From Eternity to Here (47 page)

The problem, meanwhile, should be obvious: The final state has you in a superposition of two different outcomes. The difficulty with that, of course, is that you never
feel
like you’re in such a superposition. If you actually did make an observation of a system that was in a quantum superposition, after the observation you would always
believe
that you had observed some specific outcome. The problem with the many-worlds interpretation, in other words, is that it doesn’t seem to accord with our experience of the real world.

But let’s not be too hasty. Who is this “you” of which we are speaking? It’s true: The many-worlds interpretation says that the wave function of the universe evolves into the superposition shown above, with an amplitude for you seeing the cat on the sofa, and another amplitude for you seeing her under the table. Here is the crucial step: The “you” that does the seeing and perceiving and believing is not that superposition. Rather, “you” are either one of those alternatives, or the other. That is, there are now two different “yous,” one who saw Ms. Kitty on the sofa and another who saw her under the table, and they both honestly
exist
there in the wave function. They share the same prior memories and experiences—before they observed the cat’s location, they were in all respects the same person—but now they have split off into two different “branches of the wave function,” never to interact with each other again.

These are the “many worlds” in question, although it should be clear that the label is somewhat misleading. People sometimes raise the objection to the many-worlds interpretation that it’s simply too extravagant to be taken seriously—all those different “parallel realities,” infinite in number, just so that we don’t have to believe in wave function collapse. That’s silly. Before we made an observation, the universe was described by a single wave function, which assigned a particular amplitude to every possible observational outcome; after the observation, the universe is described by a single wave function, which assigns a particular amplitude to every possible observational outcome. Before and after, the wave function of the universe is just a particular point in the space of states describing the universe, and that space of states didn’t get any bigger or smaller. No new “worlds” have really been created; the wave function still contains the same amount of information (after all, in this interpretation its evolution is reversible). It has simply evolved in such a way that there are now a greater number of distinct subsets of the wave function describing individual conscious beings such as ourselves. The many-worlds interpretation of quantum mechanics may or may not be right, but to object to it on the grounds that “Gee, that’s a lot of worlds,” is wrong-headed.

The many-worlds interpretation was not originally formulated by Bohr, Heisenberg, Schrödinger, or any of the other towering figures of the early days of quantum mechanics. It was proposed in 1957 by Hugh Everett III, who was a graduate student working with John Wheeler at Princeton.
²⁰⁴
At the time (and for decades thereafter), the dominant view was the Copenhagen interpretation, so Wheeler did the obvious thing: He sent Everett on a trip to Copenhagen, to discuss his novel perspective with Niels Bohr and others. But the trip was not a success—Bohr was utterly unconvinced, and the rest of the physics community exhibited little interest in Everett’s ideas. He left academic physics to work for the Defense Department, and eventually founded his own computer firm. In 1970, theoretical physicist Bryce DeWitt (who, along with Wheeler, was a pioneer in applying quantum mechanics to gravity) took up the cause of the many-worlds interpretation and helped popularize it among physicists. Everett lived to see a resurgence of interest in his ideas within the physics community, but he never returned to active research; he passed away suddenly of a heart attack in 1982, at the age of fifty-one.

DECOHERENCE

Despite its advantages, the many-worlds interpretation of quantum mechanics isn’t really a finished product. There remain unanswered questions, from the deep and conceptual—why are conscious observers identified with discrete branches of the wave function, rather than superpositions?—to the dryly technical—how do we justify the rule that “probabilities are equal to amplitudes squared” in this formalism? These are real questions, to which the answers aren’t perfectly clear, which is (one reason) why the many-worlds interpretation doesn’t enjoy universal acceptance. But a great deal of progress has been made over the last few decades, especially involving an intrinsically quantum mechanical phenomenon known as
decoherence
. There are great hopes—although little consensus—that decoherence can help us understand why wave functions
appear
to collapse, even if the many-worlds interpretation holds that such collapse is only apparent.

Decoherence occurs when the state of some small piece of the universe—your brain, for example—becomes so entangled with parts in the wider environment that it is no longer subject to interference, the phenomenon that truly makes something “quantum.” To get a feeling for how this works, let’s go back to the example of the entangled state of Miss Kitty and Mr. Dog. There are two alternatives, with equal amplitudes: the cat is under the table and the dog is in the living room, or the cat is on the sofa and the dog is in the yard:

(table, living room) + (sofa, yard).

We saw how, if someone observed the state of Mr. Dog, the wave function would (in the Copenhagen language) collapse, leaving Miss Kitty in some definite state.

But now let’s do something different: Imagine that nobody observes the state of Mr. Dog, but we simply ignore him. Effectively, we throw away any information about the entanglement between Miss Kitty and Mr. Dog, and simply ask ourselves: What is the state of Miss Kitty all by herself?

We might think that the answer is a superposition of the form (table)+(sofa), like we had before we had ever introduced the canine complication into the picture. But that’s not quite right. The problem is that interference—the phenomenon that convinced us we needed to take quantum amplitudes seriously in the first place—can no longer happen.

In our original example of interference, there were two contributions to the amplitude for Miss Kitty to be under the table: one from the alternative where she passed by her food bowl, and one from where she stopped at her scratching post. But it was crucially important that the two contributions that ultimately canceled were contributions to
exactly the same final alternative
(“Miss Kitty is under the table”). Two contributions to the final wave function are going to interfere only if they involve truly the same alternative for everything in the universe; if they are contributing to different alternatives, they can’t possibly interfere, even if the differences involve the rest of the universe, and not Miss Kitty herself.

So when the state of Miss Kitty is entangled with the state of Mr. Dog, interference between alternatives that alter Miss Kitty’s state without a corresponding change in Mr. Dog’s becomes impossible. Some contribution to the wave function can’t interfere with the alternative “Miss Kitty is under the table,” because that alternative isn’t a complete specification of what can be observed; it could only interfere with the alternatives “Miss Kitty is under the table and Mr. Dog is in the living room” that are actually represented in the wave function.
²⁰⁵

Therefore, if Miss Kitty is entangled with the outside world but we don’t know the details of that entanglement, it’s not right to think of her state as a quantum superposition. Rather, we should just think of it as an ordinary
classical
distribution of different alternatives. Once we throw away any information about what she is entangled with, Miss Kitty is no longer in a true superposition; as far as any conceivable experiment is concerned, she is in either one state or the other, even if we don’t know which. Interference is no longer possible.

That’s decoherence. In classical mechanics, every object has a definite position, even if we don’t know what the position is and can ascribe probabilities only to the various alternatives. The miracle of quantum mechanics was that there is no longer any such thing as “where the object is”; it’s in a true simultaneous superposition of the possible alternatives, which we know must be true via experiments that demonstrate the reality of interference. But if the quantum state describing the object is entangled with something in the outside world, interference becomes impossible, and we’re back to the traditional classical way of looking at things. As far as we are concerned, the object is in one state or another, even if the best we can do is assign a probability to the different alternatives—the probabilities are expressing our ignorance, not the underlying reality. If the quantum state of some particular subset of the universe represents a true superposition that is un-entangled with the rest of the world, we say it is “coherent”; if the superposition has been ruined by becoming entangled with something outside, we say that it has become “decoher ent.” (That’s why, in the many-worlds view, setting up surveillance cameras counts as making an observation; the state of the cat became entangled with the state of the cameras.)

WAVE FUNCTION COLLAPSE AND THE ARROW OF TIME

In the many-worlds interpretation, decoherence clearly plays a crucial role in the apparent process of wave function collapse. The point is not that there is something special or unique about “consciousness” or “observers,” other than the fact that they are complicated macroscopic objects. The point is that any complicated macroscopic object is
inevitably
going to be interacting (and therefore entangled) with the outside world, and it’s hopeless to imagine keeping track of the precise form of that entanglement. For a tiny microscopic system such as an individual electron, we can isolate it and put it into a true quantum superposition that is not entangled with the state of any other particles, but for a messy system such as a human being (or a secret surveillance camera, for that matter) that’s just not possible.

In that case, our simple picture in which the state of our perceptions becomes entangled with the state of Miss Kitty’s location is an oversimplification. A crucial part of the story is played by the entanglement of us with the external world. Let’s imagine that Miss Kitty starts out in a true quantum superposition, un-entangled with the rest of the world; but we, complicated creatures that we are, are deeply entangled with the outside world in ways we can’t possibly specify. The wave function of the universe assigns distinct amplitudes to all the alternative configurations of the combined system of Miss Kitty, us, and the outside world. After we observe Miss Kitty’s location, the wave function evolves into something of the form

(sofa, you see her on the sofa, world
₁
) + (table, you see her under the table, world
₂
),

where the last piece describes the (unknown) configuration of the external world, which will be different in the two cases.

Because we don’t know anything about that state, we simply ignore the entanglement with the outside world, and keep the knowledge of Miss Kitty’s location and our own mental perceptions. Those are clearly correlated: If she is on the sofa, we believe we have seen her on the sofa, and so forth. But after throwing away the configuration of the outside world, we’re no longer in a real quantum superposition. Rather, there are two alternatives that seem for all intents and purposes classical: Miss Kitty is on the sofa and we saw her on the sofa, or she’s under the table and we saw her under the table.

That’s what we mean when we talk about the branching of the wave function into different “worlds.” Some small system in a true quantum superposition is observed by a macroscopic measuring apparatus, but the apparatus is entangled with the outside world; we ignore the state of the outside world and are left with two classical alternative worlds. From the point of view of either classical alternative, the wave function has “collapsed,” but from a hypothetical larger point of view where we kept all of the information in the wave function of the universe, there were no sudden changes in the state, just a smooth evolution according to the Schrödinger equation.

This business about throwing away information may make you a little uneasy, but it should also sound somewhat familiar. All we’re really doing is coarse-graining, just as we did in (classical) statistical mechanics to define macrostates corresponding to various microstates. The information about our entanglement with the messy external environment is analogous to the information about the position and momentum of every molecule in a box of gas—we don’t need it, and in practice can’t keep track of it, so we create a phenomenological description based solely on macroscopic variables.

In that sense, the irreversibility that crops up when wave functions collapse appears to be directly analogous to the irreversibility of ordinary thermodynamics. The underlying laws are perfectly reversible, but in the messy real world we throw away a lot of information, and as a result we find apparently irreversible behavior on macroscopic scales. When we observe our cat’s location, and our own state becomes entangled with hers, in order to reverse the process we would need to know the precise state of the outside world with which we are also entangled, but we’ve thrown that information away. It’s exactly analogous to what happens when a spoonful of milk mixes into a cup of coffee; in principle we could reverse the process if we had kept track of the position and momentum of every single molecule in the mixture, but in practice we keep track of only the macroscopic variables, so reversibility is lost.

In this discussion of decoherence, a crucial role was played by our ability to take the system to be observed (Miss Kitty, or some elementary particle) and isolate it from the rest of the world in a true quantum superposition. But that’s clearly a very special kind of state, much like the low-entropy states we start with by hypothesis when discussing the origin of the Second Law of Thermodynamics. A completely generic state would feature all kinds of entanglements between our small system and the external environment, right from the start.