How to Teach Physics to Your Dog (11 page)

“That’s . . . pretty radical. I don’t think I like that.”

“You’re not alone, believe me.”

The Copenhagen interpretation raises a great many problems, among them that there’s no obvious reason for the absolute distinction between microscopic and macroscopic physics. As we’ve already seen, while it gets more difficult to detect quantum behavior as objects get larger and more complicated, it is still possible to see wave behavior in rather large molecules. Macroscopic objects
ought
to be described by quantum wave-functions and quantum rules.

Another problem is who or what counts as an “observer” for the purposes of collapsing the wavefunction. The requirement that somebody observe the outcome of a measurement before the measurement really “counts” seems to assign some sort of mystical quality to “consciousness,” and that idea makes many physicists uncomfortable.

Even the idea of the “collapse” itself is problematic. No mathematical formula exists to describe the collapse—you can use the Schrödinger equation to describe how a wavefunction changes
between measurements, but there is no way to describe the “collapse” process. All you can do is choose a result, and start over with a new wavefunction after the measurement. Many physicists find this a little too magical for comfort.

The most famous illustrations of the problems with the Copenhagen interpretation are the infamous “Schrödinger’s cat” thought experiment, and the follow-up thought experiment of “Wigner’s friend.” Despite his role in creating quantum theory, Erwin Schrödinger, like Einstein, had deep philosophical problems with its interpretation, and became disillusioned with the entire field. Schrödinger’s cat, which is arguably more famous than his equation, is a diabolical thought experiment through which Schrödinger attempted to illustrate the absurdity of the Copenhagen interpretation. He imagined placing a cat in a sealed box with a radioactive atom that has a 50% chance of decaying within one hour, and a device that will release poison gas if the atom decays, killing the cat. What, he asked, is the state of the cat at the end of the hour?

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.

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 interpretation, 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.