Math II (Несколько текстов для зачёта), страница 24

Many Worlds

By the 1950s this ongoing parade of successes had made it abundantly clear that quantum theory was far more than a short-lived temporary fix. And so, in the mido1950s, a Princeton University student named Hugh Everett III decided to revisit the collapse postulate in his doctoral thesis. Everett pushed the quantum idea to its extreme by asking the following question: What if the time evolution of the entire universe is always unitary? After all, if quantum mechanics suffices to describe the universe, then the present state of the universe is described by a wave function (an extraordinarily complicated one). In Everett's scenario, that wave function would always evolve in a deterministic way, leaving no room for mysterious nonunitary collapse or God playing dice.

Instead of being collapsed by measurements, microscopic superpositions would rapidly get amplified into byzantine macroscopic superpositions. Our quantum card would really be in two places at once. Moreover, a person looking at the card would enter a superposition of two different mental states, each perceiving one of the two outcomes. If you had bet money on the queen's landing face up, you would end up in a superposition of smiling and frowning. Everett's brilliant insight was that the observers in such a deterministic but schizophrenic quantum world could perceive the plain old reality that we are familiar with. Most .important, they could perceive an apparent randomness obeying the correct probability rules [see illustration above].

Everett's viewpoint, formally called the relative-state formulation, became popularly known as the many-worlds interpretation of quantum mechanics, because each component of one's superposition perceives its own world. This viewpoint simplifies the underlying theory by removing the collapse postulate. But the price it pays for this simplicity is the conclusion that these parallel perceptions of reality are all equally real.

Everett's work was largely disregarded for about two decades. Many physicists still hoped that a deeper theory would be discovered, showing that the world was in some sense classical after all, free from oddities like big objects being in two places at once. But such hopes were shattered by a series of new experiments.

Could the seeming quantum randomness be replaced by some kind of unknown quantity carried about inside particles--so-called hidden variables? CERN theorist John S. Bell showed that in this case quantities that could be measured in certain difficult experiments would inevitably disagree with the standard quantum predictions. After many years, technology allowed researchers to conduct the experiments and to eliminate hidden variables as a possibility.

A "delayed choice" experiment proposed by one of us (Wheeler) in 1978 was successfully carried out in 1984, showing another quantum feature of the world that defies classical descriptions: not only can a photon be in two places at once, but experimenters can choose, after the fact, whether the photon was in both places or just one.

The simple double-slit interference experiment, in which light or electrons pass through two slits and produce an interference pattern, hailed by Richard Feynman as the mother of all quantum effects, was successfully repeated for ever larger objects: atoms, small molecules and, most recently, 60-atom buckyballs. After this last feat, Anton Zeilinger's group in Vienna even started discussing conducting the experiment with a virus. In short, the experimental verdict is in: the weirdness of the quantum world is real, whether we like it or not.

Quantum Censorship--Decoherence

The experimental progress of the past few decades was paralleled by great advances in theoretical understanding. Everett's work had left two crucial questions unanswered. First, if the world actually contains bizarre macroscopic superpositions, why don't we perceive them?

The answer came in 1970 with a seminal paper by H. Dieter Zeh of the University of Heidelberg, who showed that the Schr6dinger equation itself gives rise to a type of censorship. This effect became known as decoherence, because an ideal pristine superposition is said to be coherent. Decoherence was worked out in great detail by Los Alamos scientist Wojciech H. Zurek, Zeh and others over the following decades. They found that coherent superpositions persist only as long as they remain secret from the rest of the world. Our fallen quantum card is constantly bumped by snooping air molecules and photons, which thereby find out whether it has fallen to the left or to the right, destroying ("decohering") the superposition and making it unobservable [see box on preceding page].

It is almost as if the environment acts as an observer, collapsing the wave function. Suppose that your friend looked at the card without telling you the outcome. According to the Copenhagen interpretation, her measurement collapses the superposition into a definite outcome, and your best description of the card changes from a quantum superposition to a classical representation of your ignorance of what she saw. Loosely speaking, decoherence calculations show that you do not need a human observer (or explicit wave-function collapse) to get much the same effect--even an air molecule bouncing off the fallen card will suffice. That tiny interaction rapidly changes the superposition to a classical situation for all practical purposes.

Decoherence explains why we do not routinely see quantum superpositions in the world around us. It is not because quantum mechanics intrinsically stops working for objects larger than some magic size. Instead macroscopic objects such as cats and cards are almost impossible to keep isolated to the extent needed to prevent decoherence. Microscopic objects, in contrast, are more easily isolated from their surroundings so that they retain their quantum behavior.

The second unanswered question in the Everett picture was more subtle but equally important: What mechanism picks out the classical states--face up and face down for our card--as special? Considered as abstract quantum states, there is nothing special about these states as compared to the innumerable possible superpositions of up and down in various proportions. Why do the many worlds split strictly along the up/down lines that we are familiar with and never any of the other alternatives? Decoherence answered this question as well. The calculations showed that classical states such as face up and face down were precisely the ones that are robust against decoherence. That is, interactions with the surrounding environment would leave face-up and face-down cards unharmed but would drive any superposition of up and down into classical face-up/face-down alternatives.

Decoherence and the Brain

physicists have a tradition of analyzing the universe by splitting it into two parts. For example, in thermodynamics, theorists may separate a body of matter from everything else around it (the "environment"), which may supply prevailing conditions of temperature and pressure. Quantum physics traditionally separates the quantum system from the classical measuring apparatus. If unitarity and decoherence are taken seriously, then it is instructive to split the universe into three parts, each described by quantum states: the object under consideration, the environment, and the observer, or subject [see box at left].

Decoherence caused by the environment interacting with the object or the subject ensures that we never perceive quantum superpositions of mental states. Furthermore, our brains are inextricably interwoven with the environment, and decoherence of our firing neurons is unavoidable and essentially instantaneous. As Zeh has emphasized, these conclusions justify the long tradition of using the textbook postulate of wave function collapse as a pragmatic "shut up and calculate" recipe: compute probabilities as if the wave function collapses when the object is observed. Even though in the Everett view the wave function technically never collapses, decoherence researchers generally agree that decoherence produces an effect that looks and smells like a collapse.

The discovery of decoherence, combined with the ever more elaborate experimental demonstrations of quantum weirdness, has caused a noticeable shift in the views of physicists. The main motivation for introducing the notion of wave-function collapse had been to explain why experiments produced specific outcomes and not strange superpositions of outcomes. Now much of that motivation is gone. Moreover, it is embarrassing that nobody has provided a testable deterministic equation specifying precisely when the mysterious collapse is supposed to occur.

An informal poll taken in July 1999 at a conference on quantum computation at the Isaac Newton Institute in Cambridge, England, suggests that the prevailing viewpoint is shifting. Out of 90 physicists polled, only eight declared that their view involved explicit wave function collapse. Thirty chose "many worlds or consistent histories (with no collapse)." (Roughly speaking, the consistent-histories approach analyzes sequences of measurements and collects together bundles of alternative results that would form a consistent "history" to an observer.)

But the picture is not clear: 50 of the researchers chose "none of the above or undecided." Rampant linguistic confusion may contribute to that large number. It is not uncommon for two physicists who say that they subscribe to the Copenhagen interpretation, for example, to find themselves disagreeing about what they mean.

This said, the poll clearly suggests that it is time to update the quantum textbooks: although these books, in an early chapter, infallibly list explicit nonunitary collapse as a fundamental postulate, the poll indicates that today many physicists--at least in the burgeoning field of quantum computation--do not take this seriously. The notion of collapse will undoubtedly retain great utility as a calculational recipe, but an added caveat clarifying that it is probably not a fundamental process violating the Schr6dinger equation could save astute students many hours of confusion.

Looking Ahead

After 100 years of quantum ideas, what lies ahead? What mysteries remain? How come the quantum? Although basic issues of ontology and the ultimate nature of reality often crop up in discussions about how to interpret quantum mechanics, the theory is probably just a piece in a larger puzzle. Theories can be crudely organized in a family tree where each might, at least in principle, be derived from more fundamental ones above it. Almost at the top of the tree lie general relativity and quantum field theory. The first level of descendants includes special relativity and quantum mechanics, which in turn spawn electromagnetism, classical mechanics, atomic physics, and so on. Disciplines such as computer science, psychology and medicine appear far down in the lineage.

All these theories have two components: mathematical equations and words that explain how the equations are connected to what is observed in experiments. Quantum mechanics as usually presented in textbooks has both components: some equations and three fundamental postulates written out in plain English. At each level in the hierarchy of theories, new concepts (for example, protons, atoms, cells, organisms, cultures) are introduced because they are convenient, capturing the essence of what is going on without recourse to the theories above it. Crudely speaking, the ratio of equations to words decreases as one moves down the tree, dropping near zero for very applied fields such as medicine and sociology. In contrast, theories near the top are highly mathematical, and physicists are still struggling to comprehend the concepts that are encoded in the mathematics.

The ultimate goal of physics is to find what is jocularly referred to as a theory of everything, from which all else can be derived. If such a theory exists, it would take the top spot in the family tree, indicating that both general relativity and quantum field theory could be derived from it. Physicists know something is missing at the top of the tree, because we lack a consistent theory that includes both gravity and quantum mechanics, yet the universe contains both phenomena.

A theory of everything would probably have to contain no concepts at all. Otherwise one would very likely seek an explanation of its concepts in terms of a still more fundamental theory, and so on in an infinite regress. In other words, the theory would have to be purely mathematical, with no explanations or postulates. Rather an infinitely intelligent mathematician should be able to derive the entire theory tree from the equations alone, by deriving the properties of the universe that they describe and the properties of its inhabitants and their perceptions of the world.

The first 100 years of quantum mechanics have provided powerful technologies and answered many questions. But physics has raised new questions that are just as important as those outstanding at the time of Maxwell's inaugural speech--questions regarding both quantum gravity and the ultimate nature of reality. If history is anything to go by, the coming century should be full of exciting surprises.

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