THE EPR PARADOX
Let’s go back to our cat and dog, and imagine that they are in the quantum state described above, a superposition of (table, living room) and (sofa, yard). But now let’s imagine that if Mr. Dog is out in the yard, he doesn’t just sit there; he runs away. Also, he is very adventurous, and lives in the future, when we have regular rocket flights to a space colony on Mars. Mr. Dog—in the alternative where he starts in the yard, not in the living room—runs away to the spaceport, stows away on a rocket, and flies to Mars, completely unobserved the entire time. It’s only when he clambers out of the rocket into the arms of his old friend Billy, who had graduated from high school and joined the Space Corps and been sent on a mission to the Red Planet, that the state of Mr. Dog is actually observed, collapsing the wave function.
What we’re imagining, in other words, is that the wave function describing the cat/dog system has evolved smoothly according to the Schrödinger equation from
(table, living room) + (sofa, yard)
to
(table, living room) + (sofa, Mars).
There’s nothing impossible about that—implausible, maybe, but as long as nobody made any observations during the time it took the evolution to happen, we’ll end up with the wave function in this superposition.
But the implications are somewhat surprising. When Billy unexpectedly sees Mr. Dog bounding out of the spaceship on Mars, he makes an observation and collapses the wave function. If he knew what the wave function was to begin with, featuring an entangled state of cat and dog, Billy immediately knows that Miss Kitty is on the sofa, not under the table. The wave function has collapsed to the possibility (sofa, Mars). Not only is Miss Kitty’s state now known even without anyone interacting with her; it seems to have been determined instantaneously, despite the fact that it takes at least several minutes to travel between Mars and Earth even if you were moving at the speed of light.
This feature of entanglement—the fact that the state of the universe, as described by its quantum wave function, seems to change “instantaneously” throughout space, even though the lesson of special relativity was supposed to be that there’s no unique definition of what “instantaneously” means—bugs the heck out of people. It certainly bugged Albert Einstein, who teamed up with Boris Podolsky and Nathan Rosen in 1935 to write a paper pointing out this weird possibility, now known as the “EPR paradox.”203 But it’s not really a “paradox” at all; it might fly in the face of our intuition, but not of any experimental or theoretical requirements.
The important feature of the apparently instantaneous collapse of a wave function that is spread across immense distances is that it cannot be used to actually transmit any information faster than light. The thing that bothers us is that, before Billy observed the dog, Miss Kitty back here on Earth was not in any definite location—we had a 50/50 chance to observe her on the sofa or under the table. Once Billy observes Mr. Dog, we now have a 100 percent chance of observing her to be on the sofa. But so what? We don’t actually know that Billy did any such observation—for all we know, if we looked for Mr. Dog we would find him in the living room. For Billy’s discovery to make any difference to us, he would have to come tell us about it, or send us a radio transmission—one way or another, he would have to communicate with us by conventional slower-than-light means.
Entanglement between two far-apart subsystems seems mysterious to us because it violates our intuitive notions of “locality”—things should only be able to directly affect other nearby things, not things arbitrarily far away. Wave functions just don’t work like that; there is one wave function that describes the entire universe all at once, and that’s the end of it. The world we observe, meanwhile, still respects a kind of locality—even if wave functions collapse instantaneously all over space, we can’t actually take advantage of that feature to send signals faster than light. In other words: As far as things actually bumping into you and affecting your life, it’s still true that they have to be right next to you, not far away.
On the other hand, we shouldn’t expect that even this weaker notion of locality is truly a sacred principle. In the next chapter we’ll talk a little bit about quantum gravity, where the wave function applies to different configurations of spacetime itself. In that context, an idea like “objects can affect each other only when they are nearby” ceases to have any absolute meaning. Spacetime itself is not absolute, but only has different amplitudes for being in different configurations—so the notion of “the distance between two objects” becomes a little fuzzy. These are ideas that have yet to be fully understood, but the final theory of everything is likely to exhibit non-locality in some very dramatic ways.
MANY WORLDS, MANY MINDS
The leading contender for an alternative to the Copenhagen view of quantum mechanics is the so-called many-worlds interpretation. “Many worlds” is a scary and misleading name for what is really a very straightforward idea. That idea is this: There is no such thing as “collapse of the wave function.” The evolution of states in quantum mechanics works just like it does in classical mechanics; it obeys a deterministic rule—the Schrödinger equation—that allows us to predict the future and past of any specific state with perfect fidelity. And that’s all there is to it.
The problem with this claim is that we appear to see wave functions collapsing all the time, or at least to observe the effects of the collapse. We can imagine arranging Miss Kitty in a quantum state that has equal amplitudes for finding her on the sofa or under the table; then we look for her, and see her under the table. If we look again immediately thereafter, we’re going to see her under the table 100 percent of the time; the original observation (in the usual way of talking about these things) collapsed the wave function to a table-eigenstate. And that way of thinking has empirical consequences, all of which have been successfully tested in real experiments.
The response of the many-worlds advocate is simply that you are thinking about it wrong. In particular, you have misidentified yourself in the wave function of the universe. After all, you are part of the physical world, and therefore you are also subject to the rules of quantum mechanics. It’s not right to set yourself off as some objective classical observing apparatus; we need to take your own state into account in the wave function.
So, this new story goes, we shouldn’t just start with a wave function describing Miss Kitty as a superposition of (sofa) and (table); we should include your own configuration in the description. In particular, the relevant feature of your description is what you have observed about Miss Kitty’s position. There are three possible states you could be in: You could have seen her on the sofa, you could have seen her under the table, and you might not have looked yet. To start with, the wave function of the universe (or at least the bit of it we’re describing here) gives Miss Kitty equal amplitude to be on the sofa or under the table, while you are uniquely in the state of not having looked yet. This can be schematically portrayed like this:
(sofa, you haven’t yet looked) + (table, you haven’t yet looked).
Now you observe where she is. In the Copenhagen interpretation, we would say that the wave function collapses. But in the many-worlds interpretation, we say that your own state becomes entangled with that of Miss Kitty, and the combined system evolves into a superposition:
(sofa, you see her on the sofa) + (table, you see her under the table).
There is no collapse; the wave function evolves smoothly, and there is nothing special about the process of “observation.” What is more, the entire procedure is reversible—given the final state, we could use the Schrödinger equation to uniquely recover the original state. There is no intrinsically quantum mechanical arrow of time in this interpretation. For many reasons, this is an altogether more elegant and satisfying picture of the world than that provided by the Copenhagen picture.
The problem, meanwhile, should be obvious: The final state has you in a superposition of two different outcomes. The difficulty with that, of cou
rse, 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 w
orld, 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.
From Eternity to Here: The Quest for the Ultimate Theory of Time Page 32
