The Future of Theoretical Physics and Cosmology: Celebrating Stephen Hawking's Contributions to Physics

, by Edited by G. W. Gibbons , E. P. S. Shellard , S. J. Rankin

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ISBN: 9780521820813 | 0521820812
Cover: Hardcover
Copyright: 11/17/2003

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Based on lectures given in honour of Stephen Hawking's sixtieth birthday, this book comprises contributions from some of the world's leading theoretical physicists. It begins with a section containing chapters by successful scientific popularisers, bringing to life both Hawking's work and other exciting developments in physics. The book then goes on to provide a critical evaluation of advanced subjects in modern cosmology and theoretical physics. Topics covered include the origin of the universe, warped spacetime, cosmological singularities, quantum gravity, black holes, string theory, quantum cosmology and inflation. As well as providing a fascinating overview of the wide variety of subject areas to which Stephen Hawking has contributed, this book represents an important assessment of prospects for the future of fundamental physics and cosmology.

List of contributors

xvii

Preface

xxv

Introduction

(14)

Gary Gibbons

Paul Shellard

Popular symposium

(1)

Spacetime singularities

(1)

Black holes

(1)

Hawkins radiation

(1)

Quantum gravity

(1)

M theory and beyond

(1)

De Sitter space

(1)

Quantum cosmology

(1)

Cosmology

(1)

Postscript

(5)

Part 1 Popular symposium

(104)

Our complex cosmos and its future

(21)

Martin Rees

Introduction

(1)

The universe observed

(5)

Cosmic microwave background radiation

(2)

The origin of large-scale structure

(2)

The fate of the universe

(4)

The very early universe

(5)

Multiverse?

(1)

The future of cosmology

(2)

Theories of everything and Hawking's wave function of the universe

(13)

James Hartle

Introduction

(1)

Different things fall with the same acceleration in a gravitational field

(2)

The fundamental laws of physics

(5)

Quantum mechanics

(1)

A theory of everything is not a theory of everything

(2)

Reduction

(1)

The main points again

(2)

References

(2)

The problem of spacetime singularities: implications for quantum gravity?

(23)

Roger Penrose

Introduction

(1)

Why quantum gravity?

(3)

The importance of singularities

(4)

Entropy

(3)

Hawking radiation and information loss

(2)

The measurement paradox

(7)

Testing quantum gravity?

(4)

Useful references for further reading

(1)

Warping spacetime

(31)

Kip Thorne

Introduction

(6)

A first glimpse of the Golden Age: 1964-74

(1)

LISA: mapping black holes with gravitational waves

(6)

The Golden Age again: colliding black holes

(2)

LIGO/VIRGO/GEO: probing colliding black holes with gravitational waves

(3)

Quantum behavior of human-sized objects

(2)

Probing the big bang with gravitational waves

(2)

Cosmic censorship: betting with Stephen

(4)

Time travel

100

(5)

Useful references for further reading

103

(2)

Sixty years in a nutshell

105

(14)

Stephen Hawking

Introduction

105

(1)

How it began

105

(1)

General relativity and cosmology

106

(1)

Mach's principle and Wheeler-Feynman electrodynamics

107

(2)

The steady state

109

(1)

Gravity and the expanding universe

110

(1)

Collapsing stars

111

(1)

Hawking radiation

112

(2)

Inflation

114

(1)

M theory and the future

115

(2)

Conclusion

117

(2)

Part 2 Spacetime singularities

119

(84)

Cosmological perturbations and singularities

121

(40)

George Ellis

Introduction

121

(1)

Part A: Cosmological perturbations

122

(1)

Fluids and scalar fields

122

(8)

Cosmic background radiation

130

(5)

Issues

135

(4)

Part B: Cosmological singularities

138

(1)

Analytic direct approach

139

(2)

Indirect method

141

(2)

Issues

143

(10)

Conclusion

153

(8)

References

153

(8)

The quantum physics of chronology protection

161

(16)

Matt Visser

Why is chronology protection even an issue?

161

(2)

Paradoxes and responses

163

(2)

Elements of chronology protection

165

(2)

Semiclassical arguments

167

(2)

The failure of semiclassical gravity

169

(2)

Where we stand

171

(6)

References

173

(4)

Energy dominance and the Hawking--Ellis vacuum conservation theorem

177

(8)

Brandon Carter

Introduction

177

(2)

The energy dominance condition

179

(2)

The vacuum conservation theorem

181

(4)

References

183

(2)

On the instability of extra space dimensions

185

(18)

Roger Penrose

The issue of functional freedom

185

(4)

Functional freedom in higher-dimensional theories

189

(6)

Classical instability of extra dimensions

195

(3)

The holographic conjecture

198

(5)

References

200

(3)

Part 3 Black holes

203

(86)

Black hole uniqueness and the inner horizon stability problem

205

(12)

Werner Israel

Introduction

205

(1)

The traiblazers: Moscow 1964

206

(1)

Cambridge 1965-71

207

(2)

Descent into the interior

209

(1)

Internal evolution problem

210

(2)

Spherical models

212

(2)

The generic case

214

(1)

Conclusions

215

(1)

Acknowledgements

215

(2)

References

215

(2)

Black holes in the real universe and their prospects as probes of relativistic gravity

217

(19)

Martin Rees

Introduction

217

(1)

Stellar mass holes

218

(1)

Supermassive holes

219

(1)

Scenarios for black hole formation

220

(2)

The galactic context

222

(2)

Do the candidate holes obey the Kerr metric?

224

(6)

Gravitational radiation as a probe

230

(6)

References

233

(3)

Primordial black holes

236

(28)

Bernard Carr

Preface

236

(1)

Historical overview

237

(3)

PBHs as a probe of primordial inhomogeneities

240

(3)

PBHs as a probe of cosmological phase transitions

243

(4)

PBHs as a probe of a varying gravitational constant

247

(1)

PBHs as a probe of gravitational collapse

248

(2)

PBHs as a probe of high energy physics

250

(6)

Postscript

256

(8)

References

259

(5)

Black hole pair creation

264

(14)

Simon Ross

Introduction

264

(2)

Constructing instantons: the C metric

266

(2)

Calculation of the action

268

(4)

Pair creation rate

272

(6)

References

275

(3)

Black holes at accelerators

278

(11)

Steve Giddings

Introduction

278

(1)

TeV-scale gravity

279

(2)

Black holes on brane worlds

281

(3)

Black hole decay and signatures

284

(2)

The future of high energy physics

286

(3)

References

287

(2)

Part 4 Hawking radiation

289

(60)

Black holes and string theory

291

(11)

Malcolm Perry

References

300

(2)

M theory and black hole quantum mechanics

302

(8)

Joe Polchinski

A story

302

(1)

`Finding Stephen's mistake'

303

(4)

The strong interaction and black holes

307

(3)

References

308

(2)

Playing with black strings

310

(20)

Gary Horowitz

Introduction

310

(2)

Existence of new (vacuum) solutions

312

(4)

Properties of the new solutions

316

(3)

New charged black strings

319

(5)

Open questions

324

(3)

Conclusions

327

(3)

References

328

(2)

Twenty years of debate with Stephen

330

(19)

Leonard Susskind

Crisis and paradigm shift

330

(1)

Stephen's argument for coherence loss

331

(2)

Horizon Complementarity

333

(1)

The Holographic Principle

334

(1)

The ultraviolet/infrared connection

335

(2)

Counting black hole microstates

337

(2)

De Sitter space

339

(4)

Correlations in finite entropy systems

343

(6)

References

345

(4)

Part 5 Quantum gravity

349

(104)

Euclidean quantum gravity: the view from 2002

351

(22)

Gary Gibbons

Introduction

351

(3)

Some historical recollections

354

(3)

The path integral

357

(8)

The AdS/CFT correspondence

365

(1)

The volume canonical ensemble

366

(2)

Hyperbolic 4-manifolds

368

(1)

Action and complexity

369

(1)

Euclides ab omni naevo vindicatus?

370

(3)

References

370

(3)

Zeta functions, anomalies and stable branes

373

(11)

Ian Moss

Introduction

373

(1)

ζfunctions

374

(1)

Heat kernel coefficients

375

(2)

Anomalies

377

(1)

Brane worlds

378

(3)

Outlook

381

(3)

References

382

(2)

Some reflections on the status of conventional quantum theory when applied to quantum gravity

384

(25)

Chris Isham

Introduction

384

(2)

The danger of a priori assumptions

386

(7)

Alternative conceptions of spacetime

393

(3)

Presheaves and related notions from topos theory

396

(5)

Presheaves of propositions, and valuations in quantum theory

401

(4)

Conclusions

405

(4)

References

406

(3)

Quantum geometry and its ramifications

409

(27)

Abhay Ashtekar

Introduction

409

(2)

A bird's eye view of loop quantum gravity

411

(9)

Applications of quantum geometry

420

(8)

Outlook

428

(8)

References

431

(5)

Topology change in quantum gravity

436

(17)

Fay Dowker

Introduction

436

(1)

A top down framework for topology change

437

(2)

Morse metrics and elementary topology changes

439

(2)

Good and bad topology change

441

(2)

Progress on the Borde-Sorkin conjecture

443

(2)

Looking to the future

445

(8)

References

449

(4)

Part 6 M theory and beyond

453

(84)

The past and future of string theory

455

(8)

Edward Witten

String theory

463

(10)

David Gross

Motivations for quantum gravity

463

(3)

The achievements of string theory

466

(4)

The future of string theory

470

(3)

A brief description of string theory

473

(11)

Michael Green

Introduction

473

(1)

Historical background

474

(3)

String theory today

477

(4)

Duality and M theory

481

(1)

Future perspective

482

(2)

The story of M

484

(10)

Paul Townsend

Introduction

484

(1)

The supermembrane

485

(3)

Backgrounds of reduced holonomy

488

(2)

The sigma model limit

490

(4)

References

492

(2)

Gauged supergravity and holographic field theory

494

(21)

Nick Warner

Gauged supergravity and a thesis project

494

(2)

The ups and downs of maximal gauged supergravity

496

(2)

Exploring higher dimensions

498

(3)

Holographic field theory and AdS/CFT correspondence

501

(2)

Bulk gravity and brane renormalization: where are the branes?

503

(3)

Holographic renormalization group flows: an example

506

(5)

Final comments

511

(4)

References

512

(3)

57 Varieties in a NUTshell

515

(22)

Chris Pope

Introduction

515

(1)

Four-dimensional self-dual metrics

516

(1)

Non-compact self-dual 4-metrics

517

(4)

Compact self-dual 4-metrics: K3

521

(3)

Special holonomy in higher dimensions

524

(1)

Ricci-flat Kahler 6-metrics and the conifold

525

(3)

Seven-dimensional metrics of G2 holonomy

528

(4)

Spin(7) holonomy

532

(1)

Conclusion

533

(4)

References

534

(3)

Part 7 De Sitter space

537

(76)

Adventures in de Sitter space

539

(31)

Raphael Bousso

Introduction

539

(2)

De Sitter space

541

(2)

Entropy and temperature of event horizons

543

(2)

Entropy bounds from horizons

545

(3)

Absolute entropy bounds in spacetimes with Λ > 0

548

(7)

Quantum gravity in de Sitter space

555

(4)

Instabilities of the Nariai solution

559

(11)

De Sitter space in non-critical string theory

570

(22)

Andrew Strominger

Alexander Maloney

Eva Silverstein

Introduction

570

(3)

De Sitter compactifications of super-critical string theory

573

(7)

Metastability of the De Sitter vacuum

580

(12)

References

589

(3)

Supergravity, M theory and cosmology

592

(21)

Renata Kallosh

Introduction

592

(4)

Extended supergravities with dS vacua

596

(3)

Hybrid inflation with D-branes

599

(7)

M theory on a four-fold with G-fluxes

606

(7)

References

609

(4)

Part 8 Quantum cosmology

613

(110)

The state of the universe

615

(6)

James Hartle

Introduction

615

(1)

Final theories

616

(1)

Effective theories

617

(2)

Directions

619

(2)

References

620

(1)

Quantum cosmology

621

(28)

Don Page

Motivation for a quantum state of the cosmos

621

(1)

The Hartle--Hawking proposal for the quantum state

622

(2)

Zero-loop quantum cosmology and FRW-scalar models

624

(3)

Real classical solutions for the FRW-scalar model

627

(2)

Complex classical solutions for the FRW-scalar model

629

(3)

FRW-scalar models with an exponential potential

632

(14)

Summary

646

(3)

References

647

(2)

Quantum cosmology and eternal inflation

649

(18)

Alexander Vilenkin

Introduction

649

(1)

Quantum cosmology

650

(1)

The tunnelling wave function

651

(4)

Alternative proposals for the wave function

655

(2)

Semiclassical probabilities

657

(1)

Comparing different wave functions

658

(2)

Do we need quantum cosmology?

660

(1)

Is quantum cosmology testable?

661

(6)

References

663

(4)

Probability in the deterministic theory known as quantum mechanics

667

(8)

Bryce DeWitt

Quantum measurement

667

(1)

Reality

668

(1)

Signalling by permutations

669

(2)

Equal likelihood

671

(1)

The case of degeneracy

672

(1)

Unequal probabilities

673

(2)

The interpretation of quantum cosmology and the problem of time

675

(18)

Jonathan Halliwell

Introduction

675

(3)

The classical case

678

(6)

The decoherent histories approach to quantum theory

684

(1)

The induced inner product

685

(1)

The class operators

686

(2)

Decoherence and the decoherence functional

688

(1)

Summary and discussion

689

(4)

References

690

(3)

What local supersymmetry can do for quantum cosmology

693

(30)

Peter D'Eath

Introduction

693

(5)

No-boundary state

698

(1)

The classical Riemannian boundary-value problem

699

(4)

Self-duality

703

(6)

Canonical quantum theory of N=1 supergravity: `traditional variables'

709

(6)

Canonical quantization of N=1 supergravity: Ashtekar--Jacobson variables

715

(2)

Comments

717

(6)

References

717

(6)

Part 9 Cosmology

723

(150)

Inflation and cosmological perturbations

725

(30)

Alan Guth

The origin of inflationary fluctuations

725

(4)

The 1982 Nuffield workshop

729

(6)

Observational evidence for inflation

735

(5)

Eternal inflation

740

(3)

A new singularity theorem

743

(7)

The origin of the universe

750

(5)

References

750

(5)

The future of cosmology: observational and computational prospects

755

(26)

Paul Shellard

Empirical cosmology

755

(1)

The cosmic microwave sky

756

(5)

Cosmological perturbations and cosmic concordance?

761

(8)

Critical observational tests

769

(3)

Primordial gravitational waves

772

(1)

Computational prospects

773

(3)

Afterword

776

(5)

References

777

(4)

The ekpyrotic universe and its cyclic extension

781

(20)

Neil Turok

Introduction

781

(2)

Homage to the Ancients

783

(1)

The ekpyrotic universe model

784

(2)

The main problem

786

(2)

Flatness

788

(1)

Density perturbations

788

(2)

Brane collisions

790

(3)

The inter-brane potential

793

(1)

The cyclic universe

793

(1)

Back to the singularity

794

(4)

Conclusions

798

(3)

References

798

(3)

Inflationary theory versus the ekpyrotic/cyclic scenario

801

(38)

Andrei Linde

Introduction

801

(2)

Chaotic inflation

803

(3)

Hybrid inflation

806

(1)

Quantum fluctuations and density perturbations

807

(2)

From the Big Bang to eternal inflation

809

(2)

Inflation and observations

811

(1)

Alternatives to inflation?

812

(2)

Ekpyrosis

814

(5)

Cyclic universe

819

(11)

Conclusions

830

(9)

References

833

(6)

Brane (new) worlds

839

(21)

Pierre Binetruy

Why study brane cosmology?

839

(2)

Life on the brane

841

(4)

Ads/CFT correspondence

845

(1)

Moduli fields. Moduli space approximation

846

(2)

Cosmological constant

848

(3)

Bulk scalars

851

(2)

Infinite dimensions

853

(2)

Open problems

855

(5)

References

856

(4)

Publications of Stephen Hawking

860

(13)

Index

873

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The Future of Theoretical Physics and Cosmology: Celebrating Stephen Hawking's Contributions to Physics

Summary

Table of Contents

Supplemental Materials