How to Teach Relativity to Your Dog


By Chad Orzel

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They say you can’t teach an old dog new tricks. But what about relativity?

Physics professor Chad Orzel and his inquisitive canine companion, Emmy, tackle the concepts of general relativity in this irresistible introduction to Einstein’s physics. Through armchair- and sometimes passenger-seat-conversations with Emmy about the relative speeds of dog and cat motion or the logistics of squirrel-chasing, Orzel translates complex Einsteinian ideas — the slowing of time for a moving observer, the shrinking of moving objects, the effects of gravity on light and time, black holes, the Big Bang, and of course, E=mc2 — into examples simple enough for a dog to understand.
A lively romp through one of the great theories of modern physics, How to Teach Relativity to Your Dog will teach you everything you ever wanted to know about space, time, and anything else you might have slept through in high school physics class.


How to Teach Relativity to Your Dog
"For the price of a book, Orzel delivers the heady, joyful experience of taking a small college class with a brilliant and funny professor who really knows how to teach. A thoroughly winning romp through a rock-solid presentation of a beautiful subject."
—Louisa Gilder, author of The Age of Entanglement
"Move over, Krypto—there's a new superdog in town! Chad Orzel's dog Emmy, having mastered quantum physics, now helps us understand Einstein's theories of relativity in a deep and accessible way. Get this dog a cape!"
—James Kakalios, Professor of Physics, University of Minnesota, and author of The Physics of Superheroes and The Amazing Story of Quantum Mechanics
"Everyone's favorite physics-loving canine is back, this time giving us a dog's eye view of Einstein and relativity. Physics professor Chad Orzel leads Emmy (and us) through an engaging tour of light speed, time dilation, and amazing shrinking bunnies (length contraction)—not to mention what all this means for the search for the elusive 'bacon boson.'"
—Jennifer Ouellette, author of The Calculus Diaries
"With Nero, the egocentric cat who believes it is the center of the universe, and Emmy, the student dog whose questions and misunderstandings would drive any teacher to distraction, and whose interest in relativity is how E = mc2 can turn squirrels into energy, Chad Orzel has created a delightful cast of characters to make his introduction to relativity relatively painless. A cleverly crafted and beautifully explained narrative that guides readers carefully into the depths of relativity. Whether you are a hare or a tortoise, or even a dog, you will enjoy this."
—Frank Close, author of The Infinity Puzzle
"Emmy may be one smart dog, but her owner also happens to be an uncommonly gifted communicator. Chad Orzel's treatment of special and general relativity is comprehensive, informative, and amazingly accessible, yet it's funny too. This is, by far, the most entertaining discussion of the subject that I've ever had the pleasure of reading."
—Steve Nadis, coauthor of The Shape of Inner Space

For Claire.
Did I type today?
Yes I did, honey.
I typed a lot.

IT'S COLD AND FLU SEASON AGAIN, and between teaching at the college and a toddler in day care, I get every single bug that goes around. I'm sitting at the dining room table grading exams when a coughing fit hits. When it finally stops, I take a drink of water, and then notice a thumping sound. I look over toward Emmy, on the floor next to the couch, and she's thumping her tail on the floor with her tongue lolling out the side of her mouth: the dog equivalent of a laugh.
"Yeah, laugh it up, fuzzball. You think this is funny?"
"Sorry," she says, "but at the end there, it sounded like you said—." She barks twice, sounding a little like a cough. "That's really funny in Dog."
"Yeah? What's it mean?"
"Well, it's . . . umm . . . You know, if you can't sniff your own butt, you won't get the joke."
"I'll try to contain my disappointment, then." I turn back to my grading.
"I'll think about it, and see what I can come up with, but translating humor is really hard."
"Translating anything is hard." I say, not looking up.
"Yeah? What do you know about translation?"
"Well, it's what I do for a living."
"You're a physicist, not a diplomat."
"I'm a physics professor," I say, putting my pen down. "In addition to doing physics, I teach physics to other people."
"And dogs!"
"Yes, and dogs. Teaching physics necessarily involves translation. The natural way to express physics is through math, but most people don't think in mathematical terms. So, a lot of the business of teaching physics is finding ways to translate physical ideas from mathematical equations into concepts drawing on everyday language and experience."
"So, making analogies and stuff like that?"
"That's part of it, yes. I also spend a lot of time dealing with people's preconceptions about how the world works. Sometimes, our intuition about how everyday objects behave leads us astray when we think about physics, and the first step in teaching the subject is to break down those preconceptions. Basically, to start over."
"You wouldn't have that problem if you stuck to teaching dogs," she says, looking pleased with herself and her species.
"Nope. I have no clue at all about how things work. I'm a clean slate, when it comes to physics."
"I wouldn't go that far, but you at least have a different set of preconceptions than most humans do. Which means that thinking about physics as it appears to a dog can be a useful thing to do—looking at the problem from a different angle, and with an open mind, can sometimes give you insight that you wouldn't get by going straight at your own misconceptions."
"So, when you think about it, teaching physics to me helps you teach physics to humans."
"Yeah, it does."
"Which means that in a sense, it's part of your job, right?" She trots over to me and sits down, looking hopeful.
"I know where you're going with this, so let me remind you that grading these papers is also part of my job. I need to turn my final grades in tomorrow, so that's the more important part right this minute."
"Oh." She deflates a little.
"But tomorrow is also the start of our break, so I'll have time to spend talking to you about physics, if you want."
"Preferably while taking long walks!"
"Sure, that works. So, let me finish grading these exams, while you think about what areas of physics you'd like to learn about, OK?"
"OK!" She trots off in the direction of the library, and I go back to my grading. As I start on the next paper, I hear her saying "Maybe I can finally find out what this Einstein guy was all about . . ."
Ask any human, or most dogs, to picture a scientist, and odds are good that their mental image will look a lot like the iconic pictures of Albert Einstein—white hair sticking in all directions, rumpled clothes, maybe even a German accent and a distracted air. This is a little unfair to scientists1—great scientists come in all sizes, shapes, races, genders, and nationalities (though not yet species)—but Einstein has captured the popular imagination to an amazing degree and dominates the popular image of a scientist. Even more than fifty years after his death, Einstein was the second most popular answer in a poll asking people to name a living scientist2.
Asked why Einstein is a famous scientist, even dogs can come up with the equation E=mc2, and possibly the words "theory of relativity." Explaining what those mean, and where they come from, is beyond most humans, though, let alone dogs. This is an unfortunate state of affairs, as Einstein's theory of relativity is one of the cornerstones of modern physics. Along with quantum mechanics, relativity completely revolutionized the way scientists view our universe. It provides insight into problems that classical physics can't handle, and poses new problems that physicists still grapple with a hundred years later.
Unfortunately, the features that make relativity so essential to physics also make it extremely intimidating to non-physicists. Relativity deals with situations that are very foreign to our everyday experience of the universe—objects moving thousands of times faster than the fastest man-made objects, astronomical objects packing enormous masses into tiny spaces—and its predictions defy all our normal expectations. Relativity tells us that quantities that seem fundamental—distances through space, and duration in time—in fact vary from one observer to another. A moving clock ticks at a different rate than a stationary one. A clock near a massive object ticks at a different rate than one farther away. And space itself is stretched by the presence of mass, so the length of a path between two points depends on what you pass along the way.
These are all surprising predictions made by the theory of relativity. They are also unequivocally true, confirmed by countless experiments in the century since Einstein first introduced relativity in 1905. The universe we live in is a far stranger place than our everyday intuition leads us to expect. To fully understand it, we have to expand our conception of the universe to include the counterintuitive predictions of the theory of relativity.
This can seem a daunting task, but one way to make it more approachable is to think like a dog. As any pet owner knows, dogs look at the world in a very different way—not entirely without preconceptions, but at least with different preconceptions than their humans, often in ways that make physics easier to understand. To a dog, any time should be dinner time, so the idea of clocks running at different rates for moving observers, or observers in different places, is easier to accept.
If you can learn to think like a dog, to approach the world as an endless source of surprise and wonder, modern physics is much less intimidating. Looking at physics from a dog's point of view allows us to shake off some of our human expectations about how things ought to work, and lets us appreciate the weird and wonderful world revealed by relativity.
This book reproduces a series of conversations with my dog about aspects of both special and general relativity. Each conversation is followed by a more detailed discussion of the physics involved, aimed at interested human readers. Some of the topics covered have achieved fame, or at least notoriety, in the wider culture, like Einstein's famous equation E=mc2 (Chapter 7) or the idea of black holes (Chapter 10); others are less familiar to non-physicists, such as the merging of space and time (Chapter 5) or the effects of gravity on time (Chapter 9), but are just as essential to the modern understanding of physics. We'll also talk about some of the innumerable experiments and observations confirming that the universe is a weird and wonderful place.
We won't be able to cover everything that's interesting about relativity—generations of scientists have dedicated their careers to the subject without managing to exhaust its wonders—but we hope this will provide an introduction to the subject giving human and canine readers some sense of what it's about, and why it's important. And the next time some pesky cat asks you to explain why Einstein is famous, you'll have a good answer for them.
"Don't forget me!"
"I'm not forgetting you. How am I forgetting you?"
"Oh, sure, you mention the conversations at the start of the chapters. But you didn't tell them that I'll be keeping an eye on you in the middles, too. If you try to leave anything out, or sneak something past without explanation, I'll make sure you get it right."
"You mean, like you're doing now?"
"Yeah. Oh, wait—is this bit going in the book?"
"Oh. Well, then, I guess they're informed. But they should know that I'll be keeping an eye on you, and I'm an excellent watchdog."
"I think you've made that point."
"Also, I'm really cute, and I like long walks, and belly rubs, and chasing bunnies, and bacon. I really like bacon. Also, cheese. And peanut butter."
"I fail to see how this is relevant."
"Well, you know, in case they want to mail me presents. You know, because I'm an excellent physics dog, and all. You are going to put our address in the book, right? So they can send me stuff."
"I think that's just about enough out of you."
"Oh, all right. You're no fun, though."
"Can we please get started with the physics discussions?"
"Sure, absolutely. Lay some physics on me—I'm ready for anything!"

Chapter 1
AS I'M DRIVING DOWN THE STREET, a squirrel darts out into the road a block or so ahead of me. From the back seat, Emmy says, "Gun it! Hit the squirrel, hit the squirrel, hitthesquirrel!"
"Will you sit down and be quiet?" We're having some work done on the house, and I'm taking her to campus with me so she's not underfoot for the contractors.
The squirrel makes it to the other side of the road and up a tree to safety. "Aw.w.ww," Emmy says. "Dude, you totally could've gotten that one. This car is way faster than a stupid squirrel."
"That may be, but I have a class to teach. I don't have time to careen around like a maniac chasing squirrels with the car."
"No, no—you'd have plenty of time. Time slows down when you go faster."
I look in the rearview mirror. Emmy's standing on the seat, wagging her tail and looking pleased with herself.
"Oh, God," I say. "Don't tell me you've started reading about relativity."
"OK, I won't tell you." She's quiet for a few seconds, then, "Relativity is pretty cool, though. I can slow time!"
This is not going anywhere good, I can tell. We come to a traffic light, and I stop.
"One thing I don't understand, though . . ."
I sigh. "OK, what is it you want me to explain?"
"Why do they call it that?"
"Why do they call what, what?"
"Why do they call relativity 'relativity'? Why not something cooler, like superfast time-slowing squirrel-catching dynamics?"
"Well, for starters, physicists don't care much about squirrels. More importantly, though, the name 'relativity' comes from one of the theory's most basic elements: the idea that relative motion is the only thing that matters. There is no absolute frame of reference against which we can measure the motion of everything in the universe." The light changes, and I start driving again.
"Yeah, but that's silly. Of course there's a fixed frame of reference."
"Really? What is it?"
"Well, our house, silly. And the yard, with the big oak tree. And the other tree. And the other, other tree. And—"
"OK, OK, I get it."
"The house is where I keep my stuff!"
"Yeah, OK. But the house only looks like it's a fixed frame of reference. I mean, it's on the Earth, right? And the Earth is rotating."
"I guess so . . ."
"And it also moves around the sun, which is why we have seasons. The thing you're using as a fixed reference point is really in constant motion, and all you're doing is measuring your motion relative to it."
"OK, but I can still tell the difference between when I'm standing still and when I'm moving."
"Well, when I'm moving, I walk past stuff, and sniff things, and chase bunnies and squirrels. When I'm not, I just sit there."
"Sure, but how can you tell the difference between a situation where you're moving, and a situation where you're sitting still and everything else is moving in the opposite direction?"
"Well, that would be silly." We come to another red light, and I stop again. "Anyway, I can tell that I'm the one moving, because my legs are moving."
"OK, but how about when you're in the car, like we are now?"
"What do you mean?"
"Well, we're sitting still right now, but when we start moving again . . ." The light changes, just at the right moment. I accelerate a bit, then cruise at a constant speed. "How can you tell that we're moving, rather than sitting still and watching the rest of the world move by?"
"Ummm . . . the engine is going."
"Yeah, but we could be on a treadmill, with fake scenery moving past us. This whole trip could be a fiendish illusion."
Emmy looks worried. "I don't like fiendish illusions."
"Calm down, it's just a hypothetical." She looks somewhat mollified. "Anyway, the answer is that there's no physics measurement you can do to distinguish between sitting still and moving at a constant velocity, the way we are now. You can detect acceleration, like this"—I step on the gas and speed up—"but when we're moving at a constant speed, all the laws of physics are exactly the same as when you're standing still."
"So how do you tell when you're moving?"
"You can't. All you can say is that you're moving relative to some other object—which is why the theory is called relativity."
I check the mirror, and she's looking thoughtful. "So," she says, "the only thing we can measure is relative velocity?"
"Like your velocity relative to that car with the lights?"
"What?" I look behind us and see a police car pulling out, lights flashing. I look down and realize my foot is still on the gas. "Crap! Well, maybe he's after someone else . . ."
The cop car pulls in behind me. "I don't think so," Emmy says cheerfully. "He's got you nailed."
I pull over. "This is all your fault, you know," I say as I kill the engine.
"Yeah? Good luck explaining that to the cop." She turns toward the window and wags her tail cutely, just in case the police officer has dog treats.
Einstein's theory of relativity is one of the cornerstones of modern physics and requires a complete and dramatic rethinking of ordinary concepts of space and time. Its most famous predictions—the equivalence of mass and energy, the slowing of time for fast-moving observers, the warping of space near black holes—have captured the popular imagination and are staples of science fiction.
Relativity is exotic and exciting precisely because it runs so counter to our usual intuition—we don't notice its effects when going about our everyday lives. The effects of relativity only show up when we are dealing with either extremely small, fast-moving objects, like the subatomic particles being smashed together in particle accelerators, or extremely large, massive objects like black holes and galaxy clusters. It may seem surprising, then, that the place to start understanding the physics of relativity is with the motion of ordinary, everyday objects like dogs and cars.


While we associate the word "relativity" most strongly with Albert Einstein, the central idea goes back long before him. Einstein himself, in his popular book Relativity: The Special and the General Theory,3 attributes the concept to Galileo Galilei (1564–1642) and Sir Isaac Newton (1643–1727), who lived almost three centuries before he was even born.
The central idea of relativity is that the laws of physics must appear the same to all observers. Whether you're moving or standing still, physics should work in exactly the same way: objects should accelerate when pushed, energy and momentum should be conserved, and so on. This is just common sense—if the laws of physics were different for running dogs than dogs sitting calmly on the ground, it would be almost impossible to understand the world around us or to predict the motion of objects like bouncing balls or thrown treats. Since even dogs without a deep knowledge of physics can track down tennis balls and snatch treats out of the air, the simple version of relativity must be true.
Of course, human physicists aren't satisfied with "Watch me catch this tennis ball" as proof, so we need to be more precise about what we mean when we talk about moving objects. The key insights that led Einstein to the theory of relativity start from very careful and exact definitions of motion. Following in his footsteps, then, we need to talk about how physicists describe moving objects.
Emmy the canine physicist, sitting in her living room watching the world outside, can describe the positions of moving objects—Winthrop the basset hound walking by on the street, say, or a human child bicycling past—by measuring the distance from her spot by the window to the object in question. At some instant, Winthrop may be 9 meters (m) due south of her, for example. A child on a bike may be 8m south and 6m east.
Emmy can measure the motion of the creatures on the street by recording their positions at one time, waiting a bit, then looking at their new positions and comparing the two, as shown in Figure 1.1. If the small human on wheels moved from 8m south and 6m east to 8m due south in one second, our canine physicist would say that the child has a velocity of 6 meters per second (m/s) due west.4 If Winthrop moves from 9m due south to 9m south and 3m east in the same time, he has a velocity of 3 m/s due east.
Figure 1.1.
To start thinking about relativity, we need to ask how these objects appear to another observer—for example, my parents' yellow Lab, Bodie, in a car headed east along the street at, say, 10 m/s. That dog would measure the motion of the various other creatures by recording their distances from his own position in the car—
"No way, dude. Don't even go there."
"You're about to say that dogs are very self-centered creatures and always measure positions relative to themselves. It's an unfair stereotype of dogs, and I won't stand for it."
"But that's how the whole thing works. If you want to understand relativity, you need to look at positions and velocities as measured by a moving observer."
"That may be, but that's not how dogs do it. We always measure positions relative to fixed points, like our houses."
"Look, I need a moving observer for this explanation to work out. Otherwise, this book is going to be a huge mess."
"You can have a moving observer, just don't make it a dog."
Figure 1.2.
"Fine. How about a cat, then?"
"Oh, yeah, that's fine. Cats are incredibly self-centered."
To start thinking about relativity, we need to ask how these objects appear to another observer, for example, my sister's cat Nero riding in a car headed east along the street at, say, 10 m/s. The cat, being incredibly self-centered, would measure the motion of the various other creatures by recording their distances from his own position in the car. From Nero's point of view, shown in Figure 1.2, he is perfectly stationary, and the rest of the world moves around him. The barking dog at the window is actually moving west at 10 m/s, as are the house, the trees in the yard, and everything else in the world, according to Nero.
According to Nero in the car heading east, the westbound child on the bike is not moving at the 6 m/s measured by the stationary dog but at a higher speed. If the child is 20m east of the cat at some instant, one second later, the distance is down to just 4m: the child has pedaled her way west by 6m, while the road and everything on it has moved 10m west. The velocity of the bicycling child is now 16 m/s due west, or the speed of the car plus the speed of the bike.
Regarding Winthrop the eastbound hound, Emmy at the window and Nero in the car disagree about not only his speed but also his direction of motion. In the one-second interval between measurements, Winthrop has moved 3m east, but the road he is on has moved 10m west (according to Nero), so the distance between the two has actually decreased. According to Nero in the car, Winthrop is headed west at 7 m/s, rather than east at 3 m/s, as measured by Emmy in the window.
"I like this version much better. Cats are so dumb."
"He's got it right, though, at least in a mathematical sense."
"What do you mean? The house isn't moving west—that would be ridiculous."
"It seems ridiculous because we're used to thinking of the Earth as a fixed reference point and measuring motion relative to it. If you want to calculate what happens in interactions between Nero and some other object, though, it's much easier to work things out using his frame of reference."
"Frame of reference? Is the cat in a picture, now?"
"Sorry. Frame of reference is a physics term that refers to the measurements made by a particular observer. The dog in the window occupies a frame of reference in which she is stationary, and all distances are measured from her position. The cat in the car is in a different frame of reference, in which he is stationary, and all distances are measured from his position in the car."
"Yeah, but he's moving, and I'm not."


On Sale
Feb 28, 2012
Page Count
368 pages
Basic Books

Chad Orzel

About the Author

Chad Orzel received his BA in physics from Williams College, his Ph.D. in chemical physics from the University of Maryland, and his postdoctorate from Yale University. He maintains a regular blog, Uncertain Principles, and is author of How to Teach Physics to Your Dog. He is currently a professor at Union College in Schenectady, New York. He lives near campus with his wife, their daughter, and, of course, Emmy.

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