The End of Time: The Next Revolution in Physics

CONTENTS

The Story in a Nutshell

Preface

Acknowledgements

PART 1 THE BIG PICTURE IN SIMPLE TERMS

CHAPTER 1 The Main Puzzles

The Next Revolution in Physics

The Ultimate Things

Getting to Grips with Elusive Time

The Properties of Experienced Time

Newton’s Concepts

Laws and Initial Conditions

Why is the Universe so Special?

CHAPTER 2 Time Capsules

The Physical World and Consciousness

Time Without Time

Time Capsules

Examples of Time Capsules

CHAPTER 3 A Timeless World

First Outline

The Crisis of Time

The Ultimate Arena

Is Motion Real?

The Big Picture

PART 2 THE INVISIBLE FRAMEWORK AND THE

ULTIMATE ARENA

CHAPTER 4 Alternative Frameworks

Absolute or Relative Motion?

An Alternative Arena

CHAPTER 5 Newton’s Evidence

The Aims of Machian Mechanics

Apparent Failure

Space and Spin

Energy

CHAPTER 6 The Two Great Clocks in the Sky

Where is Time?

The First Great Clock

The Inertial Clock

The Second Great Clock

CHAPTER 7 Paths in Platonia

Nature and Exploration

Developing Machian Ideas

Exploring Platonia

PART 3 THE DEEP STRUCTURE OF GENERAL

RELATIVITY

CHAPTER 8 The Bolt from the Blue

Historical Accidents

Background to the Crisis

Einstein and Simultaneity

The Forgotten Aspects of Time

CHAPTER 9 Minkowski the Magician

The New Arena

From Three to Four Dimensions

Are There Nows in Relativity?

CHAPTER 10 The Discovery of General Relativity

Funny Geometry

Einstein’s Way to General Relativity

The Main Advances

The Final Hurdle

General Relativity and Time

CHAPTER 11 General Relativity: The Timeless Picture

The Golden Age of General Relativity

Platonia for Relativity

Best Matching in the New Platonia

Catching up with Einstein

A Summary and the Dilemma

PART 4 QUANTUM MECHANICS AND QUANTUM

COSMOLOGY

CHAPTER 12 The Discovery of Quantum Mechanics

CHAPTER 13 The Lesser Mysteries

Introduction

The Wave Function

Interpreting the Wave Function

States Within States

The Copenhagen Interpretation

Heisenberg’s Uncertainty Principle

The Enigmatic Gem

CHAPTER 14 The Greater Mysteries

Schrödinger’s Vast Arena

Correlations and Entanglement

The EPR Paradox

Bell’s Inequalities

The Many-Worlds Interpretation

A Dualistic Picture

CHAPTER 15 The Rules of Creation

The End of Change

Creation and the Schrödinger Equation

Quantum Mechanics Hovering in Nothing

CHAPTER 16 ‘That Damned Equation’

History and Quantum Cosmology

A Simple-Minded Approach

‘That Damned Equation’

PART 5 HISTORY IN THE TIMELESS UNIVERSE

CHAPTER 17 The Philosophy of Timelessness

CHAPTER 18 Static Dynamics and Time Capsules

Dynamics Without Dynamics

Why do we Think the Universe is Expanding?

The Idea of Time Capsules: The Kingfisher

CHAPTER 19 Latent Histories and Wave Packets

Smooth Waves and Choppy Seas

History Without History

Airy Nothing and a Local Habitation

Schrödinger’s Heroic Failure

CHAPTER 20 The Creation of Records

History and Records

The Creation of Records: First Mechanism

The Prerequisites of History

The Improbability of History

The Creation of Records: Second Mechanism

CHAPTER 21 The Many-Instants Interpretation

Many Histories in One Universe

Bell’s ‘Many-Worlds’ Interpretation

The Many-Instants Interpretation

CHAPTER 22 The Emergence of Time and its Arrow

Causality in Quantum Cosmology

Soccer in the Matterhorn

Timeless Descriptions of Dynamics

A Quantum Origin of the Universe?

Vision of a Timeless Universe

A Weil-Ordered Cosmos?

EPILOGUE Life Without Time

Notes

Further Reading

Bibliography

Index

LIST OF DISPLAY ITEMS

BOXES

1 The Great Revolutions in Physics

2 The Two Big Mysteries

3 Possible Platonias

4 Centre of Mass

5 The Galilean Relativity Principle

6 The Equation of Time

7 Tait’s Inertial Clock

8 Intrinsic Difference and Best Matching

9 Relativity in One Diagram and 211 Words

10 The Impossible Becomes Possible

11 The Two-Slit Experiment

12 Entangled States

13 How Creation Works

14 The Semiclassical Approach

15 Static Wave Packets

ILLUSTRATION

The Ariel in a Snowstorm

FIGURES

1 Absolute Space and Time

2 Motion as an Illusion

3 Triangle Land

4 Triangle Land with Frontiers

5 Platonia

6 Platonia with Mist Distribution

7 Triangle Land with Similar Triangles

8 Shape Space

9 Three-Body History in Shape Space

10 Another History in Shape Space

11 Centre of Mass

12 Effect of Galilean Relativity

13 ‘Spaghetti Diagrams’ in Absolute Space

14 Nine Histories in Shape Space

15 A Spiral Galaxy

16 Saturn and its Rings

17 Potential Energy

18 Galileo’s Diagram of Parabolic Motion

19 Coordinates in Tait’s Problem

20 A Solution of Tait’s Problem

21 Trial Placing of Two Triangles

22 Illustration of Interference Fringes

23 Magnetic Lines of Force

24 The Pond Argument

25 Einstein’s Definition of Simultaneity

26 Mutual Contraction of Rods

27 Space-Time Diagram

28 Space-Time with Light Cones

29 Three Kinds of Space-Time

30 Three-Spaces in Space-Time

31 Space-Time as a Tapestry

32 Distribution of Hits Behind One Slit

33 Expected Distribution for Two Slits

34 Actual Distribution

35 Behaviour of Wave Function

36 Wave Function of Momentum State

37 Superposition of Waves

38 Superposition of ‘Spiky’ Waves

39 Two-Dimensional Configuration Space

40 Configuration Space with Probability Density

41 Collapse of Wave Function

42 Entangled States

43 Measurement Based on an Entangled State

44 Two Nearly Sinusoidal Wave Patterns

45 A Regular Wave Pattern

46 Explanation of Fermat’s Principle

47 Effect of Wave Interference

48 Wave Patterns with Spikes

49 A Moving Wave Packet

50 Creation of an Alpha-Particle Track

51 Multiple Tracks of Elementary Particles

52 Division of Platonia

53 Schematic Representation of Platonia

54 Chronology of the Universe

55 From Big Bang to Big Crunch