Coming of Age in the Milky Way - Timothy Ferris (2003)

Part III. CREATION

O landless void, O skyless void,
O nebulous, purposeless space,
Eternal and timeless,
Become the world, extend!

—Tahitian creation tale

What really interests me is whether God had any choice in the creation of the world.

—Einstein

Chapter 15. THE QUANTUM AND ITS DISCONTENTS

What is the path? There is no path.

—Niels Bohr, quoting Goethe

Progress in physics has always moved from the intuitive toward the abstract.

—Max Born

           The act of exploration alters the perspective of the explorer; Odysseus and Marco Polo and Columbus returned home as changed men. So it has been with scientific investigation of the extremities of scale, from the grand sweep of cosmological space down to the cramped and frantic world of the subatomic particles: These journeys changed us, challenging many of the scientific and philosophical conceptions we had most cherished. Some had to be discarded, like baggage left behind on a trek across a desert. Others were altered and repaired almost beyond recognition, like the veteran mountaineer’s hand-hammered pitons or the old seaman’s knife with its twine-encrusted handle and bone-thin blade. Exploration of the realm of the galaxies extended the reach of human vision by a factor of some 1026 larger than the human scale, and brought about the revolution we identify with relativity, which revealed that the Newtonian world view was but a parochialism in a wider universe where space is curved and time becomes pliant. Exploration of the subatomic realm carried us far into the realm of the small, to some 10•15 of the human scale, and it, too, wrought a revolution. This was quantum physics, and all that it touched it transformed.

Quantum theory was born in 1900, when Max Planck realized that he could account for what was called the black-body curve—the spectrum of energy generated by a perfectly radiating object —only if he abandoned the classical assumption that energy is emitted continuously and replaced it with the unprecedented hypothesis that energy comes in discrete units. Planck called these units quanta, after the Greco-Latin word for “how much” (as in quantity), and he defined them in terms of the quantum of action, symbolized by the letter h. Planck was no revolutionary—at age forty-two he was an old man by the standards of mathematical science, and a pillar of nineteenth-century German high culture to boot—but he readily appreciated that the quantum principle would shatter much of the classical physics to which he had devoted his career. “The greater [its] difficulties,” he wrote, “… the more significant, it finally will show itself to be for the broadening and deepening of our whole knowledge in physics.”1 His words proved prophetic: Constantly changing and developing, altering its coloration as unpredictably as a reflection in a soap bubble, quantum physics soon expanded into virtually every area of physics, and Planck’s h came to be regarded as a fundamental constant of nature, on a par with Einstein’s c, the velocity of light.

The quantum principle was very strange—it was, as Gamow remarked, as if one could drink a pint of beer or no beer at all, but were barred by a law of nature from drinking any quantity of beer between zero and one pint—and it got stranger as it evolved. The decisive break with classical physics came in 1927, when the young German physicist Werner Heisenberg arrived at the indeterminacy principle. Heisenberg found that one can learn either the exact position of a given particle or its exact trajectory, but not both. If, for instance, we watch a proton fly through a cloud chamber, we can by recording its track discern the direction in which it is moving, but in the process of plowing through the water vapor in the chamber the proton will have slowed down, robbing us of information about just where it was at any given instant. Alternately, we can irradiate the proton—take a flash photograph of it, so to speak—and thus determine its exact location at a given instant, but the light or other radiation we employ to take the photograph will knock the proton off its appointed rounds, depriving us of precise knowledge of where it would have gone had we left it alone. We are, therefore, limited in our knowledge of the subatomic world: We can extract only partial answers, the nature of which are decided to some extent by the questions we choose to ask. When Heisenberg calculated the inescapable minimum amount of uncertainty that limits our understanding of events on the small scale, he found that it is defined by nothing other than h, Planck’s quantum of action.

The Scale of the Known Universe

Radius (meters)

Characteristic Objects

1026

Observable universe

1024

Superclusters of galaxies

1023

Clusters of galaxies

1022

Groups of galaxies (e.g., the Local Group)

1021

Milky Way galaxy

1018

Giant nebulae, molecular clouds

1012

Solar system

1011

Outer atmospheres of red giant stars

109

Sun

108

Giant planets (e.g., Jupiter)

107

Dwarf stars, Earthlike planets

105

Asteroids, comet nuclei

104

Neutron stars

1

Human beings

10−2

DNA molecules (long axis)

10−5

Living cells

10−9

DNA molecules (short axis)

10−10

Atoms

10−14

Nuclei of heavy atoms

10−15

Protons, neutrons

10−35

Planck length: Quantum of space; radius of “dimensionless” particles in string theory

Quantum indeterminacy does not depend upon the design of the experimental apparatus employed to investigate the subatomic world. It is, so far as anyone can tell, an absolute limitation, one that the most wizardly scholars of an advanced extraterrestrial civilization would share with the humblest string-and-sealing-wax physicist on Earth. In classical atomic physics it had been assumed that one could, in principle, measure the precise locations and trajectories of billions of particles—protons, say—and from the resulting data make exact predictions about where the protons would be at some time in the future. Heisenberg showed that this assumption was false—that we can never know everything about the behavior of even one particle, much less myriads of them, and, therefore, can never make predictions about the future that will be completely accurate in every detail. This marked a fundamental change in the world view of physics. It revealed that not only matter and energy but knowledge itself is quantized.

The more closely physicists examined the subatomic world, the larger indeterminacy loomed. When a photon strikes an atom, boosting an electron into a higher orbit, the electron moves from the lower to the upper orbit instantaneously, without having traversed the intervening space. The orbital radii themselves are quantized, and the electron simply ceases to exist at one point, simultaneously appearing at another. This is the famously confounding “quantum leap,” and it is no mere philosophical poser; unless it is taken seriously, the behavior of atoms cannot be predicted accurately. Similarly, we saw earlier, it is by virtue of quantum indeterminacy that protons can leap the Coulomb barrier, permitting nuclear fusion to occur at a sufficiently robust rate to keep the stars shining.

Those who find such considerations nonsensical are in good company; as Niels Bohr remarked, when one of his students at Copenhagen complained that quantum mechanics made him giddy, “If anybody says he can think about quantum problems without getting giddy, that only shows he has not understood the first thing about them.”2 The reason, however, is simply that we human beings, having grown up in the macroscopic world, tend to think of things in terms of macroscopic similes—subatomic particles are like buckshot, light waves are like waves in the ocean, atoms are like little solar systems, and so forth—and these similes break down on the microscopic scale.

Our mental pictures are drawn from our visual perceptions of the world around us. But the world as perceived by the eye is itself exposed as an illusion when scrutinized on the microscopic scale. A bar of gold, though it looks solid, is composed almost entirely of empty space: The nucleus of each of its atoms is so small that if one atom were enlarged a million billion times, until its outer electron shell was as big as greater Los Angeles, its nucleus would still be only about the size of a compact car parked downtown. (The electron shells would be zones of insubstantial heat lightning, each a mile or so thick, separated by many miles of space.) Nor, to return to the old classical metaphor, does a cue ball strike a billiard ball. Rather, the negatively charged fields of the two balls repel each other; on the subatomic scale, the billiard balls are as spacious as galaxies, and were it not for their like electrical charges they could, like galaxies, pass right through each other unscathed.

The quantum revolution has been painful, but we can thank it for having delivered us from several of the illusions that afflicted the classical world view.

One such was the delusion of apartness—the assumption that man is separate from nature and that acts of observation can, therefore, be conducted with complete objectivity. Traditionally, scientists were free to think of themselves as passive observers, sealed off by a pane of laboratory glass or a telescope’s lens from the outer world they examined. But on the microscopic level, every act of observation is disruptive—countless photons of starlight die upon the eye, protons smash into accelerator targets—and the manner in which we choose to make the observation (to “collapse the wave function,” as the physicists say) influences the results of the interaction. Subatomic particles sometimes resemble particles, sometimes waves, depending upon how we examine them. They are not “really” one or the other—and, in any event, the two images are mathematically equivalent. Rather, they are participants in an act of observation, the nature of which influences the qualities they present to us. Quantum physics obliges us to take seriously what had previously been a more purely philosophical consideration: That we do not see things in themselves, but only aspects of things. What we see in an electron path in a bubble chamber is not an electron, and what we see in the sky are not stars, any more than a recording of Caruso’s voice is Caruso. By revealing that the observer plays a role in the observed, quantum physics did for physics what Darwin had done in the life sciences: It tore down walls, reuniting mind with the wider universe.

Likewise with the dilemma of strict causation. Classical physics was deterministic: If A, then B; the bullet fired at the window shatters the glass. On the quantum scale this is only probably true: Most of the particles in the bullet encounter those of the glass, but some go elsewhere, and the trajectory of any one of them can be predicted only by invoking the statistics of probabilities. Einstein was deeply troubled by this aspect of the new physics. “God does not play dice,” he said, and he argued that the indeterminacy principle, though useful in practice, does not represent the fundamental relationship between mind and nature. As he wrote to his friend and colleague Max Born:

I find the idea quite intolerable that an electron exposed to radiation should choose of its own free will, not only its moment to jump off, but also its direction. In that case, I would rather be a cobbler, or even an employee in a gaming-house, than a physicist.3

Einstein presented Bohr with a series of thought experiments aimed at disproving the theory of quantum indeterminacy. He was then near the peak of his powers, and his ideas were often startling in their originality and ingenuity, but Bohr and his students found flaws in them all. Nothing in nature, then or now, indicates that the universe is built upon a strictly deterministic underpinning, and no philosopher has been able to prove that we need to believe in hidden, deterministic mechanisms—“hidden variables”—that produce no observable results.

Defeated in battle if unbowed in the greater campaign, Einstein took refuge in the long view: “Quantum mechanics is certainly imposing,” he told Born, “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.”4 Ultimately, Einstein insisted, he would be proved right: “I am quite convinced that someone will eventually come up with a theory whose objects, connected by laws, are not probabilities but considered facts.”5

That might conceivably be so, but it is not clear why we should wish it to be so. Strict causation, for all its classical pedigree, was ultimately a monstrous doctrine. Consider its stark formulation by the French mathematician Pierre-Simon de Laplace:

An intelligence knowing, at a given instance of time, all forces acting in nature, as well as the momentary position of all things of which the universe consists, would be able to comprehend the motions of the largest bodies of the world and those of the lightest atoms in one single formula, provided his intellect were sufficiently powerful to subject all data to analysis; to him nothing would be uncertain, both past and future would be present in his eyes.6

What was there here worth clinging to, against the hard evidence of quantum physics? The invocation of an all-knowing intelligence, which could only be that of God? The depiction of men as machines, deprived of free will? The pretense that every occurrence, from the radioactive decay of a barium atom to the Battle of Hastings, was fated to occur just when and how it did, in a universe devoid of originality and surprise? We are free (or fated) to answer, none of the above, and to recoil from Laplace’s deterministic vision with a revulsion just as deep as Einstein’s over Bohr’s interpretation of Heisenberg. Quantum indeterminacy may have nothing to do with human will, but as a matter of philosophical taste there are good reasons to celebrate the return of chance to the fundamental affairs of the world.

And, of course, the test of a scientific theory has to do less with whether one finds it philosophically palatable than with whether it works. Quantum physics works. It depicts the world as an assembly of animated fields, and the field equations are often too abstract to seem familiar, but they tell the story of the subatomic world more accurately than do the homier metaphors to which the prior intellectual history of our species had accustomed us.

Not that the quantum precept escaped without its share of growing pains. Far from it: In charting the unfamiliar terrain of the small, its practitioners embroiled themselves in misconceptions and perplexities that made the astronomers’ earlier bewilderments over spiral nebulae and the age of the sun look inviting by comparison. Quantum numbers and airy abstractions were hurled at tough problems with both hands, until microphysics in its darkest days was justly and scathingly compared to Ptolemaic cosmology, with its wheels within wheels and its abandonment of all but the most abstract claim to model the real world. There were too many particles, so many that physicists eventually were obliged to consult a booklet, the Particle Properties Data Handbook, just to keep track of them. “If I could remember the names of all these particles I would have been a botanist,”7 fumed Enrico Fermi, and the physicist Martinus Veltman later mused that “as the number of particles increases all we are doing is increasing our ignorance.”8 There were, for some decades, too many theories as well, and many inconsistencies among them. A few physicists became so frustrated that they quit science altogether.

Yet it is turmoil and confusion and not calm assurance that mark the growth of the mind, and when the dust began to clear, quantum physics emerged as not only a vital and rapidly developing field of science, but as one of the greatest intellectual achievements in the history of human thought. Though by no means complete, it was now able to make accurate predictions about an imposing array of phenomena, from optics and computer design to the shining of the stars, and to do so in terms of theoretical structures that could already be seen to possess a beauty and scope worthy of the universe they sought to describe.

The patchwork of theories that came to constitute quantum physics by the final quarter of the century was known collectively as the standard model. Viewed by its lights, the world is composed of two general categories of particles—those of fractional spin (Vi), called fermions, after Enrico Fermi, and those of integer spin (0, 1 or 2), called bosons, after Satyendra Nath Bose, who, with Einstein, developed the statistical laws that govern their behavior.*

Fermions comprise matter. They obey what is called the Pauli exclusion principle, enunciated by the Austrian physicist Wolfgang Pauli in 1925, which establishes that no two fermions can occupy a given quantum state at the same time. It is owing to this characteristic of fermions that only a limited number of electrons can occupy each shell in an atom, and that there is an upper limit to the number of protons and neutrons that can be assembled to form a stable atomic nucleus. Protons, neutrons, and electrons are all fermions.

Bosons convey force. To hazard a hyperbolic image, one might think of the fermions as akin to ice skaters who are busy tossing medicine balls back and forth; the medicine balls are bosons, and the change in the trajectory of each skater that occurs when they throw or catch the balls betrays, in Newtonian language, the presence of a force.* Bosons do not obey the exclusion principle, and consequently several different forces can operate in the same place at the same time: The atoms in this book, for instance, are simultaneously subject both to the electrical attraction among their protons and electrons and to the gravitational force of the earth.

There are four known fundamental forces (or classes of interactions, in quantum terminology)—gravitation, electromagnetism, and the strong and weak nuclear forces. Each plays a distinct role. Gravitation, the universal attraction of all particles of matter for one another, holds each star and planet together, and retains planets in their orbits around stars and stars in their orbits in galaxies. Electromagnetism, the attraction of particles with opposite electrical or magnetic charge for one another, produces light and all other forms of electromagnetic radiation, including the long-wavelength radiation called radio waves and the short-wavelength radiation called X rays and gamma rays. Electromagnetism also bundles atoms together as molecules, making it responsible for the structure of matter as we know it. The strong nuclear force binds protons and neutrons (known as nucleons) together in the nuclei of atoms, and binds the elementary particles called quarks together to form each nucleon. The weak nuclear force mediates the process of radioactive decay, the source of energy emitted by the chunks of radium studied by Rutherford and the Curies.

The differing behavior of the forces is reflected in the nature of the bosons that convey them. Gravitation and electromagnetism are infinite in range—which is why our galaxy “feels” the gravitational pull of the Virgo Cluster of galaxies, and why we can see starlight coming from billions of light-years away—because the bosons that carry these two forces, known respectively as gravitons and photons, have zero mass. The weak nuclear force has a very short range because the particles that convey it, called weak bosons, are massive. The strong force is carried by particles called gluons; they are massless, but have the curious and quite beautiful property of increasing, not decreasing, in strength when the quarks between which they are exchanged move apart: A quark that starts to stray from its two companions soon finds itself hauled back by a gluon lattice, like a finger trapped in a woven Chinese finger-cuff. Consequently quarks in the contemporary universe remain bound up inside their protons and neutrons; no free quark has yet been observed, though they have been searched for in everything from accelerator collisions to moon dust to oysters (which filter seawater and so might catch stray quarks).

The four fundamental forces known to operate in nature today are here depicted in terms of characteristic interactions. In a typical electromagnetic interaction, a pair of electrons (symbolized e) exchange a photon. In the weak force interaction portrayed here, a neutron (n) decays into a proton (p) via the exchange of a weak boson; the event also converts a positron (e+) into a neutrino (v). In a strong interaction, quarks (q) exchange a gluon. Gravitation involves the exchange of a graviton between any two massive particles (m).

The fermions that constitute matter, though notoriously numerous and varied, can all be classified as either quarks, which respond to the strong force, or leptons, which do not. Leptons are light particles; their ranks include the electrons that orbit atomic nuclei. Quarks are the building blocks of protons and neutrons: Three quarks make a nucleon.* There are thought to be six varieties each of leptons and quarks. Neither quarks nor leptons show any sign of having an internal structure, though their anatomy has been probed on scales down to some 10−18 meter. This is to say that if a single atom were enlarged to the dimensions of the earth, any subcomponents of quarks and leptons would have to be smaller than a grapefruit to have escaped detection. So quarks and leptons are the bedrock particles of matter, so far as we know.

The Building Blocks of Matter

Particle

Description

Examples

Leptons

“Dimensionless” (i.e., radius < 10−35 meter); do not participate in the strong force.

Electron
Muon
Neutrino

Quarks

Small (< 10−18 meter) but finite in size; do participate in the strong force.

Hadrons (three quarks) Mesons (two quarks)

Trios of quarks are thought to compose the nucleons—protons and neutrons—that in turn constitute the nuclei of atoms. According to this model, a proton consists of two “up” quarks, each of which carries an electrical charge of +⅔, and one “down” quark, which has a charge of -⅓ the total charge of the proton therefore is 4/3 - 1/3 = + 1. A neutron consists of two down quarks and one up quark; consequently its charge equals 0.

Every fundamental—meaning simple—event in the universe can in principle be interpreted by means of the standard model. When a child looks at a star, photons of starlight strike electrons in the outer atoms of the receptors of the child’s retina, setting off further electron interactions that convey the image to the brain; all this is the work of electromagnetism. The nuclear processes that produced the starlight are generated by the strong and weak nuclear forces at work inside the star. And gravitation is the force that holds the star together and keeps the child’s feet (if only intermittently) on the ground.

Electromagnetic energy is generated by natural processes across a wide range of wavelengths, including gamma rays and X rays from gas falling into black holes, light from stars, microwaves from the cosmic background radiation, and radio from interstellar clouds.

The scientific accounts of how the various particles of matter behave under the influence of three of the four forces are known as relativistic quantum field theories. They are so called because they incorporate both the quantum precept and the special theory of relativity, in order to take into account such effects as increases in the mass of particles traveling at close to the velocity of light. Electromagnetism is described, with exquisite accuracy, by the theory of quantum electrodynamics, or QED. The strong force is described by quantum chromodynamics, or QCD. (The “chromo” comes from a quantum number, whimsically called “color,” that plays a role for quarks comparable to that played by electrical charge in the affairs of electrons.) The weak force, as we will see, has recently come under the purview of the “electroweak” unified theory.

Gravitation remains the odd man out. Its workings are still described by Einstein’s general theory of relativity, which is a classical theory, meaning that it does not incorporate the quantum principle. This does not cause problems under most conditions, but relativity breaks down when it comes to extremely intense gravitational fields, like those inside a black hole or in the universe at the very beginning of its expansion. There the curvature of space goes to infinity, at which point the theory tips its hat and makes a graceful exit. There was, by the late 1980s, still no quantum theory of gravitation with which to supplement general relativity. One reason for this is that gravity is weak. Individual subatomic particles normally are so little influenced by the gravitational force exerted by their colleagues that gravity can be ignored. Another reason is that gravitational interactions are interpreted, through Einstein’s general theory of relativity, as resulting from the geometry of space itself. The “gravitons” thought to convey gravitation must therefore dictate the very shape of space, and for a theory to elucidate how they manage that is no simple matter.

Particle physics today is a house divided, and though the standard model gets results, few imagine that it represents the last word on the subject. The model is a crazy quilt, not a mándala. To fire it up on all cylinders requires inputting some seventeen separate parameters, numbers the values of which have been determined experimentally but whose fundamental significance is not yet understood. We know, for instance, that the electrical charge carried by an electron is equal to 1.6021892 × 10−19 coulomb, and that the mass of the proton is 938.3 MeV, equal to 0.9986 the mass of the neutron, but nobody knows why these numbers are as they are and not otherwise. The roots of discontent with the standard model were described this way by Leon Lederman, the director of the Fermilab particle accelerator in Illinois:

The trouble we’re in now is that the standard model is very elegant, it’s very powerful, it explains so much—but it’s not complete. It has some flaws, and one of its greatest flaws is aesthetic. It’s too complicated. It has too many arbitrary parameters. We don’t really see the creator twiddling seventeen knobs to set seventeen parameters to create the universe as we know it. The picture is not beautiful, and that drive for beauty and simplicity and symmetry has been an unfailing guidepost to how to go in physics.9

So it was that physicists late in the century were still searching for a simpler and more efficient account of the fundamental interactions. The object of their quest went by the name “unified” theory, by which they usually meant a single theory that would account for two or more of the forces currently handled by separate theories. They were guided, to be sure, by experimental data and by the challenges immediately at hand—the theorist resembles, as Einstein said, an “unscrupulous opportunist,” more often trying to find a specific solution to an immediate problem than to write a grand explication of everything. But they were guided as well, as Lederman mentions, by the hope that their accounts of nature could more nearly approach the elegant simplicity and superlative creativity of nature herself.

*The “spin” referred to here is a familiar, mechanical spin, though it is quantized, and is measured in terms of h, the quantum of action.

*The medicine balls are purely repulsive, as in the interaction between two electrons or other fermions of like charge. For attractive forces (as between a proton and an electron), imagine that the bosons are elastic bands that stretch when the skaters move apart, drawing them together. For the exclusion principle, let each skater wear a hoopskirt that forbids their colliding…. And that is quite enough of that.

*The name “quark” was conferred by Murray Gell-Mann, the Caltech physicist who came up with the idea. It comes from a line in James Joyce’s Finnegans Wake, “Three quarks for Muster Mark!” George Zweig, a physicist at Caltech who arrived at the same idea independently, called the entities “aces,” a term that lost out to Gell-Mann’s, perhaps because there are four aces, not three, in a deck of cards.