How to Teach Physics to Your Dog (5 page)

Following the experiments of Davisson and Germer and Thomson, scientists showed that all subatomic particles behave like waves: beams of protons and neutrons will diffract off samples of atoms in exactly the same way that electrons do. In fact, neutron diffraction is now a standard tool for determining the structure of materials at the atomic level: scientists can deduce how atoms are arranged by looking at the interference patterns
that result when a beam of neutrons bounces off their sample. Knowing the structure of materials at the atomic level allows materials scientists to design stronger and lighter materials for use in cars, planes, and space probes. Neutron diffraction can also be used to determine the structure of biological materials like proteins and enzymes, providing critical information for scientists searching for new drugs and medical treatments.

So, if all material objects are made up of particles with wave properties, why don’t we see dogs diffracting around trees? If a beam of electrons can diffract off two rows of atoms, why can’t a dog run around both sides of a tree to trap a bunny on the far side? The answer is the wavelength: as with the sound and light waves discussed earlier, the dramatically different behavior of dogs and electrons encountering obstacles is explained by the difference in their wavelengths. The wavelength is determined by the momentum, and a dog has a lot more momentum than an electron.

The wavelength of a material object is given by Planck’s constant divided by the momentum, which is mass multiplied by velocity. Planck’s constant is a tiny number, but so is the mass of an electron—about 10
^-30
kilograms, or 0.0000000000000000 00000000000001 kg. Davisson and Germer’s electrons, moving at the brisk speed of six million meters per second, had a wavelength of about a tenth of a nanometer (0.0000000001 m). That’s extremely small, but it’s about half the distance between two nickel atoms, just right for seeing diffraction (just like sound waves with half-meter wavelengths will readily diffract through one-meter-wide doors).

The wavelength of a 50-pound (about 20 kg) dog out for a stroll, on the other hand, is about 10
^-35
meters (0.00000000000
000000000000000000000001 m), or a millionth of a billionth of a billionth of the wavelength of Davisson and Germer’s electrons. How does that compare to the size of a tree? Well, a dog’s wavelength compared to the distance between two atoms is like the distance between two atoms compared to the diameter of the solar system. There’s no chance of seeing the wave associated with a dog diffract off a crystal of nickel, let alone pass around both sides of a tree at the same time.

There’s a lot of room between a beam of electrons and a dog, though, so what is the biggest material object that has been shown to have observable wave nature?

In 1999, a research group at the University of Vienna headed

The interference pattern produced by a beam of molecules passing through an array of narrow slits. The extra lumps to either side of the central peak are the result of diffraction and interference of the molecules passing through the slits. (Reprinted with permission from O. Nairz, M. Arndt, and A. Zeilinger,
Am. J. Phys.
71, 319 [2003]. Copyright 2003, American Association of Physics Teachers.)

by Dr. Anton Zeilinger observed diffraction and interference with molecules consisting of 60 carbon atoms bound together into a shape like a tiny soccer ball, each with a mass about a million times that of an electron. They shot these soccer-ball-shaped molecules toward a detector, and when they looked at the distribution of molecules downstream, they saw a single narrow beam. Then they sent the beam through a silicon wafer with a collection of very small slits cut into it, and looked at the distribution of molecules on the far side of the slits. With the slits in place, the initial narrow peak grew broader, with distinct “lumps” to either side. Those lumps, like the bright and dark spots seen by Thomas Young shining light through a double slit, or the electron diffraction peaks seen by Davisson and Germer, are an unmistakable signature of wave behavior. Molecules passing through the slits spread out and interfere with one another, just like light waves.

In subsequent experiments, the Zeilinger group demonstrated the diffraction of even larger molecules, adding 48 fluorine atoms to each of their original 60-carbon-atom molecules. These molecules have a mass about three million times the mass of one electron, and stand as the current record for the most massive object whose wave nature has been observed directly.

As the mass of a particle increases, its wavelength gets shorter and shorter, and it gets harder and harder to see wave effects directly. This is why nobody has ever seen a dog diffract around a tree; nor are we likely to see it any time soon. In terms of physics, though, a dog is nothing but a collection of biological molecules, which the Zeilinger group has shown have wave properties. So, we can say with confidence that a dog has wave nature, just the same as everything else.

“So, which are they
really
?”

“What do you mean?”

“Well, are electrons really particles acting like waves, or are photons waves acting like particles?”

“You’re asking the wrong questions. Or, rather, you’re giving the wrong answers. The real answer is ‘Door Number Three.’ Electrons and photons are both examples of a third sort of object, which is neither just a wave nor just a particle, but has some wave properties and some particle properties at the same time.”

“So, it’s like a squirunny?”

“A what?”

“A critter that’s something like a squirrel, and something like a bunny. A squirunny.”

“I prefer ‘quantum particle,’ but I guess that’s the basic idea. Everything in the universe is built of these quantum particles.”

“That’s pretty weird.”

“Oh, that’s just the beginning of the weird stuff . . .”

*
Sir Isaac Newton, of the falling apple story, set forth three laws of motion that govern the behavior of moving objects. The first law is the principle of inertia, that objects at rest tend to remain at rest, and objects in motion tend to remain in motion unless acted on by an external force. The second law quantifies the first, and is usually written as the equation
F = ma,
force equals mass times acceleration. The third law says that for every action there is an equal and opposite reaction—a force of equal strength in the opposite direction. These three laws describe the motion of macroscopic objects at everyday speeds, and form the core of classical physics.

*
You might wonder why you can’t put together two low-energy photons to provide enough energy to free an electron. This would require two photons to hit the same electron at the same instant, and that almost never happens.

*
Millikan thought the Einstein model lacked “any sort of satisfactory theoretical foundation,” and described its success as “purely empirical,” which is pretty nasty by physics standards. Ironically, those quotes are from the first paragraph of the paper in which he conclusively confirms the predictions of the theory.

*
A nanometer is 10
^-9
m, or one billionth of a meter (0.000000001 m).

*
A few die-hard theorists still resisted the idea of photons, because even the Compton effect can be explained without photons, though it’s very complicated. The last resistance collapsed in 1977, when incontrovertible proof of the existence of photons was provided in an experiment by Kimble, Dagenais, and Mandel that looked at the light emitted by single atoms. The seventy-two-year gap between Einstein’s proposal and its final acceptance tells you something about the stubbornness of physicists confronted with a new idea. It can be as difficult to separate a physicist from a cherished model as it is to drag a dog away from a well-chewed bone.

*
The proper pronunciation of Louis de Broglie’s surname (his collection of names reflects his aristocratic background—he was the 7th Duc de Broglie) is the source of much confusion among American physicists. I’ve heard “de-BRO-lee,” “de-BRO-glee,” and “de-BROY-lee,” among others. The correct French pronunciation is apparently something close to “de-BROY,” only with a gargly sort of sound to the vowel that you need to be French to make.

*
“Crystal,” to a physicist, refers to any solid with a regular and orderly arrangement of atoms in it. This includes the clear and sparkly things that we normally associate with the word, but also a lot of metals and other substances.

†
Ironically, Davisson and Germer succeeded only because they broke a piece of their apparatus. They didn’t see any diffraction in the first experiments they did, because their nickel target was made up of many small crystals, each producing a different interference pattern, and the bright spots from the different patterns ran together. Then they accidentally let air into their vacuum system. In the process of repairing the damage, they melted the target, which recrystallized into a single large crystal, producing a single, clear diffraction pattern. Sometimes, the luckiest thing a physicist can do is to break something important.

*
In one of the great bits of Nobel trivia, Thomson’s father, J. J. Thomson of Cambridge, won the 1906 Nobel Prize in Physics for demonstrating the particle nature of the electron. This presumably led to some interesting dinner-table conversation in the Thomson household.

I’m grading papers on the couch when Emmy comes into the room, looking concerned. “What’s the matter?” I ask.

“I can’t find my bone,” she says. “Do you know where my bone is?”

“I have no idea where your bone is,” I say, “but I can tell you exactly how fast it’s moving.”

There’s silence in response, and when I look up, she’s staring at me blankly.

“It’s a physics joke,” I explain, because that always makes things funnier. “You know, Heisenberg’s uncertainty principle? The uncertainty in the position of an object multiplied by the uncertainty in the momentum is greater than Planck’s constant over four pi? Which means that when one uncertainty is small, the other must be very large.”

Now she’s glaring at me, almost growling. “Stop doing that!” she says.

“What? It’s not all that funny, but it wasn’t that bad.”

“It’s your fault that I can’t find my bone.”

“How is it my fault?”

“You went and measured how fast it’s moving, and the position got all uncertain. And now I can’t find my bone.”

“That’s not what happened,” I say. “The uncertainty principle doesn’t work like that.”

“Yes it does. You just said. You know how fast my bone is moving, and now I can’t find it.”

“First of all, that was a joke. I didn’t really measure the velocity of your bone. Second, that’s a slightly mistaken view of the uncertainty principle. It’s not just that measurement changes the state of the system, it’s that what we
can
measure is limited by the fact that position and momentum are undefined until we measure them.”

She looks puzzled. “I don’t see the difference.”

“Well, in the picture where you attribute everything to the effects of measurement, you implicitly assume that whatever you’re measuring has some definite and well-defined properties, and the uncertainty in those values arises only from perturbations that occur through the act of measuring them. That’s not what happens, though—in quantum theory, there are no definite values for those quantities. They’re not uncertain because of limits on your measurement, they’re uncertain because they are not defined, and they can’t
be
defined, due to the quantum nature of reality.”

“Oh.” She looks thoughtful for a moment, then resumes glaring. “I think you lost my bone, and you’re just trying to weasel out of this by being all confusing.”

“No, that’s really how the theory works. It’s a moot point, though, since even if I had perturbed the position of your bone by measuring its velocity, there’s no way that would’ve prevented you from finding it.”

“Yeah? Why not?”

“Well, because the uncertainty involved would be tiny. I mean, your bone has a mass of a couple hundred grams, and if I measured its velocity to within one millimeter per second, that would give an uncertainty in position of only about 10
^-31
meters. That’s a trillionth of the size of a proton—you’d never even notice that.”

“Yeah? Well, where’s my bone, smart guy?”

“I don’t know. Did you look under the TV cabinet? Sometimes it gets kicked under there.”

She trots over to the TV, and sticks her nose under the cabinet. “Oooh! Here’s my bone!” She paws at it for a minute, and eventually succeeds in knocking it out from under the cabinet. “I have a bone!” she announces proudly, and begins chewing it noisily, the uncertainty principle forgotten.

The Heisenberg uncertainty principle is probably the second most famous result from modern physics, after Einstein’s
E = mc
²
(the most famous result from relativity). Most people wouldn’t know a wavefunction if they tripped over one, but almost everyone has heard of the uncertainty principle: it is impossible to know both the position and the momentum of an object perfectly at the same time. If you make a better measurement of the position, you necessarily lose information about its momentum, and vice versa.