How to Teach Physics to Your Dog

by CHAD ORZEL

  For LHV theories to slip through this loophole the universe would need to be somewhat perverse, but it’s possible, so they did a second experiment, published in 1982, using two detectors for each photon.

  They closed the detector efficiency loophole by directly detecting both possible polarizations, and only counting experiments where they detected one photon on each side of the apparatus. They replaced the polarizers with polarizing beam splitters that directed each polarization to its own detector. If one of the detectors failed to record a photon, that run of the experiment was discarded.

  Their measured value in the second experiment exceeded the LHV limit by an astonishing 40 times the uncertainty, and the odds of that happening by chance are so small it’s ridiculous. So, why did they do the third experiment? As impressive as the second experiment was, it still left a loophole, because something could have passed messages between their detectors and their source.

  The second Aspect experiment. The entangled photons leave the source and head toward a pair of detectors with a polarizing beam splitter in front of them. These beam splitters direct the “0” polarization to one detector and the “1” polarization to another, ensuring that no photons are missed in the experiment.

  To test Bell’s theorem, it needs to be impossible for the measurement at one detector to depend on what happens at the other detector without some faster-than-light interaction. If there’s a way to send messages between the detectors at speeds less than that of light, all bets are off. In the first two experiments, they chose the detector settings in advance, and left them set for much longer than it took light to pass between the source and the detector. Something might have communicated the polarizer settings from the detectors to the source, which then sent out photons with definite polarization values chosen to match the quantum predictions. When the experimenters changed the angles, the new values would be sent to the source, which would change the polarizations sent out. Their results seemed to prove quantum theory, but they might have been the victims of a cosmic conspiracy.

  The third experiment found an ingenious way to close that loophole, as well. Aspect and his colleagues ruled out any possibility of some sort of universal conspiracy mimicking the quantum results by changing their detector settings faster than light could go from the source to the detector.

  They replaced the beam splitters with fast optical switches that could direct the photons to one of two detectors, each set for a different polarization. The switches flipped between the detectors every 10 nanoseconds, while it took the photons 40 ns to reach the detector. In effect, which detector a given photon would hit was not decided until after the photon had already left the source.

  The third experiment’s results exceeded the LHV limit by five times the uncertainty. The chances of such a result happening by accident were about one in a hundred billion—better than the chances for the other two experiments, but still low enough to be convincing.

  The third Aspect experiment. The two entangled photons leave the source, and head toward fast optical switches that send each photon toward one of two different polarizers, with the choice not being made until after the photons have left the source.

  Even the third experiment doesn’t close every loophole,* but Aspect stopped there, because the experiments were extraordinarily difficult. A number of people have repeated these experiments, using more modern sources of entangled photons,† and a 2008 experiment has even tested Bell’s theorem using entangled states of ions instead of photons, but no loophole-free test has been done. As a result, there are still a few people who argue that LHV theories have never been completely ruled out.

  These few die-hard theorists aside, the vast majority of physicists agree that the Bell’s theorem experiments done by Aspect and company have conclusively shown that quantum mechanics is nonlocal. Our universe cannot be described by any theory in which particles have definite properties at all times, and in which measurements made in one place are not affected by measurements in other places.

  Aspect’s experiments represent a resounding defeat for the view of the world favored by Einstein and presented in the Einstein, Podolsky, and Rosen paper in 1935. But while the EPR paper is wrong, it’s brilliantly wrong, forcing physicists to grapple with the philosophical implications of nonlocality. Exploring the ideas raised in the paper has deepened our understanding of the bizarre nature of our quantum universe. The idea of quantum entanglement exploited in the EPR paper also turns out to allow us to do some amazing things using the nonlocal nature of quantum reality.

  “Physicists are really weird.”

  “Yeah, nonlocality is strange.”

  “Not that, the loopholes. Do physicists really believe that there are messages being passed back and forth between different bits of their apparatus? What would carry the messages?”

  “I’m not sure anybody ever suggested a plausible mechanism, but it really doesn’t matter. They could be carried by invisible quantum bunnies, for all the difference it makes.”

  “Quantum bunnies?”

  “Invisible quantum bunnies. Moving at the speed of light. Don’t get your hopes up.”

  “Awww . . .”

  “Anyway, the third Aspect experiment pretty much rules out any means of carrying messages between parts of the apparatus, involving bunnies or anything else. The point is, prior to that, it was at least possible in principle for there to be another explanation. And in science, you have to rule out all possible explanations, even the ones that seem really unlikely, if you want to convince anybody of an extraordinary claim.”

  “Even the ones involving bunnies?”

  “Even the ones involving bunnies. And anyway, the idea that distant particles can be correlated in a nonlocal fashion isn’t all that much weirder than quantum bunnies would be.”

  “Good point. So, what’s this good for?”

  “What do you mean?”

  “You dropped a really broad hint in that last paragraph that this entanglement stuff is good for something. What’s it good for, sending messages faster than light?”

  “No, you can’t use it for faster-than-light communication, because the detections are random. There are correlations between particles, but the polarization of each pair will be random. I can’t send a message to somebody else using EPR correlations—all I can send is a random string of numbers.”

  “So what good is it?”

  “Well, random strings of numbers can be useful for quantum cryptography, making unbreakable codes. And the idea of entanglement is central to quantum computing, which could solve problems no normal computer can tackle. And there’s quantum teleportation, using entanglement to move states from one place to another. There’s all sorts of stuff out there, if you look for it.”

  “Ooh! Teleportation sounds cool! Talk about that.”

  “Well, that’s next . . .”

  * The process of decoherence (described in chapter 4) involves the interaction of a single quantum particle with a much larger environment, but we care only about the state of the single particle.

  * We’re assuming that Truman’s photon is measured first, for the sake of clarity. The result is the same if we assume RD’s photon is the first one measured.

  † The horizontal photon has a 75% chance of passing through the polarizer to the detector in either position. A “0” to match Truman’s result happens only when RD’s photon is blocked, a 25% probability.

  * This raises the question of whether a sufficiently clever experiment might distinguish between, say, the Copenhagen interpretation and the many-worlds interpretation. This is a much harder problem than distinguishing between quantum and LHV theories. Some future John Bell may yet come along and find the right test, but no one has managed yet.

  * John Clauser and a couple of other people had done earlier tests, but the Aspect (pronounced “As-PAY”) experiments had better precision, and so are regarded as the definitive tests.

  * This uncertainty is a technical limitation based
on the details of their experiment, and not anything to do with the Heisenberg uncertainty principle.

  † 1036 is a billion billion billion billion, a number so large that it might have made even Carl “Billions and Billions” Sagan blink.

  * The third experiment actually reopens the detector efficiency loophole, because they used only one detector for each polarizer.

  † One experiment by Paul Kwiat (who was part of the Innsbruck–Los Alamos team doing quantum interrogation experiments in chapter 5) and colleagues at Los Alamos saw an effect a mind-boggling 100 times larger than the uncertainty.

  * Werner Heisenberg, who developed the uncertainty principle while working with Bohr, once described Bohr as “primarily a philosopher, not a physicist.”

  † In almost all of those cases, Bohr’s argument depended on the effect of measurement on the system. Something in the process by which Einstein proposed to measure the position would cause a change in the momentum (as in the case of the Heisenberg microscope thought experiment discussed in chapter 2 [page 38]), or vice versa. Measuring the system requires an interaction, and that interaction changes the state of the system in a way that introduces some uncertainty in the quantities being measured.

  * Bohr was somewhat famous for the opacity of his writing, but he outdid himself in this case. The crucial paragraph of his paper refers to the quantum connection between distant objects as “an influence on the very conditions which define the possible types of predictions regarding the future behavior of the system” (italics in original), and declares that the quantum view “may be characterized as a rational utilization of all possibilities of unambiguous interpretation of measurement, compatible with the finite and uncontrollable interaction between the objects and the measuring instruments of quantum theory.”

  † This light-speed limit is one of the main consequences of Einstein’s theory of relativity, and thus very important to his conception of physics.

  * Or even longer, depending on what the dog is doing when called.

  * If you prefer the Copenhagen view, this projection involves a real collapse of the wavefunction into a single state. If you prefer many-worlds, the apparent projection onto a single state comes because we perceive only a single branch of the wavefunction. In either case, the resulting correlation is the same, and the effect is instantaneous.

  * We get the maximum value of 100% if the system has a 50% chance of being in state 1 and a 50% chance of being in state 8. We get the minimum value of 33% by never letting the system be in state 1 or state 8, and making the other six states equally likely. If you look at states 2 through 7, you’ll see that no matter what two different angles you choose, there are always two states that give you the same answer for both detectors.

  * As a result the predictions of Bell’s theorem are often called “Bell inequalities.”

  CHAPTER 8

  Beam Me a Bunny: Quantum Teleportation

  Emmy trots into my office, looking pleased with herself. This is never a good sign.

  “I have a plan!” she announces.

  “Really. What sort of plan is this?”

  “A plan to get those pesky squirrels.” They keep escaping up the trees in the backyard, and she’s getting frustrated.

  “Is this a better plan than the one where you were going to learn to fly by eating the spilled seed from the bird feeder?”

  “That was going to work,” she says, indignantly. “And for your information, yes, it’s a much better plan than that.”

  “Well, then, I’m all ears. What’s this brilliant plan?”

  “Teleportation.” She looks smug, and wags her tail vigorously.

  “Teleportation?”

  “Yep.”

  “Okay, you’re going to have to unpack that a little.”

  “Well, I figured, the problem is, they can see me coming from the house, and they get to the trees before I do. If I could get between them and the trees, though, I could get them before they get away.”

  “Okay, I’m with you so far.”

  “So, I just need to teleport out into the backyard, instead of going through the door.” Her whole back end is wagging now.

  “Uh-huh. And how, exactly, did you plan to accomplish this feat?”

  “Well . . .” The tail slows down, and she does her very best cute-and-pathetic look. “I was hoping you would help me.”

  “Me?”

  “Yeah. I read where some physicists have done quantum teleportation, and you’re a physicist, and you’re really smart, and you know about quantum, so I was hoping you would help me build a teleporter.” She puts her head in my lap. “Pleeeeease? I’m a good dog.”

  I scratch behind her ears. “You are a good dog, but I really can’t help. For one thing, I don’t do teleportation experiments in my lab. But even if I did, I wouldn’t be able to help you use teleportation to catch squirrels.”

  “Why not?”

  “Well, the existing teleportation experiments all deal with single particles, usually photons. You’re made up of probably 1026 atoms—a hundred trillion trillion—which is way more than anybody has ever teleported.”

  “Yeah, but you’re really smart. You can just . . . make it bigger.”

  “I appreciate your confidence, but no. The bigger problem is that the quantum teleportation people do in the real world isn’t like the teleportation you see with the transporters on Star Trek.”

  “How so?”

  “Well, all that quantum teleportation does is transmit the state of a particle from one place to another. If I have an atom here, for example, I can ‘teleport’ it to the backyard, and end up with an atom there that’s in the exact same quantum state as the atom I started with here. At the end of the process, though, I still have the original atom here where it started—it doesn’t move from one place to another.”

  “That’s pretty lame. What’s the point of that?”

  “Well, quantum mechanics won’t let you make an exact copy of a state without changing the original state, and quantum states of things like atoms are pretty fragile. If you really needed to get a particular quantum state from one place to another, your best bet might be to teleport it.” She looks a little dubious. “You could use it to make a quantum version of the Internet, if you had a couple of quantum computers that you needed to connect together.”

  “Well, okay. So just teleport my state into the backyard, and I’ll use it to catch squirrels.”

  “Even if I knew how to entangle your state with a whole bunch of photons—which I don’t—I would need to have raw material out in the backyard. There would need to be another dog out there, one that looked just like you.”

  Her tail stops dead. “We don’t like those dogs,” she says. “Dogs that look just like me. In my yard. We don’t like those dogs at all.” She looks distressed.

  “No, we don’t. One of you is all the dog we need.” She perks up a bit. “So, you see, teleportation isn’t a good plan, after all.”

  “No, I guess not.” She’s quiet for a moment, and looks thoughtful. “Well,” she says, “I guess it’s back to plan A.”

  “Plan A?”

  “Can I have some birdseed?”

  “Quantum teleportation” is probably the best-known application of the nonlocal correlations discussed in the previous chapter. The name certainly fires the imagination, conjuring up images of Star Trek and other fictional settings in which people, either through fictional science or just plain magic, can instantaneously transport objects from one place to another. The object starts at point A, disappears with a soft *bamf*, and reappears at point B, some distance away.

  The high expectations created by science fiction make the reality of quantum teleportation seem disappointing. Real quantum teleportation involves only the transfer of a quantum state from one location to another, and not the movement of complete objects. The transfer is also slower than the speed of light, because information needs to be sent from one place to another. This is a great disappointment to d
ogs hoping to beam themselves out into places where unsuspecting critters are waiting.

  Nevertheless, it’s a marvelously clever use of quantum theory, tying together several of the topics that we’ve already talked about. In this chapter, we’ll see how indeterminacy and quantum measurement make it difficult to transmit information about quantum states from one place to another. We’ll see how the “quantum teleportation” scheme makes ingenious use of nonlocality and entangled states to avoid these problems, and why you might want to.

  Quantum teleportation is a complex and subtle subject, probably the most difficult topic discussed in this book. It’s also the best example we have of the strangeness and power of quantum physics.

  DUPLICATION AT A DISTANCE: CLASSICAL “TELEPORTATION”

  We can’t teleport in the way envisioned in science fiction and fantasy, but the essence of teleportation is just duplication at a distance—you take an object at one place, and replace it with an exact copy at some other location. By that definition, we do have an approximation of teleportation using classical physics: a fax machine.

  If you have a document that you want to send instantly from one place to another—for example, if Truman has just gotten a really nice bone, and wants to taunt RD by sending him a picture of it—you can do this with a fax machine. The machine works by scanning the document, converting it to electronic instructions for creating an identical document, and sending that information over telephone lines to another fax machine at a distant location, which prints a copy. What’s transmitted is not the document itself, but rather information about how to make that document.