From Timothy Ferris' The Whole Shebang: A State-of-the-Universe(s) Report (1997).

Timothy Ferris

Quantum Weirdness

"What is the answer?"
"In that case, what is the question?"
-GERTRUDE STEIN, last words [1]

The quantum is the greatest mystery we've got. Never in my life was I more up a tree than today.

GERTRUDE STEIN said of modern art, "A picture may seem extraordinarily strange to you and after some time not only does it not seem strange but it is impossible to find what there was in it that was strange." [3]

Quantum physics isn't like that. The longer you look at it, the stranger it gets. The colloquial term is quantum weirdness, and it's not just a matter of getting used to the Alice-in-Wonderland oddities of a world in which particles are also waves and can leap from one place to another without traversing the intervening space. [4] Quantum weirdness goes deeper: It implies that the logical foundations of classical science are violated in the quantum realm; and it opens up a glimpse of an unfamiliar and perhaps older aspect of nature that some call the implicate universe.

There's no crisis within quantum physics itself. The standard model of quantum mechanics is internally consistent, and its equations accurately predict the behavior of all natural phenomena to which they have been applied. (Indeed, they have produced some of the most precisely verified predictions in science.) The trouble is border, trouble. It arises along the quantum-classical frontier, when we try to reconcile quantum mechanics with the characteristics of the macroscopic world-to conform quantum phenomena to a more general philosophy that would satisfy what Vladimir Nabokov called the "ominous and ludicrous luxury. . . of human consciousness." [5] Limited though they may be, these border skirmishes raise questions sufficiently baffling as to constitute the scientific equivalent of a Zen koan. Quantum weirdness is so counterintuitive that to comprehend it is to become not enlightened but confused. As Niels Bohr liked to say, "If someone says that he can think about quantum physics without becoming dizzy, that shows only that he has not understood anything whatever about it." [6]

The subject is a large one, and its subtleties have filled the pages of many capable books. [7] Here we will restrict ourselves to sketching its essentials, then reviewing how this mystery has been analyzed by the thinkers who have looked into it the most deeply.

Quantum weirdness arises when a quantum system is enlarged to a macroscopic scale and then measured in a way that would violate the indeterminacy principle if all the measurements were fruitful. In a typical experiment of this sort, we start with a beam of, say, light, and run it through a beam splitter that divides it in two. (A garden-variety beam splitter consists of a pane of glass half of which has been silvered, so that it's half mirror and half transparent glass. If we think of the photons as waves, the beam splitter divides each into two waves. If we think of them as particles, then the division occurs because each photon has an even chance of hitting the mirror rather than passing through the transparent glass.) The two beams are allowed to travel apart for some macroscopically significant distance, typically several meters. Then they are bounced off mirrors and reconverged at the input of a detector. The apparatus in its initial state looks something like this:

Schematic diagram of a beam-splitter apparatus.

The two beams can be regarded as parts of a single, quantum system. We can verify the validity of this analysis by using a wavechecking device as our final detector and firing a single photon through the system. The photon (having, as it does, wavelike as well as particlelike properties) will display an interference pattern in the detector. The photon is interfering with itself, confirming that even though it's just one photon, it's been deployed across meters of space.

Now that we've dragged the photon out onto a macroscopic stage, what if we try to make one measurement of it on path A, and simultaneously try to make another measurement on path B-such that the two measurements, together, would yield information forbidden us by quantum indeterminacy? The answer is weird: The system denies us the forbidden information on path B, instantly, as soon as we make a measurement on path A . Fiddling with the system here results in an instantaneous change way over there. It does so even if a signal would have to travel at a velocity faster than light in order to convey news of our fiddling from A to B.

Let's look at the situation more closely. This time, just in case we're worried that there's something peculiar about photons, we'll use electrons. [8] To minimize technical jargon, let's suppose that electrons have two sets of states, a complete knowledge of both of which is prohibited by the indeterminacy principle. We'll call one set sweet/sour and the other hard/soft. The words don't matter: The important point is that, according to Heisenberg, we can learn whether an electron is sour or sweet, or whether it is hard or soft, but not both. To test this assumption, we employ two kinds of measuring devices. One box separates sour electrons from sweet ones, spitting the sour ones out of one output window and the sweet ones out the other. The other box does the same, according to whether the electrons are hard or soft.

In an effort to circumvent the indeterminacy principle, we put a sweet/sour box upstream of the beam splitter, near the origin of our electron stream, and admit only sweet electrons to the rest of the apparatus. This works well: Another sour/sweet box, employed as our final detector, confirms that the system now contains sweet electrons only. We're ready to make an assault on indeterminacy. Into each path we insert a hard/soft box. The boxes divert all the hard electrons, permitting only soft ones to continue through the apparatus. At this point, according to classical concepts, we have set things up so that all the electrons arriving at the final detector are both soft and sweet. We know they're all sweet, because we only allowed sweet electrons into the apparatus to start with, and we know they're all soft, because we thereafter discarded all the hard ones. Yet Heisenberg says we cannot know both these things about any one electron. So we've got around the indeterminacy principle, right?

Wrong. When this is done, the final detector ceases to report that all the electrons are sweet. Instead, it starts spitting out electrons in equal numbers from both the sweet and sour windows, even though we admitted none but sweet electrons in the first place! So Heisenberg was right: We can know about sour/sweet or hard/soft, but not both. Indeed, all we've done so far is to verify the validity of quantum indeterminacy. This much of the problem is often explained by saying that the act of making a measurement "interferes" with a particle in such a way as to alter its state-that is, that making sour/sweet measurements randomizes the hard/ soft characteristics of electrons, and vice versa. But does that really get to the heart of the issue?

To find out, we change the setup, while continuing to admit only "sweet" particles to the apparatus. This time, we remove the hard-soft detector from path B; and we also divert the output of

Measuring "hardness" randomizes "the sweet/sour" results.

the hard/soft box on path A so that none of its output gets to the final detector. The result is really weird. The final detector again reports that the particles are half sweet and half sour. Yet it is receiving only path B particles-and we didn't interfere with those particles! So how did path B "learn" to randomize its flavor output? How did it "know" that we had made a forbidden measurement way over on path A?

This is quantum weirdness: Interfering with one part of a quantum system alters the results observed in another part, even when the system has been enlarged to enormous dimensions. The result is the same even if only a single particle is admitted into the apparatus at a time. It's the same if we wait until the particle has cleared the beam splitter before making a random decision whether to insert a detector into path A. It would be the same if the two paths were diverted to opposite sides of the galaxy. In every case, the system reacts instantaneously. It is as if the quantum world had never heard of space-as if, in some strange way, it thinks of itself as still being in one place at one time. Such behavior is called nonlocal. Classical physics assumes locality-that is, it assumes that changes in systems are caused by direct physical contact, comparable to the push-and-pull interactions characteristic of internal combustion engines and other machines (which is why the science of dynamic systems is called "mechanics"). Since measuring one part of a quantum system instantly alters the other parts of the system,

Making measurements on one side of the apparatus instantly alters results obtained on the other side.

even if the two parts are too far apart for a message to traverse the intervening distance by any identified agency, quantum systems are said to exhibit nonlocality: They act like an intimately connected whole, regardless of whether their parts are far removed from each other. [9]

Whatever we elect to call it-nonlocality, "quantum observership," or the "quantum measurement" problem-weirdness is as knotty a conundrum as the physical world has ever presented to the human mind. Three explanations for it, called "interpretations," have emerged. The first, the Copenhagen interpretation, asserts that we should simply accept that we cannot know the state of a quantum system until it is measured, and so should stop worrying about it. The second, or many worlds interpretation, begins with the astounding premise that the entire universe splits, with each act of measurement, into two universes, in one of which the particle has the qualities that we measure and in the other of which it resolves itself into the other potential state. This doctrine was advanced in the 1957 doctoral thesis of Hugh Everett III of Princeton University. (We encountered a latter-day version of it in the previous chapter, as the "many histories" approach.) The third interpretation preserves locality: It portrays quantum systems as mechanically linked, so that the particles on either side of our beam-splitter experiment do have a definite state throughout, and actually do alter that state when part of the system is interfered with. They are said to accomplish this by means of a "guiding wave" that has not yet been observed, and perhaps never can be. Consequently, this view is also known as the hidden-variables interpretation. -Originally advanced by the French theorist Louis de Broglie, it was worked out more fully by the American theorist David Bohm.

Before examining the three interpretations more closely, we should consider another position, popular among working scientists disinclined toward philosophy. They simply shrug their shoulders at quantum weirdness and ask, "So what?" As Isidor Rabi advised Gerald Edelman, "Quantum mechanics is just an algorithm. Use it. It works, don't worry." [10] Richard Feynman told a seminar audience, "The theory of quantum electrodynamics describes nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you can accept nature as she is-absurd." [11] Their point is that quantum physics is successful within its own domain, and can account for all of classical physics, too, so why fret over whether it "makes sense" in classical terms?

This minimalist position is perfectly satisfactory as a matter of pure science. One can simply say that we live in a quantum world, of which classical physics is a subset, and that quantum phenomena are not obliged to make sense in classical terms. But there is more to life than just science, and we all, scientists included, live in a world that we are accustomed to making sense of. Scientists aren't really content just to wield equations; they expect them to relate, not just to one another, but to the "real" world of experience. And they are, like the rest of us, accustomed to thinking of reality in terms of images-metaphors, really-drawn from experience. As the Dutch physicist Peter Debye put it, "I can only think in pictures." [12] Similarly Lord Kelvin: "I never satisfy myself until I can make a mechanical model of a thing. If I can make a mechanical model I can understand it. As long as I cannot, make a mechanical model all the way-through I cannot understand." [13] And-Einstein: "Physical theories try to form a picture of reality and to establish its connection with the wide world of sense impressions. Thus the only justification for our mental structures is whether and in what way our theories form such a link." [14]

As with pictures, so with words. Scientists put a lot of stock in their ability to explain their theories in ordinary language. The indeterminacy principle can be expressed in a few lines of mathematics-in terms, say, of the noncommutative matrix algebra that Heisenberg originally employed for this purpose. Yet scientists don't just leave it at that. They also go out of their way to tell stories and construct explanations of indeterminacy in words, and these tales and models form a nimbus surrounding the hard-core scientific literature-a nimbus that is very much a part of the scientific culture. Scientists know that they belong to a wider society and find it appropriate to relate their work to outsiders, for much the same reasons that architects and athletes do. As Erwin Schrödinger said, "If you cannot-in the long run-tell everyone what you have been doing, your doing has been worthless." [15] The scientists' insistence on resorting to nontechnical language also serves a utilitarian function, that of promoting objectivity and clear thinking while discouraging the subjective and obscurantist tendencies that can beguile even the most caustic mind. Niels Bohr was a lifelong champion of the view that theoretical physics is no place for fancy talk. "Our task must be to account for experience in a manner independent of individual subjective judgment and therefore objective in the sense that it can be unambiguously communicated in the common human language," he wrote. [16] Ernest Rutherford used to advise his students to distrust any concept (or their command of any concept) that they could not explain to a barmaid. Leon Lederman said, "If the basic idea is too complicated to fit on a T-shirt, it's probably wrong." [17] Einstein objected to theories that can "be judged only on the basis of [their] mathematical-formal qualities, but not from the point of view of ´truth.' " [18] Admittedly, the effort to translate physics into common sense becomes more difficult as physics becomes more sophisticated. But the tradition endures, and as long as quantum weirdness remains baffling, there will be physicists and philosophers who keep trying to make sense of it.

How, then, do the three leading interpretations seek to reconcile quantum weirdness with the common sense pictures and language of the macroscopic world?

The Copenhagen interpretation was the first, and for decades has remained the foremost, method of keeping peace along the quantum-classical borderline. It declares that the wave function describing a particle constitutes a complete description of that particle. Since the uncertainties expressed by the wave function are not resolved until the particle is observed, the particle cannot be said to have any definite state until it is observed. Its potential states (such as whether it is a particle or a wave, or has a certain position or momentum, or possesses, in our schematic illustration, the qualities of being hard or soft and sweet or sour) are said to be "superposed." The act of measurement turns potentiality into actuality, resolving the question of what the particle actually "is" through a combination of the particle's inherent potentials and the manner in which it is observed. So the Copenhagen interpretation implicates the observer in what he or she observes. Observers cannot arbitrarily alter reality-cannot violate the laws of nature, any more than a painter can paint a square that is both all white and all black -but they can make of a photon either particle or wave.

Heisenberg discovered quantum indeterminacy while working under Bohr, who was quick to appreciate its implications. Bohr was a wide-reaching thinker Heisenberg regarded him as "primarily a philosopher, not a physicist"-and it was due chiefly to his influence that the world soon came to regard quantum weirdness as a significant philosophical problem. [19] Although many capable theorists are like composers who play only the piano, Bohr and Einstein were both universalist thinkers, akin to those composers who can play every instrument in the orchestra. The world knows Einstein; perhaps we may take a moment to meet Bohr.

He was one of the physical physicists, blessed with a lifelong appetite for fresh air and exercise. He saw life as a whole and was immune to the scholarly delusion that brain power is superior to muscle power. Heisenberg tells a story that illustrates Bohr's integrated view of thought, action, and mystical philosophy: "Once, when on a lonely road I threw a stone at a distant telegraph post, and contrary to all expectations the stone hit, he said, ´To aim at -such-a-distant-object and-hit it-is-of course impossible . But if one has the impudence to throw in that direction without aiming, and in addition to imagine something so absurd as that one might hit it, yes, then perhaps it can happen. The idea that something perhaps could happen can be stronger than practice and will.'" [20] Bohr's younger brother Harald was a soccer star-a member of the Danish team that won a silver medal in the 1908 London Olympics-and Niels might have matched him athletically had he not been so preoccupied. Playing goalie against a German club, he busied himself tracing equations with his index finger on the goalpost, nearly letting an errant ball roll slowly into the goal. Like Einstein, Bohr was a sailor, but while Einstein liked to trace broad reaches on lakes, Bohr preferred blue water. (The greatest tragedy of his life came when his eldest son, Christian, was swept to his death from the deck of Bohr's cutter, the Cbita, in a summer storm in 1934. Only the restraining grip of friends on deck prevented Bohr from leaping into the sea after him.) Bohr viewed ignorance as an integral part of the learning process and regarded confusion and paradox as signposts on the road of inquiry. He complained on his deathbed that the philosophers too often "have not that instinct that it is important to learn something, and that we must be prepared to learn." [21]

Blunt and tenacious to a fault, Bohr was too serious to be pompous and too honest to be facile. If his way of speaking was often confusing, that was because he was himself frankly confused and liked to think out loud, and held that one should, as he put it, "never express yourself more clearly than you think." [22] (When Carl Friedrich von Weizsacker wrote in his diary on meeting Bohr, "I have seen a physicist for the first time. He suffers as he thinks," he meant that Bohr suffered out loud. [23]) His habit of being both frank and frankly uncertain could get Bohr in trouble. Winston Churchill, having been urged by Bohr to reveal nuclear secrets to the Soviets since they were bound to learn them anyway, responded in an outraged note to his science adviser, Lord Cherwell, who had arranged the meeting, "It seems to me Bohr ought to be confined or at any rate made to see that he is very near the edge of mortal crimes .... I did not like the man when you showed him to me, with his hair all over his head, at Downing Street .... I do not like it at all:" [24] Bohr fared little better-with -the -American secretary of state, Dean Acheson, with whom he met in the spring of 1950 to discuss a planned open letter to the United Nations. "The meeting began at, say, two o'clock, Bohr doing all the talking. At about two thirty Acheson spoke to Bohr about as follows. Professor Bohr, there are three things I must tell you at this time. First, whether I like it or not, I shall have to leave you at three for my next appointment. Secondly, I am deeply interested in your ideas. Thirdly, up till now I have not understood one word you have said." [25]

Bohr's explications of the Copenhagen outlook can sound as oracular as if he had uttered them from atop a tripod while chewing laurel leaves, but he was earnestly trying to bring as much clarity to quantum weirdness as he could, and his position is not all that difficult to understand. Briefly put, it is that since, owing to quantum indeterminacy, neither we nor any other observers anywhere in the universe can know everything about a given microscopic particle or system, it is pointless to speculate about whether the missing information "exists." Physics is not the pursuit of imaginary ideals, and physicists need not waste time speculating about quantities (such as whether a photon is "really" particle or wave) that are known to be unascertainable: "It is wrong to think that the task of physics is to find out how nature is," Bohr wrote. "Physics concerns what we can say about nature .... Our task is not to penetrate into the essence of things, the meaning of which we don't know anyway, but rather to develop concepts which allow us to talk in a productive way about phenomena in nature." [26] The Copenhagen interpretation asserts, to paraphrase John Wheeler (who was paraphrasing Bohr), that no elementary phenomenon is a phenomenon until it is an observed phenomenon.

To clarify this ontology, Bohr spoke of what he called complementarity. The wavelike or particlelike potential states of an undisturbed photon (or its polarization states, or the hard/soft and sweet/sour states of the particles in our schematic experiment) complement each other, like the black and white sides of the yin-yang diagram that Bohr incorporated into his family coat of arms. Bohr saw complementarity as a kind of chiaroscuro, an essential embracing by nature of opposites and contradictions that had been revealed to us by Heisenberg indeterminacy but that has wider implications. The more closely one looks at one side of the issue (e.g., studies the photon as a wave), the more paradoxical the other side (but it's a particle!) becomes.

Every interpretation of quantum weirdness amounts to sweeping the weirdness under one or another carpet, and a magic carpet at that. The magic carpet of the Copenhagen interpretation is the act of observation. It is by making an observation-a measurement-that one "collapses the wave function," thus resolving the superposed system into one or the other of its states. But what, exactly, is an observation? From this question have sprung the most enduring thought experiments to have probed the dark realms of quantum weirdness.

The best known of them is "Schrödinger's cat." It consists of a system with two potential states, A and B. This could be a piece of radium with a 50 percent chance of decaying within one hour, or a sweet/sour box into which is introduced a single particle that has a 50 percent chance of emerging from the sweet output window -any probabilistic quantum setup. The important point is that, according to Bohr, the system has no definite state-neither decayed nor undecayed, neither sweet nor sour-until it is observed. Instead it exists in a superposed state, one fully designated by the probabilities of its wave function. The radium or other quantum object is set up to trigger one of two devices located inside an opaque box that also contains a cat. If the system goes one way (if, say, the radium atom decays) it opens a canister of cyanide gas inside a sealed box, killing the cat. If it goes the other way (no decay), the cat survives. We set up the apparatus, then wait one hour before opening the box. Question: Right before we open the box, is the cat dead or alive? The Copenhagen interpretation answers that until we open the box and observe it, the cat is neither dead nor alive but exists in a superposed state of dead/alive. This seems implausible, and that is the point of the thought experiment: Schrodinger's cat critiques the Copenhagen interpretation by reducing it to absurdity. Its object is to deny the plausibility of a bifurcated, quantum-classical universe by demonstrating that such segregation yields nonsensical results. (Minimalists comfortable with a bifiircated physics can and do shrug it off. Stephen Hawking, paraphrasing Hermann Goering, says, "When I hear of Schrödinger's cat, I reach for my gun." [27])

The issue can be illuminated by considering our frame of reference. Suppose that the cat experiment is conducted in a locked laboratory, at night, with only one scientist keeping watch. At the end of the hour, he opens the box and sees . . . what? Until the scientist picks up the phone and announces the result, or runs into the street shouting "Eureka!" we don't know the outcome. [28] The wave function was collapsed in that scientist's frame of reference, but not in ours. That this is problematical is not terribly surprising: In science as in art, the choice of frame counts for a lot. (G. K. Chesterton: "Art is limitation; the essence of every picture is the frame." [29]) It amounts to saying that the Copenhagians are vague when it comes to defining just what, exactly, is meant by "measuring" or "observing" a phenomenon or "collapsing the wave function"-all of which mean the same vague thing.

Another thought experiment, more subtle than the cat but no less telling, was composed in 1935 by Einstein and two of his young associates at the Institute for Advanced Study in Princeton, Boris Podolsky and Nathan Rosen. It is known as the EinsteinPodolsky-Rosen ("EPR") "paradox," and works rather like our beam-sputter experiment. We start with a particle that decays into two other particles, X and Y, that must have a total spin equal to zero. So if one particle has a spin of + 1, the spin of the other must be -1. We let the particles fly far apart-this is the now-familiar amplification part of the experiment-and when they are separated by, say, one light-year, a physicist measures one of them, particle X, and finds that its spin is -1. He then knows that particle Y, a light-year away, must have a spin of + 1, as can be verified by a second physicist, off yonder where particle Y is. That would be perfectly sensible for a macroscopic system-if, say, the particles were replaced by a pair of one-ton gyroscopes that had been spinning in opposite directions all the way out. But according to the Copenhagen interpretation, remember, the particles were in neither spin state until their spin was observed. It seemed to Einstein-and has seemed to like-minded thinkers since-that if in fact a particle's spin is indeterminate, then the only way for Y to "know" that X had suddenly resolved itself into a spin -1 state would be if some sort of signal propagated instantaneously across a light-year of space, bringing the news from X to Y. And that, of course, would violate both special relativity and common sense. Einstein called it "spooky action at a distance." "No reasonable definition of reality could be expected to permit this," wrote Einstein, Podolsky, and Rosen. [30]

Much of the subsequent discussion of the Copenhagen interpretation-and such critiques of it as Schrödinger's dead-and-alive cat and the EPR "paradox"-has been infected with confusion. It helps in dispelling the mists to keep in mind that Bohr did not exactly maintain that a quantum system has no state prior to its being observed. Rather, he said that its state, prior to observation, cannot in principle be determined, and that attempts to define it are therefore meaningless. Bohr was an agnostic on the issue of what might be going on in nature beneath the threshold of its theoretical observability. Einstein used to poke fun at the Copenhagen interpretation by asking colleagues whether they really believed that the moon existed only when they looked at it. Bohr's answer was not that the moon does not exist when unobserved, but that we cannot know whether it, or some thoroughly unobserved moon of a remote and uninhabited planet, exists, until it is observed. His position sports a certain tough-minded bluntness: It confronts quantum weirdness and refuses to blink. But in doing so, it amounts, in the words of David Z. Albert, a physicist who holds a chair in philosophy at Columbia University, to a "radical undermining . . . of the very idea of an objective physical reality" [31]-which, I would add, has long been regarded as the whole point of science. [32] So it is understandable that at least a few philosophically minded scientists kept searching for a more accommodating way to draw quantum weirdness into the embrace of macroscopic logic.

Of these, some came to favor Hugh Everett's many worlds interpretation. Everett arrived at Princeton in 1955, the year of Einstein's death, and did his graduate work there under Wheeler, who took the problem of quantum weirdness seriously and never succumbed to the scientific conceit of dismissing it as a philosophical superfluity. [33] Like Einstein, Everett was troubled by the fact that to accept the Copenhagen interpretation is to entertain a worldview in which the probabilities expressed in a particle's wave function are said to exhaust our potential knowledge of that particle. If, for instance, an electron that had a 10 percent likelihood of turning up in a detector field X is actually observed to land at X, we are asked to accept that prior to its being observed the electron really was 10 percent here, at X, and 90 percent at other locations. This seems nonsensical. It's like saying that a woman is 10 percent pregnant, or a cat 50 percent dead, rather than making the more sensible statement that these are the odds produced by our limited knowledge of the system in question. Einstein regarded it as unworthy of the Old One, as he called the universal Logos without which science would in his view be reduced to the status of a casino game. (It was to this aspect of Copenhagenism that Einstein objected with his famous declaration "God does not play dice with the universe." [34]) Everett's formulation paints nature in the old-fashioned, classical way, as operating according to strict rules of cause and effect, uncomplicated by concerns about who constitutes an observer or how a measurement of a system is made. In the many worlds picture, the photon in our experiment is a particle, or a wave, and we simply record its existence, as we might that of a planet or a trumpet blast.

The interpretation attains this simplicity, however, at the price of making a genuinely flabbergasting supposition: It states that the universe is constantly splitting apart, making copies of itself that are identical except for the outcome of each particular observation. Every time a physicist checks to see whether a photon is a particle or a wave, the universe divides, creating two laboratories containing two physicists, one of whom sees a particle and the other a wave. Every time the. position of an electron is observed, an infinity of other universes are born, each containing an electron at each of its other possible. locations.

This notion is certainly sufficiently bold to satisfy Bohr's demand that new ideas be "crazy enough" to contribute to quantum theory. But it is also vulnerable to straightforward criticisms of the sort memorialized by Samuel Johnson, who, on being asked about Bishop Berkeley's belief that nothing can be shown to exist except ideas, kicked a stone and said, "I refute it thus." Such critiques have been abundant, their tone ironically understated. "The idea of 101 100+ slightly imperfect copies of oneself all constantly splitting into further copies, which ultimately become unrecognizable, is not easy to reconcile with common sense, writes Bryce, DeWitt. [35] The theorist Philip Pearle archly calls it "uneconomical." [36] David Lindley remarks that "when you think about how many of these parallel universes you have to provide"-to account, for instance, for the universe having split every trine a photon bumps off a proton in the course of its long climb out of the sun-"the whole idea begins to seem cumbersome, to say the least."[37]

Nevertheless, a derivation of the many worlds interpretation has become the most widely employed approach to quantum cosmology today, in the form of the "many histories" formulation that we encountered in the previous chapter. There are several reasons that so radical an idea has managed to evolve into something approaching a working set of scientific tools. For one, Everett was among the first theorists to take seriously the central idea of quantum cosmology-that one can apply quantum mechanics to the universe as a whole-and so his treatment lends itself rather well to ongoing efforts to accomplish that goal today. Specifically, it seems to make sense when combined with Richard Feynman's "sum over histories" method-the approach that equates the probabilities in the wave function with various alternative developments that might have occurred in cosmic history but didn't (or didn't, at least, in the part of the universe that we observe). From this perspective, a cosmologist can make quantum calculations without concerning himself overmuch with the vexing question of whether the outcomes that we don't observe actually exist, in some of the infinite number of alternative universes. So science marches on, even if its philosophical implications here seem at least as preposterous as under the Copenhagen interpretation.

That leaves the hidden-variables interpretation of David Bohm. Bohm was a young physicist whose Marxist convictions encouraged him in the belief that nature is fully deterministic-in which case, any theory that restricts itself to probabilities cannot be complete. He studied the Copenhagen interpretation and even wrote a book defending it, but a subsequent conversation with Einstein left him dissatisfied with the limitations the Copenhagians placed on the scope of scientific knowledge. ("He talked me out of it," Bohm told Murray Gell-Mann. "I'm back where I was before I wrote the book." [38]) In the Copenhagen approach, Bohm complained, "All that counts in physical theory is supposed to be the development of mathematical equations that permit us to predict and control the behavior of large statistical aggregates of particles . . . . This sort of presupposition is indeed in accord with the general spirit of our age, but . . . we cannot thus simply dispense with an overall world view... Indeed; one finds that physicists are not actually able just to engage in calculations aimed at prediction and control: They do find it necessary to use images based on some kind of general notions concerning the nature of reality, such as ´the particles that are the building blocks of the universe'; but these images are now highly confused (e.g., these particles move discontinuously and are also waves)." [39]

Bohm's search for a simpler and more complete interpretation led to his formulation of a new, deterministic account of quantum theory, which he published in 1952. By then, however, his career had been shipwrecked in the political typhoons of the times. Held in contempt of Congress for refusing to testify before the House Un-American Activities Committee, Bohm was fired from his post as assistant professor at Princeton and banned by a pliant university administration from visiting the campus in any capacity. He spent the rest of his life in a species of exile, teaching in Brazil, Israel, and thereafter at Birkbeck College in England. His insistence on examining quantum weirdness in a broad context further separated him from most of his fellow scientists, among whom arose the common judgment that he was a talented physicist who had squandered his potential by mucking about in philosophy.

But Bohm was onto something-a view of nature so revolutionary that he himself could not see it clearly at first. His interpretation has at least two levels, one relatively straightforward and the other, which followed clarifying research by John Stewart Bell, as startling and new as anything to have come from quantum mechanics and relativity. Let's consider each level in turn.

Bohm started with the deterministic premise that subatomic particles really are in one state or another-that quantum uncertainty is a statement of human ignorance and not a state of nature. Schrödinger's cat is dead or alive, and there is no need to imagine that it or any other system abides in a "superposed" state. This much is happily commonsensical, but it is paid for in two heavy coins.

First, Bohm was obliged to invent an agency-a guiding wave-to manipulate the particles. He called this guiding wave the "quantum potential." He envisioned it as a gently acting field with the unique property that its strength does not decrease with distance. To modify an analogy of Bohm's, consider a B1 bomber flying on autopilot in its ground-hugging mode. The B1's flight is powered by its mammoth twin jet engines (which here stand for conventional quantum force fields) but its guidance comes from the much weaker pulses emitted by its radar equipment, which reads the ground and adjusts the flight controls accordingly: (The guidance system represents the quantum potential.) Appealing as this picture may be, there is no experimental evidence to indicate that Bohm's quantum potential exists. Nor is it clear how such evidence can ever be found, since Bohm's equations produce exactly the same predictions as those of conventional quantum mechanics. (That's why the variables are "hidden.")

The other problem confronting Bohm's interpretation is that the quantum potential would seem to violate special relativity. In order for it to control the behavior of far-flung particles (in, e.g., an EPR experiment), it must act simultaneously on them. From the perspective of contemporary physics, this would mean sending signals that travel at faster-than-light speed. This is a lot to swallow, especially for the likes of Albert Einstein-who, on the day that he talked Bohm out of belief in the Copenhagen interpretation, was motivated by a distaste for just the "spooky action at a distance" that Bohm was to resurrect.

Nevertheless, Bohm's interpretation clarifies aspects of quantum weirdness and continues to gain advocates. David Z. Albert recently has been championing a Bohmian interpretation on the ground that, its philosophical penumbra aside, it is simpler than the Copenhagen approach. "What's so cool about this theory," writes Albert, going on to sound a bit like Gertrude Stein, is that

this is the kind of theory whereby you can tell an absolutely low-brow story about the world, the kind of story (that is) that's about the motions of material bodies, the kind of story that contains nothing cryptic and nothing metaphysically novel and nothing ambiguous and nothing inexplicit and nothing evasive and nothing unintelligible and nothing inexact and nothing subtle and in which no questions ever fail to make sense and in which no questions ever fail to have answers and in which no two physical properties of anything are ever "incompatible" with one another and in which the whole universe always evolves deterministically and which recounts the unfolding of a perverse and gigantic conspiracy to make the world appear to be quantum-mechanical.[40]

That it does so by invoking faster-than-light effects doesn't ruffle Albert's hair. If a relativistic version of Bohmian quantum mechanics can be written, he claims, its predictions will be in accordance with special relativity "even though the underlying [i.e., Bohmian] theory won't be; and so taking Bohm's theory seriously will entail being instrumentalist about special relativity." [41] But there is as yet no Bohmian relativistic quantum field theory, and there may never be; nor is it clear that other theorists will be as blithe about demoting the status of special relativity.

Yet what Bohm's interpretation lacks as a scientific theory it gains as an admittedly clouded but evocative glimpse into the mists of a possible fixture science. Bohm was unable to describe this Ultima Thule with any great clarity, but he insisted on its existence and predicted that its elucidation would bring about not just a new theory but a new "order," a revolution comparable to the world-shaking changes we associate with such names as Copernicus and Einstein. Bohm was a modest man, but he insisted on this one great claim. "We have . . . yet to perceive a new order," he wrote. "We are in a position which is in certain ways similar to where Galileo stood when he began his inquiries." [42] In his view, quantum weirdness is a keyhole through which we have caught a first glimpse of another side of nature, one in which the universe is neither deployed across vast reaches of space and time nor harbors many things. Rather it is one, interwoven thing, which incorporates space and time but in some sense subordinates them-perhaps by treating them as important but nonfundamental aspects of the interface between the universe and the observer who investigates it.

The quantum universe may be thought of as the other side of the coin from the spatiotemporal, relativistic universe that has to date dominated cosmological thought. We humans, having come along when the universe was already billions of years old and being rather big creatures, able to see stars in the sky but not atoms in an apple, naturally got into cosmology from the large-scale side of things-by observing galaxies and developing theories, such as relativity, to interpret their behavior. But the universe was not always big and classical. Once it was small and quantum, and possibly it has not lost the memory of those times. It may well turn out that over there-or, more properly, inside and underfoot, marbled through the very fabric of the space that is in turn marbled through every material object-the universe remains as it was in the beginning, when all places were one place, all times one time, and all things the same thing.

To investigate that side of the coin we need to consider one final technical development, and that is Bell's inequality. John Stewart Bell was an Irish physicist who concerned himself with the hidden-variables interpretation and worked out a way of testing it experimentally. Without going into specifics, Bell's proposed experiment was a variation on the EPR apparatus-a setup in which two particles that start out together are dispatched across a macroscopic distance before one is observed in a fashion that instantly defines the state of the other. Bell's contribution was to outline how an EPR-like experiment could be employed to test the classical assumption that nature works in a "local"-that is, mechanistic-way. The results were to reveal that the classical assumption is wrong-that nature is in some sense nonlocal. From this odd finding sprang considerations so astonishing as to render plausible the physicist Henry Stapp's opinion that Bell's theorem constitutes "the most profound discovery in science." [43]

We encountered the concept of locality earlier in this chapter, as the supposition that one system can change another only if there is some sort of mechanical interaction between the two. According to relativity, no such interaction can occur at faster-than-light speed, and what bothers physicists about the hidden-variables interpretation is that it seems to mandate such superluminal interactions. [44] To say that fiddling with one particle over here can instantly influence its sister particle over there is to assert that subatomic particles behave in a nonlocal way. This would overthrow the timehonored assumption of locality, and that is what Einstein found so repugnant about the situation, and why he constructed the EPR thought experiment to highlight its apparent irrationality.

Bell-a red-bearded experimentalist who spoke with a soft, Northern Irish burr, and whose unassuming wit concealed an exceptional tenacity of mind-pondered this matter for years, focusing on its essential question of whether natural processes obey locality, as had traditionally been thought, or are in some way nonlocal on the quantum level. In a paper published in 1964, he proposed an experiment that could finally settle the matter. Years passed before technology had advanced to the point that it could be implemented. Then, in the 1970s, John Clauser and Stuart J. Freedman at Berkeley, and later Alain Aspect and colleagues at the University of Paris's Institute of Theoretical and Applied Optics, in Orsay, conducted Bell experiments. The specifics need not detain us: They involved testing the polarization of large numbers of photons. Their significance was that they would produce different results if the particles behaved in a local way, as Einstein insisted, or in a nonlocal way, as the quantum mechanics equations mandate. This distinction is, after all, what all the bother over quantum weirdness is about. In both cases, and in all experiments conducted since, the verdict is clear: Bohr was right (nonlocal effects do occur in quantum systems) and Einstein wrong (there are no hidden variables to explain nonlocality). Nature-on the subatomic scale at least-really is nonlocal. Fiddling with one particle really does mean that its sister particle is altered, instantly, even if it is far away, and neither hidden variables nor any other mechanistic scheme can rescue Einstein's belief in locality. As the physicist F. David Peat puts it, "The choice before us is either to abandon any hope of knowing the nature of quantum reality or to accept a nonlocal universe." [45]

Some are comfortable with the first of Peat's alternatives. They believe that we cannot reconcile common sense with quantum reality, and so shouldn't try. But history has dealt harshly with many previous efforts to declare absolute limits to human inquiry, and had that option been popular in this case, there would not have been seventy years of debate about quantum weirdness. So let's look at the alternative-"to accept," in Peat's words, "a nonlocal universe."

What might that mean? It might mean that the universe is interconnected in some deep and as yet only dimly perceived way, on a level where time and space don't count. Bohm, who lived long enough to absorb the experimental results confirming that quantum effects are nonlocal, wrestled with this remarkable idea in his book Wholeness and the Implicate Order, published in 1980 . A capable etymologist, Bohm used the word "implicate" in its sense of "enfolded." He suggested that nonlocal effects are woven through the universe in something like the way that a chef folds a cream into a sauce. For Bohm, classical physics dealt with an explicate order, the mechanical world of Newton's gravity and Einstein's relativity, while quantum mechanics was the first science to examine the implicate world of nonlocalities. A scientific clue to this new vision may be found in the odd consideration that photons do not "experience" time. We understand from special relativity that time slows down for space travelers as they approach the velocity of light. At light speed, the speed that photons move in a vacuum, there is no time at all. So a photon "traveling" from point A to point B does so, from its point of view, in zero time-meaning that, in some sense, the two points aren't separate! Another clue comes from the work of John Wheeler and others on the hypothesis that space is interconnected by multitudes of wormholes, little tunnels linking localities that to us seem far apart. A similar outlook has been investigated by Roger Penrose, who sees spacetime as jumbled and dynamic on the quantum scale. Penrose compares space to a photographic plate, one that develops into a "normal," macroscopic picture only when "fixed" by measurement.

Bohm and others have likened the implicate universe to a hologram (from the Greek, "to write the whole"). One makes a hologram by illuminating the subject with a beam of laser light that has been run through a beam splitter, creating two beams-a process akin to the dual-slit experiments central to thinking about quantum weirdness-and exposing a sensitized glass plate to the light reflected from the subject. The plate contains no visible image, but when illuminated by a similar pair of coordinated beams of light it produces a three-dimensional replica of the hologrammed subject that seems to hover in space. This image is intriguing in itself-there is no lower limit to its resolution except that imposed by the wavelength of the light used to make it-but of particular interest, in terms of a cosmological metaphor, is the way information is recorded on the plate: Shatter a hologram, put one of its fragments in the laser beam, and what you see is not a piece of the original image but all of it. The image is dimmer and a bit "noisier," but spatially the whole thing is there, in this and every other fragment.

What if the universe is like that? I don't know how to frame such a concept in contemporary scientific terms, so I won't try: Such difficulties may, of course, be a signal that there is no "implicate" side to the universe-that this line of thought is just hot air. But they also might mean that, as Bohm believed, we are indeed dealing with a new "order," which must therefore evolve its own concepts and language and cannot properly be analyzed, in Bohm's words, "to make it fit well-defined and preconceived notions as to what this order should be able to achieve." [46] So let me describe the concept more generally, as a kind of fable.

Suppose that, as string theory implies, the universe began as a hyperdimensional bubble of space, all but four of the dimensions of which compacted to form what we today call subatomic particles. Those particles look to us like zillions of individual things, but that is merely their appearance in the four dimensions of spacetime. In hyperspace they could very well still be one thing-could, therefore, be not only connected but identical. (Wheeler to Richard Feynman: "Feynman, I know why all electrons have the same charge and the same mass." "Why?" "Because they are all the same electron!" [47]) In that case, we live in a universe that presents two complementary aspects. One obeys locality and is large, old, expanding, and in some sense mechanical. The other is nonlocal, is built on forms of space and time unfamiliar to us, and is everywhere interconnected. We peer through the keyhole of quantum weirdness and see a little of this ancient, original side of the cosmos.

To assert that the universe is deeply interconnected is to echo what mystics have been saying for thousands of years. This can be a liability in the scientific community, which has heard more than enough of complacent, shallow-draft assertions to the effect that science amounts to little more than proving what Lao Tzu and Chief Seattle were saying all along. Yet some of the most important scientific and philosophical thinking in history has been impelled by mystical motives. (Einstein: "The most beautiful emotion we can .experience is the mystical. It is the source of all true art and science. He to whom this emotion is a stranger, who can no longer wonder and stand rapt in awe, is as good as dead." [48]) We remember the paradoxes of Zeno of Elea, the philosopher and mathematician who sought to demonstrate that motion is impossible because, for example, a flying arrow must keep traversing half the distance to the target in finite intervals of time, and the number of times the distance can be halved is infinite. But we less often recall why Zeno constructed his paradoxes. He did so to support the assertion of a fellow Eleatic, Parmenides, that all is one, and to disprove, by reduction to absurdity, the contrary philosophy espoused by Pythagoras, that nature is made not of one but of many things. Science up to the present is descended mainly from Pythagoras. Zeno's point is that this Pythagorean, many-things view of the universe is incomplete, that from a deeper outlook we would realize that the many things, spacetime universe reflects but one side of creation. As Dante's Virgil says:

Yes, many things there are, which seem to be
Perplexing, though quite falsely so, because
They have good reasons which we cannot see. . . [49]

If the many threads of history are revealed to be cuts through one knot Parmenides' sun will rise anew, and Zeno's insight will emerge as an intimation of the nonlocal universe.

That would mean that the role of the observer has scarcely begun, and the poking of one's head through a starry local sphere, as illustrated in the famous woodcut depicting the Copernican revolution, is to be recapitulated on a grander scale. One of the first to see this was Wheeler-who, like Gertrude Stein, has sometimes been underestimated as a thinker, owing to his taste (like hers) for examining questions without pretending to have answers to them. Wheeler wonders aloud whether quantum observership represents an alternative vision of genesis. "How did the universe come into being?" he asks. [50]

Is that some strange, far-off process, beyond hope of analysis? Or is the mechanism that came into play one which will all the time shows itself?

Of the signs that testify to "quantum phenomenon" as being the elementary act of creation, none is more striking than its untouchability. In the delayed-choice version of the split-beam experiment, for example, we have no right to say what the photon is doing in all its long course from point of entry to point of detection. Until the act of detection the phenomenon-to-be is not yet a phenomenon. We could have intervened at some point along the way with a different measuring device; but then regardless whether it is the new registering device or the previous one that happens to be triggered we have a new phenomenon. We have come no closer than before to penetrating to the untouchable interior of the phenomenon. For a process of creation that can and does operate anywhere, that reveals itself and yet hides itself, what could one have dreamed up out of pure imagination more magic-and more fitting-than this?

All interpretations of quantum weirdness sweep it under a carpet, but carpets have patterns that cannot be perceived by isolating their parts. If we have to date perceived only the spacetime threads in the carpet, that may be because perception is itself the discernment of parts. If we could take in the whole, would we see that the here and now is the same as the then and there? Can mere observers behold both the disparate, explicit universe and the implicate universe that wove it? What does it mean, anyway, to be an observer, to be alert, alive? With that question, we descend from the icy cliffs of genesis and quantum weirdness to wander in grassy valleys, where, amid luxuriant life, our wondering and discontented species asks what might be its proper place in the universe.

NOTES: Quantum Weirdness

[1] Stein's last words were reported by her lifelong companion and secretary Alice B. Toklas, whose silence prompted them. (In Toklas, What Is Remembered. New York: Holt, Rinehart, 1963. Quoted in Dennis Flanagan, Flanagan's Version. New York: Vintage, 1988; p. 13.) Inasmuch as Ms. Stein is still routinely disparaged in newspapers and second-rate encyclopedias as a social butterfly famous solely for having known a lot of famous people, perhaps I may reassert the claim that she was both a subtle thinker and one of the most original writers of her time. Much of the essence of quantum philosophy is contained in her dying words and elsewhere, as in her remark that "The minute you or anybody else knows what you are you are not it, you are what you or anybody else knows you are and as everything in living is made up of finding out what you are it is extraordinarily difficult really not to know what you are and yet to be that thing." (Gertrude Stein, Everybody's Autobiography. New York: Random House, 1937, chapter 3.)

[2] In T. A. Heppenheimer, "Bridging the Very Large and Very Small," Mosaic, Fall 1990, p. 33.

[3] In Alan Burns, editor, Gertrude Stein on Picasso. New York: Liveright, 1970, p. 21.

[4] Though that's pretty strange, especially in view of recent experiments confirming that "leaping" particles would have to move faster than light speed if they did cross the intervening gap, meaning that they really do disappear from one spot and reappear, instantaneously, at another.

[5] In John Updike, "A Jeweler's Eye," New York Review of Books, October 29, 1995, p. 7.

[6] In Murray Gell-Mann, The Quark and the Jaguar. New York: Freeman, 1994, p. 165. Bohr liked to joke about the difficulty of expressing quantum precepts in ordinary language by telling the following story: "A young rabbinical student went to hear three lectures by a famous rabbi. Afterwards he told his friends: ´The first talk was brilliant, clear and simple. I understood every word. The second was even better, deep and subtle. I didn't understand much, but the rabbi understood all of it. The third was by far the finest, a great and unforgettable experience. I understood nothing and the rabbi didn't understand much either.' " (In Abraham Pais, Niels Bohr's Times in Physics, Philosophy, and Polity. Oxford: Clarendon Press, 1991, p. 439.) Similar in spirit is Alice B. Toklas's remark made she and Gertrude Stein were leaving a dinner party in the company of Robert Hutchins, the president of the University of Chicago,, that "Gertrude has said things tonight that will take her years to understand." (In Owen Gingerich, editor, The Nature of Scientific Discovery: Symposium Commemorating the 500th Anniversary of the Birth of Nicolaus Copernicus. Washington: Smithsonian Institution Press; New York: Braziller, 1975, p. 501.)

[7] See, e.g., David Lindley, Where Does the Weirdness Go? New York: Basic Books, 1996; David Z. Albert, Quantum Mechanics and Experience. Cambridge: Harvard University Press, 1992; F. David Peat, Einstein's Moon. Chicago: Contemporary Books, 1990; Bas C. Van Fraassen, Quantum Mechanics- An Empiricist View. Oxford: Clarendon Press, 1991; Nick Herbert, Quantum Reality. New York: Anchor, 1985; and John Gribbin, In Search of Schrodinger's Cat. New York: Bantam, 1984.

[8] Any particle will do. An entire atom was put in two quantum states in 1996, when scientists at the National Institute of Standards and Technology, using lasers, teased a beryllium atom into two spin states and separated them by the microscopically significant distance of 83 billionths of a meter.

[9] Quantum mechanics is not inherently nonlocal. But it exhibits nonlocal behavior when examined on a classical level. Quantum weirdness is, remember, an interpretation issue. It's a matter of trying to understand, in classical terms, the strange side of nature revealed when quantum systems are amplified to a classical scale.

[10] In Gerald Edelman, Bright Air, Brilliant Fire: On the Matter of the Mind. New York: Penguin, 1992, p. 216.

[11] In Abraham Pais, Niels Bohr's Times in Physics, Philosophy, and Polity. Oxford: Clarendon Press, 1991, p. 349.

[12] In Robert Scott Root-Bernstein, Educating the Eye of the Mind. Unpublished ms., 1985.

[13] In P N. Johnson-Laird, "The Ghost-Hunters," (London) Times Literary Supplement, December 14, 1984, p. 1441.

[14] Albert Einstein and Leopold Infeld, The Evolution of Physics. New York: Simon & Schuster, 1938, p. 294.

[15] In The Cartoon Guide to Physics CD-ROM. New York: HarperCollins Interactive, 1995.

[16] Bohr, "Unity of Human Knowledge," in his Atomic Physics and Human Knowwledge. Bungay, U.K. Clay, 1963, pp. 9-10.

[17] Leon Lederman, introducing Carlo Rubbia and congratulating him on having just won the Nobel Prize in physics, Santa Fe, New Mexico, November 3, 1984.

[18] Einstein, statement on Schrodinger's "The Final Affine Laws" (1947), in Walter Moore, Schrodinger: Life and Thought. Cambridge: Cambridge University Press, 1989, p. 432.

[19] The professional philosophers have not been entirely charitable toward Bohr, whose nonsicientific writings many dismiss as vague and amateurish. Doubtless this is due in part to Bohr's having composed no formal (i.e., Cartesian) statement of his philosophy. But it may also represent the philosophers' wounded response to his blunt contempt for their profession. "It is hopeless to have any kind of understanding between scientists and philosophers directly," Bohr said. "All that philosophers

have ever written is pure drivel." (In Abraham Pais, Niels Bohr's Times in Physics, Philosophy, and Polity. Oxford: Clarendon Press, 1991, p. 421.).

[20] Werner Heisenberg, "Quantum Theory and Its Interpretation," in S. Rozental, editor, Niels Bohr. His Life and Work. New York: North-Holland, 1967, p. 97.

[21] Interview by Thomas Kuhn, in E. M. MacKinnon, Scientific Explanation and Atomic Physics. Chicago: University of Chicago Press, 1982, p. 375.

[22] In Abraham Pais, Niels Bohr's Times in Physics, Philosophy, and Polity. Oxford: Clarendon Press, 1991, p. 170.

[23] In A. P French and P J. Kennedy, editors, Niels Bohr: A Centenary Volume. Cambridge: Harvard University Press, 1985, p. 183.

[24] In Abraham Pais, Niels Bohr's Times in Physics, Philosophy, and Polity. Oxford: Clarendon Press, 1991, p. 502.

[25] Abraham Pais, "Niels Bohr and the Development of Physics," in M. Jacob, editor, A Tribute to Niels Bohr on the Hundredth Anniversary of His Birth. Geneva: CERN, 1985, preprint p.11 .

[26] In Abraham Pais, Niels Bohrs Times in Physics, Philosophy, and Polity. Oxford: Clarendon, 1991, pp. 426-427. Emphasis added by T.F.

[27] The Nazi leader Hermann Goering may or may not have said, "Whenever I hear the word ´culture,' I reach for my revolver." The line appears in Schlageter, by the Nazi playwright Harms Johst, where a storm trooper says, Wenn ich Kultur höre . . . entsichere ich meinen Browning ("I cock my Browning"). Hawking's joke was made in a conversation with T.F., in Pasadena, California, April 4, 1983. The complete exchange was as follows:

HAWKING: I regard [the many worlds interpretation] as selfevidently correct.

T.F.: Yet some don't find it evident to themselves.

HAWKING: Yeah, well, there are some people who spend an awful lot of time talking about the interpretation of quantum mechanics. My attitude-I would paraphrase Goering-is that when I hear of Schrodinger's cat, I reach for my gun.

T.F.: That would spoil the experiment. The cat would have been shot, all right, but not by a quantum effect.

HAWKING (laughing): Yes, it does, because I myself am a quantum effect. But, look: All that one does, really, is to calculate conditional probabilities-in other words, the probability of A happening, given B. I think that that's all the many worlds interpretation is. Some people overlay it with a lot of mysticism about the wave function splitting into different parts. But all that you're calculating is conditional probabilities.

[28] This is known in the literature as the question of Wigner's friend, after the physicist Eugene Wigner, who asked whether the cat is dead or alive during the interval between when his friend opens the box

and observes the cat and when he tells Wigner about it. It is ´akin to quantum erasure, experiments which suggest that if Wigner's friend were to drop dead before he could announce the result, no observation would have been made. Is the cat then still neither dead nor alive, or did it return to a superposed, dead/alive state upon the death of Wigner's friend. Both alternatives are paradoxical-and this, again, is the point of the exercise, to deny the Copenhagen insistence that quantum mechanics provides a complete description of a system.

[29] In Stephen Jay Gould, New York Review of Books, November 5, 1992.

[30] A. Einstein, B. Podolsky, and N. Rosen, "Can QuantumMechanical Description of Physical Reality Be Considered Complete?" Physical Review 47, 777, 1935, p. 780.

[31] David Z. Albert, "Bohm's Alternative to Quantum Mechan ics," Scientific American, May 1994, p. 66.

[32] To be sure, there have always been philosophers who maintained that the scientific enterprise has to do strictly with making accurate predictions or, even more strictly, with learning how to manipulate the forces of nature. Essentially this is a view of science as power. But many of the strongest minds in science and philosophy have objected to this position. They insist that science is primarily about knowledge, and that genuine knowledge is necessarily objective knowledge.

[33] Disheartened by the chilly reception his ideas met with, Everett left physics after receiving his Ph.D. and found work with a defense contractor. Bryce DeWitt, a leading quantum-gravity theorist, promoted Everett's ideas from about 1968, and in the late 1970s Everett was invited to give some talks at the University of Texas, Austin, where Wheeler had joined the faculty. Everett arrived driving a Cadillac with longhorns adorning the hood and lectured with the intensity of an exiled intellectual. (He smoked so heavily that the auditorium's strict no-smoking rule had to be suspended so that he could speak.) Encouraged by an increasing willingness among scientists to take his ideas seriously, Everett was planning a return to physics when he died of a heart attack in 1982.

[34] Einstein may have had in mind Proverbs 16:33: "The lot is cast into the lap; but the whole disposing thereof is of the Lord." To Max Born he wrote, "Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the 'Old One.' I, at any rate, am convinced that He is not playing at dice' (Max Born, The Born-Einstein Letters. New York: Walker, 1971, p. 91.)

[35] In Eduard Prugovecki, "Foundational Problems in Quantum Gravity and Quantum Cosmology." Foundations of Physics, vol. 22, no. 6, 1992, p. 766. As Prugovecki notes, the actual number of universes referred to as "many" in this interpretation is actually much larger than 10 100+: In one formulation it is infinity raised to an infinite power.

[36] In Max Jammer, The Philosophy of Quantum Mechanics. New York: Wiley, 1974, p. 278.

[37] David Lindley, Where Does the Weirdness Go? New York: Basic Books, 1996, p. 109.

[38] In Murray Gell-Mann, The Quark and the Jaguar. New York: Freeman, 1994, p. 170.

[39] David Bohm, Wholeness and the Implicate Order. London, U.K.: Routledge, 1981, p. xiii.

[40] David Z. Albert, Quantum Mechanics and Experience. Cambridge: Harvard University Press, 1992, p. 169.

[41] Ibid., p. 161. "Instrumentalism" is the argument that physics deals not with physical reality but with patterns in observations that can be tested empirically-e.g., patterns in instrument readings. But even an instrumentalist must believe that there is some connection between his observations and physical reality; otherwise why bother doing physics? A gas-meter reader would soon lose interest if he thought that the readings he recorded had nothing to do with gas consumption.

[42] David Bohm, Wholeness and the Implicate Order. London, U.K.: Roudedge, 1981, p. 138.

[43] In F. David Peat, Einstein's Moon: Bell's Theorem and the Curious Quest for Quantum Reality. Chicago: Contemporary Books, 1990, p. 113.

[44] Actually, it bothered scientists even before relativity, since locality is essential to the mechanical, causal view of nature that predated Einstein. Isaac Newton, for one, was deeply troubled that his law of gravitation included no mechanical way of getting gravitational force across what he presumed to be empty space; this was his version of Einstein's worries about "spooky action at a distance."

[45] F. David Peat, Einstein's Moon. Chicago: Contemporary Books, 1990, p. 124.

[46] David Bohm, Wholeness and the Implicate Order. London, U.K.: Routledge, 1981, p. 148.

[47] Richard Feynman, Nobel Lecture, December 11, 1965. This conversation with Wheeler took place in the 1940s, when Feynman was a graduate student at Princeton. As Feynman recounts it, Wheeler "explained on the telephone, ´Suppose that the world lines which we were ordinarily considering before in time and space, instead of only going up in time were a tremendous knot. Then, when we cut through the knot by the plane corresponding to a fixed time, we would see many, many world lines and that would represent many electrons. Except for one thing. If in one section that is an ordinary electron world line, in the section in which it reversed itself and is coming back from the future, we

have the wrong sign to the proper time .... That's equivalent to changing the sign of the charge, and, therefore, that part of a path would act like a positron.' " (The editing of the published transcript has been altered slightly by T.F.)

[48] Einstein, The World as I See It. New York: Philosophical Library, 1934.

[49] Dante, Purgatorio, Dorothy Leigh Sayers, translator. New York: Penguin Books, 1969, 22:28.

[50] John Archibald Wheeler, "Law Without Law," in Wheeler and Wojciech Hubert Zurek, editors, Quantum Theory and Measurement. Princeton: Princeton University Press, 1982, vol. 1, unpaginated manuscript edition.