Learning What Is,From What Doesn't
Alan H.Guth

When Alice protested in Through the Looking Glass that one can't believe impossible things," the White Queen tried to set the issue straight. "I daresay you haven't had much practice," she said. "When I was your age, I always did it for half an hour a day. Why sometimes I've believed as many as six impossible things before breakfast."
Although science is in principle the study of what is possible, the advice of the White Queen is on target. No one yet understands the laws of nature at their most fundamental level, but the search for these laws has been both fascinating and fruitful. And the view of reality that is emerging from modern physics is thoroughly reminiscent of Lewis Carroll. While the ideas of physics are both logical and extremely beautiful to the people who study them, they are completely at odds with what most of us regard as "common sense".

Of all the "impossibilities" known to science, probably the most impressively impossible is the set of ideas known as quantum theory. This theory was developed in the early part of the twentieth century, because no one could find any other way to explain the behaviour of atoms and molecules. One of the greatest physicists of recent times, Richard Feynman, described his feelings toward quantum theory in his book QED. "It is not a question of whether a theory is philosophically delightful, or easy to understand, or perfectly reasonable from the point of view of common sense," he wrote. The quantum theory "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. I'm going to have fun telling you about this absurdity, because I find it delightful."

As one example of the absurdity of quantum theory, consider a discovery made in 1970 by Sheldon Glashow, John Iliopoulos, and Luciano Maiani. Six years earlier, Murray Gell-Mann and George Zweig had proposed that the constituents of an atom's nucleus- the proton and the neutron-are composed of more fundamental particles, which Gell-Mann called "quarks." By 1970, the quark theory had become well known, but was not yet generally accepted.

Many properties of subatomic particles were well explained by the quark theory, but a few mysteries remained. One of these mysteries involved a particle called the neutral K-meson. This particle can be produced by particle accelerators, but it decays into other types of particles in less than a millionth of a second. The neutral K-meson was found to decay into many combinations of other particles, and everything that was seen made perfect sense in terms of the quark theory. The surprising feature, however, was something that was not seen: The neutral K-meson was never seen to decay into an electron and a positron. (A positron is a particle with the same mass as an electron, but with the opposite electrical charge-it is often called the "antiparticle" of the electron.) In the quark theory, this decay was expected, so its absence seemed to indicate that the theory was not working.

The quark theory held that there are three types of quarks, which were given the whimsical names up, down, and strange. (The word quark itself is associated with the number three; according to Gell-Mann, it was taken from the line, "Three quarks for Muster Mark!" in James Joyce's novel Finnegans Wake.) For each type of quark, there is also an antiquark. The neutral K-meson, according to the theory, is composed of a down quark and an anti-strange quark. The decay of a neutral K-meson into an electron and positron was expected to take place by a four-step process, as is illustrated below. There is no need to understand this process in detail, but for completeness, I have shown the individual steps. In addition to the quarks, the intermediate steps of the process involve particles called the neutrino, the W+, and the W-, but the properties of these particles will not be needed for what I want to say. The following diagram is to be read as a sequence of events, from top to bottom, starting with the quarks that make up the neutral K-meson:
The Reaction That Doesn't Happen

In the first step, the down quark decays, or breaks up, into a W and an up quark. In the second step, the up quark combines with the anti-strange quark from the neutral K-meson to form a W+ particle. The W particle decays in the third step into a neutrino and an electron, and in the fourth step, the neutrino combines with the W+ to form a positron. Puzzling over the diagram above, scientists could find nothing wrong with it. The quark content of the neutral K-meson was determined unambiguously by a variety of properties-it must be one down quark and one anti-strange quark. And all four steps in the process were thought to occur, although they had not been directly seen. In fact, the W+ and W particles were not actually observed until 1983, when a mammoth experiment performed by a team of 135 physicists led to the observation of six W particles. Nonetheless, all four of the steps are also intermediate steps in other reactions-reactions that were known to happen. If any of the steps were impossible, then how could these other reactions take place? If the steps were possible, then what could stop them from taking place in the sequence shown above, producing a decay of a neutral K-meson into an electron and positron?

In 1970, Glashow, Iliopoulos, and Maiani proposed a solution to this puzzle. The solution is completely logical within the structure of quantum theory, yet it defies all common sense. It makes use of the strange way in which alternative processes are treated in quantum theory.
The physicists proposed that there is a fourth type of quark, in addition to the three types already contained in the theory. Such a fourth quark had already been suggested in 1964 by Glashow and James Bjorken, who were motivated by patterns in the table of known particles. The fourth quark had been called "charmed," a name that was revived in the much more specific proposal of Glashow, Iliopoulos, and Maiani. With the addition of another quark variety, the charmed quark, the neutral K-meson could decay into an electron and a positron by two distinct processes. The first would be the four-step process shown above; the second would be an alternative four-step process, in which the up quark produced in Step 1 and absorbed in Step 2 is replaced by a charmed quark.

Following the advice of the White Queen, it is now time to practice believing impossible things. The theory that includes the new quark allows two sequences of events, both beginning with a neutral K-meson and both ending with an electron and positron. The first sequence involves an up quark in Steps 1 and 2, and the second sequence involves a charmed quark in place of the up quark. According to the rules of common sense, the total probability for the decay of a neutral K-meson into an electron and positron would be the sum of the probabilities for each of the two sequences. If common sense ruled, the addition of the charmed quark would not help at all to explain why the decay is not seen. The rules of quantum theory, however, are very different from the rules of common sense.

According to quantum theory, if a specified ending can be achieved by two different sequences of events, then one calculates for each sequence a quantity called the "probability amplitude." The probability amplitude is connected to the concept of a probability, but the two have different mathematical forms. A probability is always a number between zero and one. A probability amplitude, on the other hand, is described by an arrow that one can imagine drawing on a piece of paper. The arrow is specified by giving its length and also its direction in the plane of the paper. The length must always lie between zero and one. If the specified ending can be achieved by only one sequence, then the probability is the square of the length of the probability amplitude arrow, and the direction of the arrow is irrelevant. For the decay of the neutral K-meson into an electron and positron, however, there are two sequences leading to the same result. In that case, the rules of quantum theory dictate that the tail of the second arrow is to be laid on top of the head of the first arrow, while both arrows are kept pointing in their original directions. A new arrow is then drawn from the tail of the first arrow to the head of the second, as shown:

The total probability for the result is then the square of the length of the new arrow. Although this rule bears no resemblance to common sense, thousands of experiments have shown that it is indeed the way nature behaves. For the decay of the neutral K-meson, Glashow, Iliopoulos, and Maiani proposed a definite procedure for calculating the way in which the charmed quark would interact with other particles. With this procedure, the probability amplitude arrow for the second sequence has the same length, but the opposite direction, as the arrow for the first sequence. When the two arrows are combined by the rules of quantum theory, the new arrow has zero length, corresponding to zero probability. Thus, by introducing an alternative mechanism through which the electron-positron decay could occur, it became possible to explain why the decay does not occur at all!

Although this explanation might not have been persuasive by itself, the decay discussed here was only one of about half a dozen processes that were expected but not observed. Glashow, Iliopoulos, and Maiani showed that the nonobservation of each of these processes could be explained by the charmed quark. The only drawback of the proposal was that none of the known particles appeared to contain a charmed quark. One must assume, therefore, that the charmed quark is much heavier than the other quarks, so that any particle containing a charmed quark would be too massive to have been produced in accelerator experiments. In November 1974, a new particle with more than three times the mass of a proton was discovered simultaneously at the Brookhaven National Laboratory and the Stanford Linear Accelerator Center. The particle was called J on the East Coast and psi on the West Coast, so today it is known by the compromise name J/psi. The properties of this particle, by now demonstrated conclusively, show that it is composed of one charmed and one anti-charmed quark. The interaction properties of the charmed quark are exactly those predicted in 1970. Glashow, and the leaders of the two teams that discovered the J/psi, have all been awarded Nobel prizes in physics for their contributions. (Today, we believe that there are two more types of quarks, called "top" and "bottom," although the experimental evidence for top quark is not yet conclusive.)

The bizarre logic of quantum theory and the counterintuitive prediction of the charmed quark are only examples of the ideas that scientists are developing in their attempts to understand the world in which we live. The White Queen reigns throughout the world of science. The evidence so far indicates that nature obeys simple laws, but that these laws are very different from anything that one would be likely to imagine.

ALAN H. GUTH is a physicist and the Victor F. Weisskopf Professor of Physics at MIT, and a member of the National Academy of Sciences and the American Academy of Arts and Sciences. After receiving his Ph.D. in physics and doing nine years of postdoctoral research, Guth reached a turning point in his career when he invented a modification of the big bang theory called the inflationary universe. This theory not only explains many otherwise- mysterious features of the observed universe, but it also offers a possible explanation for the origin of essentially all the matter and energy in the universe.
He has continued to work on the consequences of the inflationary theory, and has also explored such questions as whether the laws of physics allow the creation of a new universe in a hypothetical laboratory (probably yes, he thinks), and whether they allow the possibility of time travel (he would bet against it).

Further Reading

Book Cover

How Things Are: A Science Toolkit for the Mind
Edited by John Brockman and Katinka Matson
Alice in Quantumland Robert Gilmore





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