How to Teach Physics to Your Dog (18 page)

Making an image with an STM is like running your finger across a surface, and feeling the bumps and scratches. You scan the tip back and forth over the surface of the sample, keeping the height of the tip constant, and as you move the tip, you monitor the current flowing between the tip and the sample. The current increases whenever there’s a small bump sticking up from the surface making it easier for electrons to tunnel across, and decreases whenever there’s a small dip in the surface. If you take a large number of height measurements at points on a grid, you can put them together to create an image of the individual atoms making up the surface of your sample.

Not only can you see single atoms, but if you bring the tip

A schematic of a scanning tunneling microscope. A sharp tip is positioned close to the surface of a material, and moved back and forth in a regular pattern. Electrons from the tip will tunnel across the gap between the tip and the surface, producing a small electric current that is amplified and measured. The amount of current depends very sensitively on the distance between the tip and the surface, allowing a reconstruction of the surface sensitive enough to detect single atoms.

into direct contact with the surface, you can push individual atoms around. Scientists have used this ability to make a number of incredible structures, such as the oval-shaped “corral” shown in the picture on the next page, made at IBM’s Almaden research laboratory. The bumps making up the “corral” are individual iron atoms on a copper surface, which have been dragged into place by the STM. Such structures can be used to study the quantum behavior of electrons inside the “corral,” which accounts for the wavy features seen on the copper surface.

Scanning tunneling microscopes have revolutionized the study of solids and surfaces, and the technology may lead to new manufacturing techniques for tiny devices. Other scientists
have used STMs to study and manipulate individual strands of DNA, providing a more detailed understanding of the behavior of genetic material and possibly new drugs or treatments for genetic damage. All of this is made possible by the underlying wave nature of matter.

Iron atoms on a copper surface, arranged in a “corral” pattern using an STM. The wave pattern inside the corral is due to the wave nature of electrons on the copper surface. Image courtesy of IBM.

“That’s nice and all, but I’m not interested in microscopic bunnies. What has quantum tunneling ever done for me?”

“Well, for one thing, you wouldn’t be able to enjoy a nice sunny day if not for tunneling.”

“What do you mean?”

“Well, the Sun shines because of fusion reactions in the core, right?”

“Everybody knows that. Even the beagle down the street knows that, and that dog is really dumb.”

“Yes. Well. Anyway, fusion works by sticking protons together to make helium from hydrogen. Because protons are positively charged, they repel one another, and that repulsion sets up a barrier. And as hot as the Sun is, the protons in the Sun still don’t have enough energy to get over that barrier directly.”

“So they tunnel through?”

“Exactly. The probability of any given proton tunneling through the barrier is pretty low, but there are lots and lots of protons in the Sun, and enough of them do tunnel through to keep the reaction going. So it’s really tunneling that lets the Sun shine.”

“Hmm. I guess that is pretty cool.”

“I’m so glad you approve . . .”

“Can we go play fetch, now?”

*
Temperature measures the energy due to the motion of the individual atoms making up an object, and “absolute zero” is the imaginary temperature at which that motion would cease. No real object can be cooled all the way to absolute zero, though, and even if one could it would still have zero-point energy, as discussed in
chapter 2
(page 49).

*
Potential energy is generally much easier to calculate than kinetic energy. Potential energy usually depends only on the positions of the interacting objects, while the kinetic energy depends on the velocity, which depends on what has happened in the recent past. The easiest way to tackle an energy problem is usually to calculate the potential energy using the position, and find the kinetic energy by process of elimination. For example, when a roller coaster pauses at the top of a big hill, we know that all of its energy is potential energy. Later on, we can easily calculate the potential energy from the height of the track, and that lets us find the kinetic energy (and thus the speed) without needing to know what happened in between.

*
The total energy of an object
can
be increased, by adding energy from some other source, in the same way that a dog’s treat jar can be refilled by a friendly human. The extra energy does not come for free, though—the energy of the outside object has to decrease, in the same way that a human’s bank balance will decrease in order to supply the treats. The total energy of the entire universe—balls, dogs, treats, and humans—is a constant, and has not increased or decreased in the fourteen billion years since the Big Bang.

*
Strictly speaking, the probability is never exactly zero—the mathematical function describing the probability is an exponential, and while it gets closer to zero as the electron moves into the barrier, it never gets all the way there. Quantum physics predicts a tiny probability that a ball thrown in the air will tunnel through the forbidden region that starts at its classical maximum height, and end up on the Moon. That’s not a good bet, though—the probability is so small that it’s indistinguishable from zero, for all practical purposes.

*
Notice that the uncertainty in the position is very large—the electron could be just about anywhere to the left of the forbidden region.

*
A potential energy barrier doesn’t have to be a solid physical object. An air gap will do just fine, which is why you can’t make a lightbulb light up by just holding it close to the socket.

Emmy is napping in the living room, but wakes up as I pass through. She stretches hugely, then follows me into the kitchen looking pleased with herself. “I’m going to measure a bunny,” she announces.

“Beg pardon?” She’s always making these weird announcements.

“I’ve figured out how to measure both the position and the momentum of a bunny.”

“You have, have you? How are you going to do that?”

“I’m going to put a big grid of lines in the backyard, and then when the bunny is right on top of a grid mark, all I have to do is measure how fast it’s going.” She wags her tail proudly. “Uncertainty, unschmertainty.”

“Uh-huh. And how are you going to measure when the bunny is right on a grid mark?”

“What do you mean? I’m just going to look.”

“Sure, which means you’ll see the bunny, and the bunny will see you, and then it will change its velocity to run away.”

“Oh.” Her tail droops. “I didn’t think of that.”

“Look, we’ve been through this. There’s no way around the uncertainty principle. Really smart humans have tried to find a
way around it, and it can’t be done. Einstein spent years arguing about it with Niels Bohr.”

“Did he come up with anything?”

“He tried lots of different arguments, but none of them actually worked. He even had a really clever argument that quantum mechanics was incomplete, involving two entangled particles, prepared so that their states are correlated.”

“Correlated how?”

“Well, let’s say I have two treats in my hand—stop drooling, it’s a thought experiment—and one of them is steak, and the other is chicken.”

“I like steak. I like chicken.” She’s drooling all over the floor.

“Yes, I know. Thought experiment, remember?” I grab some paper towels to mop up the floor. “Now, imagine I throw these two treats in opposite directions, one to you, and one to some other dog.”

“Don’t do that. Other dogs don’t deserve treats.”

“It’s a hypothetical, try to keep up. Now, if you got the steak treat, you would know immediately that the other dog got the chicken treat. And—why are you looking all sad?”

“I like hypothetical chicken treats.”

“You got a hypothetical steak treat.”

“Oooh! I like hypothetical steak.”

“The point is, by measuring what sort of treat
you
got, you know what the other treat is, without ever measuring it.”

“Yeah, so? What’s weird about that?”

“Well, in the quantum version, the state of the particles is indeterminate until one of them is measured. When I throw the treats, until you get one and find out whether it’s steak or chicken, it’s not either. In some sense, it’s both.”

“Chickensteak! Steakchicken! Sticken!”

“You’re ridiculous. Anyway, Einstein thought this was a problem, and that the fact that you could predict the state of one particle
by measuring the other particle meant that both of them had to have definite states the whole time.”

“That makes sense.”

“In a classical world, sure. Einstein’s argument fails, though, because he’s assumed what’s called ‘locality’—that measuring one particle does not affect the other. In fact, measuring the state of one determines the state of the other, absolutely and instantaneously.”

She looks really bothered by this. “I don’t like that idea. Wouldn’t that require a message to travel from one treat to the other?”

“That’s what bothered Einstein, and he called it
spukhafte Fernwirkung.
”

“‘Spooky action at a distance’?” she translates.

“Since when do you know German?”

“Dude, look at me.” She turns sideways for a second, showing off her black and tan coloring and pointed nose. “
German shepherd,
remember?”

“Of course, how silly of me. Anyway, yes, this bothered Einstein because information cannot pass between separated objects faster than the speed of light. But quantum mechanics is
nonlocal,
and the entangled particles act like a single object. A guy named John Bell showed that it’s possible to put limits on what you can measure in theories where the particles have definite states, and showed that those limits are different than the limits for entangled quantum particles. People have done the experiments and found that the quantum theory is right. The state of the particles really is indeterminate until they’re measured.”

“So Einstein was wrong?”

“About this, yes. And generally, about the basis of quantum theory.”

“But he was really smart, wasn’t he?”

“Yes. Einstein was arguably smarter than Bohr. Bohr won all their debates, though, because he had the advantage of being right.” I bend over to scratch behind her ears. “You’re pretty smart, but you’re no Einstein.”

“I’m, like, the canine Einstein, though, right?”

“Sure. As far as I know, you’re the Einstein of the dog world.”

“Can I have some steak, then? Or chicken?”

“Maybe.” I grab a treat out of the jar on the counter. “You’ll find out when you measure it.” I throw the treat out the back door, and she goes bounding after it.

“Oooh! Indeterminate treats!”

Everything we have talked about so far has been a one-particle phenomenon. Most of the experiments need to be repeated many times to see the effects, using different individual particles prepared the same way, but at a fundamental level, all the interference, diffraction, and measurement effects we’ve talked about work with one particle at a time. Each particle in an interference experiment can be thought of as interfering with itself, and measurement phenomena like the quantum Zeno effect involve the state of a single particle.
*

Of course, the world we live in involves a great many particles, so we need to look at what happens when we apply quantum physics to systems involving more than one particle. When we do, it’s no surprise that we find some weird things going on, starting with the idea of “entangled states.”

In this chapter, we’ll look at the idea of “entangled” particles, whose states are correlated so that measuring one particle determines the exact state of the other. Entangled particles are the basis for the most serious challenge Einstein mounted against
quantum theory, known as the Einstein, Podolsky, and Rosen (EPR) paradox. We’ll talk about John Bell’s famous theorem resolving the EPR paradox, and its disturbing implications for the commonsense view of reality. Finally, we’ll talk about the experiments that prove Bell’s theorem, and show the lengths that physicists go to in challenging new ideas.