How to Teach Quantum Physics to Your Dog

Chad Orzel

• Publisher: Scribner
• Year: 2009
• ISBN:
  9781416579014
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

Learn the basics of quantum physics with this clever, fun, and lighthearted introduction to modern physics based on a series of conversations with Chad Orzel and his dog Emmy. When physics professor Chad Orzel went to the pound to adopt a dog, he never imagined Emmy. She wasn't just a friendly mutt who needed a home. Soon she was trying to use the strange ideas of quantum mechanics for the really important things in her life: chasing critters, getting treats, and going for walks. She peppered Chad with questions: Could she use quantum tunneling to get through the neighbor's fence and chase bunnies? What about quantum teleportation to catch squirrels before they climb out of reach? Where are all the universes in which Chad drops steak on the floor? With great humor and clarity, Chad Orzel explains to Emmy, and to human readers, just what quantum mechanics is and how it works—and why, although you can't use it to catch squirrels or eat steak, it's still bizarre, amazing, and important to every dog and human.

CHAPTER 1
Which Way? Both Ways: Particle-Wave Duality

We’re out for a walk, when the dog spots a squirrel up ahead and takes off in pursuit. The squirrel flees into a yard and dodges around a small ornamental maple. Emmy doesn’t alter her course in the slightest, and just before she slams into the tree, I pull her up short.

“What’d you do that for?” she asks, indignantly.

“What do you mean? You were about to run into a tree, and I stopped you.”

“No I wasn’t.” She looks off after the squirrel, now safely up a bigger tree on the other side of the yard. “Because of quantum.”

We start walking again. “Okay, you’re going to have to explain that,” I say.

“Well, I have this plan,” she says. “You know how when I chase the bunnies in the backyard, when I run to the right of the pond, they go left, and get away?”

“Yes.”

“And when I run to the left of the pond, they go right, and get away?”

“Yes.”

“Well, I’ve thought of a new way to run, so they can’t escape.”

“What, through the middle of the pond?” It’s only about eight inches deep and a couple of feet across.

“No, silly. I’m going to go both ways. I’ll trap the bunnies between me.”

“Uh-huh. That’s an . . . interesting theory.”

“It’s not a theory, it’s quantum physics. Material particles have wave nature and can diffract around objects. If you send a beam of electrons at a barrier, they’ll go around it to the left and to the right, at the same time.” She’s really getting into this, and she doesn’t even notice the cat sunning itself in the yard across the street. “So, I’ll just make use of my wave nature, and go around both sides of the pond.”

“And where does running headfirst into a tree come in?”

“Oh, well.” She looks a little sheepish. “I thought I would try it out on something smaller first. I got a good running start, and I was just about to go around when you stopped me.”

“Ah. Like I said, an interesting theory. It won’t work, you know.”

“You’re not going to try to claim I don’t have wave nature, are you? Because I do. It’s in your physics books.”

“No, no, you’ve got wave nature, all right. You’ve also got Buddha nature—”

“I’m an enlightened dog!”

“—which will do you about as much good. You see, a tree is big, and your wavelength is small. At walking speed, a twenty-kilogram dog like you has a wavelength of about 10^-35 meters. You need your wavelength to be comparable to the size of the tree—maybe ten centimeters—in order to diffract around it, and you’re thirty-four orders of magnitude off.”

“I’ll just change my wavelength by changing my momentum. I can run very fast.”

“Nice try, but the wavelength gets shorter as you go faster. To get your wavelength up to the millimeter or so you’d need to diffract around a tree, you’d have to be moving at 10^-30 meters per second, and that’s impossibly slow. It would take a billion years to cross the nucleus of an atom at that speed, which is way too slow to catch a bunny.”

“So, you’re saying I need a new plan?”

“You need a new plan.”

Her tail droops, and we walk in silence for a few seconds. “Hey,” she says, “can you help me with my new plan?”

“I can try.”

“How do I use my Buddha nature to go around both sides of the pond at the same time?”

I really can’t think of anything to say to that, but a flash of gray fur saves me. “Look! A squirrel!” I say.

“Oooooh!” And we’re off in pursuit.

Quantum physics has many strange and fascinating aspects, but the discovery that launched the theory was particle-wave duality, or the fact that both light and matter have particle-like and wavelike properties at the same time. A beam of light, which is generally thought of as a wave, turns out to behave like a stream of particles in some experiments. At the same time, a beam of electrons, which is generally thought of as a stream of particles, turns out to behave like a wave in some experiments. Particle and wave properties seem to be contradictory, and yet everything in the universe somehow manages to be both a particle and a wave.

The discovery in the early 1900s that light behaves like a particle is the launching point for all of quantum mechanics. In this chapter, we’ll describe the history of how physicists discovered this strange duality. In order to appreciate just what a strange development this is, though, we need to talk about the particles and waves that we see in everyday life.

PARTICLES AND WAVES AROUND YOU: CLASSICAL PHYSICS

Everybody is familiar with the behavior of material particles. Pretty much all the objects you see around you—bones, balls, squeaky toys—behave like particles in the classical sense, with their motion determined by classical physics. They have different shapes, but you can predict their essential motion by imagining each as a small, featureless ball with some mass—a particle—and applying Newton’s laws of motion.* A tennis ball and a long bone tumbling end over end look very different in flight, but if they’re thrown in the same direction with the same speed, they’ll land in the same place, and you can predict that place using classical physics.

A particle-like object has a definite position (you know right where it is), a definite velocity (you know how fast it’s moving, and in what direction), and a definite mass (you know how big it is). You can multiply the mass and velocity together, to find the momentum. A great big Labrador retriever has more momentum than a little French poodle when they’re both moving at the same speed, and a fast-moving border collie has more momentum than a waddling basset hound of the same mass. Momentum determines what will happen when two particles collide. When a moving object hits a stationary one, the moving object will slow down, losing momentum, while the stationary object will speed up, gaining momentum.

The other notable feature of particles is something that seems almost too obvious to mention: particles can be counted. When you have some collection of objects, you can look at them and determine exactly how many of them you have—one bone, two squeaky toys, three squirrels under a tree in the backyard.

Waves, on the other hand, are slipperier. A wave is a moving disturbance in something, like the patterns of crests and troughs formed by water splashing in a backyard pond. Waves are spread out over some region of space by their nature, forming a pattern that changes and moves over time. No physical objects move anywhere—the water stays in the pond—but the pattern of the disturbance changes, and we see that as the motion of a wave.

If you want to understand a wave, there are two ways of looking at it that provide useful information. One is to imagine taking a snapshot of the whole wave, and looking at the pattern of the disturbance in space. For a single simple wave, you see a pattern of regular peaks and valleys, like this:

As you move along the pattern, you see the medium moving up and down by an amount called the “amplitude” of the wave. If you measure the distance between two neighboring crests of the wave (or two troughs), you’ve measured the “wavelength,” which is one of the numbers used to describe a wave.

The other thing you can do is to look at one little piece of the wave pattern, and watch it for a long time—imagine watching a duck bobbing up and down on a lake, say. If you watch carefully, you’ll see that the disturbance gets bigger and smaller in a very regular way—sometimes the duck is higher up, sometimes lower down—and makes a pattern in time very much like the pattern in space. You can measure how often the wave repeats itself in a given amount of time—how many times the duck reaches its maximum height in a minute, say—and that gives you the “frequency” of the wave, which is another critical number used to describe the wave. Wavelength and frequency are related to each other—longer wavelengths mean lower frequency, and vice versa.

You can already see how waves are different from particles: they don’t have a position. The wavelength and the frequency describe the pattern as a whole, but there’s no single place you can point to and identify as the position of the wave. The wave itself is a disturbance spread over space, and not a physical thing with a definite position and velocity. You can assign a velocity to the wave pattern, by looking at how long it takes one crest of the wave to move from one position to another, but again, this is a property of the pattern as a whole.

You also can’t count waves the way you can count particles—you can say how many crests and troughs there are in one particular area, but those are all part of a single wave pattern. Waves are continuous where particles are discrete—you can say that you have one, two, or three particles, but you either have waves, or you don’t. Individual waves may have larger or smaller amplitudes, but they don’t come in chunks like particles do. Waves don’t even add together in the same way that particles do—sometimes, when you put two waves together, you end up with a bigger wave, and sometimes you end up with no wave at all.

Imagine that you have two different sources of waves in the same area—two rocks thrown into still water at the same time, for example. What you get when you add the two waves together depends on how they line up. If you add the two waves together such that the crests of one wave fall on top of the crests of the other, and the troughs of one wave fall in the troughs of the other (such waves are called “in phase”), you’ll get a larger wave than either of the two you started with. On the other hand, if you add two waves together such that the crests of one wave fall in the troughs of the other and vice versa (“out of phase”), the two will cancel out, and you’ll end up with no wave at all.

This phenomenon is called interference, and it’s perhaps the most dramatic difference between waves and particles.

“I don’t know . . . that’s pretty weird. Do you have any other examples of interference? Something more . . . doggy?”

“No, I really don’t. That’s the point—waves are dramatically different than particles. Nothing that dogs deal with on a regular basis is all that wavelike.”

“How about, ‘Interference is like when you put a squirrel in the backyard, and then you put a dog in the backyard, and a minute later, there’s no more squirrel in the backyard.’ ”

“That’s not interference, that’s prey pursuit. Interference is more like putting a squirrel in the backyard, then putting a second squirrel in the backyard one second later, and finding that you have no squirrels at all. But if you wait two seconds before putting in the second squirrel, you find four squirrels.”

“Okay, that’s just weird.”

“That’s my point.”

“Oh. Well, good job, then. Anyway, why are we talking about this?”

“Well, you need to know a few things about waves in order to understand quantum physics.”

“Yeah, but this just sounds like math. I don’t like math. When are we going to talk about physics?”

“We are talking about physics. The whole point of physics is to use math to describe the universe.”

“I don’t want to describe the universe, I want to catch squirrels.”

“Well, if you know how to describe the universe with math, that can help you catch squirrels. If you have a mathematical model of where the squirrels are now, and you know the rules governing squirrel behavior, you can use your model to predict where they’ll be later. And if you can predict where they’ll be later . . .”

“I can catch squirrels!”

“Exactly.”

“All right, math is okay. I still don’t see what this wave stuff is for, though.”

“We need it to explain the properties of light and sound waves, which is the next bit.”

WAVES IN EVERYDAY LIFE: LIGHT AND SOUND

We deal with two kinds of waves in everyday life: light and sound. Though these are both examples of wave phenomena, they appear to behave very differently. The reasons for those differences will help shed some light (pardon the pun) on why it is that we don’t see dogs passing around both sides of a tree at the same time.

Sound waves are pressure waves in the air. When a dog barks, she forces air out through her mouth and sets up a vibration that travels through the air in all directions. When it reaches another dog, that sound wave causes vibrations in the second dog’s eardrums, which are turned into signals in the brain that are processed as sound, causing the second dog to bark, producing more waves, until nearby humans get annoyed.

Light is a different kind of wave, an oscillating electric and magnetic field that travels through space—even the emptiness of outer space, which is why we can see distant stars and galaxies. When light waves strike the back of your eye, they get turned into signals in the brain that are processed to form an image of the world around you.

The most striking difference between light and sound in everyday life has to do with what happens when they encounter an obstacle. Light waves travel only in straight lines, while sound waves seem to bend around obstacles. This is why a dog in the dining room can hear a potato chip hitting the kitchen floor, even though she can’t see it.

The apparent bending of sound waves around corners is an example of diffraction, which is a characteristic behavior of waves encountering an obstacle. When a wave reaches a barrier with an opening in it, like the wall containing an open door from the kitchen into the dining room, the waves passing through the opening don’t just keep going straight, but fan out over a range of different directions. How quickly they spread depends on the wavelength of the wave and the size of the opening through

On the left, a wave with a short wavelength encounters an opening much larger than the wavelength, and the waves continue more or less straight through. On the right, a wave with a long wavelength encounters an opening comparable to the wavelength, and the waves diffract through a large range of directions.

which they travel. If the opening is much larger than the wavelength, there will be very little bending, but if the opening is comparable to the ...