Einstein's Genius Club

by Feldman, Burton, Williams, Katherine

  In the world of drama, only Shakespeare can be said to rival Sophocles. Literary works are unique and their truths timeless. But the same cannot be said of science. If Einstein had not modified Newton, someone else would have sooner or later, with whatever variations. Science guarantees that all its members will be challenged and essentially usurped—though it might be more accurate to say superseded, displaced, corrected, or improved. Einstein was challenged in just this way when quantum mechanics emerged in 1925, for its view of the universe contradicted Einstein's most fervent beliefs. If gravity is ever joined successfully to quantum mechanics, even the theory of relativity may well be modified.

  Are we to imagine that if Einstein at fifty had retained his youthful powers of imagination, he would have been able to find a unifying theory? That does not seem realistic. No matter how much genius was applied, the time was not ripe: Too little was known about electromagnetism and the fundamental forces of the atom. Strong and weak nuclear forces had yet to be discovered. Yet Einstein, trusting to his formalisms and intuition, dismissed the new evidences of quantum mechanics.

  ON THE QUANTUM PATH

  In 1905, Einstein, working on a problem called the “photoelectric effect,” wrote a paper that some say gave birth to the quantum revolution.23 This paper, modestly titled “On a Heuristic Viewpoint Concerning the Production and Transformation of Light,” offered to solve problems rather than build theory. Still, its language portended radical change:

  It seems to me that the observations associated with black-body radiation, fluorescence, the production of cathode rays by ultraviolet light, and other related phenomena connected with the emission or transformation of light are more readily understood if one assumes that the energy of light is discontinuously distributed in space. In accordance with the assumption to be considered here, the energy of a light ray spreading out from a point source is not continuously distributed over an increasing space but consists of a finite number of energy quanta which are localized at points in space, which move without dividing, and which can only be produced and absorbed as complete units.24 [emphasis added]

  “Discontinuously… not continuously distributed… quanta”—these are words that fly in the face of Newton and his classical world. It was as if, in his most productive year, Einstein spoke what much later he would, like Shelley's Prometheus, “re-pent me.”

  Like all science, quantum physics was built on the shoulders of history. As we have seen, by 1900, the world of physics had split into warring camps or worldviews, each still under the sway of classical Newtonian physics. On one side was the Enlightenment faction, which believed the world a clockwork mechanism. On the other side were the converts to electromagnetic theory, which under Maxwell had wedded electricity and magnetism into a unified theory. Yet problems remained that could not be explained by either side. Among them were three bedeviling conundrums: black-body radiation, the photoelectric effect, and bright-light spectra, which could neither be explained by classical physics nor ignored (certainly not by young physicists out to make their name). Solving them led inexorably to the quantum revolution.25

  The first inkling of quantum theory came from a lab in Berlin. In 1900, Max Planck was a forty-year-old physicist with expertise in chemistry and thermodynamics. He was also a fervent believer in the second law of thermodynamics, which states that in a closed system, entropy (loosely translated as “disorder,” but also meaning heat loss) increases and, once achieved, cannot be reversed. It was Planck's appreciation of this law and his refusal to give it up that led him to the black-body solution.

  Planck was one of the few theoretical physicists amid the cadres of experimental scientists populating German universities. He was to some extent off the academic radar, and thus had the freedom to contemplate problems that spanned disciplines. Although focused on thermodynamics, he knew of electromagnetism. Maxwell, remember, had demonstrated that light is an electromagnetic wave. Planck believed in Maxwell's findings. More obviously, he noted in the black-body question the intersection of heat (his field), light, and electromagnetism.

  Planck set out to examine black-body radiation in the context of the second law. Again, the black-body problem had resisted explanation by classical physics, but held out much practical promise. The reason is that radiation is emitted from the black body in the form of light—specifically, color. For centuries, potters had observed that heat within their kilns turned colors, like a spectrum. From blue through white, each successive color indicates hotter temperature. What can black-body radiation tell us about the behavior of radiation?

  As was their wont, German physicists tackled the problem experimentally. They created a black body—an enclosure that would absorb all the electromagnetic radiation it could—with a small hole through which electromagnetic waves could escape. Then they observed the color distribution of radiation coming through the hole. They hoped in this way to study the electromagnetic waves within, just as Maxwell had studied heated gases. To be sure, the question was of more than theoretical interest. Electricity was big business at the turn of the century. If a means for measuring emitted energy could be discovered, electrical companies would be able to quantify their product and provide the greatest amount of power using the least energy.

  Two formulas emerged. Unfortunately, one worked well for high frequencies, but not for low frequencies; the other worked only for low frequencies. In fact, at higher frequencies, the second formula produced an impossible result. Light, as had been established, comes in waves, and waves, unlike particles, can multiply infinitely—they just get closer and closer together. As the waves moved closer and closer at higher frequencies, the power (or temperature) would, theoretically, enter the ultraviolet zone and beyond, to infinity. It would become an “ultraviolet catastrophe,” emitting radiation with infinite power! Fortunately, nothing like that happens in real life. The black-body heat finds equilibrium, just as Maxwell's gas had. The problem was how to formulate an equation that would explain what was happening.

  Planck tried formulae that were tied to the second law of thermodynamics, using standard theories of radiation. Nothing worked. At last, he tried a thought experiment. What if, instead of waves, the black-body chamber was full of oscillating and discrete charges? As the interior heats up, the charges would continue to oscillate at all of the possible frequencies. Planck reworked his formula to fit the experimental results, using a constant to make the equation work. With great consternation, he pondered the result. Only by imagining the electromagnetic waves as discrete elements, using statistics, as Maxwell had with heated gas, and ascribing to the resulting discontinuity a constant (h), could he fit the formula to reality. Planck, forever the enemy of what would become quantum physics, had “quantized” radiation, at least within the black body. At the time, however, he preferred to think of his “constant” as a useful trick rather than a key to atomic architecture.

  Ironically, it was Einstein, implacable foe of later quantum theory, who established a theoretical basis for Planck's constant. In essence, he quantized light. He also solved a second conundrum: the photoelectric effect. As Planck was pondering the black-body problem, another German, Philipp Lenard, was experimenting with cathode rays and light beams. He tried shining a light of a single frequency onto a thin metal foil. The result was startling, to say the least. Out of the foil came electrons. The light had somehow ejected electrons. If light were a wave and the electrons were ejecting because they were being disturbed by the energy of the light, then it follows that if the light were of greater intensity, the electrons would carry more energy when they were ejected. But Lenard found otherwise: At low frequencies, even with a very bright beam, no electrons were ejected; at increasingly higher frequencies, the energy of the ejected electrons remained the same. Nothing in classical physics explained Lenard's findings.

  The explanation came in Einstein's second paper published in 1905. If, Einstein argued, we consider light not as waves but as photons, we can then explain the p
hotoelectric effect—the emission of electrons that occurs when light is shined on metal. If light acts not as a continuous wave, but as a collection of particles, then the photoelectric effect is nothing more than photons colliding with electrons—tiny particle colliding with tiny particle. His idea of photons explained another problem: that of cooling bodies, which gave off heat not in a neat, continuous way, but discontinuously, “jumping” from temperature to temperature. Newtonian physics could not account for this phenomenon. Quantum physics did. For his discovery of photons—not for relativity—Einstein won the Nobel Prize.

  It was not long before someone—it turned out to be the French aristocrat turned experimental physicist Louis de Broglie—asked the obvious question: If light waves behaved like particles, could particles of matter behave like waves?

  Before we hear de Broglie's answer, we must take a detour into the atom itself. As Einstein was investigating the large story of gravity and the universe, others searched in the opposite direction, trying to understand the architecture and behavior of invisible particles.

  The idea of the atom was first proposed in fifth-century Greece by the philosopher Democritus. If one chisels away at a rock, he reasoned, one is left, eventually, with a fragment so small that it cannot be divided again. These are atomos—the Greek word for “indivisible.” In the battle over scientific theory, Democritus lost out when Aristotle sided with Empedocles, who defined matter in terms of the four basic elements of fire, water, air, and earth. The atom was lost for more than a millennium. When it resurfaced, in the seventeenth and eighteenth centuries, science found its way back to the atom through the successive findings of Nicolaus Copernicus, Isaac Newton, Christian Huygens, Robert Boyle, Daniel Bernoulli, Joseph Priestley, and Antoine Lavoisier. In 1778, Lavoisier renamed the gas Priestley had isolated “oxygen.” It was the first element to be isolated and named.

  Then came John Dalton, a teacher and scientist in Manchester, a city at the heart of the English Industrial Revolution. Blessed with typical British weather, Manchester was an ideal location for Dalton, a keen observer who kept meticulous notes, to study fog. He knew from Lavoisier that oxygen combined with hydrogen to make water. In fog he found clarity: Water could behave as air, just as it could ice. What made this possible? The answer was—atoms. In air, the atoms were spaced far apart; in solids, atoms bunched together. For the next century, scientists discovered, analyzed, and classified elements. Still, the atomic structure, by definition invisible, remained a mystery.

  Toward the end of the century, the veil began to lift. At Cambridge, a young mathematician, J. J. Thomson, was put in charge of the Cavendish Laboratory. Under Thompson, the Cavendish flourished, attracting first-rate students and researchers. Its fame was solidified in 1897, when Thompson discovered the electron (which he called “corpuscle”) by isolating the particles that make up cathode rays. With the venerable Lord Kelvin, Thompson proposed a rather chunky atomic structure, a souplike concoction with floating electrons, dubbed the “plum pudding model.”

  As one might expect, the plum pudding model found few backers besides Thompson and Kelvin. Fortunately, the Cavendish nurtured great students. In 1895, when applicants from abroad were first admitted, Ernest Rutherford, fresh off the boat from New Zealand, appeared at the door.26 The experience of working with Thompson changed Rutherford's life. He became an atomic specialist, landed at the University of Manchester, and, in 1909, conducted a “most incredible” experiment. With his students Hans Geiger and Ernest Marsden, he shot alpha particles (bundles of neutrons and protons emitted by radium) through a thin sheet of gold foil. Most of the particles passed through. A few, though, bounced back. The plum pudding model had no hard centers to stop the alpha particles. How to model this phenomenon? Rutherford borrowed the image of the solar system, with electrons circling an interior nucleus. The Rutherford model was not without problems. Still, it “worked,” just as Newton's gravity had. By envisioning the solar system model, Rutherford and his students measured the nuclei of different elements. They could now explain atomic number and nuclear weight with much greater clarity. Over the next few years, Rutherford looked deep into the atom, and in 1917 he became the first scientist to “split” the atom by bombarding a nitrogen nucleus, transforming it into oxygen and emitting hydrogen. The “solar system” model is still with us. It is useful and easy to visualize.

  As Rutherford had revised Thompson's plum pudding model, so would a Rutherford student rethink the atom as solar system. Niels Bohr came to Manchester in 1911, armed with a complete set of Dickens from which to learn English. He had a doctorate from Copenhagen University and an impressive background in electron theory. Little wonder that he had sought out Rutherford's laboratory. Rutherford was an ideal teacher—cheerful, avuncular, and inspirational. His laboratory, if a bit rollicking, teemed with ideas and energy. He was known to sing “Onward Christian Soldiers” to his student-troops, his booming voice preceding him as he swept from room to room.

  At Manchester, Bohr tackled the inherent problem of the solar system model with typical Continental audacity. He knew that Rutherford's model was wrong according to classical physics. An electron circling the nucleus would emit energy (because of angular momentum) and thus fall into the nucleus. The atom would collapse, and matter would not exist. Bohr stabilized the model by abandoning classical physics. His electrons would move in fixed orbits around the nucleus. Each orbit corresponded to an energy level. The lowest energy level was closest to the nucleus.

  To reach these conclusions, Bohr himself made a quantum leap. If, rather than continuously emitting energy, the energy loss, like Planck's quanta, is discrete and particle-like, not continuous and wavelike, then electrons would emit fixed amounts of radiation when they move from one orbit to another. This “jump,” Bohr reasoned, is as discontinuous as Planck's black-body charges and Einstein's photons. The momentum of a particle changes (rises or falls) in discrete quantities. In other words, like Isaac Asimov's spaceships, electrons “jump” instantaneously through space, from one orbit to another. When an electron jumps from a higher energy orbit to a lower one, it emits light. When an electron jumps from a lower energy orbit to a higher one, farther from the nucleus, it does so because it has absorbed energy from some other source. This happens, for instance, when a chlorophyll molecule in a maple leaf or the metal hood of a black SUV absorbs light. The chlorophyll molecule absorbs heat and converts it into food for the tree; the black SUV atoms radiate heat, electron by electron, sufficient to fry an egg. They do so not by emitting heat continuously, but discontinuously, by emitting “quantum” amounts of heat generated when an electron “jumps” from a higher to a lower energy state.

  Discontinuity is the key concept here. No longer was physics solely within the classical realm. The quantum moment had arrived. Into the fray stepped a new generation of young theorists unattached to classical physics and chafing at its inadequacies. Of these, Pauli, Heisenberg, Paul Dirac, Louis de Broglie, and Max Born stood out. In rapid succession, from 1914 to 1927, came the building blocks of quantum physics: confirmation of stationary solid states (James Franck and Gustav Hertz); confirmation that matter was both particle and wave (Arthur Compton and de Broglie); Pauli's exclusion principle; matrix mechanics; and two sets of statistics for counting particles (Bose-Einstein and Fermi-Dirac).

  Far from settling matters, though, these discoveries demolished Bohr's atomic model. Its death knell sounded in 1924, when de Broglie's doctoral thesis proved that matter was not just particles, but also waves. He did so in part by applying to all matter the lessons of Einstein's photon. The “pilot” waves that follow matter through space are not incidental, but have frequencies directly related to the particle's motion.

  Matter, like radiation and light, now possessed this dual nature. No longer was physics divided into two camps, as de Broglie remarked in his Nobel Prize speech. The two conceptions of physics—matter, governed by Newtonian mechanics, and radiation, envisioned as traveling waves—w
ere now “united.”27 Bohr's model, shackled to the image of electrons as particles, no longer stood. Its demise plunged the subatomic world into the same state of disarray that had befallen macrophysics with Einstein's theories of relativity. Suddenly, our intuitive sense of the world no longer held true. Beneath (and above) our world of appearances, there exist wholly different worlds. In one, all motion is relative except for the speed of light. In the other, particles are waves and the reverse, obeying laws that contradict even Einstein's revolutionary laws.

  THE COPENHAGEN INTERPRETATION

  Into the breach of Bohr's atomic theory, now in tatters, stepped Werner Heisenberg. Fresh from a year of apprenticeship with Max Born, Heisenberg was acknowledged to be a brilliant theorist with an aversion to experimental physics.28 He and Pauli met Bohr at the Göttingen lectures of 1922. So taken was Bohr with Heisenberg's questions that he proposed a walk up Hain Mountain. During that afternoon, wrote Heisenberg, “my real scientific career… began.”29 It was the first of many conversations, often heated, between the father of quantum physics and the daring and inspired Heisenberg. Pauli often served as intercessor when disputes between the two threatened progress. It worked. Together, Heisenberg and Bohr forged a complete theory that would become known as the “Copenhagen interpretation.”

  Still, it was a tangled relationship—one that became more tangled in 1941 when Heisenberg and Bohr took their famous evening stroll through a park in German-occupied Copenhagen. At that meeting between the German patriot and the Danish Jew, Heisenberg did or did not try to extract from Bohr atomic secrets; did or did not hope to discover the extent of the Allies atomic program; did or did not suggest the immorality of atomic weapons. What happened during that evening stroll has been a matter of dispute ever since and fodder for Michael Frayn's play “Copenhagen.” (That their meeting took place in a woodland is in itself interesting. Nature was the backdrop for several “leaps” in quantum theory, most famously when Heisenberg's hay fever forced him into seclusion on a North Sea island, where he pondered atomic structure and thought up matrix mechanics, the first formulation of quantum mechanics.)