Wizards, Aliens, and Starships: Physics and Math in Fantasy and Science Fiction

by Adler, Charles L.

  1.3 ORGANIZATION

  There are four large sections of the book. Each of them contains several chapters centered on a given theme. The sections are:

  1. “Potter Physics.” This first section explores physics as used and abused in fantasy novels and series. I’ve chosen two examples of “urban fantasy” novels to focus on, the Harry Potter series by J. K. Rowling and the Dresden Files novels by Jim Butcher. The issues here are different from those in the rest of the book, for fantasy, by its very nature, cannot adhere strictly to scientific laws. However, we can ask whether the series are at least internally consistent, and whether the magic used in the series makes sense when in contact with the muggle world.

  2. “Space Travel.” This is the largest single section, consisting of nine chapters, as befits the subject. Space travel is perhaps the theme of science fiction, to the point that it almost defined the genre from the 1930s to the 1980s. One goal of this section is to examine not only the scientific issues involved in space travel but also the economic ones. The big question is, why isn’t space travel cheap and common now, as it was certainly foretold to be in almost all of “golden age”1 science fiction?

  3. “Worlds and Aliens.” This section consists of four chapters exploring the other major theme of science fiction, the possibility of life on other worlds in our Solar System and elsewhere.

  4. “Year Googol.” This part explores the potential survival of humanity (or other intelligent species) into the far distant future, along lines laid down originally by the writer Olaf Stapledon and the physicist Freeman Dyson.

  My choice of subject matter, like the organization of the book, is idiosyncratic. The book is a loose collection of essays more than a unified text. I write about those aspects of science fiction and fantasy that most interest me. My hope is that my readers are similarly interested. By necessity, I concentrate on those writers whom I know the best, meaning American and British science fiction writers. Since I know the “golden age,” New Wave, and early cyberpunk literature best, this may give the book an antiquated feel. I try to include ample description of these stories so that anyone reading the book can understand the scientific points I am trying to make.

  A set of problems has been prepared for instructors intending to use this book as a class text. For space reasons, we have placed these problems, organized by chapter, on a website (press.princeton.edu/titles/10070.html). I’ve also included solutions and hints for the problems. This book cannot be used to replace a physics textbook, but it could be used in a specialized course.

  1.4 THE MATHEMATICS AND PHYSICS YOU NEED

  I expect the readers of this book to be able to read and use algebraic equations, and to understand them on some level. I intend the book as a working book for science fiction enthusiasts who have at least a decent knowledge of algebra and know what calculus means.

  The equations I introduce don’t exist in a vacuum; they are mostly drawn from physics, and represent physical quantities. That is, unlike pure mathematics, there is always some connection with the real (or, at least, science fiction) world that is expressed by them. In most cases I explain the equations in detail but do not derive them from basic principles. This is unlike what happens in most physics courses, where the emphasis is as much on deriving the equations as on using them. Since most of my readers aren’t physicists, I will explain how the equations are used and why they make sense. I also want my readers to have a conceptual understanding of calculus. There are only a few places where this will crop up, so it isn’t essential, but it is useful to know what is meant when I use the terms “derivative” and “integral.”

  Physics is the science central to this book. Appendix 1 at the end of the book reviews Newton’s laws of motion, which are central to any understanding of physics. Just as a knowledge of grammar and spelling is needed for reading and writing, a knowledge of Newton’s laws is needed for any understanding of physics. Newton’s laws describe how things move on the macroscopic scale; that is, they are a good description of things larger than atomic size. However, they are only approximations to the truth. The laws of quantum mechanics are the real way things work. It is characteristic of physics that the underlying laws are difficult to see directly. Why this is so, and why Newton’s laws are good approximations to the true fundamental laws of nature, are questions beyond the scope of this book to answer. If readers are interested in this, there are dozens of good books that examine these questions. I strongly recommend two books by Richard Feynman, The Character of Physical Law and (for those who have a physics background) The Feynman Lectures on Physics, particularly book 2, chapter 20 [81][85].

  1.5 ENERGY AND POWER

  Energy and power, which is the rate at which energy is converted from one form to another, are the key points to understand for this book. Energy is useful because it is conserved: it can be transformed from one form to another, but not created or destroyed. I use energy conservation, either implicitly or explicitly, in almost every chapter of the book. A few of the forms that energy can take are the following:

  • Gravitational potential energy: This is the energy that pairs of objects possess by virtue of the gravitational attraction between the members of the pair. This form of energy is very important for any discussion of space travel.

  • Chemical potential energy: This is the energy resulting from the spacing, composition, and shape of chemical bonds within a molecule. Chemical reactions involve changes in these properties, which usually means changes in chemical potential energy. In an exothermic reaction, the chemical potential energy is less after the reaction than before it. Energy is “released” during the course of the reaction, usually in the form of heat. An endothermic reaction is the opposite: energy must be added to the reaction to make it proceed.

  • Nuclear energy: This is the energy resulting from the structure and composition of the atomic nucleus, the part of the atom containing the protons and neutrons. Transformations of nuclei either require or release energy in the same way that chemical reactions do, except on an energy scale about one million times higher.

  • Mass: Mass is a form of energy. The amount of energy equivalent to mass is given by Einstein’s famous formula

  where E is the energy content of mass M and c is a constant, the speed of light (3×108 m/s, in metric units). This is the ultimate amount of energy available from any form of mass.

  • Kinetic energy: This is the energy of motion. Newton’s formula for kinetic energy is

  where K is the kinetic energy, M is the mass of the object, and v is its speed. This formula doesn’t take relativity into account, but it is good enough for speeds less than about 10% the speed of light. If an object slows down, it loses kinetic energy, and this energy must be turned into another form. If it speeds up, energy must be converted from some other form into kinetic energy.

  • Heat: Heat is energy resulting from the random motion of the atoms or molecules making up any object. In a gas at room temperature, this is the kinetic energy of the gas molecules as they move every which way, plus the energy resulting from their rotation as they spin about their centers. For solids or liquids, the energy picture is more complicated, but we won’t get into that in this book.

  • Radiation: Light, in other words. Light carries both energy and force, although the force is almost immeasurable under most circumstances. Most light is invisible to the eye, as it is at wavelengths that the eye is insensitive to.

  In the units most often used in this book, energy is expressed in joules (J). The joule is the unit of energy used in the metric system. To get a feel for what a joule means, take a liter water bottle in your hand. Raise it 10 cm in the air (about 4 inches). You have just increased the potential energy of the water bottle by 1 J.2 Other units are also used; in particular, the food calorie, or kilocalorie (kcal), will be used in several chapters. The kilocalorie is the amount of energy required to increase the temperature of 1 kg of water by 1°C (Celsius). It is equivalent to 4,190 J. Other units ar
e defined as they come up in the chapter discussions.

  Power is the rate at which energy is transformed from one form to another. The unit of power is the watt (W), which is 1 J transformed per second from one form of energy to another form. For example, if we have a 60 W light bulb, 60 J is being transformed from the kinetic energy of electrons moving through the tungsten filament in the light bulb into radiation, every second.

  The different forms of energy and their transformations are the most important things you need to know to read this book. With this brief introduction to the subject, we are ready to start.

  NOTES

  1. Science fiction readers and critics divide up science fiction of the last century into different subgenres, which typically also follow one another chronologically. For example, the “golden age” covers the period from the end of World War II through the mid-1960s, when authors such as Robert Heinlein, Isaac Asimov, and Arthur Clarke were at the peak of their popularity. The major science fiction themes of this time period are space travel and alien contact. I also refer to the New Wave writers of the 1960s and 1970s, such as Brian Aldiss, and cyberpunk literature from the 1980s and later. Of course, many authors, such as Philip K. Dick, resist easy classification. Fantasy is similarly divided, into “sword and sorcery,” “magic realism,” and “urban fantasy,” among other subgenres. Urban fantasies are very useful for this book because they allow side-by-side comparison of fantasy worlds with the real world in which the laws of physics hold sway.

  2. To be specific, you have increased the potential energy of the pair of objects, the Earth plus the water bottle, by 1 J. Potential energy is always the property of a system, that is, of two objects or more, not of an individual object. However, because the Earth essentially hasn’t moved, owing to its high mass, we typically talk about the lighter object of the pair as the one whose potential energy changes. Being specific about this is important only when the masses of the two objects in question are about equal.

  PART I

  POTTER PHYSICS

  CHAPTER TWO

  HARRY POTTER AND THE GREAT CONSERVATION LAWS

  2.1 THE TAXONOMY OF FANTASY

  The “physics of fantasy” seems like an oxymoron: by definition, fantasy doesn’t concern itself with science but with magic. However, a lot of fantasy writers follow in the tradition of science fiction writers in trying to set up consistent rules by which their fantasy worlds operate. This is because many fantasy writers are science fiction writers as well. It is almost a universal trait: those who write quasi-realistic science fiction will also write quasi-realistic, rules-based fantasy; those who don’t generally won’t set up rules by which magic works.

  Among the former is Ursula K. Le Guin, whose Earthsea trilogy has long descriptions of the “rule of names” underlying all magic. Her books include several lectures by magicians on exactly how this works. Many writers have found her works compelling enough to copy her rules in their own stories. Others base their magic rules on outdated scientific or philosophical ideas, as Heinlein did in his novella, Magic, Incorporated. Magicians in that book use the “laws” of similarity and so forth, to perform their magic. Randall Garrett in his Lord Darcy stories writes of a world in which magic (following these laws) has developed instead of science. The stories are full of descriptions of how the magic works and is used in solving crimes.

  The popular writer J. K. Rowling in her Harry Potter novels does not attempt to have the magic in her books follow any known laws of science. Please don’t misunderstand me: I love her books, but not for any attempt on her part to be consistent in how magic works. This is why this section of the book is called “Potter Physics”: her body of work contains innumerable examples of magic being used in ways that violate physical law and are also internally inconsistent. She belongs solidly to the second class of writers.

  These rules of magic don’t have to follow known laws of physics—indeed, they can’t, or else we’d call them science fiction instead of fantasy. The laws that many rules-based fantasy writers choose to keep are typically the most fundamental of the physical laws: the great conservation principles—the conservation of mass, energy, and momentum—and the second law of thermodynamics.

  2.2 TRANSFIGURATION AND THE CONSERVATION OF MASS

  Harry spun around. Professor Moody was limping down the marble staircase. His wand was out and it was pointing at a pure white ferret, which was shivering on the stone-flagged floor, exactly where Malfoy had been standing.

  —J. K. ROWLING, HARRY POTTER AND THE GOBLET OF FIRE

  The issue of shape-changing in the world of the Harry Potter novels is vexing. Since the 1800s one of the principal ideas of science has been the conservation of mass: the total mass in a closed system cannot change. In turning Draco Malfoy into a ferret, what did Professor Moody do with the rest of his mass? If we assume that Draco at age fifteen had a mass of about 60 kg and a small ferret has a mass of about 2 kg, where did he stash the other 58 kg? This is an issue for most fantasy writers when dealing with shape-changers. In Swan Lake, when Odette is changed into a swan by the evil wizard Rothbart, what happened to the rest of her? One can imagine some sort of weird biological process by which flesh morphs from one animal form to another, but where does the excess go?

  A number of fantasy writers have dealt with this issue head-on. In Poul Anderson’s Operation Chaos, the hero is a werewolf who explicitly states in the course of the book that his mass is the same in both states. This is OK for a werewolf, as the average adult wolf has about the same weight as a very light adult male, but it raises problems later on when the hero meets a weretiger. In human form, the magic user must maintain a weight of nearly 400 pounds simply to make a fairly small tiger. This entails health problems and severe psychological stress. In Niven’s story “What Good Is a Glass Dagger?,” the hero implicitly invokes the principle of conservation of mass when he says that he doesn’t look too overweight as a human, but as a wolf he’d look ten years’ pregnant.

  This doesn’t bother most fantasy writers, perhaps because it would impose too strong constraints on many fantasy stories if writers stuck to the conservation of mass. For example, when trapped by the sword-wielding barbarian, the beautiful sorceress can’t turn herself into a dove and fly away. Instead, she’d have to turn into an ostrich and kick him in the ribs. (Actually, that would make a good story.) Thinking about where the mass goes leads to headaches. Einstein tells us mass is convertible into energy at a “cost” of 9 × 1016 J/kg. If somehow the mass turns into energy, then even a very small imbalance makes a very big boom. (The Hiroshima bomb blast was about the equivalent of 1 gram of matter converted into energy.) Whenever Professor McGonagall transforms herself from a human into a cat, she ought to release as much energy as all of the atom bomb tests ever done, all at the same time. And where does she get the extra mass when she turns back into a human?

  There doesn’t seem to be any good answer to this problem. If mass isn’t conserved, maybe it is sloughed off somewhere during the transformation (yuck) or stored in some extra dimension or something. It is a vexation. You have even more problems if you are transforming material from one element to another: it can be done, but with difficulty. Consider Medusa’s problem of turning people into stone. People are made up mostly of carbon and water, whereas stone is mostly silicon. Carbon has atomic number 6 and atomic mass 12, and has six protons, six electrons, and six neutrons. Silicon has atomic number 14 and atomic mass 28, with 14 protons, 14 electrons, and 14 neutrons. You can’t turn one elementary particle into another willy-nilly: to convert the carbon in a living body into silicon, you have to provide the extra particles somehow. Perhaps Medusa bombards her victims with high-energy particles? And if she can do that, why bother turning them into stone at all?

  2.3 DISAPPARITION AND THE CONSERVATION OF MOMENTUM

  Morris got bugeyed. “You can teleport?”

  “Not from a speeding car,” I said with reflexive fear. “That’s death. I’d keep the velocity.�
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  —LARRY NIVEN, “THE FOURTH PROFESSION”

  In the Harry Potter novels, the power of disapparition is used commonly. This is the ability to vanish from one spot and reappear instantly in another. In other works this maneuver is more commonly referred to as teleportation. In Star Trek the transporter is used for this purpose. Issues of conservation of energy plague teleportation in a similar manner to shape-changing. In disapparating, is Harry being converted to energy, zapped off somewhere at the speed of light, and converted back? If so, this is an awful lot of energy to manage: 9 × 1016 J for every kilogram we teleport. If even 1% of the energy isn’t contained somehow, we have the equivalent energy of an H-bomb going off. We also have all the other problems from the last section: turning 80 kg or so of matter into “pure energy” violates all sorts of conservation laws, and also involves a rather bad issue related to entropy. Or murder, if you’d rather think of it that way. A human being is a very complicated structure, and by transforming the body into pure energy, as far as I can tell, you are killing the person. Bringing a person back to life after doing this by reconstituting him or her elsewhere is implausible.