How to Teach Physics to Your Dog

by CHAD ORZEL

  The initial demonstration used only one of the four possible Bell states in the measurement step, for reasons of experimental convenience, and teleported the polarization state all of half a meter. Subsequent experiments have expanded the measurements to include all four outcomes and extended the distance considerably. In 2004 the Zeilinger group teleported photons from one side of the Danube River* to the other (a distance of about 600 meters) over an optical fiber, showing that teleportation is practical over longer distances.†

  “Yeah, but what’s the point?”

  “What do you mean?”

  “Well, who cares if you can teleport photon states?”

  “Photons aren’t the only things whose states can be tele-ported. The math is exactly the same for any two-state system, so you can use the same scheme to teleport the state of a single electron spin, for example, or transfer a particular superposition of two energy levels from one atom to another.”

  “Yeah, but if you can exchange the entangled atoms or electrons, why don’t you just send them, instead of teleporting them?”

  “Atomic states and electron spins are kind of fragile, and it’s hard to send them long distances without the state getting messed up. What you can do is to take an atom, say, and entangle it with one photon from an entangled pair, and use the other photon to teleport the state of the first atom onto another atom in a distant place.”

  “Okay, that’s a little better, but it’s still just one atom.”

  “It doesn’t have to be. In 2006, a group at the Niels Bohr Institute in Copenhagen used teleportation to transfer a collective state from one group of atoms to another. There were about a trillion atoms in each of the two groups, which is still pretty small compared to dogs and people, but it shows that you can apply the technique to a larger system.”

  “That still sounds pretty useless, but I guess it’s getting better.”

  “Thank you. You’re very kind.”

  WHAT IS IT ALL FOR? APPLICATIONS OF TELEPORTATION

  The quantum teleportation protocol lets us use entanglement to faithfully move a particular quantum state from one location to another, without physically moving the initial object. It can be used to reproduce photon states at distant locations, or to transfer a superposition state from one atom or group of atoms to another. Of course, it’s still a long way from the science fiction ideal.

  As with the classical fax machine, the only thing transmitted is information. Quantum teleportation allows us to transfer a particular state or superposition of states from one place to another, in the same way that the fax machine allows us to send a facsimile of what’s printed on a paper document over telephone lines. If the state being “teleported” is the state of an atom, however, there have to be appropriate atoms waiting at the other end of the teleportation scheme, in the same way that the receiving fax machine needs to be loaded with paper and ink.

  If the goal is to transfer an object from one place to another, though, it’s not obvious that you need quantum teleportation. Quantum teleportation moves a particular state from one place to another, but if you’re sending an inanimate object like a dog treat from one place to another, you may not need to preserve the exact state. As long as you have the right molecules in the right places relative to one another, it doesn’t make much difference to the taste or texture of the treat if the atoms in the facsimile treat are not in precisely the same states as the original. All you really need is a fax machine that works at the molecular level, and there’s nothing inherently quantum about that.

  So why should we care about quantum teleportation? Quantum teleportation may not be needed to move inanimate objects, but it may be crucial for moving conscious entities. Some scientists believe that consciousness is essentially a quantum phenomenon—Roger Penrose, for example, promotes this idea in The Emperor’s New Mind. If they’re right, we would need a quantum teleporter, not just a fax machine, to move people or dogs, in order to properly reproduce their brain state. Quantum teleportation may be the key to ensuring that when Scotty beams you up to the Enterprise, you arrive thinking the same thoughts as when you left.

  We’re not even close to teleporting people, though, so the current interest in quantum teleportation involves much smaller objects. Quantum teleportation is useful and important for situations where state information is the critical item that needs to be moved from one place to another. The primary application for this sort of thing today is in quantum computing.

  A quantum computer, like the classical computers we use today, is essentially a large collection of objects that can take on two states, called “0” and “1.”* You can string these “bits” together to represent numbers. For example, the number “229” would be represented by eight bits in the pattern “11100101.”

  In a quantum computer, however, the “qubits”† can be found not just in the “0” and “1” states, but in superpositions of “0” and “1” at the same time. They can also be in entangled states, with the state of one qubit depending on the state of another qubit in a different location. These extra elements let a quantum computer solve certain kinds of problems much faster than any classical computer—factoring large numbers, for example. The modern cryptography schemes used to encode messages—whether they’re government secrets or credit card transactions on the Internet—rely on factoring being a slow process. A working quantum computer might be able to crack these codes quickly, leading to intense interest in quantum computing from governments and banks.*

  The precise quantum state of an individual qubit is critical to the functioning of a quantum computer, and it’s here that quantum teleportation may find useful applications. A calculation involving a large number of qubits may require the entanglement of two qubits that are separated by a significant distance in the computer. Teleportation might be useful as a way of doing the necessary operations.

  Further down the road, if we want to connect together two or more quantum computers in different locations, to make what Jeff Kimble of Caltech calls the “Quantum Internet,” schemes based on entanglement and teleportation may be essential. This would allow still greater improvements in computing, in the same way that the classical Internet does for everyday computers.†

  Whatever its eventual applications, quantum teleportation is a fascinating topic. It shows us that the nonlocal effects of quantum entanglement and the “spooky action at a distance” explored in the EPR paper can be put to use, moving information around in a way that can’t be done by more traditional means. It may not help dogs to catch squirrels (not yet, anyway), but it’s another source of insight regarding the deep and bizarre quantum nature of the universe.

  “I don’t know, dude. I still think it’s lame.”

  “How’s that?”

  “Well, I mean, if you call something ‘teleportation,’ I expect it to be good for more than just moving state information.”

  “That is kind of unfortunate, I agree. I’m not the one who made up the name, though.”

  “So, that’s it for entanglement, then? Just Aspect experiments and teleportation?”

  “No, not at all. There are lots of things you can use quantum entanglement for. It’s the key to quantum computing, as I said, and you can use it for ‘dense coding,’ sending two bits of information for every one bit transmitted.”

  “That’s still just moving information around.”

  “There’s also quantum cryptography, where you use entanglement to transmit a string of random numbers from one person to another, numbers that they can then use to encode messages in a completely secure way. There’s no possibility of anyone eavesdropping on their messages, because the eavesdropping would change the particle states, and mess up the code in a way that can be detected.”

  “Still just information.”

  “Well, okay, sure, but there are people who think that the proper way to think about quantum physics is in terms of information. In some sense, the whole science of physics is really all about information.”
>
  “Yeah? Well, I’m a dog, and I’m all about getting squirrels.”

  “Okay, but that’s really about information, too.”

  “How so?”

  “Well, for your information, there’s a big fat squirrel sitting right in the middle of the lawn.”

  “Ooooh! Fat, squeaky squirrels!”

  * We’ll talk about why he might want to do such an odd thing at the end of the chapter.

  † Of course, it may also lead to quantum e-mail from dogs in Nigeria offering nine billion pounds of kibble if we’ll just provide the bank account information to help with a simple transaction . . .

  † Strictly speaking, a2 is the probability of finding vertical polarization, and b2 the probability of horizontal polarization and a2 + b2= 1. So for a photon at 30° from the vertical, with a 75% chance of passing a vertical polarizer, , and b = 1/2.

  * Strictly speaking, then, before its state is measured, Schrödinger’s cat can be in one of two states: “alive plus dead,” or “alive minus dead.”

  * The same Anton Zeilinger was seen in chapter 1 heading the group that demonstrated diffraction of molecules, and chapter 5 doing quantum interrogation. He has made a long and distinguished career doing experiments to demonstrate the weird and wonderful features of quantum mechanics.

  * In the seven years between the two experiments, Professor Zeilinger moved from Innsbruck to Vienna.

  † There’s no inherent problem with sending photons over very long distances—light manages to reach us from distant galaxies, after all—but interactions with the environment can destroy entangled states through the process of decoherence discussed in chapter 4. The Vienna experiment shows that decoherence can be avoided long enough to send entangled photons over useful distances.

  * A classical computer uses millions of tiny transistors on silicon chips; quantum computers could use anything with at least two states—atoms, molecules, electrons.

  † The “qu” is for “quantum.” Physicists are not widely admired for their ability to think up clever names.

  * In fact, the National Security Agency is one of the largest funders of quantum computing research in the United States.

  CHAPTER 9

  Bunnies Made of Cheese: Virtual Particles and Quantum Electrodynamics

  Emmy is standing at the window, wagging her tail excitedly. I look outside, and the backyard is empty. “What are you looking at?” I ask.

  “Bunnies made of cheese!” she says. I look again, and the yard is still empty.

  “There are no bunnies out there,” I say, “and there are certainly not any bunnies made of cheese. The backyard is empty.”

  “But particles are created out of empty space all the time, right?”

  “You’re still reading my quantum physics books?”

  “It’s boring here when you’re not home. Anyway, answer the question.”

  “Well, yes, in a sense. They’re called virtual particles, and under the right conditions, the zero-point energy of the vacuum can occasionally manifest as pairs of particles, one normal matter and one antimatter.”

  “See?” she says, wagging her tail harder. “Bunnies made of cheese!”

  “I’m not sure how that helps you,” I say. “Virtual particles have to annihilate one another in a very short time, in order to satisfy the energy-time uncertainty principle. A virtual electron-positron pair lasts something like 10-21 seconds before it disappears. They’re not around long enough to be real particles.”

  “But they can become real, right?” She looks a little concerned. “I mean, what about Hawking radiation?”

  “Well, sure, in a sense. The idea is that a virtual pair created near a black hole can have one of its members sucked into the black hole, at which point the other particle zips off and becomes real.”

  The tail-wagging picks back up. “Bunnies made of cheese!”

  “What?”

  She gives an exasperated sigh. “Look, virtual particles are created all the time, right? Including in our backyard?”

  “Yes, that’s right.”

  “Including bunnies, yes?”

  “Well, technically, it would have to be a bunny-antibunny pair . . .”

  “And these bunnies, they could be made of cheese.”

  “It’s not very likely, but I suppose in a Max Tegmark* sort of ‘everything possible must exist’ kind of universe, then yes, there’s a possibility that a bunny-antibunny pair made of cheese (and anticheese) might be created in the backyard, but—”

  “And if I eat one, the other becomes real.” She’s wagging her tail so hard that her whole rear end is shaking.

  “Yeah, but they wouldn’t last very long before they annihilated each other.”

  “I’m very fast.”

  “Given the mass of a bunny, they’d only last 10-52 seconds. If that.”

  “In that case, you’d better let me outside. So I can catch the bunnies made of cheese.”

  I sigh. “If you wanted to go outside, why didn’t you just say that?”

  “What fun would that be? Anyway, bunnies made of cheese!”

  I look out the window again. “I still don’t see any bunnies, but there is a squirrel by the bird feeder.”

  “Ooooo! Squirrels!” I open the door, and she goes charging outside after the squirrel, who makes it up a tree just in time.

  Back in chapter 2, we saw that the wave nature of matter gives rise to zero-point energy, meaning that no quantum particle can ever be completely at rest, but will always have at least some energy. Incredibly, this idea applies even to empty space. In quantum physics, even a perfect vacuum is a constant storm of activity, with “virtual particles” popping into existence for a fleeting moment, thanks to zero-point energy, then disappearing again.

  The idea of “virtual particles” popping in and out of existence in the middle of empty space is one of the most compelling and bizarre ideas in modern physics. In this chapter, we’ll talk about quantum electrodynamics (“QED” for short), the underlying theory that gives rise to the idea of virtual particles. We’ll also talk about the experiments that make QED arguably the most precisely tested theory in the history of science. Ironically, though, our discussion of this ultraprecise theory needs to start with the Heisenberg uncertainty principle.

  COUNTING TAKES TIME: ENERGY-TIME UNCERTAINTY

  The best-known version of the uncertainty principle is the one that we talked about in chapter 2 (page 48), which puts a limit on the uncertainties in the position and momentum of a particle. At a very fundamental level, the more we know about the position of a particle, the less we can know about how fast it is moving, and vice versa.

  Slightly less well known is the uncertainty relationship between energy and time, which says that the uncertainty in energy multiplied by the uncertainty in time has to be larger than Planck’s constant divided by four pi:

  ΔE Δt ≥ h/4π

  As with position-momentum uncertainty, this means that the more we know about one of these two quantities, the less we can know about the other.

  The idea that energy is somehow related to time may seem strange at first, but we can understand it by thinking about light. As we saw in chapter 1 (page 21), the energy of a photon is determined by the frequency associated with that color of light. A low-uncertainty measurement of energy, then, requires a precise measurement of frequency.

  So, how do you make a precise measurement of frequency? Imagine that you want to measure the rate at which an excited dog is wagging her tail, which is a fairly regular oscillation with small fluctuations in the frequency and amplitude: sometimes she wags a little faster, sometimes a little slower, sometimes farther to the right, sometimes farther to the left. What is the best way to measure the wagging frequency?

  Frequency is measured in oscillations per second, so you need to count the number of wags that take place in some fixed time interval. If you wait five seconds, and count ten tail wags, that’s a frequency of two oscillations per second. Any such me
asurement will always have some uncertainty, though—when you counted ten oscillations, was it really ten full oscillations, or ten-and-a-little-bit? Had her tail gotten all the way to the right, or was she wagging it farther that time around?

  To minimize that uncertainty, you need to look over a much longer time. The uncertainty in your count of wags will tend to be a constant—one tenth of a tail wag, say—so the more oscillations you count, the better you do in terms of the relative uncertainty.

  If you watch a tail wagging for five seconds, and count ten oscillations, plus or minus one tenth, the frequency you measure is

  f = (10 ± 0.1 oscillations)/(5 seconds) = 2.00 ± 0.02 Hz*

  That is, the frequency is somewhere between 1.98 and 2.02 oscillations per second.

  If you watch for fifty seconds (assuming the dog doesn’t explode from impatience), you’ll count a hundred wags, plus or minus one tenth, and the frequency is then

  f = (100 ± 0.1 oscillations)/(50 seconds) = 2.000 ± 0.002 Hz

  Increasing the number of oscillations that you measure leads to a decrease in the uncertainty of the frequency, and a more precise determination of just how happy the dog is.

  The cost of that decrease in frequency uncertainty is an increase in the time uncertainty. To get one tenth the energy uncertainty, you spent ten times as long making the measurement, which means you can’t say exactly when you measured the frequency. You know the average frequency over those fifty seconds, but you can’t point to a specific instant and say that the frequency right then was 2.000 Hz. All you can say is that over that fifty-second interval, the dog’s tail was wagging at about 2 Hz, but at any given instant, it may have been faster or slower.