How to Teach Physics to Your Dog

by CHAD ORZEL

  As Schrödinger noted, according to the Copenhagen interpretation the wavefunction describing the cat would be equal parts “alive” and “dead.” This would last until the experimenter opens the box, at which point it would collapse into one of the two states.* This seems completely absurd, though—the idea of a cat that is both dead and alive at the same time is outlandish. And yet this is exactly what seems to happen with photons.

  The Copenhagen interpretation also seems to be saying that physical reality does not exist until a measurement is made, which poses its own philosophical problems. Eugene Wigner brought this out by adding another layer to the cat experiment, imagining that the entire thing was conducted by a friend, and only reported to him later. Wigner asked when the wavefunction collapsed: When the friend opened the box, or later, when Wigner heard the result? Has a tree in a forest really fallen before your dog tells you that it’s on the ground?

  None of the Copenhagen interpretation’s answers to these questions are very satisfying, philosophically. While quantum mechanics does an outstanding job of describing the behavior of microscopic objects and collections of objects, the world we see remains stubbornly, infuriatingly classical. Something mysterious happens in the transition from the weird world of simple quantum objects to the much larger world of everyday objects. The Copenhagen approach of insisting on an absolute division between microscopic and macroscopic strikes many physicists as simply dodging the question: it says what happens, but not why.

  How best to handle the transition between quantum and classical remains a subject of active debate. Some future theory may lead to a detailed understanding of what, exactly, happens when we make a measurement of a quantum object. Until then, we’re stuck with one of the various interpretations of quantum mechanics.

  “I don’t think I like this interpretation. It’s awfully solipsistic, isn’t it?”

  “You’re not alone. There aren’t very many physicists these days who are really happy with the Copenhagen interpretation.”

  “So, what interpretation do you like?”

  “Me? I tend to go with the ‘shut up and calculate’ interpretation. The name is sometimes attributed to Richard Feynman,* but the idea is just to avoid thinking about it. Quantum mechanics gives us very good tools for calculating the results of experiments, and the question of what goes on during measurement is probably better left to philosophy.”

  “I don’t think I like that one, either. It’s hard to work a calculator without opposable thumbs.”

  “Well, there are all sorts of different interpretations—there’s the many-worlds interpretation, David Bohm’s nonlocal mechanics, and something called the ‘transactional interpretation.’ There are almost as many interpretations of quantum mechanics as there are people who have thought deeply about quantum mechanics.”

  “I like the many-worlds interpretation. You should talk about that.”

  “Good idea. That’s the next chapter.”

  “I knew that.”

  * See chapter 4, page 101.

  † The word “collapse” has come to be strongly associated with Copenhagen-type interpretations. There are other approaches to the problem of the projection of a multicomponent wavefunction onto a single measurement result that don’t involve a physical change in the wavefunction. We’ll look at the best-known example of these “no-collapse” interpretations in chapter 4.

  * Or, as the British writer Terry Pratchett described it in his novel Lords and Ladies, applied to a particularly nasty cat: “Technically, a cat locked in a box may be alive or it may be dead. You never know until you look. In fact, the mere act of opening the box will determine the state of the cat, although in this case there were three determinate states the cat could be in: these being Alive, Dead, and Bloody Furious” (p. 226, Harper paperback).

  * Feynman tends to get credit for anything clever said by a physicist in the latter half of the twentieth century. “Shut up and calculate” probably isn’t Feynman, though—its first appearance in print seems to be a David Mermin column in Physics Today (April 1989, p. 4), as he explains in the May 2004 issue (p. 10).

  * Sort of like “Thou shalt not climb on the furniture” for dogs living with humans.

  † Schrödinger was almost as notorious for his womanizing as for his contributions to physics. He came up with the equation that bears his name while on a ski holiday with one of his many girlfriends, and fathered daughters with three different women, none of them his wife (who, incidentally, knew about his affairs). His unconventional personal life cost him a position at Oxford after he left Germany in 1933, but he carried on living more or less openly with two women (one the wife of a colleague) for many years.

  * As we discussed at the end of chapter 2.

  * Einstein had many negative things to say about the probabilistic nature of quantum mechanics, but the origin of the usual formulation is a letter to Max Born in 1926, in which he wrote, “The theory delivers a lot, but hardly brings us closer to the secret of the Old One. I for one am convinced that He does not throw dice” (quoted in David Lindley’s Uncertainty, p. 137).

  * Werner Heisenberg went so far as to say that the results of measurements were the only reality—that it made no sense to talk about where an electron was or what it was doing between measurements.

  * The April 2007 issue of Scientific American even describes a quantum-eraser experiment that you can do at home, using a laser pointer, tinfoil, wire, and a few pieces of cheap polarizing film.

  * And electrons, and atoms, and molecules . . .

  * As we said last chapter (page 49), Bohr’s first great contribution to physics was a simple quantum model of hydrogen. It was a cobbled-together mix of quantum and classical ideas with no clear justification that happened to give the right result, and it’s unclear what led Bohr to put it forth. It did, however, point the way toward the modern quantum theory that we’re discussing in this book.

  CHAPTER 4

  Many Worlds, Many Treats: The Many-Worlds Interpretation

  I’m sitting at the computer typing, when Emmy bumps up against my legs. I look down, and she’s sniffing the floor around my feet intently.

  “What are you doing down there?”

  “I’m looking for steak!” she says, wagging her tail hopefully.

  “I’m pretty certain that there’s no steak down there,” I say. “I’ve never eaten steak at the computer, and I’ve certainly never dropped any on the floor.”

  “You did in some universe,” she says, still sniffing.

  I sigh. “All right, what ridiculous theory has your silly little doggy brain come up with now?”

  “Well, it’s possible that you would eat steak at the computer, yes?”

  “I do eat steak, yes, and I sometimes eat at the computer, so sure.”

  “And if you were to eat steak at the computer, you’d probably drop some on the floor.”

  “I don’t know about that . . .”

  “Dude, I’ve seen you eat.” Yes, the dog calls me “dude.” There may be obedience classes in her future.

  “All right, we’ll allow the possibility.”

  “Therefore, it’s possible that you dropped steak on the floor. And according to Everett’s many-worlds interpretation of quantum mechanics, that means that you did drop steak on the floor. Which means I just need to find it.”

  “Well, technically, what the many-worlds interpretation says is that there’s some branch of the unitarily evolving wavefunction of the universe in which I dropped steak on the floor.”

  “Ummm . . . yeah. Right. Anyway, I just need to find the unitary whatsis.”

  “The thing is, though, we can only perceive one branch of the wavefunction.”

  “Maybe you can only perceive one branch. I have a very good nose. I can sniff into extra dimensions. They’re full of evil squirrels. With goatees.”

  “That’s Star Trek, not science, and anyway, extra dimensions are a completely different thing. In the many-worlds interpretatio
n, once there has been sufficient decoherence between the branches of the wavefunction that there’s no possibility of interference between the different parts, they’re effectively separate and inaccessible universes.”

  “What do you mean, decoherence?”

  “Well, say I did have a piece of steak here—stop wagging your tail, it’s hypothetical—quantum mechanics says that if I dropped it on the floor, then picked it back up, there could be an interference between the wavefunction describing the bit of steak that fell and the wavefunction describing the bit of steak that didn’t fall. Because, of course, there’s only a probability that I’d drop it, so you need both bits.”

  “What would that mean?”

  “I’m not really sure what that would look like. The point is, though, it doesn’t really matter. The steak is constantly interacting with its environment—the air, the desk, the floor—”

  “The dog!”

  “Whatever. Those interactions are essentially random, and unmeasured. They lead to shifts in the wavefunctions of the different bits of steak, and those shifts make it so the wavefunctions don’t interfere cleanly anymore. That process is called decoherence, and it happens very fast.”

  “How fast?” she asks, looking hopeful.

  “It depends on the exact situation, but as a rough guess, probably 10-30 seconds or less.”

  “Oh.” She deflates a little. “That’s fast.”

  “Yeah. And once that decoherence has happened, the different branches of the wavefunction can’t interact with one another anymore. Which means, essentially, that the different branches become separate universes that are completely inaccessible to one another. Things that happen in these other ‘universes’ have absolutely no effect on what happens in our universe.”

  “Why do we only see one branch of the whatchamacallit?”

  “Ah, now that’s the big question. Nobody really knows. Some people think this means that quantum mechanics is fundamentally incomplete, and there’s a whole community of scientists doing research into the foundations of quantum theory and its interpretations. The important thing is, there’s no way you’re going to find steak under my desk in this universe, so please get out of there.”

  “Oh. Okay.” She mopes out from under the desk, head down and tail drooping.

  “Hey, look on the bright side,” I say. “In the universe where a version of me dropped a piece of steak on the floor, there’s also a version of you.”

  “Yeah?” Her head picks up.

  “Yeah. And you’re a mighty hunter, so you probably got to the steak before I could pick it up.”

  “Yeah?” Her tail starts wagging.

  “Yeah. So, in the universe where I dropped steak, you got to eat steak.”

  “Oooh!” The tail wags furiously. “I like steak!”

  “I know you do.” I save what I was working on. “Tell you what, how about we go for a walk?”

  “Ooooh! Good plan!” And she’s off, clattering down the stairs for the back door and the leash.

  Few physicists have ever been entirely happy with the Copenhagen interpretation discussed in the previous chapter. Numerous alternatives have been proposed, each attempting to find a more satisfying way to deal with the problem of quantum measurement. The most famous of these is commonly known as the many-worlds interpretation, which has achieved a dominant position in pop culture, if not among physicists, thanks to its prediction of a nearly infinite number of alternate universes in which events took a different path than the one we see. It’s a wonderful science fiction conceit, turning up in books, movies, and the famous Star Trek episode featuring an evil Spock with a goatee.

  In this chapter, we’ll talk about the many-worlds interpretation, and how it addresses some of the problems raised by the Copenhagen interpretation. We’ll also discuss the physical process known as “decoherence,” in which fluctuating interactions with the environment obscure the effects of interference between different parts of the wavefunction. Decoherence is central to the modern understanding of quantum mechanics, and may be the critical factor for understanding the move from the microscopic world of quantum physics to the classical world of everyday objects.

  THEN A MEASUREMENT OCCURS: PROBLEMS WITH COPENHAGEN

  The most disturbing element of the Copenhagen interpretation by far, for a physicist at least, is the lack of a mathematical procedure for describing what happens when you make a measurement of some quantity. The Schrödinger equation allows you to calculate what happens to the wavefunction between measurements, but at the instant of a measurement the Copenhagen interpretation says that normal physics stops, and something happens to select a single outcome in a way that does not involve any known mathematical equation.

  The ad hoc nature of the Copenhagen interpretation, with its arbitrary division between microscopic and macroscopic physics and its mysterious “wavefunction collapse,” is tremendously disturbing, because the whole project of modern theoretical physics is to find a single consistent mathematical description of the world. The unexplained process of wavefunction collapse is like the famous Sidney Harris cartoon of a scientist who has written “Then a miracle occurs” as the second step of a problem. Normal science has no room for miracles, and the Copenhagen collapse idea is a little too miraculous for comfort.

  Most physicists (particularly experimentalists) are content to use the idea of wavefunction collapse as a calculational shortcut and go about the business of predicting and measuring the physical world, for which regular quantum theory works astound-ingly well. In this “shut up and calculate” interpretation, the problem of finding a consistent explanation for quantum measurement is pushed aside to be dealt with by philosophers. Some better theory may eventually come along, but until then, we should do what we can with what we’ve got (which turns out to be an awful lot).

  The nature of measurement has been a problem from the first days of quantum theory, though, and a few physicists have always chosen to think deeply about these issues. Many of these physicists think that the lack of a clear explanation for the “collapse” of the wavefunction indicates that the Copenhagen interpretation is fundamentally flawed. Thus, they have always searched for some alternative interpretation.

  THERE IS NO COLLAPSE: HUGH EVERETT’S MANY-WORLDS INTERPRETATION

  In 1957, a graduate student at Princeton named Hugh Everett III suggested a solution to the “collapse” problem that’s breathtaking in its simplicity. The reason there is no mathematical method to describe the collapse of the wavefunction, Everett said, is because there is no such thing as the collapse of the wavefunction. The wavefunction always and everywhere evolves according to the Schrödinger equation, but we only see a small piece of the larger wavefunction of the universe.

  Let’s return to the previous chapter’s example of dog treats in sealed boxes to see how this works. If we imagine that we have one dog treat in two boxes, the Copenhagen picture says that we initially have a wavefunction for the treat that consists of two pieces at the same time. This wavefunction changes in time according to the Schrödinger equation. When we open a box and let the dog look inside, the wavefunction instantaneously collapses into only one of those two states, with the treat in either the left-hand box or the right-hand box. We predict future changes by starting over with the Schrödinger equation using the new one-part wavefunction.

  In the Everett picture, there is no collapse. The wavefunction starts out in a superposition, a two-part wavefunction with pieces corresponding to the treat in both left-hand and right-hand boxes, and when we open a box that superposition just becomes a little bigger. Now the superposition includes not just the apparatus but also the dog measuring the position of the treat. One piece is “treat in the left-hand box plus a dog who knows the treat is in the left-hand box,” and the other is “treat in the right-hand box plus a dog who knows the treat is in the right-hand box.” This process continues as you move into the future. If the next step in the experiment involves the dog either eating the t
reat or not (a low probability outcome, but it’s possible), the wavefunction contains four pieces: a dog who ate the treat from the left-hand box; a dog who didn’t eat the treat from the left-hand box; a dog who didn’t eat the treat from the right-hand box, and a dog who ate the treat from the right-hand box.

  The increase in complexity is even more striking in mathematical notation. We start with a two-component wavefunction for just the treat:

  where the angled brackets represent wavefunctions for the treat being in the left or right boxes. Then we bring in the dog:

  and finally, the decision to eat the treat or not:

  As you can see, this gets very complicated very quickly, but its evolution is always described by the Schrödinger equation.

  “You know, I’m not getting a lot out of these equations.”

  “You’re not supposed to understand them in detail. They’re just there to illustrate the increasing complexity of the wave-function in a more compact manner.”

  “So, basically, they’re just supposed to look scary?”

  “Pretty much.”

  “Oh. Good job, then.”

  • • •

  The Everett picture doesn’t immediately appear to be an improvement. The mysterious “collapse” is removed, but at the price of a wavefunction that’s expanding exponentially. At first glance, it also seems to defy reality, as we never see systems in more than one state. If all these extra pieces of the wavefunction are running around, why don’t we perceive objects as being in multiple states at the same time?