String Theory For Dummies

Unravel the secrets of the universe and untangle cutting-edge physics

Yes, you actually can understand quantum physics! String Theory For Dummies is a beginner’s guide, and we make it fun to find out about the all the recent trends and theories in physics, including the basics of string theory, with friendly explanations. Build a foundation of physics knowledge, understand the various string theories and the math behind them, and hear what the opponents to string theory have to say. It’s an exciting time to be alive in advanced physics, and this updated edition covers what’s new in the string world—the Large Hadron Collider, the Higgs Boson, gravitational waves, and lots of other big headlines. Unleash your inner armchair physicist with String Theory For Dummies.

• Brush up on the basics of physics and the approachable math needed to understand string theory
• Meet the scientists who discovered string theory and continue to make waves (and particles) in the physics world
• Understand what it’s all about with real-world examples and explanations
• Learn why string theory is called "The Theory of Everything"—and what it means for technology and the future

Aspiring scientists or life-long learners will both be able to gain valuable information from this book. This accessible intro into string theory is for the theorists inside anyone.

Andrew Zimmerman Jones, PhD, is the physics guide at About.com, where he writes lessons and explanations for common physics problems and questions. Andrew earned his degree in physics from Wabash College and his PhD in mathematics from Purdue University. He is the author of the previous edition of String Theory For Dummies.

Alessandro Sfondrini is a theoretical physicist. He obtained his bachelor’s and master’s degrees in physics from the University of Padova. He is currently a Rita Levi-Montalcini Fellow and assistant professor in theoretical physics and mathematical methods and models at the University of Padova, as well as a member and IBM Einstein Fellow at the Institute for Advanced Study in Princeton, New Jersey.

Introduction 1

About This Book 1

Foolish Assumptions 2

Icons Used in This Book 3

Beyond the Book 4

Where to Go from Here 4

Part 1: Introducing String Theory 5

Chapter 1: So What Is String Theory Anyway? 7

String Theory: Seeing What Vibrating Strings Can Tell Us about the Universe 8

Using tiny and huge concepts to create a theory of everything 8

A quick look at where string theory has been 10

Introducing the Key Elements of String Theory 11

Strings and branes 11

Quantum gravity 13

Unification of forces 13

Supersymmetry 13

Extra dimensions 14

Understanding the Aim of String Theory 15

Quantizing gravity 15

Unifying forces 15

Explaining matter and mass 16

Defining space and time 17

Appreciating the Theory’s Amazing (and Controversial) Implications 18

Landscape of possible theories 18

The universe as a hologram 19

Why Is String Theory So Important? 19

Chapter 2: The Physics Road Dead-Ends at Quantum Gravity 21

Understanding Two Schools of Thought on Gravity 22

Newton’s law of gravity: Gravity as force 22

Einstein’s law of gravity: Gravity as geometry 24

Describing Matter: Physical and Energy-Filled 25

Viewing matter classically: Chunks of stuff 25

Viewing matter at a quantum scale: Chunks of energy 26

Grasping for the Fundamental Forces of Physics 26

Electromagnetism: Super-speedy energy waves 27

Nuclear forces: What the strong force joins, the weak force tears apart 28

Infinities: Why Einstein and the Quanta Don’t Get Along 28

Singularities: Bending gravity to the breaking point 29

Quantum jitters: Space-time under a quantum microscope 30

Unifying the Forces 31

Einstein’s failed quest to explain everything 32

A particle of gravity: The graviton 32

Supersymmetry’s role in quantum gravity 33

Chapter 3: Accomplishments and Failures of String Theory 35

Celebrating String Theory’s Successes 36

Predicting gravity out of strings 36

Explaining what happens to a black hole (sort of) 36

Explaining quantum field theory using string theory 37

String theory keeps making a comeback 38

Being the most popular theory in town 38

Considering String Theory’s Setbacks 39

The universe doesn’t have enough particles 40

Dark energy: The discovery string theory should have predicted 40

Where did all these “fundamental” theories come from? 41

Looking into String Theory’s Future 42

Theoretical complications: Can we figure out string theory? 43

Experimental complications: Can we prove string theory? 43

Part 2: The Physics Upon Which String Theory Is Built 45

Chapter 4: Putting String Theory in Context: Understanding the Method of Science 47

Exploring the Practice of Science 48

The myth of the scientific method 48

The need for experimental falsifiability 50

The foundation of theory is mathematics 52

The rule of simplicity 53

The role of objectivity in science 53

Understanding How Scientific Change Is Viewed 54

Precision and accuracy: Science as measurement 54

Old becomes new again: Science as revolution 55

Combining forces: Science as unification 56

What happens when you break it? Science as symmetry 57

Chapter 5: What You Must Know about Classical Physics 61

This Crazy Little Thing Called Physics 62

No laughing matter: What we’re made of 62

Add a little energy: Why stuff happens 64

Symmetry: Why some laws were made to be broken 65

All Shook Up: Waves and Vibrations 67

Catching the wave 67

Getting some good vibrations 69

Newton’s Revolution: How Physics Was Born 71

Force, mass, and acceleration: Putting objects into motion 72

Gravity: A great discovery 73

Optics: Shedding light on light’s properties 74

Calculus and mathematics: Enhancing scientific understanding 74

The Forces of Light: Electricity and Magnetism 75

Light as a wave: The ether theory 75

Invisible lines of force: Electric and magnetic fields 76

Maxwell’s equations bring it all together: Electromagnetic waves 78

Two dark clouds and the birth of modern physics 79

Chapter 6: Revolutionizing Space and Time: Einstein’s Relativity 81

What Waves Light Waves? Searching for the Ether 82

No Ether? No Problem: Introducing Special Relativity 84

Unifying space and time 86

Unifying mass and energy 88

Changing Course: Introducing General Relativity 89

Gravity as acceleration 89

Gravity as geometry 91

Testing general relativity 93

Surfing the gravitational waves 96

Applying Einstein’s Work to the Mysteries of the Universe 97

Kaluza-Klein Theory — String Theory’s Predecessor 98

Chapter 7: Brushing Up on Quantum Theory Basics 101

Unlocking the First Quanta: The Birth of Quantum Physics 102

Fun with Photons: Einstein’s Nobel Idea of Light 104

Waves and Particles Living Together 107

Light as a wave: The double slit experiment 107

Particles as a wave: The de Broglie hypothesis 108

Quantum physics to the rescue: The quantum wavefunction 110

Why We Can’t Measure It All: The Uncertainty Principle 111

Dead Cats, Live Cats, and Probability in Quantum Physics 112

Does Anyone Know What Quantum Theory Means? 114

Quantum Units of Nature: Planck Units 115

Chapter 8: The Standard Model of Particle Physics 119

Atoms, Atoms, Everywhere Atoms: Introducing Atomic Theory 120

Popping Open the Atomic Hood and Seeing What’s Inside 122

Discovering the electron 122

The nucleus is the thing in the middle 123

Watching the dance inside an atom 124

The Quantum Picture of the Photon: Quantum Electrodynamics 125

Dr Feynman’s doodles explain how particles exchange information 125

Discovering that other kind of matter: Antimatter 128

Sometimes a particle is only virtual 129

Digging into the Nucleus: Quantum Chromodynamics 130

The pieces that make up the nucleus: Nucleons 130

The pieces that make up the nucleon’s parts: Quarks 131

Looking into the Types of Particles 132

Particles of force: Bosons 132

Particles of matter: Fermions 133

Gauge Bosons: Particles Holding Other Particles Together 134

Exploring the Theory of Where Mass Comes From 135

What is the Higgs field? 136

Discovering the Higgs boson at the LHC 137

From Big to Small: The Hierarchy Problem in Physics 137

Chapter 9: Physics in Space: Considering Cosmology and Astrophysics 141

The Enlightened Universe and the Birth of Modern Astrophysics 143

Everything doesn’t revolve around Earth 143

Beholding the movements of heavenly bodies 144

Introducing the Idea of an Expanding Universe 145

Discovering that energy and pressure have gravity 145

Hubble drives it home 147

Finding a Beginning: The Big Bang Theory 148

Going to bat for the big bang: Cosmic microwave background radiation 149

Understanding where the chemical elements came from 151

Using Inflation to Solve the Universe’s Problems of Flatness and Horizon 152

The universe’s issues: Too far and too flat 153

Rapid expansion early on holds the solutions 154

Dark Matter: The Source of Extra Gravity 155

Dark Energy: Pushing the Universe Apart 155

Stretching the Fabric of Space-Time into a Black Hole 158

What goes on inside a black hole? 158

What goes on at the edge of a black hole? 159

Part 3: Building String Theory: A Theory of Everything 161

Chapter 10: Early Strings and Superstrings: Unearthing the Theory’s Beginnings 163

Bosonic String Theory: The First String Theory 164

Explaining the scattering of particles with early dual resonance models 164

Exploring the first physical model: Particles as strings 166

Bosonic string theory loses out to the Standard Model 167

Why Bosonic String Theory Doesn’t Describe Our Universe 168

Massless particles 169

Tachyons 169

No electrons allowed 170

25 space dimensions, plus 1 of time 171

Supersymmetry Saves the Day: Superstring Theory 173

Fermions and bosons coexist sort of 173

Double your particle fun: Supersymmetry hypothesizes superpartners 174

Some problems get fixed, but the dimension problem remains 176

Supersymmetry and Quantum Gravity in the Disco Era 177

The graviton is found hiding in string theory 177

The other supersymmetric gravity theory: Supergravity 179

String theorists don’t get no respect 179

A Theory of Everything: The First Superstring Revolution 180

But We’ve Got Five Theories! 181

Type I string theory 182

Type IIA string theory 182

Type IIB string theory 182

Two strings in one: Heterotic strings 182

How to Fold Space: Introducing Calabi-Yau Manifolds 183

String Theory Loses Steam 185

Chapter 11: M-Theory and Beyond: Bringing String Theory Together 187

Introducing the Unifying Theory: M-Theory 187

Translating one string theory into another: Duality 188

Using two dualities to unite five superstring theories 192

The second superstring revolution begins: Connecting to the 11-dimensional theory 193

Branes: Stretching Out a String 194

The discovery of D-branes: Giving open strings something to hold on to 195

Creating particles from p-branes 196

Deducing that branes are required by M-theory 197

Uniting D-branes and p-branes into one type of brane 198

Using branes to explain black holes 199

Getting stuck on a brane: Brane worlds 200

Matrix Theory as a Potential M-Theory 200

Chapter 12: Exploring Strings and Their Landscape 203

Strings and Fields: String Field Theory 203

Splitting and joining of strings and how to avoid infinities 204

Trying to visualize how strings create loops 206

String Theory Gets Surprised by Dark Energy 208

Considering Proposals for Why Dimensions Sometimes Uncurl 209

Measurable dimensions 209

Infinite dimensions: Randall-Sundrum models 210

Understanding the Current Landscape: A Multitude of Theories 211

The anthropic principle requires observers 212

Disagreeing about the principle’s value 214

Chapter 13: Gaining Insights from the Holographic Principle 217

What’s a Hologram? 217

Creating optical holograms 218

More bang for your buck: Encoding information in fewer dimensions 219

Using Holograms to Understand Black Holes 222

Going down a black hole 222

Black holes and entropy 223

If it works for black holes, it works for me 224

Considering AdS/CFT Correspondence 226

Checking the predictions 227

AdS space, or living in an M C Escher painting 227

CFTs: conformal, but nonconformist 231

Understanding quantum gravity through AdS/CFT correspondence 232

Turning the Tables: Using Holography to Study Strongly Interacting Matter 233

The force is strong when using AdS/CFT 233

Cooking up a soup of quarks and gluons 235

Chapter 14: Putting String Theory to the Test 237

Understanding the Obstacles 238

Testing an incomplete theory with indistinct predictions 238

Testing versus proof 239

Analyzing Supersymmetry 240

Finding the missing sparticles 240

Testing implications of supersymmetry 241

Testing Gravity from Extra Dimensions 242

Checking the inverse-square law 242

Searching for gravity waves to understand inflation 243

Disproving String Theory Sounds Easier Than It Is 244

Violating relativity 244

Could proton decay spell disaster? 245

Seeking mathematical inconsistencies 246

Bootstrapping Our Way into String Theory 247

Looking for Evidence in the Cosmic Laboratory: Exploring the Universe 248

Using outer space rays to amplify small events 249

Analyzing dark matter and dark energy 252

Detecting cosmic superstrings 253

Looking for Evidence Closer to Home: Using Particle Accelerators 254

Accelerating heavy ions at the RHIC 254

Colliders of the future 255

LHC finds a boson, but no superpartners yet 256

Discovering the Higgs boson 257

Looking for superpartners 258

Part 4: The Unseen Cosmos: String Theory on the Boundaries of Knowledge 261

Chapter 15: Making Space for Extra Dimensions 263

What Are Dimensions? 264

2-Dimensional Space: Exploring the Geometry of Flatland 265

Euclidean geometry: Think back to high school geometry 265

Cartesian geometry: Merging algebra and Euclidean geometry 266

Three Dimensions of Space 267

A straight line in space: Vectors 267

Twisting 2-dimensional space in three dimensions: The Mobius strip 268

More twists in three dimensions: Non-Euclidean geometry 270

Four Dimensions of Space-Time 272

Adding More Dimensions to Make a Theory Work 273

Sending Space and Time on a Bender 274

Are Extra Dimensions Really Necessary? 275

Offering an alternative to multiple dimensions 276

Weighing fewer dimensions against simpler equations 277

Chapter 16: Our Universe — String Theory, Cosmology, and Astrophysics 279

The Start of the Universe with String Theory 280

What was before the bang? 280

What banged? 282

Explaining Black Holes with String Theory 286

String theory and the thermodynamics of a black hole 286

String theory and the black hole information paradox 288

The Evolution of the Universe 289

The swelling continues: Eternal inflation 289

The hidden matter and energy 291

The Undiscovered Country: The Future of the Cosmos 293

A universe of ice: The big freeze 293

From point to point: The big crunch 294

A new beginning: The big bounce 294

Exploring a Finely Tuned Universe 294

Chapter 17: Have Time, Will Travel 297

Temporal Mechanics 101: How Time Flies 298

The arrow of time: A one-way ticket 298

Relativity, worldlines, and worldsheets: Moving through space-time 299

Hawking’s chronology protection conjecture: You’re not going anywhere 302

Slowing Time to a Standstill with Relativity 303

Time dilation: Sometimes even the best watches run slow 303

Black hole event horizons: An extra-slow version of slow motion 304

General Relativity and Wormholes: Doorways in Space and Time 305

Taking a shortcut through space and time with a wormhole 306

Overcoming a wormhole’s instability with negative energy 308

Crossing Cosmic Strings to Allow Time Travel 310

A Two-Timing Science: String Theory Makes More Time Dimensions Possible 310

Adding a new time dimension 311

Reflecting two-time physics onto a one-time universe 311

Does two-time physics have any real applications? 312

Sending Messages through Time 313

Part 5: What the Other Guys Say: Criticisms and Alternatives 317

Chapter 18: Taking a Closer Look at the String Theory Controversy 319

The String Wars: Outlining the Arguments 320

50 years and counting: Framing the debate from the skeptic’s point of view 321

A rise of criticisms 323

Is String Theory Scientific? 324

Argument No 1: String theory explains nothing 324

Argument No 2: String theory explains too much 325

Turning a Critical Eye on String Theorists 329

Hundreds of physicists just can’t be wrong 329

Holding the keys to the academic kingdom 331

Does String Theory Describe Our Universe? 332

Making sense of extra dimensions 333

Space-time should be fluid 333

The ever-elusive superpartners 334

How finite is string theory? 335

A String Theory Rebuttal 335

What about the extra dimensions? 336

Space-time fluidity? 337

Does string theory need to be finite? 337

Trying to Make Sense of the Controversy 337

Chapter 19: Loop Quantum Gravity: String Theory’s Biggest Competitor 339

Taking the Loop: Introducing Another Road to Quantum Gravity 340

The great background debate 340

What is looping anyway? 341

Making Predictions with Loop Quantum Gravity 343

Gravity exists (Duh!) 343

Black holes contain only so much space 343

Gamma ray burst radiation travels at different speeds 344

Finding Favor and Flaw with Loop Quantum Gravity 344

The benefit of a finite theorem 344

Spending some time focusing on the flaws 345

So Are These Two Theories the Same with Different Names? 346

Chapter 20: Considering Other Ways to Explain the Universe 349

Taking Other Roads to Quantum Gravity 350

CDT: If you’ve got the time, I’ve got the space 351

Quantum Einstein gravity: Too small to tug 352

Quantum graphity: Disconnecting nodes 352

Tensor models: gluing the space-time together 353

Newton and Einstein Don’t Make All the Rules: Modifying the Law of Gravity 354

DSR: Twice as many limits as ordinary relativity 355

MOND: Disregarding dark matter 355

VSL: Light used to travel even faster 356

MOG: The bigger the distance, the greater the gravity 358

Massive gravity and bimetric theory: making the graviton heavy 359

Rewriting the Math Books and Physics Books at the Same Time 360

Compute this: Quantum information theory 360

Looking at relationships: Twistor theory 361

Uniting mathematical systems: Noncommutative geometry 362

Mathematics All the Way Down: Are We Living in a Simulation? 363

Part 6: The Part of Tens 365

Chapter 21: Ten Tests for a Theory of Quantum Gravity 367

Reproduce Gravity 368

Compute Quantum Corrections 368

Describe How Gravity and Matter Interact 368

Explain Inflation 369

Explain What Happens When Someone Enters a Black Hole 369

Explain Whether Singularities Are Allowed 369

Explain the Birth and Death of Black Holes 370

Explain the Holographic Principle 370

Provide Testable Predictions 371

Describe Its Own Limitations 371

Index 373

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