When the Atom Broke Down

Inward Bound is a sweeping narrative of the history and present state of atomic physics. It is something of an official history, explaining what, in the opinion of the physics community, is known, and how it came to be known. Pais was a distinguished participant in a number of the events he describes, but he distances himself from them. His erudite chronology is written from a deep love of the subject, a desire to make it intelligible, and a zest for describing the actors in his story. You could use this book to learn physics in the order that the discoveries became established. According to one school of pedagogy, that is the best way to understand the problems and the prospects of the discipline.

So it is a wonderful book, but for whom? It is superb for apprentice or journeyman physicists who want to hear, from a master colleague, about the stages in the evolution of their craft, as seen from inside the trade. But what is in it for anyone else, for most readers of The New York Review, for example? Open it at random and you will find equations that look quite daunting.

Inward Bound is not quite as hard as it may look. For most of the book, the equations are more or less intelligible to someone who is not embarrassed by the applied mathematics now taught to sophomores at run-of-the-mill colleges (or, to put it differently, expected of entering freshmen at Caltech). But only halfway through Pais interrupts himself to say: “At this point the reader may like to have at hand a simple but good book on quantum mechanics (like the one by Schiff) where results merely stated here and in the rest of this section are derived in detail.” Schiff wrote in 1949 for graduate students in physics, even if by now his material is known to a Caltech undergraduate by the end of the first year. So why should the rest of us have to read this highly touted book that has an average of one mathematical formula per page?

Because, although demanding, it is the best book about the history of physics that is both sophisticated and accessible, and that tells what the world is made of, and how we are finding that out. Had you scratched a metaphysician of long ago and asked what the universe is, as likely as not you would have been told about space, time, causality, and substance. Those are also the most memorable topics of physics, but until Pais, most general writers told us only about the first three.

Everyone knows a little about all four because of the vast upheavals in their very definitions that have occurred in this century. Relativistic thinking put paid to stable ideas about space and time. Among the lesser effects of quantum theory are gaping holes in old ideas about causality. And substance, contrary to the old metaphysicians, is not stable. Atoms are no longer indestructible, and interactions in the nucleus can produce immense power.

Relativity and quantum mechanics were each well written up almost from the moment of inception. That was because there was a moment, call it 1905 for space and time, and 1926 for the new quantum mechanics. There are good stories to tell about those years. The number of heroes is small. The dramatic unities can be preserved (even if at the expense of sound history) by making everything seem to happen in a few weeks, if not a day. Substance, however, requires a different kind of telling. Pais calls his story an epic.

So it is. There is a cast of—how many? The names of more than five hundred physicists occur in the index, and Pais is not a writer to string along a lot of names to show off his knowledge. The present installment of the epic runs from 1895 to 1945 (I’ll explain the dates shortly). That covers two thirds of the book, which concludes with the next installment, in the form of a “memoir” from 1945 to the present. This second part spans Pais’s own career, but is in no way restricted to his own work. It is simply that period during which he was an active participant. The transformations since 1895 have been intense. Nuclear weapons and nuclear power have been the stuff of policy decisions for forty years, but there was not even an atomic nucleus on the books in 1910. Ernest Rutherford first speculated that the atom might have a nucleus the next year.

Although Pais quite properly has his own favorites—he loves Niels Bohr, for example—there is no one event or any handful of heroes around which to unfold the plot. The story of substance demands a treatment different from that of relativity or quantum mechanics. Moreover, I have spoken of installments. The year 1895 does not begin the entire story. The oldest and most permanent project in that kind of Western thinking we now call physics is to reveal the inner constitution of matter. Why on earth should matter have an inner constitution at all? Some of us seem always to have thought that it has. I happen to use a seventeenth-century phrase. I might better employ Locke’s typically more cumbersome but more precise term, “the real internal, but generally (in substances), unknown constitution of things.” The cronies of Democritus could have used similar terms when they postulated, against all reason, that the world is composed of indestructible atoms and emptiness. Such speculation has been going on by fits and starts since the dawn of our civilization. So too has the rival fantasy that we live in a plenum of fields of force and energy. Both models have appealed to many of the best minds. It was James Clerk Maxwell who (with others, of course) gave us both the kinetic theory of gases, marbles bouncing around in nothingness, and also the electromagnetic equations in which everything fills everything. This traditional feature of our entire culture is one reason that the facts recounted by Pais deserve to be widely known.

By and large, every success has taken us down and down, to smaller and smaller units of matter. Hence Inward Bound is a good title. In case you missed the pun, the book is also about the forces that bind the nucleus of the atom together. There is also the play on Outward Bound, the push-yourself-to-the-limit adventure movement founded in a British preparatory school. In order to assure you that the book is not all equations, I should say that there is a slight whiff of the stories from English schoolboy magazines published between 1918 and 1939. If you had read them, you would recognize some of the characters. There is the hearty sportsman (the bluff New Zealander who has come home to England) or the quiet fellow whose Swiss father, a Manchester schoolmaster, forces him to speak French at breakfast, driving him to shyness amounting to autism. Although Pais is evenhanded with his cast of hundreds, it is clear that, in addition to Niels Bohr, those two characters are among his favorite five. The hearty one is Ernest Rutherford, greatest experimenter of his day, the first to “split the atom,” albeit a trifle inadvertently. The introvert is P.A.M. Dirac, the superb theorist, who wrote down the best sentence in this book, an array of some fourteen symbols that says what the electron is.

Those two figure in the epic. From the memoir we get some subsequent dialogue, an exchange, in Pais’s presence, written down on the spot.

“I am Feynman.”

“I am Dirac.” (Silence.)

“It must be wonderful to be the discoverer of that equation.”

“That was a long time ago.” (Pause.)

“What are you working on?”

“Mesons.”

“Are you trying to discover an equation for them?”

“It is very hard.”

“One must try.”

Incidentally, Pais’s personal admiration for Rutherford and Dirac reflects a great strength in the book to which I shall briefly return. This narrative is unusually sympathetic to both experiment and theory, and hence provides many real insights into the interplay between them. In the matter of theory/experiment, it is perhaps the most evenhanded general survey of physics ever written.

Now let’s turn to the dates. The division into two parts, epic and memoir, before and after 1945, is the result of a happy if whimsical chance. Pais was born in 1918, and was awarded a Dutch doctorate in 1941. He spent most of the war in hiding. Hence he grew up in prewar physics and began his career in postwar physics. After 1946 he seems always to have kept careful notes of what was going on around him, possibly a consequence of having spent his postdoctoral years in almost complete isolation. In two ways the book is a memoir. The choice of topics reflects the author’s taste, and the anecdotes come from his diary. He feels that events have been going on at such a pace since 1945 that it would be impossible, now, to write with the detachment and sound selection that were possible for the earlier epoch. But it is not just these accidents that make Pais’s division almost inevitable. Like a latter-day Rip van Winkle, he is also testifying to the tremendous transitions in physics effected while he was out of circulation. The era of big science and big funding had begun.

Precisely because of this institutional change—rather than any theoretical advance—1945 will appear as a fundamental date in many histories of physics until some iconoclast gets us to tear up that model.¹ What about 1895? That year allows Pais his own whimsy, saying he is telling the story of physics “from X to Z.” In 1895 Roentgen stumbled across X-rays. In 1983 a group using the CERN collider in Geneva elicited a pair of particles called W and Z. These “weak neutral bosons” are latent in prewar ideas of Enrico Fermi. When efforts were made to create a unified theory of electromagnetism and gravitation, it turned out that in addition to these forces, there were also two “nuclear forces” as well. One of these, the “weak” nuclear force, which helps to hold atomic nuclei together, was found to be conveyed by W and Z. These particles were described in some detail in 1957 and 1958, but only in 1976 could anyone figure out how to produce the events that are their signature. The report of their discovery created much excitement in the community of physicists. They were theoretically important. They confirmed a particular longterm direction of theory. The actual experimentation had many elements of brilliance. It was a gamble that paid off; a collider experiment uses a great many available resources at a given time, and in fact Fermilab in Illinois was much slower in taking a similar gamble. All in all, then, 1983 was a good year to end the book with a Z. Let us not worry about Z, however, and ask about X.

Were X-rays so important? At the time they were sensational headline stuff. Their medical use was almost immediate. Roentgen called them X-rays, perhaps meaning “Who-knows-what-rays.” They were not the first rays of something or other: cathode rays had been known for two decades, but only in 1897 did it become apparent that they were rays of negatively charged corpuscles of definite mass, namely electrons. What X-rays are rays of—photons—came later.

Pais makes a plausible story for X-rays commencing a chain of events leading to the present. The year after Roentgen’s discovery Henri Becquerel found a curious phenomenon: when a compound of uranium was placed near a photographic plate, the plate became exposed. By a natural analogy, he reasoned that there must be some more rays here. Conceivably, Roentgen rays and Becquerel rays might be the same. No, because these new “uranic rays” were soon shown to have other features, such as the ability to affect static electricity. In no time we had a wholly new phenomenon, radioactivity and radium discovered by the Curies.

Radioactivity is the spontaneous disintegration or decay of atomic nuclei by the emission of particles. Obviously radioactivity matters to a history of the nucleus of the atom. In addition, the idea of rays (or “beams,” a better translation of Roentgen’s X-Strahls) has a lot to do with the evolution of experimentation in particle physics. For despite all the ingenuity and cultivation of mental and material resources required to elicit the W and Z, most of the experiments mentioned in Pais’s book have the same underlying structure. There is a detector. A beam is sent toward the detector. A target is put in the way of the beam. The detector notes what happens. We have become more sophisticated. Beams are bent. Instead of a target, two beams are made to collide with each other (that’s the CERN collider mentioned above). In postwar physics the detectors detect so much that an echelon of computer data analysis intervenes between the detector and the experimenters.

You might think that this structure is inevitable. In order to get the nucleus to give up its secrets we must bombard it. We have to create interactions between particles to determine their decay products. That is now our set of mind, but notice how it got in place. It has a lot to do with that picture of “rays” or “beams.” Roentgen’s beam was the X-ray. One of his first targets was his own hand. His detector was a photographic plate. There’s no nuclear physics here, but now turn to the discovery of the nucleus and our first interactions with it.

In 1909 Rutherford told his assistants (Marsden and Geiger of the counter) to take some radioactive stuff and beam it toward some tin foil. It did not seem a very interesting question, asking what would happen, except that something astonishing happened. Some of the rays were bounced back. They must bounce off something, and Rutherford gradually came to think that there must be occasional little hard places on the foil, the nuclei of the atoms, no less. Here the detector was not a photographic plate. But it was still a plate of glass, coated with slightly impure zinc sulfide that gives a microscopic flash of light when a charged particle hits it.

In that experiment particles interacted only with the nucleus as a whole. They bounced off it. In 1919, again rather unexpectedly, Rutherford’s team obtained the first induced nuclear reaction, in which a particle hits atoms of a nitrogen isotope and produces atoms of an oxygen isotope and protons. In this case there was a somewhat different source and preparation of particles, there was a different target (the nitrogen), and there was a somewhat different detector. But the structure of the experiment was the same. Rutherford was of course still working with natural sources of particles, namely radioactive compounds. Once one had the idea of “smashing” the atom by “bombardment” one could hardly resist the idea that hitting atoms harder, i.e., with faster moving, more energetic, particles, would have more interesting effects on the nucleus. The era of accelerators was about to begin. Yet, from then until now, it can be said that we have been still doing the same old thing, even on the model of Roentgen’s first X-rays. I don’t know that Pais had this in mind in starting with X, but it fits.

Much experimentation is not a matter of collecting data but of building apparatus and getting it to work. Progress has come at both ends, in the preparation of the beam and in the improvement of the detector. That means, of course, preparing new kinds of beam, and inventing new kinds of detector. In the public mind, the big accelerators are what matter, for there is a vague awareness that the more the energy, the more the cost, but also, the more national kudos if it is your accelerator. So stories like the following are salutory.

By 1947 Ernest Lawrence had built and was running in Berkeley the world’s best cyclotron by far. Yet because he concentrated on the engineering problems of greater acceleration, he missed the first postwar coup. That was left for a group in Bristol, England, using cosmic radiation from the sky instead of an accelerator. They found the first of the new particles (two kinds of pi-meson that resolved a fundamental theoretical problem posed in 1936). That was thanks to their rather old-fashioned detector, which used a photographic emulsion specially designed for them by the Ilford film company. Berkeley (and Kodak) could not duplicate these results until a young Brazilian student from the Bristol group went to Berkeley. Then Lawrence’s team saw that the cyclotron was wallowing in mesons that they could not previously detect.

This example should not make one think that detectors, though essential, come cheap. The bubble chamber invented in Ann Arbor and subsequently developed at Berkeley is one of the most versatile types of detector, even today. Its development was immensely costly. It might never have been built were it not for liquid hydrogen technology (and investment) originally intended for Teller’s version of the hydrogen bomb. The “crystal ball” detection system used for the CERN collider experiment is even more expensive.

I have said that Pais, a theoretician, is exceptionally sensitive to the role of experiment and of invention. There are times when he leans over backward to avoid a theoretician’s bias, as at the end of the book: “The search for the W and the Z had not been a surprise party. It is in fact dubious whether this enormous enterprise would have been funded and executed had there not been excellent theoretical reasons for knowing where to look: near 80 GeV for M_W, near 90 GeV for M_Z.” Dubious? It is certain that without the theory this particular experiment would never have been performed. (One still might have found W and Z in some other way. The Jgq particle was discovered largely by accident in 1974 in a not dissimilar experiment.)

Now I turn to the mathematics, the chief stumbling block for the lay reader dipping into Pais’s book. Let me say first of all that it is perfectly possible to read the book silently, omitting the equations, although sometimes you may remember their shape (as some of us have done with Russian names when reading Russian novels in translation). What is important for the casual reader interested in the story is to grasp the main direction of ideas. I shall give one example—“renormalization.” It is central to the book and to physics. It may also matter, with a slight mood of nostalgia, to Pais personally. He recounts his meeting with his Dutch mentor H.A. Kramers shortly after the war. Young Pais had his own ideas of what to do next in physics, and did not attend with much dedication to Kramers’s own program of research, which in retrospect looks like renormalization. Pais just suggests that he missed the boat. What is “renormalization”?

An inevitable project of prewar theoretical physics was the linking of quantum mechanics and relativity. In 1926 and 1927 we acquired a quantum mechanical picture of the atom which pretended the world was still, in a way, Newtonian. One knew that it had to be embedded in the theory of special relativity, but the task was formidable. Diracspent all his energies on this, while many of his contemporaries thought that he could not succeed. He did, and gave us the equation for the electron which is both quantum mechanical and relativistic. That was the beginning. The end, to date, is called quantum field theory, or QFT.

Arguably QFT is the best theory of the material world yet devised. But it has a problem. Its equations are quite literally insoluble. That is, there is no direct way in which to deduce from them any experimental phenomena whatever.

Insoluble equations are nothing new in physics. The most successful theory before QFT was Newtonian physics. In a Newtonian universe there are no known exact general solutions for a universe with more than two bodies in it. What has long been called the “three body problem”—deduce the exact motion of a system of three bodies—has been a poser for centuries. This does not mean, to take an obvious example, that physicists cannot calculate the mutual influence of the gravitational fields of the earth, the moon, and the sun. They can. The three body problem concerns only the general formula for calculating such influences when no restriction is placed on the positions and velocities of any three bodies. It is of no practical significance because one makes approximate solutions for the equations, and there are procedures for making better and better approximations to the unknown exact solution. Crudely, one makes messier and messier calculations, adding in more and more corrections. Thus a first-order approximation may be some distance from the true solution, while the next, or second-order approximation, may add in more factors, thereby taking one closer to the truth. Even if an exact solution to the equation is unattainable, we don’t need one for sending rockets to Venus. We can approximate the true solution as closely as we please.

But the problem with QFT is not that we are unable to provide exact solutions to its equations. At the first approximation, one gets sensible rough figures for the properties of the electron, for example. But after that there is a disaster. The mass and charge on the electron, nice small quantities that have been known with great accuracy for seventy-five years, are—according to the second and higher-order approximate solutions for QFT—infinite. You would think people would immediately conclude that the theory is just plain false. You can certainly see why Dirac spent the rest of his life trying to discover a better theory.

Why then did I say that QFT is such a successful theory? Because there is a way of fiddling the equations, which is called renormalization. “Normalization” is a term used in mathematics for rewriting an equation so that, for example, all the quantities of interest lie between zero and unity. Renormalization in QFT means rewriting the equations so that at higher-order approximations all the appropriate quantities are finite. Like much of postwar physics, the idea had been proposed in the Thirties, but by a special bit of bad luck—a straightforward miscomputation—it looked as if it would not work. But it does. Here is what is done. We know certain quantities that are given by experiment, such as the mass and charge on the electron already mentioned. We insert these quantities, given by experiment, into the expressions with which QFT represents them. This is wholly non-theoretical. There is no reason in theory for putting in these or any other numbers. But you put them in, and then, with great delicacy, make approximations to obtain other physical quantities according to the equations that have been tampered with. What happens is that when some experimental finite quantities are introduced, everything becomes finite—“normal.”

Two things about this technique of renormalization are remarkable. First, the ensuing predictions are astonishingly accurate for the given order of approximation. Every aspect of the behavior of the electron (and much else) can be predicted, and whenever an experiment can test the predictions they are confirmed. It is this that leads one to say that QFT is at least the best predicting device ever known to the physicist. Second, in 1949 Freeman Dyson proposed that for quantum electrodynamics—the quantum field theory describing the interaction of electrons and the electromagnetic field—for any order of approximations we need only enter these two experimentally known constants, the mass and charge on the electron. The theory is finite when expressed in terms of these two observable properties. This proposal was subsequently given rigorous proof by Steven Weinberg. It shows that renormalization is what mathematicians call “conservative.” That is, nothing more than quantum mechanics and relativity is needed. The theory makes sense once you have “renormalized” it. That is mathematically elegant. Experimentally, it is marvelous, for it means that infinitely many empirical quantities can be predicted, via the equations and their approximations, from two known numbers.

That does not mean that everything is a picnic. As Pais notes in connection with our famous W and Z, in 1967, “renormalizability remained the stumbling block.” Advanced renormalization theory is one of the most difficult and subtle branches of mathematical physics, and is almost an independent subdiscipline. But that does not preclude a layman from having a rough idea of what is going on. Pais makes it possible to get such an idea.

The example bears on the widespread belief that anything mathematical, including mathematical physics, is wholly rigorous. Yes and no. There is often something quite hokey about approximation in physics, because there are many ways to procure approximate solutions, only some of which fit the facts. Approximation needs tact. But then there are also rigorous and fascinating results, such as Weinberg’s proof of renormalizability. In virtue of such results, new aspects of the entire enterprise may dawn on the community. The equations of QFT work, you may say (thanks to renormalization), but they can’t possibly be true! After all, they assert that finite quantities are infinite. But maybe there is a way to understand this. All the quantities that we measure, we do so at, from a God’s eye view, very low energies. J.J. Thomson got (pretty well) the mass of the electron and R.A. Millikan its charge, both using very little energy. In contrast, our W and Z were obtained at energies near the top of the actual energies of existing accelerators. But nevertheless, those energies are small, even compared to what we could have with larger accelerators by the end of the century. They are minute compared with the energy nature provides in the cosmic rays. One could think of the equation of QFT telling “the truth”—which we certainly don’t understand—about phenomena occurring with no upper bound on available energy. Renormalization is a procedure for bringing us down to accessible energy levels, to domains that we can know about.

Inward Bound is avowedly two books, the pre-1945 epic and the post-1945 memoir. The latter starts fascinatingly with the initial postwar enthusiasm and the chance to get back to theorizing. The mobilization of science for war also created the new system of lavish resources for experimentation. We get some sense of the multiplicity of particles delivered by the accelerators that, to some, made it look as if particle physics was going to degenerate into a bizarre scholasticism. Then there were the new and radical simplifications and unifications of theory, which happen so quickly in Pais’s book that he cannot be intending that any but the informed should understand them. Indeed one is reminded of the speculation that at high enough energies, our familiar particles will turn to mush, and space and time will become incoherent. Something of the sort happens toward the end of the book itself: not recommended reading.

In contrast the pre-1945 epic is a polished piece of exposition. At the beginning I said it was something of an official history, which is one very proper way to write the history of science. Pais says that he wanted to do the history of physics in a new way. In fact, although there are more anecdotes, the effect is not so different from a classic piece of instruction written for an earlier era, and which carries the reader up to 1900: E.T. Whittaker’s A History of the Theories of Aether and Electricity from the Age of Descartes to the Close of the Nineteenth Century.²

Pais does not describe a story of uniform advance. He notes wrong analogies, false starts, and what he calls “pitfalls” that beset the growth of knowledge. The book remains an account of marvelous results, of heroes with interesting quirks but few blemishes. One notes, in the memoir, that a couple of very famous living men drop out of the tale a little prematurely. Perhaps silence is Pais’s strongest form of criticism. Contrary, I believe, to Pais’s intentions, one gets very little idea, from this book, of what it is like to be a working physicist, either on the front lines or in the reserves. But if you stand back from the book, and view it as an account of knowledge and not of people, it does provoke a sense of wonder. The members of our species are five or six feet tall. We seem now to have investigated the inner constitution of matter down to 10^{-16 centimeter, a number pertaining to the W and Z, where theory and experimental intervention mesh astonishingly well. There seems nothing in the theory of evolution to explain how a species our size should have acquired the ability to do that.}