It may have been the ancient Greeks who first conceived of a tiniest unit of matter, the atom, or atomos, meaning “uncuttable.” Atoms were not only uncuttable. They were indestructible. Atoms protected us from the whimsy of the gods, said Democritus and Lucretius, because atoms could not be created or destroyed. Even the gods had to obey atoms. Newton also prized atoms, but as the handiwork of God rather than as a defense against Him. Newton, who understood the logic of nature better than any mortal before him, wrote: “It seems probable to me that God in the beginning formed matter in solid, massy, hard, impenetrable, moveable particles…so hard as never to wear or break in pieces; no ordinary power being able to divide what God Himself made one in the first creation.” Indeed atoms were the ultimate oneness of the material world. Perfect in their indivisibility, perfect in their wholeness and indestructibility.
Atoms also unified the world, because a leaf and a human being are made of the same atoms. Take apart a leaf or a human and we find identical atoms of hydrogen and oxygen and carbon and other elements. With atoms, we have a foundation for material reality. On that foundation, we can build systems. We can organize and construct the rest of the world. Said Lucretius: Pleasing substances are made of smooth and round atoms, bitter substances of hooked and thorny atoms. With atoms, we can make rules for the particular proportions in which different substances combine, as British chemist John Dalton did in the early nineteenth century. Carbon monoxide: one atom of carbon joined to one atom of oxygen. Carbon dioxide: one atom of carbon joined to two atoms of oxygen. Never carbon with one and a half atoms of oxygen. Because atoms cannot be divided. With atoms, we can predict the properties of the chemical elements, as Dmitri Mendeleev did in the mid-nineteenth century.
Atoms prevent us from falling forever into smaller and smaller rooms of reality, contrary to the notions of Pascal. When we reach atoms—so the thinking went—the falling stops. We are caught. We are safe. And from there, we begin our journey back up, building the rest of the world.
Although atoms had been conjectured for a couple of thousand years, their size wasn’t known until the work of Albert Einstein, in his miracle year of 1905. Among many other things Einstein studied at the time—relativity, the particle nature of light, and so on—was the jittery motion of tiny particles suspended in a fluid, so-called Brownian motion, named after the botanist Robert Brown, who in 1827 first described the random dance of pollen suspended in water. Einstein reasoned that the jittery motion must be caused by collisions with water molecules. By calculating how often and with what force a grain of pollen should collide with a water molecule and comparing this to the observed motions, Einstein was able to estimate the size and mass of a water molecule, and thus the sizes and masses of the hydrogen and oxygen atoms that made up the molecule.
At an engaging internet site hosted by the American Institute of Physics, you can listen to the voice of Joseph John Thomson talking about his discovery of electrons in 1897. Electrons were the first attack on the atom. At the time of the recording, in 1934, Thomson was seventy-eight years old and had been for many years the Cavendish Professor of Experimental Physics at Cambridge University. The recording crackles with static, but the words are unmistakable: “Could anything at first sight seem more impractical than a body which is so small that its mass is an insignificant fraction of the mass of an atom of hydrogen?” Impractical indeed! But practicality is beside the point here. We’re talking about a revolution of ideas, a bombing of the palace of Unity and Indivisibility. A photograph of Thomson at the time shows a deadly serious gentleman, balding, with spectacles and a thick walrus moustache, hands tightly clasped, starched white collar, staring unflinchingly into the camera as if he were looking two thousand years of history in the eye without apologies. “It was coming sooner or later,” his gaze seems to say. “So buck up and take it like an adult.”
Thomson made his discovery by measuring the paths of electrically charged particles as they were deflected by electric and magnetic forces. First, he and others had to develop good “vacuum pumps” for removing the air in the glass tubes through which the particles moved. Molecules of air interfere with the delicate trajectories of the tiny particles under study. I have a great deal of respect for vacuum pumps. I used them myself during my short-lived encounter with experimental physics as a university student. A vacuum pump, when working properly, starts out with a coarse, grating sound, like the chug of a locomotive, then graduates to a clicking whine, rising in pitch, and ends with a smooth hum when a good vacuum has been attained. When the vacuum is incomplete, the pump never gets past the chugging locomotive stage.
The amount of deflection of a charged particle in a good vacuum indicates the ratio of its electrical charge to its mass. From previous experiments, Thomson and others already knew that particular ratio for hydrogen atoms, the lightest of all atoms. What Thomson found was that these other particles, the electrons—which he called “corpuscles” and which could be created by heating a piece of metal—had a ratio roughly 1,800 times larger than that of hydrogen atoms. Assuming the same electrical charge, the mass was then inferred to be 1,800 times smaller. Evidently, these things were really tiny compared to atoms (although the size of the latter was not known until 1905, as mentioned above). The atom was not the smallest unit of matter.
While Thomson was discovering the electron in England, Antoine Henri Becquerel and Marie Skłodowska Curie were discovering the disintegration of atoms in France, what Madame Curie called “radioactivity.” Becquerel believed that the mysterious radiations recently observed to emanate from uranium, the so-called X-rays, were the result of the absorption of sunlight. The uranium X-rays, in turn, could be detected by nearby photographic plates. When Becquerel did his experiment, on February 26, 1896, Paris was cloudy. His uranium did not receive any energizing sunlight. On a whim, he decided to develop his photographic plates anyway. To his surprise, the photographic plates were strongly exposed, showing that the uranium emitted some kind of radiation on its own, without needing to be powered by the Sun. Later experiments by Becquerel showed that the radiations were electrically charged particles of some kind because they were deflected by magnetic fields, as were Thomson’s electrons. After the discoveries of Becquerel, Madame Curie did further studies of uranium rays and found that the uranium atoms were hurling out tiny pieces of themselves. A year later, Curie found the same atomic disintegrations with another element, radium. The indivisible atom was, after all, divisible. And what lay inside? No one knew. The bottom of the universe had fallen out.
Here is the reaction of historian Henry Adams in 1903 to these disturbing developments:
As history unveiled itself in the new order, man’s mind behaved like a young pearl oyster, secreting its universe to suit its conditions until it had built up a shell of nacre that embodied its notions of the perfect…He sacrificed millions of lives to acquire his unity, but he achieved it, and justly thought it a work of art.
“One God, one Law, one Element” [Adams quoting Tennyson]
Suddenly, in 1900, science raised its head and denied…the man of science must have been sleepy indeed who did not jump from his chair like a scared dog when, in 1898, Mme. Curie threw on his desk the metaphysical bomb she called radium.
With his new corpuscles in hand, Professor Thomson proposed what became called the “plum pudding” model of the atom: a tiny ball filled uniformly with a “pudding” of positive electrical charge, into which were sprinkled the negatively charged electrons. You needed the positively charged pudding to balance out the negatively charged electrons, since it was known that most atoms are electrically neutral.
Fifteen years later, the great physicist from New Zealand, Ernest Rutherford, and his assistants found that the atom was not a pudding at all. It was more like a peach. A hard nut resided at its center, containing all of the positive charge and nearly all of the mass. The new particles residing within that hard central nut were called protons and neutrons. Protons have positive electrical charge, neutrons have no charge. This peach picture emerged after Rutherford’s team fired subatomic particles at a thin sheet of atoms. Some of the particles veered off at large angles, as if they had hit something hard, a hard nut in the atom. With pudding, the deflections should have been small. “It was quite the most incredible event that had ever happened to me in my life,” boomed Rutherford. “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.” The hard nut at the center of each atom, the “atomic nucleus,” is a hundred thousand times smaller than the atom as a whole. To use an analogy, if an atom were the size of Fenway Park, the home stadium of the Red Sox in Boston, its dense central nucleus would be the size of a mustard seed, with the electrons gracefully orbiting in the outer bleachers. In fact, 99.9999999999999 percent of the volume of an atom is empty space, except for the haze of nearly weightless electrons. Since we and everything else are made of atoms, it is literally a fact that we are mostly empty space. That vast emptiness is perhaps the most unsettling consequence of dividing the indivisible.
Eventually, Rutherford’s protons and neutrons, at the center of the atom, would themselves be found to consist of even smaller particles called quarks.
Were we falling and falling without end? Were there unlimited infinities on all sides of us, both bigger and smaller, as Pascal believed? It is an unpleasant sensation. I am reminded of the Escher drawing Ascending and Descending, which depicts a line of cloaked men walking around a quadrangle in a medieval castle. The disturbing feature of the picture, achieved through a trick of perspective, is that the walkers are always ascending, marching up a continuously rising staircase, and yet after completing the loop they end up exactly where they began. It is a staircase without beginning or end. It is a staircase that goes nowhere.
Escher made Ascending and Descending in 1960, at a time when physicists had recently discovered hundreds of novel subatomic particles in the new “atom smashers” and in high-energy radiations from space. The field of research into elementary particles and forces was thrown into chaos. In addition to the electrons and protons and neutrons, there were now delta particles and lambda particles, sigmas and xis, omegas, pions, kaons, rhos, and more. When the Greek alphabet was exhausted, the confounded physicists resorted to using Latin letters. Some of these new subatomic particles had total lifetimes, from the moment they were created to the moment they disappeared, of a mere 10-21 seconds, or 0.000000000000000000001 seconds. Before, even with the sacred atom fractured, there had been some kind of order. There had been only the electrons and protons and neutrons. But now—this howling zoo. There seemed to be no fundamental particles, no bottom to the infinite spiral down, no organizing principles.
Then quarks were discovered in the late 1960s. Temporarily, the plummeting stopped. Each of the hundreds of new particles could be understood as a particular combination of a half-dozen basic quarks. Quarks offered a new system for organizing the subatomic zoo. Quarks were the new protons and neutrons, which, in turn, had been the new atoms. I once asked physicist Jerry Friedman, co-discoverer of quarks, whether he thought that the quark was the end of the line, the smallest unit of matter. “Probably,” he answered. He gave reasons. But he hesitated. “I could be surprised,” he said with a grin. “There are always surprises in science.” Surprises in science are good things, and bad.
The philosophers of ancient Greece developed a terrifying view of the world called Zeno’s Paradox. Suppose you want to walk 15 feet across a room. Before you travel that distance of 15 feet, however, you must go halfway, which is 7.5 feet. And before you go that 7.5 feet, you must travel half of that distance, 3.75 feet. And before you go that 3.75 feet…And so on. In their minds, the philosophers kept chopping space into halves, into smaller and smaller dimensions ad infinitum, as did Pascal centuries later. The indivisible was pitted against the divisible. The ultimate conclusion of this intellectual exercise is that you cannot cross the room. In fact, you cannot move even an inch. You are frozen in a metaphysical conundrum. You are trapped by the infinity of the small.
When scientists and mathematicians talk about infinity, they are usually imagining a sequence of bigger and bigger spaces and numbers. But infinity can go in the other direction as well. Jerry Friedman, physicist rather than philosopher, is more hopeful. He thinks that the quarks may be the end of the line.
Other physicists disagree. In the last forty years, physicists have proposed objects far smaller than quarks, called “strings.” Instead of being point particles, like electrons, strings are extremely tiny one-dimensional “strings” of energy. Their sizes would be the Planck length, where gravity and quantum physics are joined. (See the earlier chapter “Between Nothingness and Infinity.”) An important property of strings is that they occupy a space of nine or ten dimensions, instead of the familiar three. In our world of tables and trees, we would not be aware of the additional dimensions because they are curled up into ultra-tiny loops. In the same manner, a garden hose appears as a line when seen at a distance.
Strings were originally proposed as a theory of the strong nuclear force. In more recent years, they have been hypothesized as part of a theory of quantum gravity—that is, Einstein’s theory of gravity, general relativity, revised to include quantum physics. At present, no one knows how to test string theory or even whether it can be tested—the sizes are so tiny. Although the mathematics of the theory is beautiful and, in fact, the theory may be the only path to quantum gravity, some physicists have abandoned the theory. For one thing, it may be impossible to test. For another, it has turned out that there are many, many different versions of string theory, each with different outcomes and each corresponding, possibly, to a different universe, with different properties. In that case, our universe would be just one random cosmos, a throw of the dice—defeating the long-standing hope of physicists to show that our universe must necessarily be the way it is and no other way, given a small number of “first principles,” in the same way that a crossword puzzle has only one solution.
Regardless of whether strings actually exist, we know that space and time lose their meaning at the Planck size, as discussed in “Between Nothingness and Infinity.” We cannot find smaller “particles” beyond Planck; we cannot divide space into smaller elements beyond Planck. It took two thousand years to measure the size of the hypothesized atom. In 1899, Max Planck hypothesized the “Planck length” as the unique length formed by combining his newfound quantum constant with the speed of light and Newton’s gravitational constant. Will it be another two thousand years before we can test the existence of strings?