Twentieth Century and Beyond

38. Photoelectric Effect (1905)

Figure 62

Figure 62 depicts the photoelectric effect. Light (upper left) strikes a surface (bottom), breaks loose some of its electrons, and ejects them (upper right) from the surface. Soon after its discovery in 1887, scientists began exploring the curious properties of the photoelectric effect. Chief among them is that only sufficiently high frequency light can eject electrons—so-called photoelectrons—from the surface. How high a frequency is required depends on the composition of the surface. Most metals, for instance, require frequencies at least as high as that of ultraviolet light. If the frequency is too low, for instance, if its color is too red, no photoelectrons are produced no matter how intense the light. Then, in 1902, Philipp Lenard (1882–1947) discovered that when photoelectrons are produced their kinetic energy increases with the frequency of light that produced them and is independent of its intensity.

This behavior is impossible to explain in terms of the wave theory of light. All simple waves are characterized by a frequency, which determines how quickly wave crests arrive at a particular point, and by an amplitude, whose square is directly proportional to the wave intensity. Ocean waves, for instance, have these properties.

Indeed, Arthur Holly Compton (1892–1962) once made clear the absurdity of low-amplitude light waves ejecting electrons from a metal with the following simile: “There was once a sailor on a vessel in New York harbor who dived overboard and splashed into the water. The resulting wave, after finding its intricate way out of the harbor, at last found its way across the ocean, and a part of it entered the harbor at Liverpool. In this harbor there happened to be a second sailor swimming beside his ship. When the wave reached him, he was surprised to find himself knocked by the wave up to the deck.” Here Compton actually makes two comparisons. The first two sentences refer to the creation of electromagnetic radiation by electrons striking a metallic surface (see essay 41) while the last two sentences refer to a single electron absorbing, photon-like, low-amplitude electromagnetic radiation.

In 1905 Albert Einstein, then a twenty-six-year-old Swiss patent inspector, devised a simple explanation of the photoelectric effect. According to Einstein, light has both a wave-like and a particle-like character. Light must be wave-like because Maxwell’s wave theory of light had been tremendously successful. Yet, Einstein argued, in producing photoelectrons, the energy of light behaves as if it is concentrated in bundles or quanta (later called photons). The energy of a photon is proportional to the frequency of the wave with which it is associated. The proportionality constant is called Planck’s constant after the physicist Max Planck (1858–1947) who first measured its value. Greater light intensity simply means greater numbers of photons.

Since a photon is localized, one photon interacts with only one electron. Part of the photon energy goes into overcoming the forces that hold the electron in the surface while the other part produces the kinetic energy of the electron. Symbolically, . Thus, if the energy of the photon is not larger than the energy required to dislodge an electron, that is, if , no photoelectrons are created. The data available to Einstein supported his light quantum or photon interpretation of the photoelectric effect.

In 1900 Planck derived an accurate description of equilibrium or blackbody radiation, that is, a description of the electromagnetic waves contained within a cavity whose walls absorb and emit those waves. In doing so, he supposed that the material composing the cavity walls absorbs and emits electromagnetic wave energy only in quantized chunks of energy . Einstein’s explanation of the photoelectric effect shifted attention away from the way blackbody radiation interacts with the material composing the cavity walls to the radiation itself.

The title of Einstein’s 1905 paper on the photoelectric effect, “On a Heuristic Point of View about the Creation and Conversion of Light,” signals Einstein’s cautious approach. Photons are a mere heuristic, that is, a useful but ultimately provisional, approach to the photoelectric effect. Einstein came to understand that photons and other quantum phenomena presume a probabilistic dynamics. (The creation of a photoelectron is not completely predictable.) But Einstein never accepted as final the probabilistic interpretation of physics that the quantum revolution demanded.

Planck was not pleased with photons for a different reason. He asserted that if photons were accepted, “the theory of light would be thrown back by centuries”—presumably back to the seventeenth century when the adherents of light particles (following Newton) and of light waves (following Huygens) debated the issue. Thus, Planck understandably resisted the wave-particle duality of light. But wave-particle duality was here to stay. Sometimes it is asserted that the current theory of light, called quantum electrodynamics, as developed after World War II, decides the question in favor of particles. If so, these are very strange particles that carry along with them information usually ascribed to waves.

Robert Millikan (1868–1953) performed experiments in 1915–1916 that confirmed Einstein’s explanation of the photoelectric effect. Einstein received the 1921 Nobel Prize in Physics (in 1922) “especially for his discovery of the law of the photoelectric effect,” and Millikan received the 1923 Nobel Prize in Physics, in part, for his work in confirming that law. Einstein, however, was never satisfied with the photon concept. In 1951 he wrote, “All these 50 years of pondering have not brought me any closer to answering the question, ‘What are light quanta?’”

39. Brownian Motion (1905)

Figure 63

Jean Perrin’s (1870–1942) experimental work ended the long debate over whether matter was continuously divisible or not, that is, whether or not atoms exist. Perrin received the 1926 Nobel Prize in Physics for deciding the question in favor of atoms. Among his crucial experiments are those that confirmed Albert Einstein’s theory of Brownian motion—a theory that makes use of atoms and molecules.

Brownian motion—that irregular, back-and-forth, wandering motion of microscopic particles immersed in a liquid—was first observed in 1827 in grains of pollen in water. After showing that neither currents in the water nor the water’s evaporation caused the irregular motion of the pollen grains, the Scottish botanist Robert Brown (1773–1858) supposed that, in this motion, he had discovered the source of vitality common to all forms of life. But upon observing the same irregular motion in particles of fossilized wood, volcanic ash, ground glass, granite, and even a fragment of the Sphinx, Brown gave up this idea.

Investigators following Brown had, by the early twentieth century, identified the cause of Brownian motion in the impacts delivered to the microscopic particles, Brownian particles, by the molecules composing the surrounding fluid. All that was needed was a quantitative theory of the phenomenon whose predictions could be tested. Einstein provided that theory in 1905. According to Einstein, a group of Brownian particles, all starting from the same point, disperses indifferently in all directions. Also a Brownian particle’s mean squared distance from its starting point increases as the first power of the time rather than, as one might expect of uniformly moving particles, as the second power . Brownian particles randomly diffuse rather than deterministically drift.

In confirming Einstein’s theory, Perrin constructed a number of diagrams, like figure 63, in which he marked the position of a Brownian particle (often a particle of plant resin) at equal intervals (typically every thirty seconds) and connected successive positions with a straight line. The lengths and numbers of these displacements confirmed the statistical predictions of Einstein’s theory. The microscopes, with which Brownian particles are seen, in effect make visible the ordinarily invisible world of atoms and molecules.

However, a common mistake is to associate a single line segment (see figure 63) with a single molecular impact. Perrin knew that, if instead of every 30 seconds, he had marked the position of the particle a thousand times more frequently, that is, every 0.03 seconds, he would have created a diagram, except for its size, much like this one. Every tiny displacement of a Brownian particle hides within itself a pattern of random displacements that mimics the larger pattern. The displacements of a Brownian particle are said to be scale invariant.

Also in 1905 Einstein created the theory of special relativity and originated the concept of a quantum of light or photon. Einstein continued, during the next twenty years of his life, to contribute to the quantum revolution in physics. But eventually he turned his back on quantum theory. In particular, Einstein rejected the probabilistic interpretation of quantum phenomena—an interpretation that rapidly gained ground after Max Born (1882–1970) introduced it in 1926. Yet Einstein began his career by embracing a statistical, that is, a probabilistic, description of Brownian motion. Why then did he reject a probabilistic description of quantum phenomena?

Einstein was comfortable using probability to describe the incompleteness of our knowledge of the natural world. We are ignorant, but neither necessarily nor completely so. According to Einstein, probabilities, properly used, quantify the degree of knowledge and ignorance that follows from our finitude. On the other hand, Max Born’s probabilistic interpretation of quantum mechanics radically limits what we can, in principle, know. Einstein rejected Born’s use of probability. Rather, such limitation, Einstein believed, simply means that our theories are incomplete. Einstein stubbornly maintained that the fundamental laws of nature (now unknown to us) must be deterministic (not probabilistic or random) and that complete knowledge of an isolated part of the physical world is possible.

In spite of their deep disagreement, Born and Einstein remained lifelong friends. “I at any rate am convinced that He [God] is not playing at dice,” Einstein famously wrote to Born in 1926. Many years later Born said of Einstein: “He has seen more clearly than anyone before him the statistical background of the laws of physics, and he was a pioneer in the struggle for conquering the wilderness of quantum phenomena. Yet later, when out of his own work a synthesis of statistical and quantum principles emerged which seemed to be acceptable to almost all physicists, he kept himself aloof and skeptical. Many of us regard this as a tragedy—for him, as he gropes his way in loneliness, and for us who miss our leader and our standard bearer.” Born went on to say that their disagreement was “based on different experiences in our work and life. But, in spite of this, he remains my beloved master.”

40. Rutherford’s Gold Foil Experiment (1910)

Figure 64

The concept of an atom as a tiny, indivisible building block of the material world is at least as old as the fifth century BCE. Imagine dividing a chunk of matter into smaller and smaller pieces until eventually producing an object that could no longer be divided. This is appropriately an atom, since the very word means uncuttable. Lucretius, a first-century BCE Roman poet, took comfort in the idea that human affairs were mere surface phenomena. Ultimately, all was “atoms and the void.”

Atoms also comforted philosophers because the existence of atoms solved, in part, a philosophical problem. One observes that all things seem to change. But since change is a relative concept, we are moved to ask: “Change with respect to what?” “How can we evaluate change except relative to some unchanging standard that does not itself change?” “How does one account for both change and permanence?” Atoms provide one answer. Atoms are permanent. It is their spatial relationship to one another that changes.

Isaac Newton endowed Lucretius’s invisible atoms with the properties of quite visible objects: mass, weight, and the ability to deliver an impact. Daniel Bernoulli (1700–1782) used these Newtonian concepts to explain how and to what extent a gas composed of atoms can exert a pressure on its container walls. But these were speculations, even if essentially correct ones.

The first to call attention to empirical evidence for the existence of atoms was the English chemist John Dalton (1766–1844). Dalton’s evidence consisted of the regular proportions of the mass of homogeneous and unanalyzable substances or chemicals that combine with one another. While Dalton’s work reinforced the traditional picture of the atom as a solid, indivisible object, he also brought something new to the idea: each element has its own kind of atom, and atoms of the same kind are identical. Dalton’s atom remained plausible throughout much of the nineteenth century even as the number of known elements more than doubled from his day to that of the youth of Ernest Rutherford (1871–1937). Rutherford’s comment “I was brought up to look at the atom as a nice hard fellow, red or grey in colour according to taste” must have expressed what many of his generation believed.

But atoms are not so simple. Most importantly, atoms are not even atoms in the sense of being indivisible. For late in the nineteenth century, certain kinds of atoms were found to be radioactive, that is, to spontaneously emit massive particles or electromagnetic energy or both. Evidently, atoms have parts and some atoms emit their parts: alpha, beta, and gamma rays as they were then called. We now know that alpha rays are the nuclei of helium atoms, two protons and two neutrons stuck together; that beta rays are electrons; and that gamma rays are quite short-wavelength, and thus quite high-energy, electromagnetic radiation. Radioactive atoms must in some way contain these various “rays.”

Joseph John Thomson (1856–1940), who had earlier discovered that beta rays are electrons, in 1904 quite plausibly suggested that all atoms contain a number of electrons. In order to provide for the charge neutrality of most atoms, Thomson imagined that these atomic electrons reside within a sphere of positively charged, atomic fluid that leaves the entire atom electrically neutral. This model of atomic structure became known as the “plum pudding” or “currant bun” model after edible concoctions of the day. Presumably, the plums or the currants are electrons, while the pudding or the bun dough is the positive fluid that surrounds and neutralizes these electrons.

Thomson’s model did not last long. In 1910 Ernest Rutherford, his associate Hans Geiger (1882–1945), and Geiger’s student Ernest Marsden bombarded a thin gold foil with the alpha particles (helium nuclei) emitted from a sample of naturally radioactive radium. One day Geiger reported to Rutherford that the gold foil deflected alpha particles back toward their source.

Since an alpha particle is eight thousand times more massive than an electron, an electron residing within an atom could no more deflect an alpha particle from its straight-line path than a fly could deflect a rolling bowling ball. Neither could the whole mass of an atom deflect an alpha particle if, as was supposed, that mass was distributed uniformly throughout the atom’s volume. Only if most of the gold atom’s mass was concentrated within an essentially point-like core or nucleus would a few alpha particles, each directed squarely at a nucleus, bounce back toward their source. Rutherford understood all this and knew what Geiger and Marsden’s result implied. Some years later he remarked, “It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”

Figure 64 illustrates the essential physics of Rutherford, Geiger, and Marsden’s experiment. Several alpha particles approach the gold foil from the left. The foil is represented by an array of gold nuclei shown here as dots. In fact, Rutherford’s gold foils were about four thousand atoms across. Most alpha particles pass through the foil without deflection, but a few bounce directly back.

The orbit of an alpha particle scattering from a gold nucleus is structurally identical to the orbit of a comet approaching, passing around, and then receding from the sun as illustrated in figure 65. (The alpha particle and nucleus are on the left and the comet and Sun are on the right in the diagram.) Such trajectories have been understood since the time of Newton. Rutherford had only to adapt Newton’s general mathematical description to his particular experiment to quantify the observed scattering.

Figure 65

Rutherford’s gold foil experiment showed that an atom is composed of a small nucleus and attendant electrons that orbit throughout a much larger volume around that nucleus. A typical nuclear radius is to the radius of its atom as the radius of a beach ball is to the radius of the earth. Apparently, Lucretius’s void is inside as well as outside the atoms that make up our world.

41. X-rays and Crystals (1912)

Figure 66

On November 8, 1895, while experimenting with a beam of electrons created within an evacuated glass tube, Wilhelm Conrad Röntgen (1845–1923) accidentally discovered certain “rays” that propagated beyond the end of his tube. These rays seemed to travel in straight lines, made florescent materials glow, and exposed photographic plates. Because the rays traveled through flesh but not through bone, Röntgen used them to photograph the bones in his wife’s hand. He called them X-rays.

Röntgen’s X-rays were immediately hailed as a new method of photography. The New York Times covered Röntgen’s discovery early in 1896. That year more than one thousand professional and popular articles and fifty books and pamphlets were published on X-rays. Röntgen, however, was not pleased with the publicity and complained, “I could not recognize my own work in the reports.” But he had started something new. That spring the young Ernest Rutherford wrote to his fiancée that “every Professor in Europe is now on the warpath” trying to understand X-rays.

That understanding came slowly, but by 1912 evidence was accumulating that X-rays were very high frequency, short-wavelength electromagnetic waves. The left half of figure 66 depicts this understanding. Electrons are accelerated to high speeds and collide with the end of an evacuated glass tube. In the collision short-wavelength, electromagnetic waves—the X-rays—are created that carry forward the energy and momentum of the electrons. Yet not everyone was convinced. Some continued to believe that X-rays were particles.

Max von Laue (1879–1960), a near contemporary and friend of Albert Einstein, proposed an experiment (shown in the right half of the diagram) whose result secured the case for waves. Early in 1912, while listening to a student explain his research on the interaction of long-wavelength electromagnetic waves with the atoms or molecules that compose a crystal, von Laue asked himself, “Why not shine X-rays on a crystal?”

Since the spacing between the atoms or molecules in a typical crystal (10^-8 cm) is only a little larger than the estimated wavelength of X-rays (10^-9 cm), X-ray waves should, after passing through the crystal, produce an interference pattern, that is, a pattern of constructively and destructively superposing waves. This interference pattern should be similar to that produced by visible light passing through a regular series of parallel slit-shaped openings called a diffraction grating. In both cases, the interference pattern produced depends upon a wave property called diffraction, that is, a departure from straight-line propagation.

Although X-ray interference is, in its geometry, a smaller-scale version of visible light interference, physically the two cases are quite different. X-rays pass through a crystal by vibrating the charged particles in the atoms (or molecules) composing the crystal. These atoms, in turn, radiate new waves that pass on the interaction from atom to atom until the very last atoms on the far side of the crystal radiate like a string of regularly spaced radio beacons. Visible light, on the other hand, passes freely though the slits of a diffraction grating and is absorbed or reflected by the material surrounding the slits.

Von Laue convinced two colleagues, Walter Friedrich and Paul Knipping, to test his idea. Their initial experiment, with materials and equipment on hand, captured on film the X-ray interference pattern shown in figure 67. It consists of several dark splotches, each indicating the constructive interference of diffracted X-rays, surrounding a single, larger dark patch, indicating the remains of the original ray. This image attracted favorable attention and secured funding for more refined experiments that fully confirmed von Laue’s detailed analysis. Von Laue, Friedrich, and Knipping published their first results in June 1912.

Figure 67

Von Laue’s idea was brilliant and its confirmation complete. In place of pursing a single idea for many years, he had “suddenly ... perceived the way which subsequently proved to be the shortest path to success.” The Nobel committee awarded Von Laue its 1914 Prize in Physics for “his discovery of the diffraction of X-rays by crystals.” Von Laue’s rise, from privatdozent (junior faculty with no regular salary) to Nobel laureate, took less than three years.

Von Laue survived long enough to be tested by the fires of Nazism and World War II. He spoke out publicly against the persecution of the Jews and the promotion of a “German science” that, for instance, rejected relativity because Einstein was Jewish. He remained in Germany during the war, an outspoken critic of the Nazis, secretly helping his Jewish colleagues emigrate and then escape. After the war von Laue helped rebuild Germany’s institutions of science. Then, in 1960, a motorcycle struck and overturned the car he was driving to work. In the few days left to him, von Laue composed his own epitaph: “He died trusting in God’s mercy.”

42. Bohr’s Hydrogen Atom (1913)

Figure 68

The Danish public knew Niels Bohr (1885–1962) as a soccer player before it knew him as a physicist. Crucial to the evolution of Bohr’s persona from sports hero to Nobel laureate was the postdoctoral year (1911–1912) he spent in England studying atomic physics, first with John Joseph Thomson at the University of Cambridge and then with Ernest Rutherford at the University of Manchester. Recall that the earlier work of Max Planck (1900) and Albert Einstein (1905) had suggested that the concepts of classical physics were not sufficient for understanding the atom.

Bohr set for himself the task of understanding the simplest of all atoms, the hydrogen atom. Initially he was uncertain about how to proceed. Rutherford’s gold foil experiment had implied that most of the mass of an atom resides in a tiny, positive core or nucleus. And because electrical and gravitational forces were similarly structured, it was natural for Bohr and others to suppose that the electron in a hydrogen atom moves round its nuclear proton in a circular or elliptical orbit just as a planet moves around the sun. The problem with this planetary picture of the atom is simple and dramatic. According to classical concepts, an electron that orbits a nucleus will radiate for the same reason that an electron moving back and forth along a radio antenna will radiate. Both are accelerating and, therefore, both radiate energy. Consequently, an atomic electron will lose energy and spiral into the nucleus. The atom will quickly collapse.

Yet stable atoms do exist. And by 1912 scientists knew that the diameter of a hydrogen atom was about 10^-8 centimeters. Furthermore, the frequencies and wavelengths of the light that could be absorbed and emitted by atoms of different elements were known quite precisely and quantified in certain tantalizing, simple, yet unexplained formulas. Any successful model of the structure of the hydrogen atom would have to be consistent with these well-established facts.

Bohr’s working principle was to make the least modification needed to the classical physics of the hydrogen atom in order to account for its stability and its interaction with light waves. He implemented this principle by simply asserting that the hydrogen atom observes classical physics except that it does not radiate when its electron occupies one of a discrete set of special orbits. He called these special orbits stationary states. Bohr’s assertion, though quite unjustified, worked brilliantly.

Of course, in order to quantify his model, Bohr had to specify what makes an orbit a stationary state. He did this by requiring that in a stationary-state circular orbit the electron’s angular momentum—that is, the product of its radius, its mass, and its speed—is a multiple of the fundamental constant discovered by Planck during his study of blackbody radiation and now called Planck’s constant.

In order to illustrate the consequences of these assumptions, we number the allowed stationary-state circular orbits with an index , as illustrated in figure 68, so that, for example, and stand for the energy and radius of the first, most stable, ground, stationary-state orbit. In general the electron’s energy and its distance from the nucleus in a stationary state increase with increasing index . Only the three innermost, circular orbits of a hydrogen atom’s electron are shown in the diagram, but possible orbits extend out in ever larger, unevenly spaced, concentric circles.

According to Bohr, the hydrogen atom can absorb energy from light only by boosting its electron from a less energetic, lower, stationary state orbit into a more energetic, higher one—as shown in figure 69—and likewise can emit light energy only when an electron drops from a more energetic, higher, stationary state orbit into a less energetic, lower one. This hypothesis allowed Bohr to calculate the frequency of the light absorbed or emitted when the electron transitioned from one orbit to another—frequencies that exactly reproduced those observed.

Figure 69

Bohr’s model was quickly recognized as important. Rutherford’s assessment was typical: “While it is too early to say whether the theories of Bohr are valid, his contributions ... are of great importance and interest.” But Bohr and his contemporaries had less success in applying the model assumptions to multi-electron atoms. This failure should have been expected. For Bohr’s method depended upon using as much of classical physics as possible in describing an electron orbit. However, helium, the next simplest atom after hydrogen, is composed of three particles: one nucleus and two electrons. And unlike the classical two-body problem, the classical three-body problem cannot be exactly solved. The quantum revolution of the 1920s dismantled the very notion of an orbit of an atomic electron. Still, in 1913, the simplicity and success of Bohr’s model of the hydrogen atom forced physicists to take a close look at his model and ask themselves, “Why does it work so well?”

43. General Relativity (1915)

Figure 70

Each side in the Great War of 1914–1918 tried to bleed the other to death. Because newly developed machine guns and heavy artillery made traditional offensive tactics obsolete, furious battles achieved little or nothing of military value—only massive death. The Battle of Verdun, for instance, lasted nine months, created a million casualties, and left two depleted armies occupying much the same ground as before. By the time Germany sued for peace in the fall of 1918, a whole generation of “doomed youth,” in Wilfred Owen’s haunting words, had died “as cattle.”

The memory of the Great War, its chauvinism, its horror, and its futility, was still fresh on November 6, 1919—one year after the armistice—as the Royal Society and Royal Astronomical Society convened in London to announce observations that confirmed Einstein’s theory of general relativity. That English scientists had made the considerable effort necessary to test an esoteric theory of a German-speaking Swiss scientist was welcome news to a public weary of war.

The English scientists tested Einstein’s theory by placing themselves within the shadow cast by the moon as it passed in front of the sun during the total eclipse of May 29, 1919. On that date the oval-shaped shadow of total eclipse, some hundred miles across, traveled from the east coast of Brazil to the west coast of Africa. One team of observers led by the Royal Astronomer Andrew Crommelin was stationed at Sobral, Brazil, and the other led by the Cambridge physicist Arthur Eddington (1882–1944) was stationed on Principe Island off the west coast of Africa near present-day Gabon. Each team measured the angular separation of two stars as one of them passed near the edge of the obscured sun’s disc. When this separation was compared with earlier measurements of the same separation, the position of the star grazing the sun’s disc during total eclipse had shifted as if the sun had attracted its light—illustrated in figure 70 in exaggerated form.

That the sun can attract starlight was implicit in Newton’s theory of gravitation and his proposal that light is composed of tiny, massive particles traveling at high speed. Accordingly, Newton could have calculated the angle through which starlight is deflected in the circumstance illustrated in figure 70, but he did not. The first to do so, according to Newtonian principles, was Johann Georg von Soldner (1776–1833) who in 1801 predicted a deflection of 0.87 seconds of arc—somewhat less than 1/360th of a single degree of arc. (Note: One degree of arc is 1/360 of a complete circle.)

Einstein, like Newton, believed that light is composed of tiny, massive particles. A theory based simply on tiny, massive particles of light (however differently conceived by Newton and Einstein) and Newton’s theory of gravitational attraction leads to Soldner’s deflection of 0.87 seconds. However, something more is at work in the general relativistic description of space, time, and gravitation that Einstein proposed in 1915. That additional something is the idea that massive bodies curve space and time in their vicinity. When this curvature is accounted for, Einstein’s theory predicts a deflection of 1.74 seconds of arc—exactly twice that of Soldner’s prediction.

Crommelin and Eddington confirmed Einstein’s general relativistic prediction, not Soldner’s Newtonian one. Shortly after the public announcement of their results, the Times of London boldly declared that Einstein had “overthrown” Newtonian physics and the New York Times declared that he had “knocked out” Euclidean geometry. The cover of the popular Berliner Illustrirte Zeitung displayed a full-page photograph of a thoughtful Einstein. John Joseph Thomson (1856–1940), the discoverer of the electron, pronounced that “his [Einstein’s] was one of the greatest achievements of human thought.” Such coverage turned Einstein, who was already well known among physicists, into an icon of science.

That some of the consequences of the special and general theories of relativity are counterintuitive has contributed to Einstein’s long-lasting fame. Recall that general relativity sprang from special relativity—the latter a theory of moving clocks that run slow and moving meter sticks that shrink. Special relativity was and is a spectacular success. The daily, predictable operation of thousands of particle accelerators around the world attests to its correctness. Its generalization, the general theory of relativity, has been confirmed in more limited circumstances. Besides the deflection of starlight, general relativity explains, in part, the slow advance of Mercury’s closest approach to the sun and also the red shift of light emerging from massive bodies and the properties of black holes.

Yet Einstein did not set out to predict unusual phenomena. His motivation, according to the eminent physicist Subrah­manyan Chandrasekhar (1910–1995), was more aesthetic than empirical. His desire was for simplicity, system, and symmetry in physical theory rather than for successfully accounting for specific phenomena. Of course Einstein looked for and found applications of his theories, but in 1915 general relativity satisfied no outstanding empirical need.

Interestingly, what counts as a good theory has changed over time. Today general relativity has an odd reputation among physicists. While its successes cannot be denied, many are uncomfortable with the absence of a quantum theory of gravity, that is, uncomfortable with the absence of a quantum version of general relativity. This absence is felt more as a lack of conformity to current standards than as any failure of general relativity’s predictions. This is because the language of quantum mechanics has become the language of physics. And gravity alone among fundamental forces has resisted expression in that language.

44. Compton Scattering (1923)

Figure 71

Einstein invented the concept of light quanta in 1905 in order to account for the photoelectric effect—that is, for the capacity of ultraviolet light to eject electrons from metallic surfaces. According to his hypothesis, the energy in light is concentrated in bundles or quanta that are, on occasion, entirely and instantaneously transferred to a single electron. The energy in each quantum of light is determined by the frequency of the light wave with which it is associated where the proportionality constant is Planck’s constant.

Einstein’s explanation of the photoelectric effect was not experimentally confirmed until ten years after its proposal. Even then most physicists continued to resist the implication of Einstein’s explanation that light consists of quanta or photons as they would later be called. After all, the diffraction and interference of visible light only makes sense if light is composed of waves. Infrared, ultraviolet, and X-ray radiation are also waves—straightforward extensions of the visible spectrum. Furthermore, the wave theory of light is firmly grounded in Maxwell’s theory of electromagnetism—a theory so successful it could not be questioned. The few experiments that light waves did not explain concerned the interaction of light with atoms and molecules—an interaction that, because it was not fully understood, could be ignored by quantum skeptics.

Max Planck probably spoke for many when, in 1913, he signed a letter nominating Einstein for membership in the Prussian Academy of Sciences: “In sum, one can say that there is hardly one among the great problems in which modern physics is so rich to which Einstein has not made a remarkable contribution. That he may have sometimes missed the target in his speculations, as, for example, in his hypothesis of light quanta, cannot really be held too much against him, for it is not possible to introduce new ideas even in the most exact sciences without sometimes taking a risk.” Einstein himself considered light quanta to be a mere provisional device that in time would be replaced with a more foundational theory.

In the meantime, Einstein used the concept of light quanta cautiously. He spoke, for instance, of the ejection of photoelectrons as akin to drawing beer from a barrel. That beer is always drawn from barrels in pint containers does not mean the beer inside the barrel is partitioned into pints. In similar fashion, that light, in some circumstances, seems to give up its energy in standardized chunks does not mean that light is composed of quanta.

It fell to Arthur Holly Compton to endow light quanta with a reality that few could question. Figure 71 illustrates Compton’s experiment. Light (left panel) is directed at a free electron (represented by the circle on the left). Light (right panel) scatters from the electron and the electron recoils. The dotted line shows a continuation of the electron’s original trajectory. According to Compton, the angle through which the light scatters and its shift to lower frequency and longer wavelength is related to the direction of the recoiling electron and its kinetic energy exactly as if the energy and momentum of the light were concentrated in a single quantum. The light quanta and an electron collide, say, as one billiard ball with another.

In fact, Compton scattered X-rays, instead of visible light, from the weakly bound electrons in the carbon atoms of a sample of graphite, instead of from perfectly free electrons. Recall that William Röntgen had discovered X-rays in 1895 and that Max Von Laue had demonstrated in 1912 that X-rays are relatively high frequency (compared to visible light) electromagnetic waves. Now Compton had shown that X-rays, and by extension all parts of the electromagnetic spectrum, also behave as particles of electromagnetic radiation.

Interestingly the 1923 paper in which Compton announced his result did not mention Einstein’s 1905 paper on the photoelectric effect. Yet Compton’s experiment is routinely characterized, as we do here, as confirming Einstein’s light quanta hypothesis. Compton’s biographer, Roger Steuwer, claims that Compton, given the way he typically mischaracterized Einstein’s work, “quite likely never even read Einstein’s 1905 paper.” Steuwer continues, “One of the most striking aspects of Compton’s research program, when viewed in its entirety, is its relative autonomy”—that is, “his theoretical insights were derived from, and anchored in, his own precise experiments.”

The Compton effect created a sensation. Before Compton’s experiment and its interpretation, one could confine the supposed particle-like qualities of light to its ill-understood interaction with matter. After Compton’s experiment, physicists had no choice but to embrace light quanta.

But the Compton effect created a new difficulty. Two incompatible theories of light, a particle theory and a wave theory, had been found indispensable, each in different circumstances. High-frequency light interacts with electrons just as if the light were composed of particle-like photons. Yet beams of low-frequency light also create interference patterns just as waves do. Light can be treated either as a bundle of energy or as a wave with frequency . Eventually physicists became accustomed to this wave-particle duality, and the idea remains useful to this day. But a more coherent theory has now been fashioned. Shortly after World War II, the wave and particle theories of light were integrated into a single, mathematical theory called quantum electrodynamics.

45. Matter Waves (1924)

Figure 72

Louis de Broglie (1892–1987) (pronounced Louie de Broy) was born into an illustrious family that had since the seventeenth century produced prominent soldiers, politicians, and diplomats for France. Louis’s father was the fifth duc de Broglie. Louis would eventually become the seventh. Educated as a child by private tutors, he completed high school and matriculated at the University of Paris, first studying history, then law, and finally physics—especially theoretical physics. Although World War I interrupted his studies, his older brother, a prominent experimental physicist, arranged for Louis to be posted, for much of the war, to the safety of a telegraph station at the foot of the Eiffel Tower. Demobilized in 1919 Louis returned to the university to finish his doctoral dissertation.

A confidence born of his family’s privilege and means and his obvious talent for physics enabled Louis to develop ideas outside the mainstream of physics. Einstein’s 1905 work on relativity and on the photoelectric effect inspired de Broglie. In particular, Einstein’s idea that light, so successfully described as a wave, could also behave as a quantum of energy suggested to de Broglie the complementary idea that an electron, considered a particle since its discovery in 1897, could also behave as a wave.

According to de Broglie’s hypothesis, every particle is accompanied by a wave that helps determine its behavior. De Broglie found that the wavelength of the wave associated with a material particle, today called the de Broglie wavelength, is inversely proportional to the particle’s momentum so that where is Planck’s constant. The smaller the particle momentum, the larger its wavelength, and the larger its wavelength, the more evident the particle’s wave nature. These wave properties were, to de Broglie, as real as the mass of the associated particle.

De Broglie’s first application of matter waves was to the hydrogen atom. Niels Bohr had, in 1913, somewhat arbitrarily limited the continuum of its possible electron orbits to a discrete set he called stationary states. According to Bohr, only an electron in a stationary state orbit is stable and immune from the classical expectation of radiating energy. Bohr’s model was empirically successful even if based on ad hoc postulates.

De Broglie’s matter waves provided an explanation of Bohr’s arbitrary limitation of electron orbits that, in turn, opened up a new world of thought. He found that only electron orbits associated with waves that smoothly reconnect with themselves after a complete orbit are possible. Waves associated with other orbits destroy themselves. De Broglie’s smoothly reconnecting waves neatly correspond to Bohr’s stationary states. Figure 72, more conceptual than figurative, of a circular electron orbit associated with a wave of three complete wavelengths illustrates this concept. Other possible orbits are associated with waves of a whole number (1, 2, 3, ...) of wavelengths.

The idea of a wave constructively interfering with itself may already be familiar. Fix one end of an extendable, elastic cord to a post. (A Slinky in place of a cord will do.) Extend the cord, and launch waves by moving its free end up and down. Only those regular up-and-down motions with certain discrete frequencies will produce waves that constructively interfere with the waves reflected from the fixed end of the cord. With this particular setup, the only large waveforms possible are those composed of a whole number of half wavelengths. Figure 73 shows a cord, fixed at one end, supporting a wave of three half wavelengths.

Figure 73

De Broglie composed his ideas on matter waves into a doctoral dissertation in 1924. Upon reading it Einstein claimed, “He [de Broglie] has lifted a corner of the great veil.” Erwin Schrödinger (1887–1961), by developing a wave equation whose solutions described and generalized de Broglie’s matter waves, soon lifted another corner of that veil.

Experimental confirmation came quickly. Indeed, the American physicist Clinton Davisson (1881–1958) confirmed de Broglie’s matter waves even before he knew he was doing so. Davisson and his collaborator, Lester Germer, had been continuing Davisson’s earlier study of the surfaces of crystals by shining a beam of low-energy electrons on those surfaces and recording the intensity of the reflected beam as a function of its angle of incidence. Germer, on a trip to Europe in 1926, was astonished to hear a lecture in which the presenter, Max Born (1882–1970), who a year later developed the probabilistic interpretation of matter waves, showed a curve from Davisson’s earlier research that, Born claimed, showed that electrons reflect from a crystal’s surface just as waves do. On Germer’s return he and Davisson refined their experiment in the light of Born’s comment. Their result: slow electrons reflect from the surface of a crystal exactly as do waves with a wavelength equal to that of the de Broglie wavelength , where is the electron momentum.

De Broglie received the 1929 Nobel Prize in Physics “for his discovery of the wave nature of electrons.” Erwin Schrödinger received the prize in 1933, Clinton Davisson in 1937, and Max Born in 1954. De Broglie, like Einstein and Schrödinger, rejected Born’s probabilistic interpretation of matter waves. They were too strongly committed to the classical tradition of continuity and determinism in physics. Yet Born’s quantum probabilistic interpretation has proven all but inescapable.

46. The Expanding Universe (1927–1929)

Figure 74

The daily appearances of the sun and the moon, the moving planets, the starry sky, and the encircling band of hazy or “milky” light called the Milky Way have, over the centuries, invited men and women to consider the universe as a whole. Of what is it composed? Does it move? What is its shape?” are questions they asked and sometimes answered. Observations made with the naked eye or with the aid of a telescope only slightly constrained their speculations. Experiments were, of course, out of the question.

Emmanuel Kant (1704–1804) was one inquirer whose speculations were disciplined with reason. He reasoned both from what little he knew (the sun is part of the Milky Way star system) and from what he could reasonably suppose (the laws of physics are everywhere the same) to a cosmology much in advance of his time. According to Kant, the Milky Way must be an extended rotating system of stars whose apparent stability is the result of a balance between the attractive force of gravity and the centrifugal tendency of rotating systems to fly apart. While we see the Milky Way from its inside, a distant observer on its outside would see a hazy, flattened ellipse that appears much like the nebulae of unknown composition astronomers had been discovering in Kant’s day. Thus, it is likely that the Milky Way is not the only such star system—a lone island in an otherwise empty universe—but one among many similar systems scattered throughout the universe.

Empirically minded astronomers ignored Kant’s reasoning, based, as it was, on a slim foundation of physical evidence. More influential were the painstaking telescopic studies of William Herschel (1738–1822) and Harlow Shapley (1885–1972). Shapley determined the size of the Milky Way by using the characteristic relation, discovered by Henrietta Swan Leavitt (1868–1921) (one of the first female “computers” at the Harvard College Observatory), between the brightness of the variable stars called Cepheids and their period of variation. Shapley developed a method of determining the distance of a particular Cepheid variable by observing its period and consequently inferring its absolute brightness, and then by comparing the latter to its apparent brightness and inferring its distance. Since Cepheid variables are scattered throughout the Milky Way, Shapley was able to determine the Milky Way’s size—some 100,000 light years across. However, in opposition to Kant, he erroneously concluded that the nebulae were objects in the Milky Way and that the Milky Way encompassed all the matter of the universe.

This last conclusion fell apart in 1923–1924 when Edwin Hubble (1889–1953), using the recently constructed 100-inch diameter optical telescope on Mount Wilson in California, identified Cepheid variables in the Andromeda nebula. Using Shapley’s method of determining distances, Hubble found that this nebula was, in fact, a separate star system some ten times further from the Milky Way than the latter is across. Upon reading a letter from Hubble explaining this discovery, Shapley remarked to a colleague, “Here is the letter that has destroyed my universe.”

Hubble went on to study the spectra, that is, the characteristic pattern of colored light emitted from and absorbed by the gases in the atmosphere of the stars that compose distant nebulae. Interestingly, Hubble found that, more often than not, these spectra were shifted toward longer wavelengths and lower frequencies (“red-shifted”) relative to the spectra of the same gases in terrestrial laboratories. Hubble then supposed these red shifts were Doppler shifts—a consequence of a galaxy’s rapid recession from our galaxy just as the pitch of the siren of an emergency vehicle is lower (and its sound wavelength longer) when the vehicle rapidly recedes from the listener. He found that the further the galaxy, the faster its velocity of recession in direct proportion one to the other—a relation now known as Hubble’s law.

Milton Humason (1891–1972), a local Mount Wilson mule driver and observatory janitor who turned himself into a meticulous and able astronomer, assisted Hubble in this work. Their discovery at first glance seemed to place our galaxy, the Milky Way galaxy, at the center of a giant cosmic explosion. After all, the most quickly moving fragments produced in an explosion would travel, in a given interval, furthest from its center. But another idea has prevailed. All modern cosmologies assume that, on the largest scales, the matter of the universe is uniformly distributed. Thus, the distribution of galaxies looks the same in different directions and would look the same in different places. According to this assumption, called the cosmological principle, there is no center and no edge of the universe. The “cosmic explosion” happened everywhere at the same time.

Hubble’s law and the cosmological principle together imply that the density of galaxies decreases as time marches on. Figure 74 illustrates this conclusion by imaging two views of the cosmos through the frame of a single window. The right view is billions of years later than the left view and consequently shows a universe less densely populated with galaxies. It is in this sense that we can say the universe is expanding.

There is much evidence supporting this universal expansion. However, the rate of expansion and its proximate cause are still (in 2016) under investigation. Although Hubble was the first to gather data that showed galactic red shifts, he was not the first to interpret that data in terms of a universal expansion. Rather that honor is due to Georges Lemaître (1894–1966), a Belgian Roman Catholic priest and student of Arthur Eddington, the latter one of the leading general relativists of his time. Lemaitre discovered a solution, to the equations of general relativity, that describes an expanding, homogenous, and isotropic universe with nonzero density and found evidence for this solution in Hubble’s earliest data. Published in a little-known journal in 1927, Lemaître’s work, although eventually praised by Einstein and others, went, for a time, unnoticed.

Hubble eventually took the unusual step of hiring an agent to promote his case for a Nobel Prize in Physics. This was an uphill and ultimately unsuccessful battle—for in Hubble’s day, astronomers were not considered for Nobel Prizes. Even so Hubble deserves recognition at the level of a Nobel Prize for his discovery that the nebulae are independent star systems and for his crucial role in discovering the expansion of the universe.

47. The Neutrino and Conservation of Energy (1930)

Figure 75

When first discovered in the last few years of the nineteenth century, radioactivity troubled physicists. After all, atoms were supposed to be indestructible. How then could they eject their parts? And why did they even have parts? Furthermore, radioactivity seemed to be an inexhaustible source of energy. From whence came this energy? Was it from the atom itself or from the region surrounding the atom, or was it created ex nihilo at the moment of radioactive decay?

Hard work and imagination soon answered these questions. Atoms, indeed, have parts. Radioactivity consists of unstable atoms randomly ejecting those parts in alpha, beta, and gamma radiation. Alpha (helium nuclei) and beta (electron) radiations transform the original atom into one of another kind. Ernest Rutherford summarized the situation in 1904: “This theory [of transformation] is found to account in a satisfactory way for all the known facts of radioactivity and a mass of disconnected facts into one homogeneous whole. On this view the continuous emission of energy from the active bodies is derived from the internal energy inherent in the atom, and does not in any way contradict the law of conservation of energy.” Einstein’s discovery, in 1905, that anything with mass has energy in the amount and anything with energy has mass in the amount supported Rutherford’s assessment. (Here is the speed of light.) The energy of radiation is accounted for by a loss of the radioactive atom’s mass.

By 1929 physicists had made more progress. Rutherford discovered the nucleus in 1910, and Werner Heisenberg (1901–1976), Erwin Schrödinger, and Paul Dirac (1902–1984) fashioned different approaches to the quantum mechanics of atomic structure (respectively in 1924, 1926, and 1928). Soon similar ideas would be applied to the nucleus. According to Dirac, “The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the application of these laws leads to equations much too complicated to be soluble.” And yet problems remained whose solution required more than “the application of these laws.”

The electrons ejected from unstable nuclei in beta radiation were at the heart of these problems. In particular, the electron energies in beta radiation are continuously distributed over a range of possible values even when their source is a single kind of nucleus. In contrast, alpha and gamma radiation—respectively, helium nuclei and high-frequency electromagnetic waves—have well-defined energies that characterize the particular nuclei from which they come.

In 1929 physicists believed (correctly) that nuclei were composed of protons and neutrons in sufficient numbers to account for their nuclear charge and mass. Many also believed (incorrectly) that a neutron was a tightly bound system of a proton and an electron. Because a proton and electron are oppositely charged, they attract each other. For this reason these scientists thought that beta rays were produced when a neutron breaks in two and releases enough energy to drive its proton and electron apart.

As reasonable as this picture might seem, it is unacceptable. For given that both momentum and energy are conserved in any process and that the neutron is slightly more massive than the proton (each about 1,800 times more massive than an electron), the electron must carry away almost all the energy released in the beta decay of a neutron. Furthermore, betas, like alphas and gammas, should have well-defined energies that characterize the neutron from which they are emitted. But, in fact, the energy of the emitted electrons varies widely. Either identical neutrons contain different amounts of energy or, as suggested by Niels Bohr, energy is not conserved in a single decay but only on average over many decays. Most physicists rejected these possibilities.

Wolfgang Pauli (1900–1958) rescued the situation, in 1930, by suggesting that the energy released in the beta decay of a neutron is shared among the remaining proton, the electron, and an as yet undetected, lightweight particle—later named a neutrino (Italian for “little neutron”) by Enrico Fermi. Figure 75 illustrates the decay of a neutron into a proton, an electron, and a neutrino. Because the electron sometimes takes more and sometimes less of the available energy with most of the rest going to the neutrino, Pauli’s version of beta decay conserves energy while allowing for a continuous distribution of electron energies.

That the neutrino interacts only weakly with other particles explains why it had not, in Pauli’s time, been detected. Pauli’s proposal took great courage. Privately he confided to a friend, “I have done something very bad today by proposing a particle that cannot be detected; it is something no theorist should ever do.” But Pauli started something of a trend. Today we have particle physicists whose job it is to suggest new particles every time an unusual experimental result is observed.

The Italian physicist Enrico Fermi (1901–1954) took Pauli’s idea and, using the newly developing methods of quantum electrodynamics, constructed a theory of beta decay that predicted the observed distribution of electron energy. According to Fermi’s theory, a proton, electron, and neutrino are not constituents of the neutron but, rather, are created at the moment of its decay. Fermi’s theory, published in 1934, was a great success.

The neutrino is, indeed, difficult but not impossible to detect. In 1956, more than twenty-five years after Pauli’s original proposal, Clyde Cowan and Frederick Reines were confident that they had observed neutrinos produced in a nuclear reactor and sent Pauli the following exciting, if plainly phrased, confirmation: “We are happy to inform you that we have definitely detected neutrinos.”

48. Discovering the Neutron (1932)

Figure 76

James Chadwick (1891–1974) gets credit for “discovering the neutron,” but his actual contribution is not so simply described. He was neither the first to predict the existence of the neutron nor the first to find evidence for its existence. Nor was he the first to realize that neutrons must be elementary rather than composite particles.

Of course, sometimes the word discover is quite appropriate. Ernest Rutherford, for instance, certainly discovered the atomic nucleus. Its existence was unexpected in 1910 when Rutherford, his associate Hans Geiger, and their undergraduate student Ernest Marsden performed an experiment whose inescapable interpretation was that most of the mass of the atom and all of its positive charge were concentrated in a relatively small body at the center of the atom. Rutherford later called this body a nucleus.

Since the hydrogen nucleus is the least massive and least charged of the known nuclei, Rutherford took it to be a building block out of which other nuclei were composed and gave it the name proton after the Greek for “first thing.” (Rutherford was an adept eponymist. He not only gave us nucleus and proton but also neutron and alpha, beta, and gamma radiation—all names that have survived to this day.)

It soon became apparent that while the number of protons in an atomic nucleus determines an atom’s chemical properties, a nucleus composed of protons alone does not explain its physical properties—in particular, its mass. For instance, the next most massive atom after hydrogen is helium. Its nucleus has two protons but weighs approximately four times more than a single proton. Other nuclei weigh at least twice and often more than twice the weight of the protons they contain. Rutherford’s solution was to postulate the existence of a neutral particle in nuclei, the neutron, with mass approximately equal to that of a proton. Neutrons inhabit nuclei in numbers that bring each nuclear mass up to its observed value. Thus a helium nucleus contains two protons and two neutrons bound together with the strong nuclear force. So far, so good. But Rutherford mistakenly conceived the neutron itself to be a composite system containing a proton and an electron. (The electron mass is about 1/1800 a proton mass.)

Such was the common understanding and misunderstanding in 1928 when three teams of researchers—Rutherford and his assistant, James Chadwick, in Manchester, England; Walther Bothe and his student, Herbert Becker, in Berlin; and Irene Curie (Marie Curie’s daughter) and her husband, Frédérick Joliet, in Paris—began bombarding various light elements with alpha particles, that is, with helium nuclei. These teams found that when a nucleus absorbs an alpha particle, it typically becomes unstable and emits, uniformly in all directions, penetrating, high-frequency, electromagnetic (that is, gamma) radiation. But when beryllium, with a charge of 4 protons and a mass of 9 atomic mass units, was bombarded something unusual happened: the unstable nucleus emitted radiation only in the forward direction, that is, in the direction of the bombarding alpha particles.

Chadwick was the first to propose that when a beryllium nucleus absorbs an alpha particle it emits not electromagnetic radiation but another particle, a neutron, in the forward direction, and he set about devising an experiment to confirm this proposal. By February 1932 Chadwick was confident enough to submit a letter to the journal Nature entitled “Possible Existence of a Neutron.” As Chadwick later explained, “The results, and others I have obtained in the course of this work, are very difficult to explain on the assumption that the radiation from beryllium is a quantum radiation, if energy and momentum are to be conserved in the collision. The difficulties disappear, however, if it is assumed that the radiation consists of particles of mass 1 and charge 0, or neutrons.”

Figure 76 illustrates Chadwick’s idea. In the left frame, an energetic alpha particle approaches a beryllium nucleus. When a beryllium nucleus with 4 protons and 5 neutrons absorbs an alpha particle with 2 protons and 2 neutrons, the result is an unstable carbon nucleus with 6 protons and 7 neutrons. In the right frame, the unstable carbon has emitted a neutron in the forward direction. What remains behind is a stable carbon with 6 protons and 6 neutrons.

Chadwick still imagined that the neutron he had identified was Rutherford’s composite particle, a tightly bound system of an electron and proton. But between 1932 and 1935 when he received the Nobel Prize in Physics for “the discovery of the neutron,” Chadwick changed his mind. After all, Heisenberg’s newly discovered uncertainty principle made it impossible for an electron to be confined within the small volume of a neutron without having an unrealistically large energy. In addition, Chadwick had succeeded in measuring the mass of a neutron and found it to be larger than the sum of the masses of its presumed constituents, a proton and an electron—a result that doomed the idea of a composite neutron. The neutron must be an elementary particle.

A resourceful researcher trained in the art of cobbling together experiments from materials at hand, Chadwick was well positioned to make his contribution. As a young man Chadwick was studying with Hans Geiger in Germany when World War I broke out. Geiger advised Chadwick, an Englishman, to leave Germany at once, but Chadwick delayed and was imprisoned along with other enemy aliens. In accordance with the Geneva Conventions, the prisoners administered their own internal affairs. Thus, Chadwick lectured to his fellow inmates on radioactivity and conducted experiments using commercially available radioactive toothpaste as a source.

When World War II began Chadwick, now in England and a famous Nobel laureate, was asked to investigate the feasibility of building an atomic bomb based upon the fission of heavy nuclei. Subsequently he wrote the final draft of a report summarizing British efforts through 1941. Eventually the British, exposed as they were to Luftwaffe bombing, abandoned the task of building their own bomb and offered their expertise to the Americans. Chadwick then became head of the British mission to the Manhattan Project and as such traveled to its various sites in America, moved his family to Los Alamos, New Mexico, and became a confidant of General Groves, the military engineer in charge of the Los Alamos effort. While Chadwick believed it was necessary for the Allies to build an atomic bomb, he returned to Britain in 1948 disenchanted with the trend toward big, industrialized science of which the Manhattan Project was a prime example.

49. Nuclear Fission and Nuclear Fusion (1942)

Figure 77

We are used to things happening in a certain way. Massive objects fall down—not up. Certain materials, like paper, burn easily. Others do not. We may be less familiar with nuclear fission and fusion, but the same general principle applies: A system (massive object, paper, nucleus) changes in a certain way (falls, burns, transforms) only when that system can lose energy in that change. This principle helps us understand nuclear fission and nuclear fusion. The first releases energy slowly in nuclear power plants and quickly in fission bombs. The second produces the energy beaming from our sun and released explosively in a hydrogen bomb.

We know from Ernest Rutherford’s gold foil experiment of 1912 that all of the positive charge and most of the mass of an atom is confined within a tiny nucleus several fermis across (1 fermi = 10^-13 cm). By 1932 our current picture of the nucleus, as a spherical configuration of protons and neutrons, had emerged. Each proton is positively charged while each neutron is uncharged and only slightly more massive than a proton. Thus, the number of protons within a nucleus is a measure of its charge, and the number of protons and neutrons in a nucleus, collectively called nucleons, is a measure of its mass. However, a question arises: Given that like charges repel each other with a greater force the closer they are, what keeps the protons in a nucleus from flying apart? Evidently there is an even stronger attractive force that binds these nucleons together. Physicists call this force the strong nuclear force.

Competition between the repulsive electrostatic force among protons and the attractive strong nuclear force among nucleons determines the size, composition, and stability of nuclei. The different natures of these competing forces make this competition interesting. The attractive force between nucleons is strong but short range. When two nucleons are within a couple of fermis of each other, they attract one another with a strong nuclear force that overwhelms any repulsive electrostatic force. But, when two nucleons are further apart than a couple of fermis, the attractive strong nuclear force between them vanishes. As a result, the strong nuclear force acts only between a nucleon and its nearest neighbors. In contrast, the repulsive electrostatic force between two protons diminishes slowly with separation—as the inverse of their separation squared—in the same way as the gravitational force between the sun and the earth does. The electrostatic, like the gravitational, force is said to be long range.

Now, imagine adding more and more protons to an already large nucleus. As the number of protons grows the net repulsive electrostatic force among all these protons grows, while the strong nuclear force keeping a nucleon (proton or neutron) bound to its nearest neighbors remains the same. For this reason, there is a natural limit to how many protons a nucleus can have. Uranium with 92 protons occupies that limiting position. Nuclei with more than 92 protons are unstable.

This competition also explains the stability properties of relatively light nuclei. Because these nuclei contain so few protons the net repulsive electrostatic force among them is weak relative to the strong nuclear force between neighboring nucleons. Furthermore, the nucleons of hydrogen (one proton and no neutrons), of helium (two protons and two neutrons), and of lithium (three protons and four neutrons) are all on the surface of their relatively small, roughly spherical nuclei. Therefore, in these nuclei, each nucleon is not as strongly bound to its neighbors, as it would be if completely surrounded by other nucleons. As more nucleons are added to a light nucleus, a typical nucleon gains more neighbors and, consequently, the whole system becomes more tightly bound. An iron nucleus, intermediate between lighter and heavier nuclei with 56 protons and neutrons, is the most stable.

This competition between repulsive electrostatic and attractive strong nuclear forces can also be thought of in terms of energy lost and gained. Think, for instance, of a rock rolling down a hill. The final configuration of the rock-earth system has less energy than before. The energy “lost” is released in the kinetic energy of the rock as it falls. Ultimately this kinetic energy contributes to the thermal energy of the rock and the hillside.

Likewise the configuration of a system of nucleons after splitting apart (the fission process) or sticking together (the fusion process) has less energy than before. Because the number of nucleons after fission or fusion is the same as before, the energy per nucleon in the final configuration is less than the energy per nucleon in the initial configuration. The nuclear energy lost is released in the kinetic energy of the fission or fusion products and in high-energy electromagnetic radiation.

The curve in figure 77, called the curve of binding energy, encapsulates this physics. Plotted is the energy per nucleon in various nuclei from hydrogen to uranium in the units typical of nuclear energy (MeV or million electron volts), versus the nuclear mass number, that is, the number of nucleons in the nucleus. The single curved arrow (on the left) indicates the fusion of two, identical, light nuclei and the two curved arrows (on the right) the fission of one heavy nucleus. Since the fusion or fission products have less energy per nucleon than before, energy is lost in the nuclear transformation and the final configurations are more tightly bound than before. The results of both fission and fusion are nuclei with more stability than before.

Nuclear fusions within the interior of the sun are ultimately the source of all of our “non-nuclear” energy: fossil fuel, hydro, wind, and solar power. But the fusion of two light nuclei does not happen as readily as the fission of a nucleus heavier than the stable form of uranium. After all, two light nuclei must overcome their electrostatic repulsion in order to fuse. Thus, fusion requires that light nuclei be driven together with a speed characteristic of the high temperature of the sun’s interior. Fission, on the other hand, occurs when a heavy nucleus, for instance, uranium with 235 nucleons or plutonium with 239 nucleons, absorbs an extra neutron. If among the fission fragments are several neutrons, one fission reaction can cause several others and each of those several more. The result: a self-sustaining chain reaction of nuclear fissions. Enrico Fermi and his team were the first, on December 2, 1942, to initiate and control a nuclear chain reaction of fissions.

The discovery and application of nuclear fission and nuclear fusion intertwine with the development of nuclear weapons. The story of their development tells of competition between the United States, Nazi Germany, and Soviet Russia; sudden epiphanies while crossing a London street; a revelatory discussion between an aunt and her nephew, both physicists, on holiday together in Sweden; the contributions of Hungarian émigré scientists; letters to President Roosevelt signed by Einstein; a nuclear reactor under the football stadium at the University of Chicago; British commandos destroying a (Nazi-controlled) Norwegian heavy water plant; a secret, multi-billion-dollar, nuclear industry in the United States; and Russian spies working incognito in the closed city of Los Alamos, New Mexico. Numerous books relate the human drama and the interesting science of this story. Two excellent ones are The Making of the Atomic Bomb by Richard Rhodes (1987) and Nuclear Weapons: What You Need to Know by Jeremy Bernstein (2007).

50. Global Greenhouse Effect (1988)

Figure 78

The earth absorbs radiant energy from the sun, transforms that energy into longer wavelength, infrared, thermal energy, and reradiates this thermal energy skyward. By intercepting part of this reradiated, thermal energy and directing it back toward the earth’s surface, our atmosphere boosts the temperature of the earth’s surface above what it would be in its absence. Although such heating is commonly referred to as the greenhouse effect, actual greenhouses warm their contents in a different way—in particular, by inhibiting the circulation of air.

Consider two models: the no-atmosphere model (figure 78) and the absorbing and radiating atmosphere model (figure 79). Together these illustrations show how our “global greenhouse” works. The earth absorbs the energy of sunlight at an average rate of watts per square meter. The no-atmosphere model assumes the earth radiates into space as much energy as it receives from the sun. Since all objects with temperature radiate at watts per square meter where is a universal constant, the earth radiates at a rate , where is the average temperature of the earth’s surface. Thus, and so, given values of W and is found to be 254 degrees Kelvin—a frigid minus 19 degrees Celsius (minus 2 degrees Fahrenheit).

But the earth does have an atmosphere and that atmosphere absorbs thermal energy radiated from the earth’s surface and reradiates that energy downward as well as upward at a rate of watts per meter squared where is the average temperature of the atmosphere. Figure 79 shows the energy flows in the absorbing and radiating atmosphere model. Accordingly, both the earth and its atmosphere each radiate as much energy as each receives. Some algebra shows that, in this case, the average temperature of the earth’s surface is boosted over its no-atmosphere value by a factor of , that is, by approximately 19 percent. With this boost the average temperature of the earth’s surface becomes 302 degrees Kelvin, that is, a warmish 29 degrees Celsius (or 84 degrees Fahrenheit). The current average temperature of the earth’s surface, 14.8 degrees Celsius (or 58.6 degrees Fahrenheit), lies between the temperatures implied by the no-atmosphere and the absorbing and radiating atmosphere models. Apparently, our atmosphere absorbs only part of the thermal energy radiated by the earth’s surface and is transparent to the remaining part.

Figure 79

Of course, these models are simplifications that ignore changes within the atmosphere and do not account for other contributions to the temperature of the earth’s surface, such as the variable reflection of sunlight from clouds and snow. Still, they show that our atmosphere’s ability to absorb and reradiate thermal energy is an important determinant of the temperature of the earth’s surface.

But what allows our atmosphere, a thin layer of gas containing less than one-millionth the mass of the earth, to absorb and reradiate this infrared radiation? The answer is, in large part, atmospheric carbon dioxide and water. While most of the atmosphere is nitrogen and oxygen , Argon is the third most numerous kind of molecule, and carbon dioxide is the fourth. Water, , is also present in variable amounts as well as smaller amounts of other gases. Notice that among these constituents, and molecules each contain three atoms. For instance, carbon dioxide is composed of one carbon atom denoted and two oxygen molecules denoted . The more atoms in a molecule, the more ways its structure may flex and vibrate and so resonate with and absorb the thermal radiation from objects with a temperature close to that of the earth’s surface.

While human beings do not directly control the amount of in the atmosphere, we do directly contribute to its —chiefly by burning fossil fuels. In preindustrial times, the concentration of in our atmosphere was 270 parts per million (ppm) or 0.0270 percent. Now our atmosphere has over 400 ppm , that is, over 0.0400 percent. By releasing more into the atmosphere, we increase its ability to absorb thermal radiation and, consequently, increase the average temperature of the earth’s surface.

The Swedish scientist Svante Arrhenius (1859–1927), who was the first in 1896 to note that increasing the number of CO₂ molecules in the atmosphere leads to global warming, considered such warming, in the main, a positive development that would prevent future ice ages and allow more of the earth’s surface to be cultivated. Ninety years later in 1988, James Hansen (1941– ), then the director of the NASA Goddard Institute for Space Studies, warned of the hazards of global warming in testimony before committees of the United States Congress.

While the physics of the global greenhouse effect is simple, the phenomenon of global warming is not. For instance, as the temperature of the earth’s atmosphere increases, it absorbs more water vapor. This, of course, leads to even more heating, but more atmospheric also leads to more cloud cover, and since clouds reflect sunlight, clouds moderate, in some degree, this heating. Of course, we can do no experiments on the global system—or rather we can do only one irreversible experiment.

Since Hansen’s testimony, climate scientists have collected much data and constructed complex numerical models that incorporate the physics relevant to climate change. They have checked their model predictions against those produced by independent teams of researchers and against historical data and quantified the uncertainty of those predictions. Their conclusion validates Hansen’s warning more than it does Arrhenius’s rosy prediction. Average surface temperatures are increasing at an alarming rate, and human activity is a major cause of this increase.

But some resist this conclusion. The chair of the United States Senate Committee on Environment and Public Works in 2015, Senator James Inhofe of Oklahoma, quoting God’s promise to Noah after the flood, “While the Earth remains, seed time and harvest, cold and heat, summer and winter, day and night, shall not cease” (Genesis 8:22), claims that it is arrogant for humans to believe they can change the earth’s climate. Indeed, arrogance may be an occupational hazard for scientists. After all, they invariably trust that natural processes can, in fact, be understood—a trust that sometimes devolves into arrogance.

Yet Inhofe should know that God’s will is often not done. We despoil rivers and lakes. We pollute land and air. We drive species into extinction. Given time we can do worse—or we can, by God’s grace, do better. The late Reinhold Niebuhr (1892–1971), who was a wiser theologian than Inhofe, urged us to pray for “the wisdom to distinguish between those things that can and those things that cannot be changed and for the courage to change those things that should be changed.” Certainly, the distinction between those things that can and those things that cannot be changed is an important part of the understanding scientists seek. What we all need is the courage to change those things that should be changed.

51. Higgs Boson (2012)

Figure 80

As we grow older, some of us put on weight. We slowly begin to feel more massive, or, at least, heavier. And while feeling our weight or our mass is an everyday experience, we have probably never been moved to ask: “Why does anything have mass?” “Where does mass come from?”

Einstein’s or, equivalently, provides one kind of answer. Evidently, anything with energy has mass in the amount . But consider an elementary particle, for instance, an electron, isolated and at rest, that is, a particle with no parts, no apparent spatial extent, no obvious energy, and no motion. Yet an electron acts as if it has a tiny rest mass of grams. Our question then becomes “Why do elementary particles have rest mass?” Or, if you prefer: “Why do isolated elementary particles at rest have energy?”

Before 1930 scientists knew of only two elementary particles: the electron and the proton. Then James Chadwick discovered the neutron and shortly thereafter Wolfgang Pauli reasoned that another kind of elementary particle, the neutrino, must exist. Today we know that protons and neutrons are themselves each composed of three quarks. According to the standard model of particle physics, quarks are elementary particles that, like the electron, carry electric charge, have mass, and have no spatial extent. Electrons and neutrinos are also elementary particles but of a class, distinct from quarks, called leptons. Photons belong to yet a third class of elementary particles.

The theoretical concept of mass has emerged as a product of our long-standing effort to unify the fundamental forces that act among the elementary particles. Just as in the mid-nineteenth century James Clerk Maxwell, building upon Michael Faraday’s ideas, unified the separate theories of electricity and magnetism into a single theory of electromagnetism, so also in the early 1960s were the separate theories of electromagnetism and the weak nuclear force unified into a single electro-weak theory.

The main building blocks of the electro-weak theory are the several symmetries assigned to these forces. A symmetry is a property that is preserved while something else changes. For instance, we believe that the basic laws of physics are the same in every part of the universe. Or, as a physicist would say, these laws are symmetrical under translation from one part of the universe to another. Unfortunately, the simplest version of the electro-weak theory with its embedded symmetries requires that all elementary particles have zero rest mass—a claim we know to be false. For, while some elementary particles, like the photon, are massless, others, like the electron, are not.

How then can the simplest description of the electro-weak theory be modified so that some elementary particles have mass? One answer is that the universe contains a Higgs field that allows those particles with which it interacts to acquire mass.

Such acquisition is sometimes compared to a celebrity trying to move through a crowd while stopping frequently to shake hands, receive compliments, and pose for photos. Because the celebrity (the particle) interacts strongly with the crowd (the Higgs field), he or she acquires mass—at least of a certain kind. In contrast, an unknown person hardly interacts with the crowd at all just as if he or she has none of this “celebrity mass.” Quarks and leptons similarly interact, in varying degrees, with the Higgs field and, consequently, acquire mass in various amounts. On the other hand, because a photon does not interact with the Higgs field, it has no rest mass and travels at the speed of light.

The Higgs field and the mechanism with which it confers mass on otherwise massless particles makes the electro-weak theory consistent with known particle rest masses and also with our everyday experience of mass. In 2012, the Higgs boson, itself a characteristic excitation of the Higgs field, was observed in the detectors of the Large Hadron Collider of the CERN (after the French Conseil Européen pour la Recherche Nucléaire) laboratory in Geneva, Switzerland.

Apparently, early in its history, the universe transitioned from a state with no Higgs field to one with a Higgs field—a transition initiated by the emergence of a “Mexican hat” global potential energy shown in the center and right panels of figure 80. The horizontal position of the black circle indicates the strength of the universe’s Higgs field. The black circle initially resides in the center of the left panel, indicating no Higgs field. When the Mexican hat global potential emerged (center panel), the universe was for a short time in an unstable state. Then the universe transitioned to a stable state with nonvanishing Higgs field (right panel). These panels are meant to suggest the rolling of a marble, initially perched on the crest of the Mexican hat potential, into the trough between the hat’s crest and its upturned brim. In this way the fundamental forces, as represented by the Mexican hat potential, retain their symmetries while the state of the universe, represented by the position of the black circle, “breaks” this symmetry.

Peter Higgs (1929– ) and François Englert (1932– ) shared the 2013 Nobel Prize in Physics for, in 1964, postulating the Higgs field, describing the Higgs mechanism, and predicting the Higgs boson. That Higgs’s name alone is attached, in proprietary fashion, to these discoveries may well embarrass Peter Higgs. For, while Higgs certainly deserves a Nobel Prize, he is only one of several theoreticians who independently and nearly simultaneously came to the same conclusions.

Notes

161 “There was once a sailor on a vessel in New York harbor ... ” Stuewer, The Compton Effect (1975), 43.

163 “the theory of light would be thrown back by centuries.” Holton and Brush, Physics, the Human Adventure (2001), 401.

163 “especially for his discovery of the law of the photoelectric effect.” Nobel Citations (1922).

163 “All these 50 years of pondering have not brought me any closer to answering the question, ‘What are light quanta?’” Pais, Subtle Is the Lord (1982), 382.

164 Robert Brown, who thoroughly investigated Brownian motion, is usually credited with its discovery in 1827. However, Jan Ingenhousz quite clearly described the Brownian motion of coal dust particles on the surface of alcohol in 1785.

167 “I at any rate am convinced that He ... ” Einstein and Born, The Born-Einstein Letters 1916–1955 (2004), xxii.

167 “He has seen more clearly than anyone before him ... ” Schlipp, Albert Einstein; Philosopher-Scientist (1949), 163–164.

167 “based on different experiences in our work and life ... ” Schlipp, Albert Einstein; Philosopher-Scientist (1949), 177.

169 “I was brought up to look at the atom as a nice hard fellow ... ” Keller, The Infancy of Atomic Physics (2006), 9.

171 “It was quite the most incredible event that has ever happened to me ... ” Pais, Inward Bound (1986), 189.

173 “I could not recognize my own work in the reports.” Pais, Inward Bound (1986), 39.

174 “every Professor in Europe is now on the warpath.” Pais, Inward Bound (1986), 39.

176 “suddenly ... perceived the way which subsequently proved to be the shortest path to success.” Nobel Citations (1914).

176 “his discovery of the diffraction of X-rays by crystals.” Nobel Citations (1914).

180 “While it is too early to say whether the theories of Bohr ... ” Pais, Niels Bohr’s Times in Physics, Philosophy, and Polity (1991), 153.

182 “Doomed youth” and “as cattle.” From “Anthem for Doomed Youth” by Wilfred Owen, in Salter, Ferguson, and Stallworth, eds., Norton Anthology of Poetry (2005), 1386.

184 “overthrown” and “knocked out.” Pais, Subtle Is the Lord (1982), 306–309.

187 “In sum, one can say that there is hardly one among the great problems ... ” Pais, Subtle Is the Lord (1982), 382.

188 “quite likely never read Einstein’s 1905 paper.” Stuewer, The Compton Effect (1975), 217–218.

192 “He [de Broglie] has lifted a corner of the great veil.” Moore, Schrödinger (1989), 187.

193 “for his discovery of the wave nature of electrons.” Nobel Citations (1929).

196 “Here is the letter that has destroyed my universe.” Payne-Gaposchkin, An Autobiography and Other Recollections (1997), 209.

198 “This theory [of transformation] is found to account ... ” Pais, Inward Bound (1986), 113.

199 “The underlying physical laws necessary for the mathematical theory ... ” Dirac, “Quantum Mechanics of Many-Electron Systems,” 714.

201 “I have done something very bad today ... ” Solomey, The Elusive Neutrino (1997), 14.

201 “We are happy to inform you that we have definitely detected neutrinos.” Solomey, The Elusive Neutrino (1997), 65.

204 “The results, and others I have obtained ... ” Schweber, Nuclear Forces (2012), 220.

204 “for ‘the discovery of the neutron.’” Nobel Citations (1935).

214 For an example of Senator James Inhofe’s rhetoric, see the November 12, 2014, issue of the New York Times.

214  “While the Earth remains ... ” Genesis 8:22 (Revised Standard Version).

215 “The wisdom to distinguish between those things ... ” A paraphrase of the widely reproduced “serenity prayer” typically ascribed to Reinhold Niebuhr.