The Cave and the Light

by Arthur Herman

  It was a classic experiment in optics, Isaac Newton’s original home turf. It seemed innocent enough—except that no matter how Michelson moved his apparatus and no matter in what direction, when he flicked on the light and measured the light speed, he always came up with the same result: 186,000 miles per second.

  Michelson couldn’t believe it. According to Newton’s Principia, this shouldn’t happen. It was light’s duty to change speed according to how it was made to travel. Clearly something was wrong with his interferometer. Michelson went home to America deeply disappointed.

  He repeated the experiment in Chicago a year later with a chemist friend, Edward Morley. It showed the same result. No matter what they did or what deflection angle they used, the speed of light was always the same.

  Albert Michelson went on to found the American Physical Society. He was the first American to win a Nobel Prize in physics (1907). However, until his death in 1931, he considered his most famous experiment a failure. He could not believe that the problem was not his device or his skill as a scientist but Newton’s laws about space and time.22

  Einstein thought otherwise. Even as a student, he had wondered whether Newton’s most fundamental assumption—that space and time form an exact and immovable grid in which all physical events, like light traveling from one point to the next, take place—was really true. As a teenager, Einstein had once wondered, “What would the world look like if I rode a beam of light?” Around 1900, he began to work out the details and discovered that if somehow he did ride a light beam, he would cut himself off from the passage of time.23

  An interstellar horse race demonstrates Einstein’s point. Suppose the horses come out of the gate at the exact moment the course clock strikes noon. The horse I’m riding is traveling at the speed of light. In one second I move 186,000 miles; but so does the light beam carrying the image of the clock hands reaching twelve. When I look back, to me the clock hands have not changed; time is frozen. For the other riders, however, the clock is moving on and the chimes are sounding: for them, the time on the clock seems “normal.”

  What if a horse and rider could race at the speed of light?

  But normal now has no meaning—or rather, it has a provisional or relative one. The faster we approach the speed of light (and at half the speed of light, when my watch says three and a half minutes past noon, the course clock will appear to be a few seconds slower), the more we find ourselves in our own little world of experience of space as well as time. This is because the faster I go, the longer the light bearing visual images of the course will take to reach me, making them appear elongated and distorted. By the same token, those observers at the starting point will experience time as slower than the racer; and the dimensions of their space will be normal for them but different from mine.

  Objectivity, the Newtonian view, the God’s-eye view of space and time—all had been crushed. Subjectivity—what we see and experience from our own vantage point—had won. What’s left in common is the ability to share information about different perspectives. In fact, what’s usually called the theory of relativity (a term Einstein never used) should really be called the theory of perspective.24 For thanks to Einstein, what the Renaissance artists had used to represent reality had now become reality—a way to measure seeing from a particular point of view.

  What Einstein had really done, however, was to show that science was less about describing objective facts, as the Logical Positivists were claiming, than about measuring subjective observations. We can say “measure” because, thanks to Ludwig Boltzmann, the data drawn from our subjective observations still retain the power of mathematical prediction.

  Einstein had never even heard of Boltzmann from his teachers at the Polytechnic (or of Maxwell, for that matter) and began reading his works, especially his Lectures on Gas Theory, on his own. “Boltzmann is quite magnificent,” he wrote to the young woman who would become his wife. “I am completely persuaded by the correctness of the principles of the theory, that the question is really about the movement of [atoms] according to certain conditions.”25

  But he was equally persuaded by the idea that statistical probability had the power to illuminate certain otherwise-invisible features of nature that included the electromagnetic spectrum as studied by Max Planck. Planck had borrowed from Boltzmann the idea of dividing the energy of an electromagnetic wave into smaller units in order to give a theoretical deviation of the spectrum of radiation flowing out from an object. It was an elegant way of proceeding, as Boltzmann himself had shown in writing about gases. Boltzmann had even coined a term for these smaller bits, quanta, a German word meaning “quantity.”

  They behaved beautifully as statistical units. But did these smaller units or lumps, which Planck’s formulae described, really exist? Planck was stumped. And since he had rejected the rest of Boltzmann’s theory of atoms, he was permanently stumped: that is, until Albert Einstein picked up Planck’s latest work and began reading it with Boltzmann’s atoms in mind.

  The paper Einstein subsequently wrote showed that treating every “quantum” of radiation energy as a physically independent entity produced formulae for the energy and entropy of a volume of radiation that matched exactly the derivation of those quantities in terms of traditional thermodynamics. In other words, just as a physical gas was made up of individual atoms, so the “gas” of electromagnetic radiation was made up of individual and distinct particles whose presence remained invisible but whose behavior was mathematically predictable.

  This was no mere mathematical stunt. Quanta really were atoms of energy—and were the constituent parts that made up the light spectrum. Instead of a wave of energy, as Maxwell and others had conceived it, light was a stream of quanta (or photons) traveling at an incredible speed past other atoms—which incidentally is why the speed of light is constant, no matter what medium it passes through, as Michelson’s experiments had shown.

  Indeed, light turned out to be the only constant. Everything else, even time (as the relativity theory showed) and space and the objects that occupy it, are subject to the laws of the quanta—and the atoms that make it up.

  But what is the relationship between the quantum and the atom? That would be the next step in uncovering the nature of the unseen world. And it would come at the hands of Danish physicist Niels Bohr, on the eve of the great cataclysm that would engulf Europe: World War I.

  Contrary to historians, what really divided Europe in the years before 1914 was not nationalism or alliances or imperial ambitions for a “place in the sun.” It was a rift in Europe’s cultural crust separating the major portion of German-speaking Europe from its neighbors. Inside the rift, Hegel’s Plato-influenced German idealism ruled, above all the notion that ultimate reality is found not in the vicissitudes of empirical experience but in the realm of the Absolute, of mind and spirit.26

  Outside the Hegel Line and across the rest of Europe, various schools of thought and lines of inquiry competed for attention. They included Catholics and Protestants; John Stuart Mill–style liberals and Burkean conservatives; Logical Positivists and Social Darwinists; Enlightenment Deists and out-and-out atheists. But most looked to Aristotle and his intellectual offspring, including Aquinas and John Locke, as their original progenitors, if not their actual inspiration. They argued passionately among themselves in university lecture halls, academic journals, political discussion groups, writers’ and artists’ studios, even newspapers and secondary-school common rooms. Over time, however, they generally found themselves resisting the aggressive thrust of Hegel’s idealism, or being engulfed by it—and by the disciples of Hegel’s unacknowledged bastard heir, Karl Marx. For after 1848, Hegelianism—like Absolute Spirit itself—seemed destined to sweep everything before it.

  It’s not hard to describe the Hegel Line on a map. To the east, it separated Germany from the Austro-Hungarian Empire and its twin capitals, Vienna and Prague—the home not only of Logical Positivism but of the first glimmerings of Mendelian genetics.
To the west, it ran roughly along the border between Germany and France, although later in the twentieth century Paris would become one of Hegelianism’s most important outposts. To the north, Great Britain was largely sheltered from its influence by its own long empirical tradition, as well as by the rise of Darwinism. Even so, important outcroppings appeared at Cambridge and Oxford in the 1880s. In the United States they came as early as the 1850s, where American Transcendentalists like Ralph Waldo Emerson came to worship at the temple of The Phenomenology of Spirit.27

  Farther north, Scandinavians by and large resisted the spread of Hegelianism. The existentialist philosopher Søren Kierkegaard made it his principal target. To the south, however, the Hegel Line thrust deep into Italy, where Benedetto Croce (1867–1941) made his version of Hegel’s science of history a virtual orthodoxy; he became as much the intellectual dictator of Italy as Hegel had been of Germany.28 At the farther ends of Europe, in Spain and Russia, it is hard to find a serious thinker in the later nineteenth century who wasn’t influenced by the philosopher from Jena.29

  What made Hegel so irresistibly appealing? First of all, his totality as a thinker. His theories didn’t just draw together science, art, history, and philosophy into a consistent (if not always coherent) whole. His vision of totality also embraced, and subsumed, the individual. As with Plato, Hegel taught that the key to human happiness was belonging to an entity larger than ourselves. For Hegel and the Hegelian, the desire of each person to lead his or her life as he or she pleases—the Lockean individual of the Enlightenment—was as morally absurd as it was physically impossible. We are all inevitably parts of larger and larger wholes, Hegel explained, both organically (the individual and his family belong to a village or town; that local community is part of the nation; and so on) and over time, as all things become integrated into the ultimate reality of the Absolute—including the State.30

  What the Catholic Church had been for Saint Augustine, the modern political state became for Hegel and the Hegelians: the universal community of the future. The crucial difference was that Augustine’s community was bound together by belief in a supreme power greater than itself. In sharp contrast, Hegel’s State is held together by its belief in itself, and the certainty that in the long run it can do no wrong. “The State is the reality of the moral idea,” he wrote in The Philosophy of Right, “which thinks and knows itself, and fulfills what it knows.”31

  Marx had substituted the word class for the State, but the effect was same. Both for Marx and for Hegel, the illusory freedoms set forth by Locke and the Enlightenment were doomed to disappear. History and the future belonged to newer, stronger forces, and Hegel’s legacy was to prepare the way for it.

  Marx had seen the future arise from the proletariat. For Hegel himself, it had risen up from the squabbling principalities of Germany and central Europe, the trash heap left behind by the decay and collapse of the medieval Holy Roman Empire, the disasters of the Reformation, and Napoleon’s conquests. He had concluded that the full development of the Absolute in history, including the State, belonged to the German race. “The German spirit is the spirit of the new world,” he wrote. “Its aim is the realization of absolute Truth as the unlimited self-determination of freedom,” meaning freedom not in the Anglo-American sense of rights and natural law but in the sense of belonging to a greater, more real whole.32

  At the University of Berlin, Prussia’s capital, first Hegel and then his disciples held forth to generations of students on the inevitable triumph of the German spirit in History, and on the kingdom of Prussia as the state that most embodied that idea.33 The nickname for the Berlin faculty became “The First Guards Regiment of Learning.” Other German universities, like Freiburg and Heidelberg and Leipzig, also played their part in the march of German nationalism. It would be a gross error to imagine that every German scholar or thinker in 1860 was an Hegelian.§ All the same, Hegel’s Berlin became the epicenter of a series of seismic tremors, both intellectual and political, that would remake the map of Europe. They would erupt first to the east, along the German-Austrian border at Königgrätz in 1866, where the Prussian army decisively defeated the Austrian forces in a driving rainstorm.

  The battle of Königgrätz decided not only who would dominate Germany but the intellectual future of continental Europe. First the Saxons saw the writing on the wall and became a Prussian ally. The other German states, like Bavaria and Hanover, soon followed. Four years later Kaiser Wilhelm I, his first minister Otto von Bismarck, and the Prussian army would repeat their triumph, this time over the French in the Franco-Prussian War. In 1871, a united German state and empire had emerged that was poised to become the colossus of Europe and the fulfillment of Hegel’s dream.

  Germany would soon pass both Britain and France as a producer of iron and steel and coal. Its scientists pioneered the industrial development of drugs, synthetic dyes, and chemicals, while its universities became major centers of research and learning (the chief reason Albert Michelson came to Berlin in 1881). Its finest minds became cultural legends, from Goethe and Beethoven to Kant, Leibniz, and Hegel himself. To be German (or barring that, at least of Germanic racial stock) was to be in some degree a participant in Western civilization at its highest trajectory.

  Meanwhile, the efficiency of Germany’s Hegelian-inspired government bureaucracy became the envy of Europe. Its offer of unemployment insurance to workers in 1881 forced virtually every other country to take the first tentative steps to creating the modern welfare state. At the same time, its disciplined and invincible army became an inspiration to military gurus around the world—while its navy aspired to be a global presence as powerful as that of Britain’s Royal Navy.34

  By 1880, British statesman Benjamin Disraeli pronounced “the German revolution” a greater event than the French Revolution of the previous century.35 Rousseau’s revolution, after all, had ended in terror and blood. Hegel’s revolution in Germany, by contrast, seemed on the brink of universal fulfillment. History—and the march of the Absolute—were clearly on the Germans’ side.36

  By 1905, that march had advanced far enough to alarm those on the other side of the Hegel Line, especially in the West. France and Britain had made common cause and in 1904 signed an Entente Cordiale, while France brought along its traditional ally, Russia, to make a third at the table. Emperor Franz Josef of Austria and his entourage sensed where their geopolitical and strategic future lay and signed a similar alliance with Germany, as did the newly unified Italy.

  Other parts of the Austro-Hungarian Empire, including its universities, were not so sure. Indeed, the hostility on the part of Ernst Mach and the Logical Positivists to the systems of Hegel was at least in part a declaration of independence against the encroaching monolith of imperial Germany—a declaration of cultural and intellectual independence as loud and clear as the American declaration of political independence in 1776.‖37

  Something similar was happening in the new atomic physics. In 1910, Denmark stood well above the Hegel Line. So it’s not surprising that when Niels Bohr decided to study physics, he turned first not to study in neighboring Germany but with J. J. Thomson at Cambridge, and then Ernest Rutherford at the University of Manchester, who was the best experimental physicist in the world. Like Einstein, Rutherford was a convert to the atom, and in 1911, he proposed a definitive model of how its tiny world worked. Rutherford based it on the model of the solar system, with a heavy central core or nucleus akin to the sun at its center, and electrically charged particles or electrons circling the nucleus like the planets.

  It was brilliant, it worked mathematically, and it had the advantage of appealing to what had become by 1900 a robust commonsense image—the heliocentric cosmos of Copernicus and Galileo. But Bohr saw at once that there was a problem. All systems run down, even the solar system eventually—that was the lesson of entropy. What keeps the electrons in their orbits? If they really are like little planets, they must wind up falling into the nucleus. Something else must keep them f
rom losing energy—some new undiscovered principle that limits the energy every electron gives out to a fixed value so it doesn’t drain away.

  Bohr found it in Planck’s quanta. As long as the electron in a hydrogen atom, for example, stays in a single orbit, it emits no energy. When it jumps from one orbit to another, it emits a quantum of energy—and the energy difference between the two orbits is released as a tiny burst of light. That light is reflected, Bohr discovered, in the spectrum that each element generates not as a continuous range but as discrete bright lines that define that element. Hydrogen, for instance, releases three lines, one red, one blue-green, and one blue. Each is the visible trace of a release of energy as the electron jumps from orbit to orbit.

  Bohr published his paper “On the Constitution of Atoms and Molecules” in 1913. As the prospect of war hovered over Europe, an even greater event broke over Western civilization: the overthrow of Newton’s universe, and the overthrow of matter.

  Bohr’s paper revealed the precise mathematical workings of an unseen world that underlies everything, and whose only visible trace is a series of spectral lines like a footprint. Matter—the primary building block of nature for every scientist since Aristotle—turned out to be nothing but packets of energy.

  At the center of the action is the movement of electrons. When electrons remain tied to their atomic nuclei, they generate stability—the apparent solidity of objects, which are actually atoms in a low-energy state. When they jump from their ground state to the next energy level, they create the phenomenon known as electricity. When they do, however, the energy released can trigger the electrons of other atoms to do the same. If they get the right boost of quantum energy (defined as the resonant frequency multiplied by something called Planck’s constant), electrons respond to each other like tones on a musical scale. They can even bind atoms together to form molecules, the building blocks of chemistry. In short, the mechanics of the quantum revealed not only the nature of electricity but also the atomic nature of the chemical bond.38