How to Teach Physics to Your Dog (27 page)

Whether you think of it as a superposition of all possible
paths at the same time, or an average interaction being used to cover the details of many individual interactions, the effect of virtual particles shows up when we look at an electron interacting with a magnetic field. Electrons (and all other material particles) have a property called “spin” that makes them act like tiny little magnets, with north and south poles.
*
The energy of an electron whose poles are aligned with the magnetic field is very slightly different than the energy of an electron whose poles point in the opposite direction.

The energy difference between these states in a magnetic field depends on a number called the gyromagnetic ratio, or g-factor, of the electron, which basically tells you how big a magnet you get for a given amount of “spin.” The simplest quantum theory of the electron says that the value of this ratio should be exactly 2, which is what you would get if there were no virtual particles. Thanks to the contributions of virtual particles, the actual value is very slightly higher.

This value can be measured with extraordinary precision. In 2008, a team of physicists led by Gerald Gabrielse of Harvard made the most accurate measurement to date of the electron g-factor in experiments involving single electrons held in a Penning trap. The experimental value they obtained was:

g
= 2.00231930436146 ± 0.00000000000056

They compared their result to the result of a QED calculation that involved summing almost a thousand individual Feynman diagrams
^†
—including processes much more complex than
those described above—and theory and experiment were in perfect agreement, to fourteen decimal places. This is why we can say with confidence that virtual particles exist, no matter how strange the idea may seem at first glance.

While this agreement is extremely impressive, a
disagreement
would be even more interesting. The g-factor for the electron includes only the effects of virtual photons and virtual electron-positron pairs, but the analogous quantity for the muon (a type of particle similar to an electron, but with a larger mass) shows the effects of a number of other, more exotic, virtual particles.
*
The latest measurements of the g-factor of the muon show a tiny difference between the experimental value and the theoretical prediction. This difference might be merely a calculation or measurement error, or it might hint at the existence of a new particle that wasn’t included in the calculations—some particle that isn’t part of the standard model of particle physics. It’s still much too early to say for sure, but if this difference holds up, it could be the first experimental test of the many theories for physics beyond the standard model.

Experimentalists have a long way to go before they start to see the effects of virtual bunnies made of cheese, of course. But if it is possible to make bunnies out of cheese, we know that they must be out there somewhere.

“So that’s what you mean when you say ‘Quantum mechanics is the most accurately tested theory in the history of theories.’ ”

“Well, I didn’t say it like
that
. . .”

“Whatever. You say it all the time, and it sounds really pompous.”

“Fine. See if I rub your belly anymore. Anyway, yes, that’s what I mean. Quantum electrodynamics has been used to predict the g-factor of the electron to fourteen decimal places, and it agrees perfectly with experimental measurements. And QED is a relatively straightforward extension of ordinary quantum mechanics to situations where you need to think about relativity.”

“So, what else is it good for?”

“Well, as I said, you can have all sorts of different things as virtual particles. This includes particles that have been predicted by theorists, but not observed yet—if they really exist, they’ll show up as virtual particles.”

“How does that help anything?”

“Some of those hypothetical particles would allow interactions that aren’t possible with any of the particles we know about. In addition to the muon g-factor, there’s the ‘electric dipole moment’ of the electron. If the right sort of particles exist, they would change the way an electron interacts with electric fields inside atoms and molecules. It might be possible to detect the tiny shift in the allowed states in experiments with lasers.”

“So, if you saw this dipole moment thing, you would know that new types of particles exist?”

“And if you
don’t
see it, you can rule out some types of particles. The fact that nobody has observed an electric dipole moment in an electron yet has ruled out some of the simpler models that theorists like to use. If some of the new experiments don’t see anything, it could really make the theorists squirm.”

“That’s pretty cool.”

“It’s especially cool because these are tabletop experiments, not billion-dollar particle accelerators. There are a whole bunch of groups doing these experiments—at Berkeley, Yale, Washington, Colorado, and other places—and they’re our best chance of learning something really new until the Large Hadron Collider starts up, and maybe beyond that.”

“Of course, none of this helps with what’s really important.”

“That being?”

“Providing me with bunnies made of cheese.”

“Well, what can I say? In some areas, physics still has a long way to go.”

“I’ll say.”

*
Max Tegmark is a cosmologist at MIT known for proposing that our universe is one of a vast number of universes in a larger “multiverse.” According to Tegmark, this multiverse contains every possible kind of universe that can be described mathematically, even those that would make no sense to us. Tegmark’s work is somewhat similar to the “modal realism” of the philosopher David Kellogg Lewis.

*
Unless the dog is a basset hound, in which case he’ll want to thoroughly sniff
everything
.

*
The name “spin” is because this is similar to what you would see if the electron were a spinning ball of charge. The electrons are not literally spinning, but the math is the same.

†
An impressive achievement in its own right, done by the group of Toichiro Kinoshita at Cornell.

*
The muon g-factor calculations include virtual muons, tau particles, quarks, and gluons, which account for most of the known types of subatomic particles.

*
The units for frequency are “Hertz,” abbreviated Hz, after the German physicist Heinrich Hertz, who was the first physicist to demonstrate experimentally that light is an electromagnetic wave.

*
It’s even harder for humans, whose noses don’t work well enough to sniff out the really tiny crumbs in the corners.

*
Or, to put it yet another way, if the particle-antiparticle pair is around for only a short time, their masses have a large uncertainty. If the time is short enough, the uncertainty in the mass can be larger than the mass, in which case we can’t say that the mass
wasn’t
zero. In which case, they can exist for that short time, because two particles with zero mass don’t increase the energy inside the box at all.

*
This is an interval so short it may literally have no meaning—in some exotic theories, time itself is quantized, and comes in steps of 10
^-44
s (the “Planck time”). In such models, it’s impossible to have an interval shorter than that.

*
Feynman was famous for his very intuitive approach to physics, and the diagram-based technique he developed gained wide acceptance because it provides a convenient way of thinking about the complex calculations required for QED. At the same time Feynman was doing his work, Julian Schwinger developed a much more formal approach to the same problems, giving the same results as the Feynman approach in a more mathematically rigorous way. Both approaches are widely used in theoretical physics today, and Feynman and Schwinger shared the 1965 Nobel Prize with Shin-Ichiro Tomonaga, who independently developed some of the same techniques as Schwinger.

*
In a Feynman diagram, any particle that appears and disappears before the end of the “story” is a “virtual particle.”

†
A positron can be mathematically described as an electron moving backward in time, another trick invented by Feynman, hence the downward arrow.

*
Of course, there are an infinite number of things that
might
happen, and thus an infinite number of possible diagrams. In practice, though, the more complicated the diagram, the smaller the contribution it makes to the answer, so theoretical physicists need to add up only as many diagrams as they need to match the precision of an experiment.

I’m putting seed in the squirrelproof bird feeder when I hear a little voice above my head. “Pssst! Hey, human dude!”

There’s a squirrel perched on the branch of a tree, staring at me. I look around, but Emmy is on the far side of the yard, intently sniffing the base of the big oak tree. “What do you want?” I ask.

“How about you give me some of that seed?”

“I don’t think—what’s with your face? Is that a goatee?”

“It’s a fake. We wear ’em to mess with the dog—she thinks we’re from another dimension. Look, how about
selling
me some birdseed, then?”

“What’s a squirrel going to use to buy birdseed?”

“How’s free energy sound, hmm?” Somehow, despite the fake goatee, fuzzy tail, and protruding teeth, he manages to look smug.

“Free energy?”

“Yeah, we can tell you how to extract a nearly infinite amount of energy from ordinary water. That ought to be worth some bird-seed, eh?”

“Really. Free energy.”

“You bet. We extract the zero-point vibrational energy from water molecules, leaving them in a lower energy state than ordinary
molecules. You can turn that energy directly into electricity, and use it to power lights, or computers, or birdseed-making machines.” Looking closely, I see that the fake goatee is obviously held on by string.

“Sounds too good to be true. What’s the catch? Toxic waste products?”

“No, no—the only waste is still water. In fact, it’s better than water. It’s superwater!”

“What’s so super about it?”

“Well, it’s in a different quantum state, right? So it’s got, like, special properties and stuff. You can drink it, and it’ll cure diseases.”

“How’s that work?”

“Well, you drink it, and concentrate on measuring your wave-function to be in a healthy state. If you do it right, you can think your way to perfect health.”

“You don’t say.”

“Yeah, we run some workshops and classes and stuff. I’m a hundred and six, and in perfect health. For just a handful of birdseed a week, we’ll let you in on the secret.”

“Uh-huh.” The dog is still on the far side of the yard, carefully checking the bushes for bunnies.

“You can also use it to power a quantum computer, but that’ll cost more than birdseed. For a jar of peanut butter a week, you can have the schematics of a quantum computer that you can use to crack the encryption on credit card transactions.”

“Wow.”

“I know. Pretty cool, huh?”

“The dog was right. You
are
evil squirrels.”

“Yeah, like you wouldn’t do it if you knew how. So, how ’bout that birdseed?”

“Sure, I’ll give you some birdseed . . .” I put a little pile of seed down on the ground, about six feet from the trunk of the tree.

“Thanks, buddy,” says the squirrel, scampering down the trunk. “You’re a prince.”

“Don’t mention it,” I say, stepping between the squirrel and the tree. “Emmy!” Across the yard, her head snaps around. “Look! Evil squirrel!”

“Ooooh!” She comes charging across the yard, teeth bared. The squirrel tries to run back up the tree, but I block his path, so he turns and flees toward the maples at the back of the yard, with the dog snapping at his tail.

I spot something in the grass, and bend down to retrieve a tiny fake goatee. I drop it in the trash on my way back into the house.

In the preceding chapters, we have talked about a lot of weird and wonderful features of quantum mechanics. Wave-particle duality, quantum measurement, EPR correlations, virtual particles—so many aspects of quantum theory defy our everyday experience that quantum mechanics starts to seem like magic. None of the normal rules seem to apply, and it may look as though absolutely anything is possible.

This is a common misconception regarding quantum mechanics, and you’ll find it repeated in lots of places. A little time with Google will turn up dozens of sites offering “quantum” methods to produce energy for nothing, improve your health and well-being, or even amass wealth and power: lots of people out there are making money by peddling quantum mechanics as magic.

Quantum mechanics is
not
magic, though. No matter how unlikely or amazing it seems, quantum mechanics is a scientific theory that has to conform to the general principles of physics. The word “quantum” in the description of a phenomenon or device does not allow it to create energy out of nothing or send messages faster than the speed of light. These principles are built into the deep structure of the universe. Quantum mechanics is not only compatible with those rules, but in some cases, these rules arise from quantum behavior.

While many of the predictions of quantum mechanics seem to defy our everyday intuition for how the world works, they do not suspend all the rules of common sense. In particular, they do not supersede the most important commonsense rule for dealing with the world: if something sounds too good to be true, it almost certainly is.

We’ve spent the bulk of this book talking about the wonderful features of quantum theory, but I want to close on a cautionary note. There are a lot of people peddling a false version of quantum mechanics as magic, offering results beyond your most wildly unrealistic dreams. Some of them are scam artists, and some of them are sincere but deluded, but they’re all wrong. The hucksters are hard to separate from the merely confused, but it is not difficult to spot false versions of quantum theory, and in this chapter, I’ll point out a few of the most common problems.