Einstein's Genius Club (21 page)

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—were 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.

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.)

In the happy years of the 1920s, Bohr played the diffident, sometimes disapproving father, Heisenberg the rebellious and brilliant prodigy. In his three years at Copenhagen, from 1924 through 1927, Heisenberg proved his worth. His first major contribution was a formula that figured the energy states within an atom. Max Born and Pascual Jordan extended the formula into a true matrix mechanics with which all frequencies of the spectrum could be figured. Heisenberg's second contribution was less formalistic and much more incendiary. The uncertainty principle by its very nature contradicted classical physics and, in a way, challenged the very essence of modern science. Throughout the development of classical physics, it was assumed that perfectly accurate measurement was possible, in ideal conditions. Only the crudeness of
our measuring apparatus stood between our results and the object's true dimensions. Heisenberg said no, it is impossible to “see” sufficiently into the atom to know for certain what processes—specifically, wave or light—one is measuring. Further, whatever means we use to measure will inevitably disturb the element under scrutiny. Thus, the “observer” will affect and distort the “observed.”

For Bohr, Heisenberg's uncertainty principle was too limited. It focused only on conditions that occurred during observation, and in effect ignored the “wave” state. Bohr insisted (vehemently) on much more. Little was gained, he argued, from ignoring empirical evidence.

The wave-particle duality that so vexed quantum physics had a very solid empirical history. It began with an experiment, now replicated in physics classrooms throughout the world, called the “double-slit experiment.”

In 1801, Thomas Young (a physicist, physician, and Egyptologist who in his spare time deciphered the Rosetta Stone) devised a mechanism to analyze light: “I made a small hole in a window shutter, and covered it with a thick piece of paper, which I perforated with a fine needle,” he told the Royal Society in 1803. Thus began what has been called the most beautiful experiment in physics.
³⁰
When Young “split” the sunlight by dividing it with a thin card, he observed, projected onto the wall, “fringes of colour on either side of the shadow”—clear evidence of interference or diffraction. He was astonished. Light, according to Newton, was made of particles. Yet as it traveled past Young's thin card, it diffracted, just like a wave breaking on a jetty. Startling as this was for Young, a 1927 variation on the double-slit experiment came up with an even more astounding result: Electron beams from a nickel crystal produced diffraction. Matter, like light, was shown to behave like waves.

Young's experiment was the basis for much resistance to Einstein's theory of photons. After all, Young had proved that light was wave, not particle. Einstein countered with proof of light's particle nature. In 1915, Robert Millikan, after ten years of experimentation,
reluctantly concluded that Einstein's equations were correct. In 1923, Arthur Compton confirmed the particle nature of electromagnetic quanta by observing the scattering of electrons from X-rays.

Thus, the paradox: Light and, as de Broglie proved, matter are both wave and particle. If physics had challenged our intuitive sense of the world with relativity, it now seemed to have done away with intuition altogether. After all, these states—wave and particle—are quite different. A wave is continuous and nonlocal, spread out over a large area. Particles are discrete, indivisible, and local. Richard Feynman calls the uncertainty principle a “logical tightrope on which we must walk if we wish to describe nature successfully.”
³¹
We must think anew, says Feynman, “in a certain special way” to avoid “inconsistencies.” The awkward phrasing is unusually revealing. Quantum physics challenges not only our intuitive perception, but the limits of language. When Bohr and Heisenberg argued over the uncertainty principle, more was at stake than the utility of the principle itself. In order for a theory to “work,” it must not only explain evidence; it must also gain acceptance among practitioners. Bohr was older than Heisenberg and certainly more empathetic to the general state of alarm over quantum mechanics. Perhaps, too, he was more understanding of our psychological need to visualize (that is, imagine, in its etymological sense) our world. Something in addition to de Broglie's elegant proofs was needed to bridge the gap between particle/discontinuity (the side favored by Heisenberg) on the one side and wave/continuity on the other.