The physical world : an inspirational tour of fundamental physics / Nicholas Manton, Nicholas Mee.

Format:

Book

Author/Creator:

Manton, Nicholas, 1952- author.

Mee, Nicholas, author.

Language:

English

Subjects (All):

Physics.

Physical Description:

xiii, 556 pages : illustrations (some color) ; 26 cm

Edition:

First edition.

Place of Publication:

Oxford, United Kingdom : Oxford University Press, 2017.

Summary:

The book offers a grand vision of the essential unity of physics that will enable the reader to see the world through the eyes of a physicist and understand their thinking. The text follows Einstein's dictum that 'explanations should be made as simple as possible, but no simpler', to give an honest account of how modern physicists understand their subject, including the shortcomings of current theory. The result is an up-to-date and engaging portrait of physics that contains concise derivations of the important results in a style where every step in a derivation is clearly explained, so that anyone with the appropriate mathematical skills will find the text easy to digest. The book concentrates on the conceptual principles of each branch of physics and shows how they fit together to form a coherent whole. Emphasis is placed on the use of variational principles in physics, and in particular the principle of least action, an approach that lies at the heart of modern theoretical physics, but has been neglected in most introductory accounts of the subject.

Contents:

0 Introduction 1

1 Fundamental Ideas 4

1.1 Variational Principles 4

1.1.1 Geometrical optics-reflection and refraction 6

1.1.2 The scope of variational principles 9

1.2 Euclidean Space and Time 10

1.3 Partial Derivatives 14

1.4 e, π and Gaussian Integrals 18

1.4.1 Radioactive decay 19

1.4.2 Waves and periodic functions 21

1.4.3 The Gaussian integral 21

1.4.4 The method of steepest descents 24

2 Motions of Bodies-Newton's Laws 26

2.1 Introduction 26

2.2 Newton's Laws of Motion 27

2.3 The Principle of Least Action 29

2.3.1 Motion in one dimension 31

2.3.2 A simple example and a simple method 32

2.3.3 Motion in a general potential and Newton's second law 35

2.3.4 The calculus of variations 36

2.3.5 The unimportance of the endpoints 38

2.4 The Motion of Several Bodies and Newton's Third Law 39

2.5 Motion of One Body in Three Dimensions 42

2.5.1 The harmonic oscillator 43

2.6 Central Forces 44

2.6.1 Circular orbits 46

2.7 The Attractive Inverse Square Law Force 48

2.8 G and the Mass of the Earth 52

2.9 Composite Bodies and Centre of Mass Motion 53

2.10 The Kepler 2-Body Problem 56

2.10.1 Binary stars 57

2.11 Lagrangian Points 58

2.12 Conservation of Energy 63

2.13 Friction and Dissipation 65

3 Fields-Maxwell's Equations 67

3.1 Fields 67

3.2 The Scalar Field Equation 69

3.3 Waves 72

3.4 Divergence and Curl 74

3.5 Electromagnetic Fields and Maxwell's Equations 75

3.5.1 What Maxwell's equations tell us 78

3.6 Electrostatic Fields 81

3.6.1 Charge and dipole moment 84

3.7 Electromagnetic Waves 86

3.8 Magnetostatics 90

3.9 Principle of Least Action for Electromagnetic Fields 92

3.10 The Lorentz Force 93

3.10.1 The Lorentz force from the principle of least action 97

3.11 Field Energy and Momentum 98

3.12 Dynamics of Particles and Fields 100

4 Special Relativity 103

4.1 Introduction 103

4.2 Lorentz Transformations 105

4.3 Relativistic Dynamics 110

4.3.1 Comparison of Newtonian and relativistic dynamics 114

4.3.2 E = mc² 116

4.4 More on 4-Vectors 117

4.5 The Relativistic Character of Maxwell's Equations 118

4.6 Relativistic Principles of Least Action 122

5 Curved Space 126

5.1 Spherical Geometry 126

5.1.1 Geodesies 127

5.2 Non-Euclidean, Hyperbolic Geometry 128

5.3 Gaussian Curvature 129

5.4 Riemannian Geometry 132

5.4.1 Simple examples of metrics 134

5.5 Tensors 137

5.5.1 Covariant derivatives and Christoffel symbols 140

5.5.2 Christoffel symbols in plane polar coordinates 143

5.6 The Riemann Curvature Tensor 143

5.6.1 Riemann curvature in plane polar coordinates 145

5.6.2 Riemann curvature on a sphere 145

5.6.3 The 3-sphere 146

5.7 The Geodesic Equation 146

5.7.1 Geodesies in plane polar coordinates 149

5.7.2 The equation of geodesic deviation 149

5.8 Applications 152

6 General Relativity 158

6.1 The Equivalence Principle 158

6.2 The Newtonian Gravitational Field and Tidal Forces 159

6.3 Minkowski Space 162

6.4 Curved Spacetime Geometry 164

6.4.1 Weak gravitational fields 166

6.5 The Gravitational Field Equation 167

6.5.1 The energy-momentum tensor 168

6.5.2 The Einstein tensor and the Einstein equation 170

6.5.3 Determining the constant of proportionality 172

6.6 The Classic Tests of General Relativity 173

6.6.1 The perihelion advance of Mercury 173

6.6.2 The deflection of starlight 174

6.6.3 Clocks and gravitational redshift 174

6.7 The Schwarzschild Solution of the Einstein Equation 177

6.7.1 The Newtonian limit 179

6.8 Particle Motion in Schwarzschild Spacetime 180

6.9 Light Deflection in Schwarzschild Spacetime 183

6.10 The Interior Schwarzschild Solution 185

6.11 Black Holes 187

6.11.1 Eddington-Finkelstein coordinates 189

6.11.2 The Kerr metric 191

6.12 Gravitational Waves 195

6.12.1 The detection of gravitational waves 196

6.13 The Einstein-Hilbert Action 199

7 Quantum Mechanics 203

7.1 Introduction 203

7.2 Position and Momentum in Quantum Mechanics 205

7.3 The Schrödinger Equation 207

7.3.1 The free particle 210

7.3.2 The harmonic oscillator 212

7.4 Interpretation of Wavefunctions-Observables 214

7.4.1 Position probabilities 215

7.4.2 Other physical quantities-hermitian operators 216

7.4.3 Measurements of observables 218

7.5 Expectation Values 220

7.6 After a Measurement 222

7.7 Uncertainty Relations 222

7.8 Scattering and Tunnelling 225

7.9 Variational Principles in Quantum Mechanics 227

8 Quantum Mechanics in Three Dimensions 231

8.1 Introduction 231

8.2 Position and Momentum Operators 232

8.2.1 Particle in a box 234

8.3 Angular Momentum Operators 235

8.3.1 Eigenfunctions of 1² using Cartesian coordinates 237

8.4 The Schrödinger Equation with a Spherical Potential 240

8.4.1 The Coulomb potential 241

8.4.2 Spectroscopy 242

8.5 Spin 244

8.5.1 The Stern-Gerlach experiment 245

8.5.2 The Zeeman effect 246

8.5.3 Other spin representations 247

8.6 Spin 1/2 as a Quantum Paradigm 248

8.7 Quantum Mechanics of Several Identical Particles 249

8.7.1 The Fermi sphere 254

8.8 Bosons, Fermions and Spin 255

8.9 Return to the Action 256

9 Atoms, Molecules and Solids 261

9.1 Atoms 261

9.1.1 Atomic orbitals 263

9.1.2 Atomic shell model 264

9.2 Molecules 267

9.2.1 Covalent bonding 267

9.2.2 Polar bonds 274

9.2.3 Simple molecules 276

9.3 Organic Chemistry 277

9.3.1 Hückel theory-benzene 277

9.3.2 Polyenes 280

9.4 Solids 283

9.4.1 Covalent solids 284

9.5 Band Theory 286

9.5.1 Atomic lattices 286

9.5.2 Bloch'a theorem 289

9.5.3 Bloch states in a finite crystal 290

9.5.4 The tight-binding model 291

9.5.5 The nearly free electron model 293

9.5.6 Ionic solids 294

9.5.7 Example of caesium chloride 294

9.5.8 Metals 297

9.5.9 Example of copper 298

9.6 Ferromagnetism 300

10 Thermodynamics 303

10.1 Introduction 303

10.1.1 What is heat? 304

10.1.2 The ideal gas law 304

10.1.3 The microscopic origin of heat 306

10.1.4 Iced tea 306

10.2 Entropy and Temperature 307

10.3 The First Law of Thermodynamics 311

10.3.1 New variables 313

10.4 Subsystems-The Gibbs Distribution 315

10.5 The Maxwell Velocity Distribution 318

10.6 Ideal Gases-Equation of State and Entropy 320

10.7 Non-Ideal Gases 322

10.8 The Chemical Potential 323

10.9 Fermion and Boson Gases at Low Temperature 324

10.9.1 The Fermi-Dirac function 325

10.9.2 Pressure of a degenerate electron, gas 326

10.9.3 The heat capacity of an electron gas 327

10.9.4 The Bose-Einstein function 329

10.10 Black Body Radiation 334

10.11 Lasers 337

10.12 Magnetization in Spin Systems 341

10.13 A Little about Phase Transitions 343

10.14 Hawking Radiation 347

11 Nuclear Physics 351

11.1 The Birth of Nuclear Physics 351

11.2 The Strong Force 352

11.2.1 The nuclear potential 354

11.2.2 Nucleoli pairing 357

11.2.3 The liquid drop model 358

11.3 The Nuclear Shell Model 362

11.3.1 The atomic shell analogy 362

11.3.2 The harmonic oscillator 363

11.3.3 Spin-orbit coupling 365

11.3.4 Beta decay 369

11.3.5 The Nilsson model 370

11.4 Alpha Decay 372

11.5 Fission 377

11.6 Fusion 380

11.6.1 Thermonuclear fusion 381

11.6.2 Controlled nuclear fusion 385

11.7 The Island of Stability 385

11.8 Exotic Nuclei 387

11.9 Pions, Yukawa Theory and QCD 389

12 Particle Physics 393

12.1 The Standard Model 393

12.1.1 Fundamental particles 394

12.2 Quantum Field Theory 395

12.2.1 Quantizing the electromagnetic field 397

12.2.2 The quantized scalar Klein-Gordon field 398

12.3 The Dirac Field 400

12.3.1 The Dirac

equation 400

12.3.2 Quantizing the Dirac field-particles and antiparticles 403

12.4 Actions and Interactions 406

12.4.1 Quantum electrodynamics 406

12.4.2 Feynman diagrams 408

12.5 The Strong Force 410

12.5.1 Quarks 413

12.5.2 Confinement 415

12.6 QCD 417

12.6.1 Gluons 417

12.6.2 Lattice QCD 421

12.6.3 Heavy quarks and exotic hadrons 422

12.7 The Weak Force 422

12.7.1 Parity violation 424

12.8 The Theory of the Electroweak Force 426

12.8.1 The Higgs mechanism 427

12.8.2 Fermion masses 429

12.8.3 Discovering the W and Z bosons and the Higgs boson 432

12.8.4 Quark mixing 434

12.8.5 How many generations? 435

12.9 Neutrino Oscillations 437

13 Stars 443

13.1 The Sun 443

13.2 The Herzsprung-Russell Diagram 444

13.3 The Birth of Stars 447

13.3.1 Stellar composition 447

13.3.2 The virial theorem 448

13.3.3 Star formation 451

13.4 Stellar Structure 453

13.4.1 The structure functions 455

13.4.2 The mass-luminosity relationship 457

13.4.3 The density-temperature relationship 458

13.5 Nucleosynthesis 458

13.5.1 The proton-proton chain 459

13.5.2 The CNO cycle 461

13.5.3 The mass-radius relationship 463

13.5.4 The mass-temperature relationship 463

13.5.5 Minimum mass of main sequence stars 463

13.5.6 The temperature-luminosity relationship 464

13.6 Giant Stars Beyond the Main Sequence 465

13.6.1 The triple alpha process 466

13.7 Late Evolution 467

13.7.1 White dwarfs 467

13.7.2 Gravitational collapse of massive stars 470

13.8 Neutron Stars 474

13.8.1 Pulsars 476

13.9 Supernovae 477

13.9.1 Gamma-ray bursts 482

13.10 The Density-Temperature Diagram 483

14 Cosmology 487

14.1 Einstein's Universe 487

14.2 The Distance-Redshift Relationship 487

14.3 Friedmarm-Robert son-Walker Cosmology 489

14.3.1 Einstein's equation and the FRW metric 490

14.3.2 The general FRW cosmological solutions 493

14.4 Cosmological Redshift 496

14.5 Newtonian Interpretation of the FRW Cosmology 497

14.6 The Big Bang 498

14.6.1 The age of the universe 499

14.7 Dark Matter 500

14.8 The Cosmic Microwave Background 502

14.8.1 Precision measurements of the CMB 503

14.9 The Cosmological Constant 504

14.10 Galaxy Formation 505

14.11 The Inflationary-Universe 507

14.11.1 Particle horizons 508

14.11.2 Inflation 510

15 Frontiers of Physics 514

15.1 The Interpretation of Quantum Mechanics 514

15.1.2 Schrodingpj's cat and Wigner's friend 515

15.1.2 The many-worlds interpretation 518

15.1.3 The EPR paradox 518

15.1.4 The Aspect experiments 519

15.2 The Problem of Point Particles 524

15.2.1 Solitons 525

15.2.2 Skyrmioas 527

15.3 Critique of the Standard Model 529

15.4 Topology and the Standard Model 530

15.5 Beyond the Standard Model 532

15.5.1 Grand Unified Theories 533

15.5.2 Supersymmetry 534

15.6 String Theory 535

15.6.1 Compactification 538.

Notes:

Includes bibliographical references and index.

ISBN:

9780198795933

0198795939

9780198796114

0198796110

OCLC:

965461385