Uncertainty: Einstein, Heisenberg, Bohr, and the Struggle for the Soul of Scienceby David Lindley
Werner Heisenberg’s “uncertainty principle” challenged centuries of scientific understanding, placed him in direct opposition to Albert Einstein, and put Niels Bohr in the middle of one of the most heated debates in scientific history. Heisenberg’s theorem stated that there were physical limits to what we could know about sub-atomic
Werner Heisenberg’s “uncertainty principle” challenged centuries of scientific understanding, placed him in direct opposition to Albert Einstein, and put Niels Bohr in the middle of one of the most heated debates in scientific history. Heisenberg’s theorem stated that there were physical limits to what we could know about sub-atomic particles; this “uncertainty” would have shocking implications. In a riveting account, David Lindley captures this critical episode and explains one of the most important scientific discoveries in history, which has since transcended the boundaries of science and influenced everything from literary theory to television.
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Robert Brown, son of a Scottish clergyman, was the archetypal self–made scholar, sober, diligent, and careful to the point of fanaticism. Born in 1773, he trained in medicine at Edinburgh, then served for some years as a surgeon’s assistant in a Fifeshire regiment. There he put his spare time to worthy use. Rising early, he taught himself German (nouns and their declensions before breakfast, his diary records, conjugation of auxiliary verbs afterward) so that he could master the considerable German literature on botany, his chosen subject. On a visit to London in 1798, the young Scotsman met and so impressed the great botanist Sir Joseph Banks, president of the Royal Society, that on Banks’s recommendation he sailed three years later on a long voyage to Australia, returning in 1805 with close to four thousand exotic plant specimens neatly stowed on his ship. These he spent the next several years assiduously describing, classifying, and cataloging, serving meanwhile as Banks’s librarian and personal assistant. Brown’s remarkable Australian trove, along with Banks’s own equally notable collection, became the heart of the botanical department of the British Museum, of which Brown became the first professional curator. He was, said a visitor to Banks’s London house, “a walking catalogue of every book in the world.”
Charles Darwin, before he was married, passed many a Sunday with the learned Robert Brown. In his autobiography Darwin describes a contradictory man, vastly knowledgeable but powerfully inclined to pedantry, generous in some ways, crabbed and suspicious in others. “He seemed to me to be chiefly remarkable for the minuteness of his observations and their perfect accuracy. He never propounded to me any large scientific views in biology,” Darwin writes. “He poured out his knowledge to me in the most unreserved manner, yet was strangely jealous on some points.” Brown was notorious, Darwin adds, for refusing to lend out specimens from his vast collection, even specimens that no one else possessed and which he knew he would never make any use of himself.
It is ironic, then, that this dry, cautious man should be commemorated now mainly as the observer of a curious phenomenon, Brownian motion, that represented the capricious intrusion of randomness and unpredictability into the elegant mansion of Victorian science. It was indeed the very scrupulousness of Brown’s observations that made the implications of Brownian motion so grave.
In June 1827, Brown began a study of pollen grains from Clarkia pulchella, a wildflower, popular today with gardeners, that had been discovered in Idaho in 1806 by Meriwether Lewis but named by him for his co–explorer William Clark. Characteristically, he intended to scrutinize minutely the shape and size of pollen particles, hoping that this would shed light on their function and on the way they interacted with other parts of the plant to fulfill their reproductive role.
Brown had acquired a microscope of recent and improved design. Its compound lenses largely banished the rainbow–hued fringes of color that afflicted the borders of objects seen in more primitive instruments. Under Brown’s eye the ghostly shapes of the pollen grains sprang clearly into view, their edges neatly delineated. Even so, the images were not perfect. The pollen grains wouldn’t stay still. They moved about, jiggled endlessly this way and that; they shimmered and stuttered; they drifted with strange erratic grace across the microscope’s field of view.
This incessant motion complicated Brown’s planned investigations, but it was not so very surprising. More than a century and a half earlier Antony van Leeuwenhoek, a draper from Delft, Holland, had astonished and delighted the scientific world when he described tiny “animalcules” of strange and myriad form that his crude microscope revealed in droplets of pond water, in scrapings from the unbrushed teeth of old men, and even in a suspension of ordinary household pepper crushed into plain water. “The motion of most of these animalcules in the water was so swift, and so various, upwards, downwards, and round about, that ’twas wonderful to see,” the entranced Leeuwenhoek wrote. His discovery not only spurred further scientific investigation but also led well–to–do citizens to purchase microscopes for their parlors and drawing rooms, where they could amaze their guests with this new wonder of nature.
Some animalcules had tiny hairs or finny extensions that enabled them to swim about. Others wriggled like little eels. It was easy to imagine that their meanderings were purposeful in some rudimentary way. Pollen grains, on the other hand, were simple in shape and had no moving parts. Still, they were undeniably organic. It seemed to Brown not unreasonable to suppose that pollen grains—especially as they were the male parts of a plant’s reproductive equipment—might possess some vital spirit that impelled them to move in their amusing but inscrutable fashion.
But Brown distrusted vague hypotheses of this sort. Observation, not speculation, was his forte. Testing pollen from other plants, he found that those grains danced about too. But then he examined minute fragments of leaves and stems and saw that those also jogged perplexingly about under his microscope’s gaze.
His attention caught by this “very unexpected fact of seeming vitality,” Brown could not help but probe the matter further. He obtained dust from dried plant samples, some more than a century old. He scraped tiny fragments from a piece of petrified wood. All these tiny grains had once been living but were now long dead, any vital spark extinguished. Examined under a microscope, they also shimmied. He moved on to truly inorganic material, knocking tiny shards from a variety of rocks and a piece of ordinary window glass. They too jiggled about. To put the case to the ultimate test, he scratched powder from a piece of the Sphinx, to which, as a curator of the British Museum, he had easy access and which he presumably regarded as certifiably, unarguably dead, on account of its provenance.
Placed in a drop of water under his microscope lens, ancient dust from the Sphinx danced about like everything else.
Brown acknowledged that he was not the first to see things jiggling about under the microscope. A certain Mr. Bywater of Liverpool, he noted, had a few years earlier looked at fragments of both organic and inorganic materials and observed “the animated and irritable particles” that they all shed. But Brown, through a variety of ingenious and careful experiments, established that the ceaseless motion of all these tiny fragments was neither the “animalcular motion” Leeuwenhoek and others had seen nor movement produced by vibration or turbulence of the fluid suspensions, by the action of heat, or through electric or magnetic influences.
This was contradictory and baffling. Dead particles of dust clearly couldn’t move of their own volition, nor was any external influence pushing them around. Yet move they all too plainly did. Brown himself made no attempt at an explanation. He was a careful descriptive botanist, not a philosopher of nature, and as Charles Darwin said, “much died with him, owing to his excessive fear of never making a mistake.”
Faced with this impossible dilemma, science took the prudent course and ignored Brownian motion for decades. Its deep significance went unnoticed because the phenomenon was so far beyond scientific apprehension. There was no way even to begin to grasp what it meant. Anyone who used a microscope knew about Brownian motion, at least as a great nuisance, but few read carefully what Brown himself had said about it. Most botanists and zoologists persisted in the idea that it was a manifestation of vital spirits, conveniently ignoring Brown’s demonstration that inert particles jiggled about just as much. Or else they decided their specimens were buffeted by heat or vibrations or electrical disturbances, ignoring Brown's experiments that ruled out those and other influences.
It was not until after Brown's death in 1858 that a few scientists began to see their way to an understanding of the phenomenon. As often happens in science, the observations could not be understood until there was at least the glimmering of a theory by which to understand them. The theory in this case was not a new idea but a very old one that science finally had the means to make sense of.
The Greek thinker Democritus, who flourished around 400 B.C, believed that all matter was made of tiny, fundamental particles called atoms (from the Greek atomos, indivisible). No matter how prescient this notion seems in retrospect, it was really a philosophical conceit more than a scientific hypothesis. What atoms were, what they looked like, how they behaved, how they interacted—such things could only be guessed at. Modern interest in atoms revived first among the chemists. In 1803, John Dalton in England proposed that rules of proportion in chemical reactions—hydrogen and oxygen combining in a fixed ratio to produce water, for example—came about because atoms of chemical substances joined together according to simple numerical rules.
Atoms didn’t gain credibility overnight. As late as 1860 an international conference convened in Karlsruhe, Germany, to debate the atomic hypothesis. The weight of opinion by now favored atoms, but there was significant dissent. Many distinguished chemists were happy to take laws of chemical combination as basic rules in their own right, and saw no reason to indulge in extravagant speculation about invisible particles.
August Kekulé, the German chemist who famously devised the ring structure of the benzene molecule while dozing in his fireside armchair and dreaming about snakes catching their own tails, offered a more shaded opinion. He accepted the existence of the chemical atom, along the lines suggested by Dalton and others, and he noted that some physicists, for their own reasons, had also recently begun arguing for atoms. But were the chemist’s atom and the physicist’s atom the same thing? Kekulé thought not, or at least that any such judgment was premature.
To the chemist, an atom was a thing of almost tactile qualities. It possessed in some way the characteristics of the substance it represented, and it could hook up with or detach from other atoms, according to their respective qualities. Chemists mostly imagined that atoms in bulk sat still, filling space like oranges in a crate.
Physicists thought quite differently. Their atoms were tiny, hard pellets, flying about at high speed in mostly empty space, occasionally crashing into each other and bouncing off again. The role of these atoms was specific. Beginning about halfway through the nineteenth century, a number of mathematically inclined physicists began to pursue the idea that the frenetic motion of atoms could explain the hitherto mysterious phenomenon of heat. As atoms in a volume of gas gained energy, they would fly about faster, bump into each other more violently, and crash more forcefully into the walls of a container. This was why gas would expand when heated, and exert more pressure. In this so–called kinetic theory of heat, heat was nothing but the energy of atomic motion. The deeper implication was that large–scale physics of heat and gases ought to follow ineluctably from the small–scale behavior of atoms as they moved and collided in strict obedience to Newton’s laws of motion.
Thus arose the reliable cliche of the atom as a tiny billiard ball, hard but inert, banging mindlessly about. Whether this had anything to do with chemistry was another question. Physicists allowed that the atoms of one gas might be lighter or heavier than those of another, but why gases had distinct chemical properties was none of their business.
The atom, in short, was in these early days by no means a unifying hypothesis. If chemists and physicists had little to say to each other, still further excluded were the microscopists and biologists. Kinetic theory came with mathematical complexities that repelled all but a select few, while the typical mathematician, if even aware of Brownian motion, most likely assumed it was a trivial phenomenon of strictly botanical interest.
Nevertheless, a connection awaited discovery. A first hint came from Ludwig Christian Wiener, who spent most of his life teaching mathematics and geometry at German universities. In 1863, after conducting experiments that confirmed everything Brown had long ago found, Wiener felt able to publish an intriguing if speculative suggestion. If the liquid in which Brownian particles jiggle about was in reality a welter of furious atoms, then these atoms would buffet the suspended particles from all sides. The erratic but incessant agitation of the invisible atoms, he argued, would cause the larger visible particles to stagger unpredictably about.
In keeping with the tangled history of this subject, Wiener's daring proposal attracted next to no interest.
It fell to a series of French and Belgian Jesuit priests to keep digging for a scientific account of Brownian motion. During the nineteenth century many clergymen maintained an active and useful interest in the observational and collecting sciences: botany, geology, zoology, and so on. The clerical connection comes up in Middlemarch, when the determinedly atheistic man of science Dr. Lydgate visits the agreeably untheological Reverend Farebrother and finds that the clergyman has an impressive natural history collection, including specimens, books, and journals. Happy to encounter a fellow philosopher of nature, Lydgate offers to show Farebrother a few of his own items, in particular “Brown’s new thing—Microscopic Observations on the Pollen of Plants—if you don't happen to have it already.”
What’s more, Jesuits and many other churchmen had a surprisingly broad and rigorous education in philosophy, logic, and even mathematics. Such men were singularly well equipped to deal with problems that we might now call cross–disciplinary but which in those days were merely part of the broad enterprise called science. Mathematical physicists, by contrast, were by the latter half of the nineteenth century on their way to becoming a breed apart, inhabitants of their own recondite discipline, a realm that even those with an adequate amateur command of mathematics were increasingly shy of entering.
This growing divide meant that by the end of the 1870s, a number of scientists perceived the correct qualitative explanation of Brownian motion but lacked the means to put their hypothesis into convincingly quantitative terms. It’s strangely difficult to find anyone willing to take credit for seeing the answer. In an 1877 issue of the London Monthly Microscopical Journal, for example, we find Father Joseph Delsaulx, S.J., attributing to an unnamed colleague the suggestion that Brownian motion results from the constant agitation of small particles by the atoms or molecules that make up a liquid. (Chemists had by this time established the distinction between atoms, which were fundamental, and molecules, which were combinations of atoms.)
Three years later, writing for the Revue des Questions Scientifiques, Father J. Thirion, S.J., mentions that he had seen some years before a similar proposal jotted down in the unpublished laboratory notes (!) of “Fr. Carbonelle, a savant well known to our readers, to whom another of our colleagues, Fr. Renard, had shown for the first time the curious movement of libelles.” These libelles, Thirion is helpful enough to explain, are microscopic dark spots seen within little pockets of liquid trapped in samples of quartz. They are in fact tiny bubbles of gas caught within these liquid inclusions, and they jiggle about in the now–familiar fashion. Father Delsaulx also refers to libelles, and adds that since quartz is known to be very old, this is a case of Brownian motion that must have been going on unabated for millions of years. Clearly, he says, no external cause can be responsible. What Father Renard showed to Father Carbonelle must be the result, Father Delsaulx affirms, of molecules bouncing endlessly around.
The reverend gentlemen were on the right track, but their lack of mathematical sophistication prevented them from going much further. Delsaulx suggested vaguely that the observed amplitude of Brownian motion—how far and fast a particle travels on each zig or zag—must have something to do with what he called the “law of large numbers.” A molecule of liquid, it was clear by this time, is far too small for a single impact with a Brownian particle to cause any observable motion. Rather, the molecules crash constantly into the particle from all sides, but not quite uniformly. Variations in the impacts on different sides of the Brownian particles make it jiggle about; at the same time, the greater the number of molecules involved, the more their random impacts would tend to cancel each other out, making the motion smaller. The “law of large numbers,” by which Delsaulx evidently means to imply some sort of statistical reasoning, should in principle connect the magnitude of Brownian motion with the size and number and speed of molecules in the liquid. More than this he could not say.
Meet the Author
David Lindley holds a Ph.D. in astrophysics from Sussex University and has been an editor at Nature, Science, and Science News. Now a full-time writer, he is the author of The End of Physics, Where Does the Weirdness Go?, The Science of Jurassic Park, Boltzmann's Atom, and Degrees Kelvin. He was also the recipient of the Phi Beta Kappa science writing prize. He lives in Alexandria, Virginia.
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A general history of the concept. Well written and paced. A good read. More 3 and a half than 3.