in Quantum Field Theory

Fock States

Up and Down We Go…

Round and Round We Go…

The Vacuum

Operators Representing Observables

The Story So Far

Fermions and Bosons

Change of Basis

Basis for Progress

So Why Is It Called Quantum Field Theory?

Wave–Particle Duality

Interactions in Quantum Field Theory

Interaction Operators

Interaction Potentials

Vacuum Fluctuations

Number Operators Again

Fields and Numbers

Endnotes

Personal Conclusions

Appendix A: List of Important Rules

Appendix B: Glossary

Appendix C: Useful Mathematics

Appendix D: Bibliography

Index

## Reviews

… a good and thorough presentation of the philosophical issues that have come so much to the fore in recent decades. This can in many ways stand among the best treatments of this side of the subject at the non-specialist level. …

—Contemporary Physics, Vol. 52, No. 1, January 2011

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