How to Teach Physics to Your Dog (14 page)

“So, even if you
were
moving the feeder every night, I could still find the bunny wavefunction?”

“If you kept track of where the feeder was each time, yes.”

“Because the bunny would always be most likely to be underneath the feeder?”

“Right. If you put all the positions together, you’d find a mess, but if you only used cases where the feeder was under the oak tree, you’d find the bunny mostly under the oak. If you only used cases where the feeder was between the two maple trees, you’d mostly find the bunny there, and so on.”

“OK. You’re not going to do that, though, right?”

“I wouldn’t upset you like that.”

“See, this is why you’re my favorite human.”

We see, then, that the many-worlds picture removes both of the major problems with the Copenhagen interpretation. Not only does it eliminate the mysterious “collapse” of the wavefunction, it gets rid of the arbitrary division between microscopic and macroscopic in the Copenhagen picture. According to the many-worlds interpretation, macroscopic objects like cats in boxes
do
obey quantum rules, and show superposition and interference effects. We don’t
see
those effects because of decoherence caused by interactions with the environment. If we could keep track of every interaction between the cat and its environment, though, we could reconstruct the wavefunction, and verify that quantum mechanics works on every scale.

Of course, it’s impossible to keep track of the exact state of every particle making up even the simplest of scientific experiments, let alone all the particles making up a macroscopic object like a piece of steak or a hungry dog. As a result, the process of decoherence happens all the time, and happens extremely quickly. You see decoherence any time you have an object interacting with a larger environment, and all objects are always interacting with their environments. The more atoms you have, the more chances you have for the system to interact with the environment, and the faster decoherence will take place. A
piece of steak contains something like 10
²³
atoms, so decoherence will take place extremely quickly, so quickly that we’ll never get a chance to see any quantum effects.
*

Real objects are extremely difficult to isolate from the environment well enough to be able to see quantum interference, but it can be done. Experimentalists have been able to demonstrate quantum effects using small numbers of particles inside ultra-high vacuum chambers, often involving components cooled to temperatures close to absolute zero. The largest such experiment involved about a billion electrons in a loop of superconductor, at temperatures within a few degrees of absolute zero. The electrons were placed into a superposition of states corresponding to clockwise and counterclockwise flow around the loop (like a dog walking clockwise and counterclockwise around Central Park at the same time). A billion electrons sounds like a lot, but it’s still pretty tiny compared to everyday objects. It serves to demonstrate, though, that with sufficiently careful control of the environment, we can see quantum behavior with large numbers of particles.

The idea of decoherence is by no means exclusive to the many-worlds interpretation of quantum mechanics. Decoherence is a real physical process that happens in all interpretations. In the Copenhagen interpretation, it serves as the first step in the process of measurement, selecting the states you can possibly end up in. Decoherence turns a coherent superposition of two or
more states (both A and B) into an incoherent mixture of definite states (either A or B). Then some other, unknown, mechanism causes the wavefunction to collapse into one of those states, giving the measurement result. In the many-worlds view, decoherence is what prevents the different branches of the wavefunction from interacting with one another, while each branch contains an observer who only perceives that one branch.

In either case, decoherence is an essential step in getting from quantum superpositions to classical reality. All of the concrete predictions of quantum theory are absolutely identical, regardless of interpretation. Whichever interpretation you favor, you use the same equations to find the wavefunction, and the wavefunction gives you the probabilities of the different possible outcomes of any measurement. No known experiment will distinguish between the Copenhagen interpretation and the many-worlds interpretation,
*
so which you use is essentially a matter of personal taste. They are just two different ways of thinking about what happens as you move from the probabilities predicted by the wavefunction to the result of an actual measurement.

“So how do I pick my universe?”

“Pardon?”

“I want to be in the universe where I eat steak. What determines which universe I end up in, and how do I change it to give me the one that I want?”

“Well, there’s nothing you can do to affect the outcome of a quantum measurement, that we know of. It’s completely random,
whether you want to think of it as a collapsing wavefunction, or just perceiving a single branch of the entire wavefunction of the universe. Either way, you’re stuck with random outcomes.”

“But I thought you said that in many-worlds the wavefunction always followed the Schrödinger equation? Can’t you use that to predict which branch is the real one?”

“You can use it to predict the probabilities of the different branches, but each branch has its own version of you, perceiving its own set of measurement outcomes. Each of them think they’re the ‘real’ branch, and wonder why they didn’t end up in a different branch. The theory doesn’t say anything about one of them being ‘real.’ ”

“So . . . it’s a punt, basically?”

“Sorry, but yes. It’s mathematically more elegant, but not really much more satisfying than the Copenhagen interpretation, when you get right down to it. It just sort of pushes the question back a level.”

“Interpretations are stupid.”

“You’re not alone in thinking so, but we’re stuck with them for the moment.”

“Well, I don’t like them. I want to eat steak. If quantum measurement won’t help me eat steak, then I don’t want any more to do with it.”

“Interpretations aren’t the whole of quantum theory, by any stretch. There are only a few people who spend their time working on that stuff. Most physicists don’t bother worrying about interpretations, and use quantum mechanics to do useful stuff instead.”

“If measurement is random, how can you do anything useful with it?”

“Well, that’s the next chapter.”

*
In fact, all of the viable candidates to replace the Copenhagen interpretation include decoherence as an important part of the measurement process.

†
“Many-worlds,” “many-histories,” “many-minds,” “decoherent histories,” “relative state formulation,” and “theory of the universal wavefunction,” among others.

*
This is called a “Mach-Zehnder interferometer” after the German and Swiss physicists who invented it.

*
There is a small shift in the “phase” of a wave when it reflects off a beam splitter, as if the reflected beam had traveled a small extra distance. As a result, when the two paths have equal length, the waves hitting Detector 2 are in phase, and add to give a bright spot, while the waves reaching Detector 1 are out of phase, and cancel each other out. For paths with different lengths, the two detectors give complementary signals—when one sees no light, the other detects the full initial intensity, and vice versa.

*
This is a very rough definition, and doesn’t capture everything—waves from opposite ends of a single large source may not be coherent, for example—but it does get the basic idea across.

*
This is on top of the fact that the wavelength of a 10-gram piece of steak would be something like 10
^-29
meters, as discussed in
chapter 1
, making it nearly impossible to measure a steaky interference pattern even if decoherence weren’t an issue.

*
Or any of the other interpretations, for that matter. Interpretations of quantum mechanics are sort of “metatheories,” each giving a different gloss on the results of an experiment, but not changing the results. Every now and then, you will run across somebody claiming to have experimentally “proved” some interpretation or another, but they’re inevitably confused.

I’ve had a long, annoying day at work, running from one committee meeting to another, and I come home with a pounding headache. I have an hour or so until Kate gets home, and all I want is a nap. Emmy is ecstatic to see me, and does the Happy Dance all over the living room.

“Hooray! You’re home! Yippeee!!!” She’s wagging her tail so hard she almost loses her balance. This happens every afternoon when I come home.

“It’s good to see you, too.”

“Let’s do something fun! Let’s play fetch! Let’s go for a walk! Let’s play fetch on a walk!”

“Let’s let me take a nap.” She stops bounding immediately, and looks crestfallen. Her ears and tail droop.

“No walk?”

“Not right now,” I say, lying down on the couch. “Let me sleep for half an hour, and then we’ll do something fun.”

“Promise?”

“I promise. Now be quiet. The sooner I get to sleep, the sooner we’ll do something fun.”

“Oh. Okay.”

I lie down and get comfortable on the couch. I’m just starting to settle in for my nap, when a cold, wet nose pokes me in the face.

“Are you asleep?”

“No, I’m not asleep.”

“Oh.” A minute passes.

Poke.
“Are you asleep?”

“No.” Another minute passes.

Poke.
“Are you asleep?”

“No!” I sit back up. “And I’m never going to get to sleep if you don’t stop poking me with your nose and asking that question.”

“Why not?”

“Every time you poke me, you wake me back up, and I have to start over again. If you keep waking me up, I don’t get all the way asleep, and you don’t get to do anything fun.”

“Oh.” She brightens up. “Hey, it’s just like the Zero Effect!”

“The what?”

“You know. The paradox with the guy who can’t catch the turtle because he has to go half the way there, and then another half, and so on, so he never gets anywhere.”

“You mean Zeno’s paradox. Zeno, with an
n
as in ‘nap.’ The
Zero Effect
is a movie with Bill Pullman and Ben Stiller.”

“Whatever. I don’t spell so good.”

“Anyway, what you’re thinking of is the
quantum
Zeno
effect, and yes, this is kind of like that. If you have a system that’s moving from one state to another, with the probability of being in the second state increasing over time, you can prevent the state change by repeated measurements. Every time you measure it to be in the first state, you restart the process.”

“Right. So when I ask if you’re asleep, I collapse your wave-function back to the ‘awake’ state, and you need to start napping again.”

“Or you find yourself perceiving the branch of the wavefunction in which I’m awake again, in the many-worlds picture. But yes, that’s the basic idea, and a good analogy.”

“I’m a philosophical dog!”

“Yes, you’re very smart. Now shut up and let me sleep.”

“Okay. I won’t ask if you’re asleep anymore.”

“Thank you.”

I settle back down onto the couch, and start to feel warm and cozy, and feel myself drifting off . . .

Poke.
“Are you awake?”

Whether you prefer the Copenhagen interpretation, many-worlds, or one of the many others,
something
happens when you make a measurement. Whether you think this involves the physical collapse of a wavefunction, or just limiting your perception to a single branch of an expanding and evolving wavefunction, measurement is an active process. Before you measure an object’s state, it exists in a quantum superposition of all possible states, while immediately after the measurement, you observe one and only one state.

In this chapter, we’ll look at the most dramatic consequence of active measurement, the “quantum Zeno effect.” We’ll see that making repeated measurements of a quantum particle can prevent it from changing its state. We can also use the quantum Zeno effect to detect the presence of objects without hitting them with even a single photon of light.

The name of the effect is a reference to the famous paradoxes of the Greek philosopher Zeno of Elea, who lived in the fifth century
B.C.E.
There are several different versions of the paradoxes, but all of them purport to show that motion is impossible.

Here’s a modern canine version of the argument: in order to reach a treat on the far side of the room, a dog first needs to cross half the width of the room, which takes a finite time. Then, she needs to cross half of the remaining distance, which takes a finite time, and then half of the remaining distance, and so on.
The distance across the room is divided into an infinite number of half steps, each requiring a finite time to cross. If you add together an infinite number of steps, each taking a finite time, it should take an infinite amount of time to cross the room. Thus, it’s impossible for the poor dog to ever get all the way to the tasty treat.

Happily for hungry dogs everywhere, there’s a mathematical solution to the apparent paradox: as the distance gets smaller, the time required to cross it also gets smaller. If it takes one second to cross half the width of the room, it takes half a second to cross the next quarter, and a quarter of a second to cross the next eighth, and so on. Adding together all those times, we find that:

1 s + 1/2 s + 1/4 s + 1/8 s + . . . = 2 s

The total time is the sum of an infinite number of terms, but the terms get smaller as you go. Mathematicians learned how to add this sort of series when calculus was invented in the seventeenth and eighteenth centuries. The infinite sum gives a finite result: the dog crosses the room in two seconds. Motion is possible after all, and a good dog can always reach her treats.
*