O amazement of things—even the least particle!
—Walt Whitman, “Song at Sunset”
Theoretical physicists are in a state of high excitement these days, and for good reason. New discoveries in particle physics, combined with brilliant theoretical invention, suggest that they are on the verge of nothing less than explaining everything.
Well, not exactly Everything, but everything possible for physics to explain. More precisely, they believe they are close to constructing a unified field theory that will describe exactly how the universe, almost instantly after the big bang, acquired all the particles and forces that allowed it, some 15 billion years later, to grow into the universe we know. A few adventuresome theorists think they may soon be able to explain how the primeval explosion itself was caused by a random quantum fluctuation of Nothing.
One of the two books under review is by the American physicist Heinz Pagels, whose previous book The Cosmic Code is one of the best introductions to quantum mechanics I have ever read. The other volume is by the British physicist Paul Davies, author of many earlier books that are models of science writing for laymen. Both books are admirable up-to-the-minute accounts of the search for what Pagels calls the Holy Grail. Those who work in “the shadowy world of fundamental physics,” Davies writes in his first paragraph, are about to complete their long quest “for a prize of unimaginable value—nothing less than the key to the universe.”
Is it really true that physics may be nearing the end of a road, “going for broke,” as Pagels puts it? Of course, there will remain the infinite problems on what Pagels calls “the frontier of complexity”—such trifles as explaining how the basic forces and particles manage to get together and write books about themselves—but there may be nothing more to learn on a bedrock level. The situation will be something like that of plane geometry. All its theorems are implied by its axioms, but the number of theorems yet unknown is infinite. A unified field theory would in no way be the end of science or technology. There will be endless inventions to make, endless worlds out there in space to explore. It would only mean the end of the search for fundamental laws.
Unfortunately, physicists have been in previous states of euphoria about reaching the end of the road. In the late Twenties everything seemed wonderfully simple. Maxwell’s field equations had explained electromagnetism. Einstein’s field equations had explained gravity. And Einstein was hard at work on a theory to unify these two forces. All matter was made of atoms that contained just two kinds of particles: protons in the nucleus and electrons whirling around in paths described by probability waves. “Physics as we know it will be over in six months,” said Max Born, one of the great architects of quantum mechanics.
In 1932 nature began to look shaggy again. A new particle, the neutron, was found hiding in the nucleus. Paul Dirac’s theoretical work implied that the electron had an antiparticle twin exactly like it but with a positive charge, and, sure enough, in 1932 the positron was found. Then came the deluge. Dozens of entirely unsuspected particles began to turn up as physicists started clashing particles together at high speeds in the new accelerators—particles that had, in Robert Oppenheimer’s words, an “insulting lack of meaning.” When it appeared later that protons and neutrons were made of smaller particles, the physicist Murray Gell-Mann, drawing on Finnegans Wake, called these “quarks” (“three quarks for Muster Mark!”).
Two entirely new forces arrived on the scene. Neutrons and protons were found to be held together in the nucleus by a “strong force,” much stronger than gravity or electromagnetism but operating at extremely small distances. In radioactive decay, when a neutron decays into an electron, proton, and an antineutrino, the process was found to be controlled by a “weak force.”
Slowly, over the next four decades, the hundreds of newly discovered particles began to make sense. It now appears that everything material is made from combinations of six kinds of quarks and six particles called leptons. The four forces, or “interactions,” as physicists prefer to say—gravity, electromagnetism, the “strong” and the “weak” forces—are transmitted by a third set of more ghostly particles called bosons.
The leptons are pointlike particles that are influenced by the weak force. For example, when radioactivity takes place, and a neutron decays into a proton, the weak force creates two leptons, an electron and an antineutrino. Leptons have no known interior structure, but they have mass and a curious quantum property called spin, to which I will soon return. The electron is the most important lepton because it is part of all atoms, and because it carries electrical charge. (Electric currents are produced by moving electrons.) The muon is the funniest lepton. It has been called a fat electron because it is just like an electron in every respect except that it weighs more than two hundred times as much. “Consider the muon,” Columbia University’s Isidor I. Rabi once began a lecture. “Who ordered that?” The tauon, discovered in 1976, is even odder. It is a fat muon more than 3,500 times as massive as the electron. When the three particles are involved in certain interactions, each is associated with its own kind of neutrino.
Neutrinos, which make up the other three leptons, are as close to nothing as a particle can get. They have no electric charge, no known mass. Their only property seems to be spin. Quantum spin is something like the spin of a top but much more mysterious. (How can a point spin?) All three neutrinos are left-handed in the sense that when they move away from you their spin is counterclockwise. Each of the six leptons has a twin antiparticle of opposite spin (and opposite charge if not a neutrino), so if antiparticles are considered, there are twelve leptons.
The six quarks come in six types or “flavors”: up, down, charmed, strange, top (or truth), and bottom (or beauty). These words have no connection with their ordinary meanings. They are simply colorful terms for properties of quarks that can only be described by mathematical expressions. All quarks are believed to be pointlike, though some theorists have speculated that they are made of smaller particles, and a few think there may even be an infinity of sublevels. Each quark has mass, spin, a fractional electric charge of plus two-thirds or minus one-third, and a different kind of charge called color. It differs from an electric charge in that it applies to a new property of matter that comes in three varieties: red, green, and blue. Of course the quarks do not have colors in the usual sense, but the color names are useful because of analogies between the mixing of quark colors and the mixing of ordinary colors.
Each quark has its antiquark of opposite charges and spin. The heavier a particle, the harder it is to produce in an accelerator, and for this reason the heaviest quark, the top quark, was the last to be detected. Carlo Rubbia, heading a team of scientists at CERN (The European Laboratory for Particle Physics, in Geneva) announced evidence for the top quark late in 1984.
Quarks join together in only two ways, pairs or triplets, to make composite particles called hadrons. Hadrons are influenced only by the strong force. It binds together the quarks inside them and also binds them to one another. Quark doublets (each consisting of a quark and an antiquark) form hadrons called mesons. The triplets (three quarks) are the baryons, of which the most important are the proton (two up quarks and one down) and the neutron (two down, one up). Every possible combination of doublets and triplets is a hadron that has been experimentally verified.
Particles that carry the four forces go by various names: bosons, exchange particles, interaction particles, carrier particles, virtual particles, ghost particles. They can be thought of as particles that zip rapidly back and forth between the “real” particles. The photon carries the electromagnetic force, the graviton (not yet detected) carries gravity. The weak force has three carriers: a positively charged W particle, a negatively charged W particle, and a chargeless Z particle. A 1984 Nobel prize went to Rubbia and Simon van der Meer for their observations at CERN of all three particles. The strong force that glues together the quarks inside the hadrons, and the hadrons to each other, is carried by eight kinds of bosons appropriately called gluons. (Pagels uses the term gluon for all exchange particles, and color gluons for carriers of the strong or color force.)
Every force is described by a field such as the magnetic field around a magnet or the gravity field around the earth. Every field has its carrier particle, and every particle, carrier or otherwise, has its field. Pagels’s chapter on fields is especially useful in making clear the overriding importance of fields and their symmetries.
Symmetry is that property of a structure which remains the same if you perform a certain operation on it. For example, the letter H has 180 degree rotational symmetry because if you turn it upside down it doesn’t change. It also has left-right symmetry because it is unaltered by mirror reflection. It has glide symmetry because it stays the same if you slide it along the page. The letter F has glide symmetry but lacks rotational and reflection symmetry.
Fields share all the symmetry properties of their particles. A particle is simply a property of a field. Newton’s atoms were like hard little billiard balls, but in quantum mechanics such atoms have totally dematerialized. For a crude analogy, think of a sheet of paper filled with hundreds of parallel creases. Imagine that another set of parallel creases, at right angles to the first set, glides across the page. At spots where the creases intersect, little bumps move across the page. Particles resemble those bumps. They are created by the movements of fields. “The world according to this view,” Pagels writes, “is a vast arena of interacting fields manifested as quantum particles flying about and interacting with each other.”
In our analogy the fields were made of paper. What are quantum fields made of? The question is meaningless. They are not made of anything. They are irreducible in the sense that they can’t be reduced to something more fundamental. They are pure mathematical concepts. They just are.
The first great modern unification theory was James Clerk Maxwell’s joining of magnetism and electricity. They were thought to be independent forces until Maxwell’s field equations (field equations describe how a field changes in space and time) combined them. Gravity and inertia were similarly considered different until Einstein showed them to be manifestations of a single field. Einstein spent the last part of his life vainly trying to unify gravity and electromagnetism. Nobody can blame him for failing because the data he had at hand were too scant.
In 1961 Harvard’s Sheldon Glashow laid the groundwork for a unification of electromagnetism and the weak force. The theory was completed by Steven Weinberg and Abdus Salam, working independently, and for this the three received a 1979 Nobel award. The new field is called the electroweak field. The theory predicted the W and Z particles, which carry the weak force. Their discovery was such strong confirmation of the theory that it is now accepted as standard particle physics. Formerly there were four basic forces. Now there are three—gravity, the strong force, and the electroweak force.
The next step is to unify the electroweak force with the strong. Hundreds of attempts to do this, known as GUTs (grand unified-field theories) are now being proposed. The simplest and most promising is one constructed by Glashow and Howard Georgi in 1973. It makes several predictions, but none has yet been verified.
The final step of course would be a field that unified all the forces, including gravity. Such a theory would be extraordinarily difficult to confirm because it would require accelerators more powerful than any now conceivable, but that has not inhibited the theorists, especially the younger ones. They are enthusiastically at work on what are called super-GUT theories, or supersymmetry theories, or SUSYs for short. It may turn out that the only arena in which confirmations can be found is in interstellar space where stars and black holes produce extreme temperatures and energies beyond the power of earthly instruments. Pagels recalls a motto he saw on a student’s T-shirt: “Cosmology takes GUTs.”
To understand how cosmology is involved it is necessary to grasp the concept of breaking symmetry. Weinberg likes to explain it with a marble balanced on top of the glass mound at the base of certain bottles. The structure has circular symmetry in the sense that bottle and marble look the same from all sides. But the structure is unstable. The marble rolls off the mound to one side, breaking the original symmetry. Abdus Salam likes to explain it with a group of people sitting symmetrically around a circular table. In front of each is a dinner plate, and between every adjacent pair of dinner plates is a salad plate. The situation is symmetrical until the hostess decides whether to reach right or left for the salad. As soon as she decides, everybody reaches the same way. Left-right symmetry is broken. In cosmology, the symmetries that break are much more complicated. They are properties of equations that cannot be expressed in visual pictures.
SUSYs assume that immediately after the big bang, when the temperature of the universe was unthinkably high, elegant symmetries prevailed, then were broken as the universe rapidly expanded and cooled. Let’s run this script backward in time. When temperature rises to a certain point, electromagnetism and the weak force become one force. Go further back in time, when temperatures are still higher, and the electroweak force fuses with the strong. Go back some more, to less than a nanosecond (one-billionth of a second) after the big bang. All forces are now a single force field, perhaps with a single superparticle. This is the force that provides the title “superforce” of Davies’s book, and the “perfect symmetry” title of Pagels’s book.
Water has high rotational symmetry because no matter how you turn it it-looks the same. But when water freezes into a snowflake a “phase transition” occurs. It loses its rotational symmetry to acquire a beautiful hexagonal pattern that now must be turned in 60 degree increments to make it look the same. Broken symmetries like this, though far more complicated and on a vaster scale, are believed to have occurred while the universe cooled. “Our universe today,” Pagels writes, “is the frozen, asymmetric remnant of its earliest hot state.”
My favorite model of symmetry breaking is an old stunt with playing cards. On a tablecloth, using great care and patience, it is possible to balance four cards on their long edges so they radiate out from a point like the arms of a cross. Gently push four more cards into the gaps to make a wheel with eight spokes. Add more cards one at a time. The more you add the more stable the structure should become until finally you have a wheel with fifty-two spokes. It is not easy to form. It helps if you give the deck a slight bend. You can anchor the outer ends of the first four cards with small objects such as checkers or chessmen, and later remove them. The trick is prettier if you place the cards so they all face around the circle in the same direction.
Big bang your fist on the table. The jar will break the symmetry, collapsing the structure into a lovely rosette that is either right- or left-handed. Many physicists believe that an event similar to this explains why the universe we know is made of matter. Originally the cosmos was symmetrical with respect to matter and antimatter (matter made of anti-particles). When the symmetry broke, the universe collapsed into matter, but it could just as easily have gone the other way.
Davies devotes a colorful chapter to a popular SUSY known as a generalized Kaluza–Klein (KK) theory. When I was writing my Ambidextrous Universe in the early Sixties I came across a forgotten theory proposed in the Twenties by the Polish physicist Theodor Kaluza and the Swedish physicist Oscar Klein. They tried to unify gravity and electromagnetism by assuming a fourth spatial dimension, closed like a circle and with a radius smaller than an atom’s. They claimed that electromagnetism is actually a form of gravity, its waves moving in this unseen dimension of space. Think of every point in space as attached to an incredibly tiny circle that goes in a direction impossible to visualize. As Davies describes the theory, “what we normally think of as a point in three-dimensional space is in reality a tiny circle going round the fourth space dimension.” From every point in space, as Davies puts it, “a little loop goes off in a direction that is not up, down, or sideways, or anywhere else in the space of our senses. The reason we haven’t noticed all these loops is because they are incredibly small in circumference.” If time is added as a coordinate, the little loop becomes a threadlike cylinder in five-dimensional space-time. Gravity waves spiral around these threads in helixes that have either of two mirror-image forms. One direction produces positive charge, the other a negative charge.
I discussed the KK theory not only because I found it whimsical, but because it explained positive and negative charge according to left-right handedness, and also gave a reason why charge comes in discrete units. (Something going around a loop has to go completely around it to get back where it started.) Einstein took the theory seriously. “The idea of achieving [a unified theory] by means of a five-dimensional cylinder world,” Pagels quotes him as writing to Kaluza, “never dawned on me…. At first glance I like your idea enormously.” Eventually Einstein decided the theory was wrong. In 1963 I asked several top physicists what they thought of the KK theory. None had even heard of it.
You can imagine my surprise fifteen years later when the theorists suddenly remembered KK. It turns out that a simple, beautiful way to explain the properties of particles is to generalize KK by turning the tiny circles into seven-dimensional spheres! If this conjecture proves fruitful, all interactions and particles become aspects of one superforce shimmering around in a space-time of eleven dimensions. Three are the ones we know, seven are the “compacted” dimensions of the invisible hyperspheres, and the eleventh is time.
It is good to realize that when physicists talk about spaces they don’t always mean spaces that are physically real. They are usually artificial spaces devised to simplify calculations. No physicist thinks that the curves he uses to graph functions on two-dimensional paper are “out there” in physical space, or that the probability waves of quantum mechanics (they are waves in imaginary “phase spaces” of high dimensions) are out there like water or sound waves. Probability waves exist only in the minds and discourse of physicists. On the other hand, the higher spaces of the KK theories (some have more than seven new dimensions) could be as real as our familiar space of three dimensions. On this dark question KK enthusiasts are sharply divided. No one can even think of an empirical test that might settle the matter.
It is dangerous, Sherlock Holmes once said to Dr. Watson, to theorize without adequate facts. Nevertheless, it is essential to science that dangerous theorizing constantly go on, and Davies is among those superoptimists who think the ultimate unification may be as imminent as Billy Graham thinks the Second Coming is. Pagels, too, is optimistic, though more cautious:
A whole community of very smart scientists may have talked themselves into a theory of the very early universe that in the future (with the wisdom of hindsight) will be seen as a fantasy based on incomplete information and imaginative extrapolation. Theory building, while it creates a framework for thought, is never a substitute for experiment and observation. The new high-energy accelerators and telescopes currently on the drawing boards will tell us a lot about whether or not these ideas are correct.
Sometimes I wish that this book about the current ideas of physics and cosmology could be published like a loose-leaf notebook. That way, pages could be discarded and replaced with new pages describing better ideas when they come along. Much of our current scientific thinking about microscopic physics, the “wild ideas” and cosmology is probably wrong and will have to be discarded. Maybe in the future there will be a major revolution in physics that will revise our whole idea of reality. We may look back on our current attempts to understand the origin of the universe as hopelessly inadequate, like the attempts of medieval philosophers trying to understand the solar system before the revelations of Copernicus, Kepler, Galileo and Newton. What we now regard as “the origin of the universe” may be the temporal threshold of worlds beyond our imagining. But it is also possible that we are near the end of our search. No one knows.
The wildest of all the wild ideas now being tossed about is based on the assumption that a vacuum is not pure nothing because it is saturated with quantum fields. Even if we think of the vacuum as spaceless and timeless, there may be some sort of mathematical structure to it, more fundamental than space and time, with its associated quantum laws. Given enough time—whatever that means!—there is some degree of probability that the structured “nothing” will become unstable. A single spot of “something,” produced by a random quantum event, will explode into a space-time universe. Many physicists, Pagels among them, are playing with such notions, while others think it is a waste of time—as absurd as looking for something north of the North Pole.
This view of the universe as a “free lunch” is close to the medieval doctrine of creation ex nihilo, though we must be careful now to distinguish between points of view hotly debated by the Scholastics. There were many subtle variations, but the essential conflict was between those who argued that God created the universe from absolutely nothing, and those who argued that God made use of a formless, eternally existing primal matter. The two points of view are mirrored today in the views of cosmologists who are unwilling to consider creation by an Outsider. There may exist from all eternity a primal Mother Field of space and time, capable of giving rise to a singularity—the random quantum event previously mentioned—that explodes into a universe. Or there may be no field at all—just nothing, completely empty of space and time. Somehow behind this nothing are quantum laws that can spontaneously produce a space-time field that in turn explodes into the universe.
Observe that nothing is not absolutely nothing for either the Scholastics or a secular cosmologist. All the theologians of the Middle Ages assumed an eternally existing Creator. Today’s cosmologists must assume, at the least, eternally existing quantum laws. “[The] unthinkable void,” Pagels writes, “converts itself into the plenum of existence—a necessary consequence of physical laws. Where are these laws written into that void? What ‘tells’ the void that it is pregnant with a possible universe? It would seem that even the void is subject to law, a logic that exists prior to space and time.”
It would seem indeed! Because the existence of laws is not nothing, the new physics adds nothing to help answer the unanswerable superultimate question: Why is there something rather than nothing?
Davies also struggles with this impenetrable mystery, ending his book on an enigmatic note of pantheism. Although science may in a sense explain the universe, “we still have to explain science. The laws which enable the universe to come into being spontaneously seem themselves to be the product of exceedingly ingenious design. If physics is the product of design, the universe must have a purpose, and the evidence of modern physics suggests strongly to me that the purpose includes us.”
Perhaps. But I cannot see how anything in modern science suggests this more than anything in ancient science. That the universe displays an incredible order, not made by us, was as obvious to a Roman atheist like Lucretius as it is to a modern theist. The only difference is that today cosmic evolution has pushed speculation about the source of this order down to the quantum level and back to a primordial fireball. For all science and reason can tell us, a mindless Mother Field may have generated precisely the patterns we find, and be as indifferent to human destiny as it is to the fate of a symmetrical snowflake.
On this question, the deepest in philosophy, Pagels does not tell us his private views. Nowhere in his splendid book does he consider the possibility of a Mind outside the cosmos, although he confesses that the universe continues to haunt him. “This sense of the unfathomable beautiful ocean of existence drew me into science. I am awed by the universe, puzzled by it and sometimes angry at a natural order that brings such pain and suffering. Yet any emotion or feeling I have toward the cosmos seems to be reciprocated by neither benevolence nor hostility but just by silence. The universe appears to be a perfectly neutral screen onto which I can project any passion or attitude, and it supports them all.”
Yet Pagels’s epigraph for his book is that spine-tingling first verse of an old religious document from the Middle East that tells how the world was once without form and void, and darkness was on the face of the deep, and the spirit of God moved over the waters. The superultimate question remains as stark as ever. Back of the Mother Field, behind space and time and the laws of quantum mechanics, is there something analogous to human consciousness? Or is the universe, as G.K. Chesterton once wrote, “the most exquisite masterpiece ever constructed by nobody”?
“Someday,” Pagels writes “(and that day is not yet here) the physical origin and the dynamics of the entire universe will be as well understood as we now understand the stars. The existence of the universe will hold no more mystery for those who choose to understand it than the existence of the sun.”
I can (with effort) buy the first sentence but not the last. Theorems of geometry are not very mysterious. It is a formal system’s axioms that pop like magic out of nowhere. A set of laws with the awesome power to blast into reality a cosmos containing life forms as fantastic as you and I is to my mind so staggering a vision that it makes the origin and dynamics of a star seem as trivial as the origin and dynamics of an eggbeater.
June 13, 1985