Fantastic Realities

49 Mind Journeys and A Trip to Stockholm

Frank Wilczek

• Publisher: WSPC
• Year: 2006
• ISBN:
  9789814338196
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

With a contribution from Betsy Devine

Podcast of Frank Wilczek and Betsy Devine's interview with Steve Mirsky of Scientific American

The fantastic reality that is modern physics is open for your exploration, guided by one of its primary architects and interpreters, Nobel Prize winner Frank Wilczek.

Some jokes, some poems, and extracts from wife Betsy Devine's sparkling chronicle of what it's like to live through a Nobel Prize provide easy entertainment. There's also some history, some philosophy, some exposition of frontier science, and some frontier science, for your lasting edification.

49 pieces, including many from Wilczek's award-winning Reference Frame columns in Physics Today, and some never before published, are gathered by style and subject into a dozen chapters, each with a revealing, witty introduction.

Profound ideas, presented with style: What could be better? Enjoy.

Contents:

• Constructing This World, and Others
• Musing on Mechanics
• Making Light of Mass
• QCD Exposed
• Breathless at the Heights
• At Sea in the Depths
• Once and Future History
• Methods of Our Madness
• Inspired, Irritated, Inspired
• Big Ideas
• Grand Occasions
• Breaking into Verse
• Another Dimension

Readership: Students, scientists and lay people.

Once and future History

“The Dirac Equation” and “Fermi and the Elucidation of Matter” are fraternal twins. “The Dirac Equation” was a homework assignment from Graham Farmelo, for his collection of essays on great equations, It Must Be Beautiful. “Fermi and the Elucidation of Matter” was a homework assignment from Jim Cronin, for a collection of tributes to Fermi, Fermi Remembered, to commemorate the 100th anniversary of his birth.

Superficially, matter and light seem to be utterly different sorts of things. And not only superficially: until well into the 20th century, the best scientific understandings of these two elements of reality used entirely different and contradictory concepts. Discrete particles were the ingredients for matter, but continuous fields described light. Matter was permanent, but light was transient. It was Dirac and Fermi, primarily, who transcended these dualities. Their work initiated modern quantum field theory. So these pieces provide a gentle introduction to “Quantum Field Theory.”

There's a lot more in these two pieces than I'll mention here; let me only call special attention to the concluding section of “The Dirac Equation,” which has some sharp observations on mathematical creativity.

A general observation: The more I've learned about most “great” historical figures like Alexander, Napoleon, or many others I won't name, the less admirable they've appeared to me. There are exceptions, notably Benjamin Franklin and Abraham Lincoln, but they are rare. In physics I've found the proportions reversed. The more I learn about Dirac and Fermi—and also Bohr (Item 33)—the more admirable, in different ways, they seem.

“The Standard Model Transcended” is a report, for Nature News and Views, on the historic first announcement that neutrinos have mass. I was present at the conference in Osaka, and the atmosphere of release and fulfillment there was tangible. People were glowing like newlyweds.

What does it mean? As I explain in “The Standard Model Transcended,” a levitating pyramid now rests on one point.

“Masses and Molasses” and “In Search of Symmetry Lost” are half-sibs. Both are devoted to the same subject, namely the exotic superconductivity of what we see as empty space. (That phenomenon is commonly called the Higgs phenomenon, a name that manages to be both uninformative and misleading.) I know I'm the father of “Masses and Molasses” (never mind how), but it got its looks from somebody at New Scientist. Note especially the penetrance of the dominant short-sentence trait. Anyway, switching metaphors, the two pieces go together naturally: “Masses and Molasses” forms an appetizer to “In Search of Symmetry Lost,” the entrée.

“From ‘Not Wrong’ to (Maybe) Right” and “Unification of Couplings” are another pair. Both deal with a remarkable, quantitative evidence for the validity of ambitious speculations about the validity of quantum field theory at ultra-small distances, ultimate unification of the fundamental forces of nature, and supersymmetry. The Large Hadron Collider (LHC) will bring forth abundant testimonial fruit. It's a thrilling prospect, in the abstract, though I have to admit that after more than 20 years of waiting I've learned how to control my excitement and get some sleep. “From ‘Not Wrong’ to (Maybe) Right” tells the inside personal story of the key calculation, while “Unification of Couplings” explains it scientifically.

The Dirac Equation

One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them.

—H. Hertz, on Maxwell's equations for electromagnetism

A great deal of my work is just playing with equations and seeing what they give.

—P. A. M. Dirac

It gave just the properties one needed for an electron. That was really an unexpected bonus for me, completely unexpected.

—P. A. M. Dirac, on the Dirac equation

Of all the equations of physics, perhaps the most “magical” is the Dirac equation. It is the most freely invented, the least conditioned by experiment, the one with the strangest and most startling consequences.

In early 1928 (the receipt date on the original paper is January 2), Paul Adrien Maurice Dirac (1902–1984), a 25-year-old recent convert from electrical engineering to theoretical physics, produced a remarkable equation, forever to be known as the Dirac equation. Dirac's goal was quite concrete, and quite topical. He wanted to produce an equation that would describe the behavior of electrons more accurately than previous equations. Those equations incorporated either special relativity or quantum mechanics, but not both. Several other more prominent and experienced physicists were working on the same problem.

Unlike those other physicists, and unlike the great classics of physics, Newton and Maxwell, Dirac did not proceed from a minute study of experimental facts. Instead he guided his search using a few basic facts and perceived theoretical imperatives, some of which we now know to be wrong. Dirac sought to embody these principles in an economical, mathematically consistent scheme. By “playing with equations,” as he put it, he hit upon a uniquely simple, elegant solution. This is, of course, the equation we now call the Dirac equation.

Some consequences of Dirac's equation could be compared with existing experimental observations. They worked quite well, and explained results that were otherwise quite mysterious. Specifically, as I'll describe below, Dirac's equation successfully predicts that electrons are always spinning and that they act as little bar magnets. It even predicts the rate of the spin and the strength of the magnetism. But other consequences appeared inconsistent with obvious facts. Notably, Dirac's equation contains solutions that seem to describe a way for ordinary atoms to wink out into bursts of light, spontaneously, in a fraction of a second.

For several years Dirac and other physicists struggled with an extraordinary paradox. How can an equation be “obviously right” since it accounts accurately for many precise experimental results, and achingly beautiful to boot—and yet manifestly, catastrophically wrong?

The Dirac equation became the fulcrum on which fundamental physics pivoted. While keeping faith in its mathematical form, physicists were forced to reexamine the meaning of the symbols it contains. It was in this confused, intellectually painful re-examination—during which Werner Heisenberg wrote to his friend Wolfgang Pauli, “The saddest chapter of modern physics is and remains the Dirac theory” and “In order not to be irritated with Dirac I have decided to do something else for a change…”—that truly modern physics began.

A spectacular result was the prediction of antimatter—more precisely, that there should be a new particle with the same mass as the electron, but the opposite electric charge, and capable of annihilating an electron into pure energy. Particles of just this type were promptly identified, through painstaking scrutiny of cosmic ray tracks, by Carl Anderson in 1932.

The more profound, encompassing result was a complete reworking of the foundations of our description of matter. In this new physics, particles are mere ephemera. They are freely created and destroyed; indeed, their fleeting existence and exchange is the source of all interactions. The truly fundamental objects are universal, transformative ethers: quantum fields. These are the concepts that underlie our modern, wonderfully successful Theory of Matter (usually called, quite unpoetically, the Standard Model). And the Dirac equation itself, drastically reinterpreted and vastly generalized, but never abandoned, remains a central pillar in our understanding of Nature.

1. Dirac's Problem and the Unity of Nature

The immediate occasion for Dirac's discovery, and the way he himself thought about it, was the need to reconcile two successful, advanced theories of physics that had gotten slightly out of synch. By 1928 Einstein's special theory of relativity was already over two decades old, well digested, and fully established. (The general theory, which describes gravitation, is not part of our story here. Gravity is negligibly weak on atomic scales.) On the other hand, the new quantum mechanics of Heisenberg and Schrödinger, although quite a young theory, had already provided brilliant insight into the structure of atoms, and successfully explained a host of previously mysterious phenomena. Clearly, it captured essential features of the dynamics of electrons in atoms. The difficulty was that the equations developed by Heisenberg and Schrödinger did not take off from Einstein's relativistic mechanics, but from the old mechanics of Newton. Newtonian mechanics can be an excellent approximation for systems in which all velocities are much smaller than the speed of light, and this includes many cases of interest in atomic physics and chemistry. But the experimental data on atomic spectra, which one could address with the new quantum theory, was so accurate that small deviations from the Heisenberg-Schrödinger predictions could be observed. So there was a strong “practical” motivation to search for a more accurate electron equation, based on relativistic mechanics. Not only young Dirac, but also several other major physicists, were after such an equation.

In hindsight we can discern that much more ancient and fundamental dichotomies were in play: light versus matter; continuous versus discrete. These dichotomies present tremendous barriers to the goal of achieving a unified description of Nature. Of the theories Dirac and his contemporaries sought to reconcile, relativity was the child of light and the continuum, while quantum theory was the child of matter and the discrete. After Dirac's revolution had run its course, all were reconciled, in the mind-stretching conceptual amalgam we call a quantum field.

The dichotomies light/matter and continuous/discrete go deep. The earliest sentient proto-humans noticed them. The ancient Greeks articulated them clearly, and debated them inconclusively. Specifically, Aristotle distinguished Fire and Earth as primary elements—light versus matter. And he argued, against the Atomists, in favor of a fundamental plenum (“Nature abhors a vacuum”)—upholding the continuous, against the discrete.

These dichotomies were not relieved by the triumphs of classical physics; indeed, they were sharpened.

Newton's mechanics is best adapted to describing the motion of rigid bodies through empty space. While Newton himself in various places speculated on the possible primacy of either side of both dichotomies, Newton's followers emphasized his “hard, massy, impenetrable” atoms as the fundamental building blocks of Nature. Even light was modeled in terms of particles.

Early in the nineteenth century a very different picture of light, according to which it consists of waves, scored brilliant successes. Physicists accepted that there must be a continuous, space-filling ether to support these waves. The discoveries of Faraday and Maxwell, assimilating light to the play of electric and magnetic fields, which are themselves continuous entities filling all space, refined and reinforced this idea.

Yet Maxwell himself succeeded, as did Ludwig Boltzmann, in showing that the observed properties of gases, including many surprising details, could be explained if the gases were composed of many small, discrete, well-separated atoms moving through otherwise empty space. Furthermore J. J. Thomson experimentally, and Hendrik Lorentz theoretically, established the existence of electrons as building blocks of matter. Electrons appear to be indestructible particles, of the sort that Newton would have appreciated.

Thus as the twentieth century opened, physics featured two quite different sorts of theories, living together in uneasy peace. Maxwell's electrodynamics is a continuum theory of electric and magnetic fields, and of light, that makes no mention of mass. Newton's mechanics is a theory of discrete particles, whose only mandatory properties are mass and electric charge.^a

Early quantum theory developed along two main branches, following the fork of our dichotomies, but with hints of convergence.

One branch, beginning with Planck's work on radiation theory, and reaching a climax in Einstein's theory of photons, dealt with light. Its central result is that light comes in indivisible minimal units, photons, with energy and momentum proportional to the frequency of the light. This, of course, established a particle-like aspect of light.

The second branch, beginning with Bohr's atomic theory and reaching a climax in Schrödinger's wave equation, dealt with electrons. It established that the stable configurations of electrons around atomic nuclei were associated with regular patterns of wave vibrations. This established a wave-like property of matter.

Thus the fundamental dichotomies softened. Light is a bit like particles, and electrons are a bit like waves. But sharp contrasts remained. Two differences, in particular, appeared to distinguish light from matter sharply.

Fir...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Introduction
• Contents
• Constructing This World, and Others
• Musing on Mechanics
• Making Light of Mass
• QCD Exposed
• Breathless at the Heights
• At Sea in the Depths
• Once and Future History
• Methods of Our Madness
• Inspired, Irritated, Inspired
• Big Ideas
• Grand Occasions
• Breaking into Verse
• Another Dimension
• Acknowledgments
• Back Cover