Wizards, Aliens, and Starships: Physics and Math in Fantasy and Science Fiction
Page 1
WIZARDS, ALIENS, AND STARSHIPS
Copyright © 2014 by Princeton University Press
Published by Princeton University Press, 41 William Street,
Princeton, New Jersey 08540
In the United Kingdom: Princeton University Press, 6 Oxford Street,
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Jacket Illustration: Chesley Bonestell, Space Station, Ferry Rocket, and Space Telescope 1,075 Miles above Central America (1952). Reproduced courtesy of Bonestell LLC.
All Rights Reserved
Library of Congress Cataloging-in-Publication Data
Adler, Charles L.
Wizards, aliens, and starships : physics and math in fantasy and science fiction / Charles L. Adler.
pages cm
Summary: “From teleportation and space elevators to alien contact and interstellar travel, science fiction and fantasy writers have come up with some brilliant and innovative ideas. Yet how plausible are these ideas—for instance, could Mr. Weasley’s flying car in Harry Potter really exist? Which concepts might actually happen—and which ones wouldn’t work at all? Wizards, Aliens, and Starships delves into the most extraordinary details in science fiction and fantasy—such as time warps, shape changing, rocket launches, and illumination by floating candle—and shows readers the physics and math behind the phenomena. With simple mathematical models, and in most cases using no more than high school algebra, Charles Adler ranges across a plethora of remarkable imaginings, from the works of Ursula K. Le Guin to Star Trek and Avatar, to explore what might become reality. Adler explains why fantasy in the Harry Potter and Dresden Files novels cannot adhere strictly to scientific laws, and when magic might make scientific sense in the muggle world. He examines space travel and wonders why it isn’t cheaper and more common today. Adler also discusses exoplanets and how the search for alien life has shifted from radio communications to space-based telescopes. He concludes by investigating the future survival of humanity and other intelligent races. Throughout, he cites an abundance of science fiction and fantasy authors, and includes concise descriptions of stories as well as a glossary of science terms. Wizards, Aliens, and Starships will speak to anyone wanting to know about the correct—and incorrect—science of science fiction and fantasy”— Provided by publisher.
Includes bibliographical references and index.
ISBN 978-0-691-14715-4 (hardback : acid-free paper)
1. Fantasy literature—History and criticism. 2. Science fiction—History and criticism. 3. Physics in literature. 4. Mathematics in literature. 5. Physics—Miscellanea. 6. Mathematics—Miscellanea. I. Title.
PN3433.8.A35 2014
809.3’8762—dc23 2013027794
British Library Cataloging-in-Publication Data is available
This book has been composed in Minion Pro and League Gothic
Printed on acid-free paper. ∞
Typeset by S R Nova Pvt Ltd, Bangalore, India
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
To Poul Anderson, who wrote it better, shorter, and earlier
CONTENTS
1
PLAYING THE GAME 1
1.1 The Purpose of the Book 1
1.2 The Assumptions I Make 3
1.3 Organization 4
1.4 The Mathematics and Physics You Need 5
1.5 Energy and Power 6
I
POTTER PHYSICS 11
2
HARRY POTTER AND THE GREAT CONSERVATION LAWS 13
2.1 The Taxonomy of Fantasy 13
2.2 Transfiguration and the Conservation of Mass 14
2.3 Disapparition and the Conservation of Momentum 16
2.4 Reparo and the Second Law of Thermodynamics 21
3
WHY HOGWARTS IS SO DARK 27
3.1 Magic versus Technology 27
3.2 Illumination 28
4
FANTASTIC BEASTS AND HOW TO DISPROVE THEM 38
4.1 Hic sunt Dracones 38
4.2 How to Build a Giant 39
4.3 Kleiber’s Law, Part 1: Mermaids 45
4.4 Kleiber’s Law, Part 2: Owls, Dragons, Hippogriffs, and Other Flying Beasts 49
II
SPACE TRAVEL 57
5
WHY COMPUTERS GET BETTER AND CARS CAN’T (MUCH) 59
5.1 The Future of Transportation 59
5.2 The Reality of Space Travel 61
5.3 The Energetics of Computation 63
5.4 The Energetics of the Regular and the Flying Car 64
5.5 Suborbital Flights 68
6
VACATIONS IN SPACE 71
6.1 The Future in Science Fiction: Cheap, Easy Space Travel? 71
6.2 Orbital Mechanics 74
6.3 Halfway to Anywhere: The Energetics of Spaceflight 74
6.4 Financing Space Travel 82
7
SPACE COLONIES 86
7.1 Habitats in Space 86
7.2 O’Neill Colonies 87
7.3 Matters of Gravity 89
7.4 Artificial “Gravity” on a Space Station 93
7.5 The Lagrange Points 103
7.6 Off-Earth Ecology and Energy Issues 106
7.7 The Sticker Price 112
8
THE SPACE ELEVATOR 115
8.1 Ascending into Orbit 115
8.2 The Physics of Geosynchronous Orbits 116
8.3 What Is a Space Elevator, and Why Would We Want One? 118
8.4 Why Buildings Stand Up—or Fall Down 119
8.5 Stresses and Strains: Carbon Nanotubes 122
8.6 Energy, “Climbers,” Lasers, and Propulsion 123
8.7 How Likely Is It? 125
8.8 The Unapproximated Elevator 127
9
MANNED INTERPLANETARY TRAVEL 130
9.1 It’s Not an Ocean Voyage or a Plane Ride 130
9.2 Kepler’s Three Laws 131
9.3 The Hohmann Transfer Orbit 134
9.4 Delta v and All That 136
9.5 Getting Back 137
9.6 Gravitational Slingshots and Chaotic Orbits 138
9.7 Costs 142
10
ADVANCED PROPULSION SYSTEMS 145
10.1 Getting There Quickly 145
10.2 Why Chemical Propulsion Won’t Work 146
10.3 The Most Famous Formula in Physics 147
10.4 Advanced Propulsion Ideas 148
10.5 Old “Bang-Bang”: The Orion Drive 153
10.6 Prospects for Interplanetary Travel 155
11
SPECULATIVE PROPULSION SYSTEMS 157
11.1 More Speculative Propulsion Systems 157
11.2 Mass Ratios for Matter-Antimatter Propulsion Systems 168
11.3 Radiation Problems 173
12
INTERSTELLAR TRAVEL AND RELATIVITY 176
12.1 Time Enough for Anything 176
12.2 Was Einstein Right? 178
12.3 Some Subtleties 182
12.4 Constant Acceleration in Relativity 184
13
FASTER-THAN-LIGHT TRAVEL AND TIME TRAVEL 188
13.1 The Realistic Answer 188
13.2 The Unrealistic Answer 188
13.3 Why FTL Means Time Travel 190
13.4 The General Theory 193
13.5 Gravitational Time Dilation and Black Holes 195
13.6 Wormholes and Exotic Matter 198
13.7 The Grandfather Paradox and Other Oddities 205
III
WORLDS AND ALIENS 215
> 14
DESIGNING A HABITABLE PLANET 217
14.1 Adler’s Mantra 218
14.2 Type of Star 221
14.3 Planetary Distance from Its Star 226
14.4 The Greenhouse Effect 229
14.5 Orbital Eccentricity 232
14.6 Planetary Size and Atmospheric Retention 233
14.7 The Anna Karenina Principle and Habitable Planets 237
14.8 Imponderables 239
15
THE SCIENTIFIC SEARCH FOR SPOCK 242
15.1 Exoplanets and Exoplants 242
15.2 Doppler Technique 246
15.3 Transits and the Kepler Mission 249
15.4 The Spectral Signatures of Life 250
15.5 Alien Photosynthesis 251
16
THE MATHEMATICS OF TALKING WITH ALIENS 255
16.1 Three Views of Alien Intelligences 255
16.2 Motivation for Alien Contact 259
16.3 Drake-Equation Models and the Mathematics of Alien Contact 267
IV
YEAR GOOGOL 273
17
THE SHORT-TERM SURVIVAL OF HUMANITY 275
17.1 This Is the Way the World Will End 275
17.2 The Short-Term: Man-Made Catastrophes 275
18
WORLD-BUILDING 292
18.1 Terraforming 292
18.2 Characteristics of Mars 294
18.3 Temperature and the Martian Atmosphere 295
18.4 Atmospheric Oxygen 299
18.5 Economics 301
19
DYSON SPHERES AND RINGWORLDS 303
19.1 Dyson’s Sphere 303
19.2 The Dyson Net 305
19.3 Niven’s Ringworld 311
19.4 The Ringworld, GPS, and Ehrenfest’s Paradox 318
19.5 The Ringworld Is Unstable! 320
19.6 Getting There from Here—and Do We Need To? 324
20
ADVANCED CIVILIZATIONS AND THE KARDASHEV SCALE 326
20.1 The Kardashev Scale 326
20.2 Our Type 0.7 Civilization 327
20.3 Type I Civilizations 329
20.4 Moving Upward 331
20.5 Type II Civilizations 332
20.6 Type III Civilizations 334
21
A GOOGOL YEARS 336
21.1 The Future of the Future 336
21.2 The “Short Term”: Up to 500 Million Years or so 336
21.3 The “Medium Term”: Up to about 1013 Years 338
21.4 The “Long Term”: Up to a Googol Years 341
21.5 Black Hole–Powered Civilizations 344
21.6 Protons Decay—or Do They? 346
21.7 A Googol Years—All the Black Holes Evaporate 346
21.8 Our Last Bow 349
Acknowledgments 351
Appendix: Newton’s Three Laws of Motion 353
Bibliography 359
Index 371
WIZARDS, ALIENS, AND STARSHIPS
CHAPTER ONE
PLAYING THE GAME
Dear Roger,
(XXX) and I have been exchanging letters for some time. As a fan, he’s strange; he likes the science better than the fiction. Wants me to quit futzing with the plot and characters and get on with the strange environments. He plays The Game: finds the holes in the science and writes in. I like him.…
—LETTER FROM LARRY NIVEN TO ROGER ZELAZNY, JANUARY 3, 1974
1.1 THE PURPOSE OF THE BOOK
When I was young, back in the 1970s and 80s, I read a lot of science fiction. I read a lot of other stuff, as well, but science fiction (and fantasy) filled a need that other literature simply didn’t. I tended to read “hard” science fiction, that is, stories plotted around hard science: physics, astrophysics, giant engineering projects, and the like. The worlds these stories portrayed, where space travel was common, human problems such as poverty were nearly eliminated, and conflicts centered on larger-than-life issues, always seemed to me more compelling than human dramas that revolved around why someone didn’t love someone else.
My tastes have changed since then, but the initial thrill of these stories has never really left me. I am a scientist because of my initial love of these tales. A chill still runs down my spine whenever I look at a Hubble Telescope photo or learn of a new exoplanet discovered. I live in hope that I will be alive when life on other planets is discovered. I still want to take a vacation to the Moon or to an orbiting satellite. These thrills are tempered by my adult realization that much of what goes into science fiction is quite unrealistic. This book is written for my fifteen-year-old self, and other readers like him, who would like to know which parts of science fiction are based on real science, and therefore in some way plausible, and which parts are unrealistic. This is the book I would have wanted to read when I was young. Just as for Niven’s correspondent, my interest in science fiction was mostly in the strange environments, the new worlds, the alien life, the superscience it portrayed. I wanted to know which parts were (potentially) real and which weren’t. To a large extent, that is why I eventually became a physicist.
Almost any science fiction story has a lot of incorrect science. This doesn’t make the story bad or invalid. Some authors, like Larry Niven, are almost obsessive in trying to get the science right; most are more lackadaisical about it. However, the standards for the profession are pretty high: no science fiction writer can be really esteemed accomplished unless he or she has a thorough knowledge of basic physics, chemistry, biology, astrophysics, history (ancient and modern), sociology, and military tactics; and besides all this, must possess a certain something in their air and manner of writing, or their profession will be but half-deserved. (Improvement of their minds by extensive reading goes without saying.) Science fiction writers do not have the same opportunities as research scientists do to stay up-to-date in their research fields, and writing science fiction involves a lot more fields than most research scientists can keep up with.
This book is one physicist’s attempt to discuss the science, particularly the physics and mathematics, that goes into writing hard science fiction. As an added bonus, I also take a look at physics in fantasy writing: there’s more in it than meets the eye. This is not an attempt to predict the future: as G. K. Chesterton pointed out, most of the fun in predicting the future comes from burying the people who attempt to do it [50]. Rather, I stick to the science used in crafting the stories. There are many books dedicated to the literary criticism of science fiction; this book is devoted to its scientific critique. As such, my choice of which literature to use is dictated both by my own reading and by the needs of the book. I tend to avoid writers who don’t make much use of science in their stories, except occasionally to comment on their errors. I also tend to stick to literature, that is, novels and short stories, although I occasionally comment on science fiction movies or television shows as well.
Many have gone down this path before me, scientists and writers alike (and a few who were both). The preeminent standout among science fiction writers is Poul Anderson, to whom this book is dedicated, for his essays “How to Build a Planet” and “On Thud and Blunder.” I read both when I was a teen; this book would not have been written but for his example. Isaac Asimov and Arthur C. Clarke both wrote many essays on science. Larry Niven has written several essays on the scientific aspects of teleportation, time travel, and other science fiction themes. Almost from the beginning of the modern era, scientists have written essays on science fictiony ideas, and I reference them where appropriate. This book is mainly synthetic rather than original, although I think there are a few new things in it, such as the discussion of candlelight in the Harry Potter series in chapter 3.
1.2 THE ASSUMPTIONS I MAKE
David Gerrold has written that science fiction authors by necessity almost always involve bits in their work that defy the laws of science as we know them. He refers to places where this happens as instances of “baloneyum.” His advice is that beginning authors limit themselves to only one piece of baloneyum per story, experienced
authors perhaps as many as two, and only grandmasters put in three instances [94]. It’s a good rule.
In this book I have followed a similarly conservative path. In analyzing science fiction my assumptions are that the laws of physics as we understand them now are pretty much correct. They are incomplete; we don’t know all of them, but the incompleteness doesn’t really affect most science fiction stories. In particular, I assume that Newton’s laws of motion are good enough to describe things larger than atoms, that Einstein’s theory of relativity is correct, and that quantum mechanics is the correct description of nature on the microscopic scale. The one example of baloneyum I indulge in is in the consideration of faster-than-light travel and, equivalently, time travel, which appear to be impossible from almost everything we know about physics—but perhaps not quite.