by Harry Cliff
Dalton’s stroke of brilliance was to take his theory of mixed gases—that atoms only repel other atoms of their own kind—and extrapolate it to figure out how many atoms of different chemical elements bind together to make molecules. His reasoning went something like this: Imagine that two atoms of two different chemical elements, let’s call them atom A and atom B, bind together to make a molecule A-B. Now imagine that another atom of A comes along and wants to join the party. Since atoms of A repel each other it will naturally want to get as far away from the other A atom as possible and so attach to the opposite side of the B atom to make a larger molecule A-B-A. Then if a third atom of A comes along this time it will arrange itself at 120 degrees from the other two atoms of A to form a triangular shape with B at the center, and so on.
Dalton reasoned that if only one compound of A and B is known, then its molecule should have the simplest structure, which is AB. If there are two different compounds of A and B, then the second molecule will be the next simplest, ABA.
For example, two different gases made of carbon and oxygen were known in the early nineteenth century: one was called “carbonic oxide” (the colorless toxic gas that nearly killed Humphry Davy when he breathed it in, possibly in the name of science or in search of another way to get high) and what was called “carbonic acid” (the fixed air discovered by Joseph Black, which was used to suffocate a number of unlucky mice, again in the name of science). By weighing the amount of oxygen that reacted with a fixed amount of carbon to make these two gases, Dalton found that carbonic acid contained twice as much oxygen as carbonic oxide. Applying the rules of his atomic theory, this meant that carbonic oxide was the simplest molecule, made of one carbon and one oxygen atom (what we now know as carbon monoxide, CO), and carbonic acid contained one carbon and two oxygen atoms (in modern terms, carbon dioxide, CO2).
At last, Dalton could figure out the relative masses of carbon and oxygen atoms, calculating that an oxygen atom weighs about 1.30 times more than a carbon atom, which is remarkably close to the modern value of 1.33. Through a combination of guesswork, theorizing, and experimentation, he had measured a property of an atom, and in doing so had caught a glimpse of their hidden realm for the very first time.
Dalton knew that he was onto something big. He completely forgot about the original problem of dissolving gases in water and engrossed himself in his new atomic theory. After three years of work, interrupted by heavy teaching duties and the occasional walking holiday in his beloved Lake District, he was ready to reveal his ideas to the world.
In March 1807 Dalton traveled to Edinburgh, arguably Britain’s greatest intellectual and scientific center and crucible of the Enlightenment. He was there to present what was nothing short of a revolutionary new description of the chemical elements. He began his momentous lecture series in the most English way imaginable, with an apology. “It may appear somewhat like presumption in a stranger to intrude himself upon your notice in the character I am now assuming, in a city like this, so deservedly famous for its seminaries of physical science.” However, there was steel beneath Dalton’s veneer of humility. He went on to announce that if the ideas he was about to share were borne out by experiment, which he was sure they would be, they would “produce the most important changes in the system of chemistry, and reduce the whole to a science of great simplicity, and intelligible to the meanest understanding.”
The atomic theory Dalton presented at Edinburgh, and later published in his great work A New System of Chemical Philosophy, finally connected Lavoisier’s chemical elements with the ancient idea of atoms. According to Dalton, all matter was made up of solid, indivisible, indestructible atoms, and every chemical element was made of its own unique atom with a definite mass. Chemical reactions, from burning charcoal to baking apple pie, were nothing more than a process of rearranging these different atoms to make a wider variety of different molecules.
The response to Dalton’s atomic theory was immediate, both in Edinburgh and beyond. In London, Humphry Davy was quick to see its potential to help chemists understand and quantify the way that different chemical elements reacted with one another. The theory’s most important prediction was a rule known as “the law of multiple proportions.” Basically, it says that when two elements react to make compounds, they always do so in certain ratios, which is a direct consequence of the fact that elements come in discrete little atomic lumps.
Take reactions between the two dominant gases in our atmosphere, nitrogen and oxygen, to make three different compounds: nitrous oxide, nitric oxide, and nitrogen dioxide. If we did three different experiments where we started with 7 grams of nitrogen and then reacted it with oxygen to make these three compounds, we would find that the amount of oxygen that joined up with the nitrogen in each case would be 4 grams, 8 grams, and 16 grams. From this, Dalton was able to figure out that the chemical formulae of nitrous oxide, nitric oxide, and nitrogen dioxide is N2O, NO, and NO2, and the reason that oxygen only reacts in these fixed proportions is because the mass of an oxygen atom is eight-sevenths the mass of a nitrogen atom.
Within months, other experimenters were finding evidence that the elements really did react in the way that Dalton’s theory said they should, and soon Dalton was being feted around the country. In the same year that Dalton published his atomic theory, Humphry Davy tried to persuade him to become a fellow of the most prestigious scientific organization in Britain, the Royal Society in London.*1
But while chemists were happy to take and apply the consequences of his atomic theory, far fewer agreed with Dalton’s belief in real, physical atoms. In 1826, when Humphry Davy, now President of the Royal Society, presented Dalton with the Royal Medal, he was keen to emphasize that this was for his work on the law of multiple proportions—a prediction of Dalton’s atomic theory—and not for his belief in actual physical atoms.
Although Dalton had connected Lavoisier’s chemistry with atomic theory, his ideas were too far ahead of their time. The debate over whether atoms existed or not was to rage for another hundred years and was only finally resolved by an aspiring young physicist working in the Bern patent office, whose destiny it was to change science forever.
EINSTEIN AND THE ATOM
You’ve got to feel sorry for Albert Einstein’s high-school teachers. I mean, just imagine having Albert Einstein in your class. Of course, in 1895 his teachers didn’t realize they were teaching Albert Einstein, just a puckish German teenager with a mop of unruly black hair and a self-satisfied smile.
Famously, Einstein was not a good student. At a fairly early age he had realized he could teach himself more advanced mathematics and physics than his teachers, and by his midteens had decided that school was a waste of time. He seems to have had a special talent for winding his teachers up. On one occasion his father Hermann was called into school to be berated for Albert’s disruptive influence. When he asked what exactly his son had done, he was told by an exasperated teacher, “He sits at the back and smiles.”
Despite a not entirely successful or happy schooling, Einstein was determined to pursue a career in physics and after one failed attempt got himself admitted to the Swiss Federal Polytechnic, a relatively new university in the Swiss city of Zurich. His time at the “Poly,” as it was known, was a happy one. He reveled in his newfound freedom and soon formed a tight-knit group of friends, spending most of his time in coffeehouses, sailing on the lake, or at parties entertaining groups of admiring young women with his violin playing. It was at one of these shindigs that he met his lifelong friend, Michele Besso, a mechanical engineer six years his senior, with whom he would spend many happy hours discussing the latest controversies in science, philosophy, or politics amid a haze of pipe smoke at their favorite café.
During one of their wide-ranging discussions, Besso introduced Einstein to the work of the Austrian physicist and philosopher Ernst Mach. Mach was an ardent opponent of atomic theory, a
rguing that atoms were little more than a convenient fiction that just happened to explain the behavior of larger-scale objects. As long as atoms themselves remained out of the direct reach of human senses, Mach argued that belief in their existence was a matter of faith, not science.
Mach had a point. Almost a hundred years after Dalton published his chemical atomic theory, the evidence for atoms was still mostly circumstantial. That said, over the course of the nineteenth century, atomic theory had achieved several big wins. In chemistry, the marriage of atoms with chemical formulae (symbolic ways of representing different chemical compounds in terms of their atomic building blocks—such as N2O for nitrous oxide) had proved extremely useful in exploring the reactions of organic molecules. Great progress had also been made on Dalton’s project of measuring the relative weights of different atoms, resolving most of the ambiguities around the atomic makeup of molecules, including whether water was HO or H2O.
At the same time a powerful new way of understanding the behavior of gases had emerged, known as “kinetic theory.” According to this theory, a gas was a multitude of minuscule atoms flying about through empty space, bouncing back and forth off the walls of their container like a swarm of tiny angry bees. This picture allowed physicists to neatly explain measurable properties of a gas like temperature and pressure. Lavoisier had thought of heat as a physical substance called “caloric,” which he included in his list of chemical elements. Kinetic theory did away with this idea; heat was simply a consequence of the speeds that the atoms were zipping about at. The faster the atoms were moving, the hotter the gas. This also explained why the pressure of a gas increases as you heat it up. As the temperature rises the atoms move about faster and hammer against the walls more often and with greater force, causing an increase in pressure.
An early version of kinetic theory had been proposed by Daniel Bernoulli way back in 1738 and had remained more or less unchanged until after the 1860s, when James Clerk Maxwell, Josiah Willard Gibbs, and Ludwig Boltzmann revamped the theory by applying statistics to describe how atoms continually bumping into one another determine the measurable properties of a gas. This new statistical theory was able to explain familiar phenomena like the conduction of heat or how long it takes for a smelly gas released on one side of a room to be noticed by people on the other,*2 as well as predicting wholly new ones.*3
By the time Einstein was having his coffee- and tobacco-fueled discussions with Besso in 1896, progress on kinetic theory had stalled. Despite its successes, the theory had gotten snagged on a couple of particularly thorny problems, leaving open the possibility that it could yet be overturned. But worst of all, it was still true that no one had seen an atom.
At the University of Vienna, a battle was raging for kinetic theory’s very soul. On one side was Ludwig Boltzmann, the theory’s leading light, and on the other, Ernst Mach, its arch-nemesis. Boltzmann was so stung by Mach’s attacks that he devoted the last few years of his life to a valiant defense of his cherished kinetic theory, and although he won most physicists round to his side, Mach and a number of leading chemists remained intransigent.
In Zurich, the young Einstein followed the debates with increasing interest and frustration. He was convinced that Boltzmann was right and Mach was wrong. There was simply no way that all kinetic theory’s successes were a fluke. Atoms were real, and as soon as he graduated, Einstein resolved that he would settle the two-thousand-year-old debate once and for all. Unfortunately, old habits die hard, and Einstein had not acquitted himself well in his studies, gaining the lowest passing grade in his year and earning a reputation as a “lazy dog,” as his favorite professor Herman Minkowski put it. He found himself struggling to find a job, eventually having to take up temporary teaching positions to make ends meet.
A reprieve came in 1902 when he got a job at the patent office in the Swiss city of Bern. Not only did this come with a salary that was twice what he would have gotten as a professor’s assistant, but it was also undemanding enough that it allowed him to do scientific research on the side, both in his spare time and, as he later admitted, during working hours.
A steady income also made it possible for him to finally marry his university girlfriend, Mileva Marić. Mileva and Albert had met at the Poly (she had been the only female science student in his year) and formed an intense relationship that was both romantic and scientific. Einstein was clearly swept along by the prospect of a partner he could share both his life and his physics with and proposed marriage despite the opposition of his parents and the doubts of his close friends. Unfortunately, Mileva’s ambitions for her own scientific career were thwarted when she failed her final exams—perhaps in part thanks to her boyfriend’s bad influence—compounded by getting pregnant while she was doing retakes.
By 1903 the romance had clearly faded—Albert later said that he married her out of a sense of duty—but they nonetheless settled into a life of quiet domesticity. Mileva seems to have accepted the loss of a potential scientific career and the scandal of having a child out of wedlock with remarkable stoicism, cheerfully taking care of the home and more or less all of her husband’s needs. Combined with his light duties at the patent office, this trouble-free life set Einstein up for the most productive period of his entire career.
The year 1905 has mythic status in the history of science. Over a period of just a few months, Einstein published four papers, each of which sent shockwaves through the physics world that are still being felt today. Two of the four were truly revolutionary: one upended the fundamental concepts of space and time, the other heralded the dawn of the quantum age. Relativity and quantum mechanics—two beautiful, deeply unsettling ideas that challenge our most basic notions of how the world ought to work—are the pillars upon which modern particle physics is built. (We’ll come back to them again and again in the coming chapters, but we’re not quite ready to discuss them yet.)
It is incredible that the paper that finally proved the existence of atoms was arguably the least revolutionary of the four. There is a reason that 1905 is referred to as Einstein’s “miraculous year.” Einstein’s warm-up act was his PhD dissertation on what sounds like the rather curious subject of sugar solutions but was actually an ingenious method to calculate the number and sizes of sugar molecules. Even though Einstein got a result that was remarkably close to the accepted modern values, this still didn’t constitute proof of the existence of molecules or atoms—his calculations were based on the same bunch of unproven assumptions that formed the basis of kinetic theory.
What Einstein needed was a smoking gun, an unmistakable signature that could only be left by an atom. He knew that atoms were far too small to be seen directly through a microscope, but what if there was a way of seeing their influence on particles that were large enough to be visible?
In 1827, the Scottish botanist Robert Brown had discovered a peculiar phenomenon when peering through his microscope at some pollen grains. Within the grains, he noticed tiny particles endlessly jiggling about. While many suggestions had been made to account for the effect, including living molecules within the pollen and vibrations from passing carriages, no good explanation for the jiggling, which became known as “Brownian motion,” could be found at the time. Three decades later in the 1860s, a couple of scientists had suggested a new explanation: What if the pollen particles were moving about thanks to taking continuous blows from individual water molecules? The water molecules themselves might be far too small to see through a microscope, but perhaps their influence could be seen each time they crashed into a much larger particle. The problem is that a single water molecule is far too small and moves far too slowly to have any noticeable effect on the position of a relatively ginormous pollen particle. It would be the equivalent of an aircraft carrier being noticeably deflected by a collision with an anchovy.
Einstein realized that even though an individual water molecule couldn’t visibly move something as l
arge as a pollen particle, the accumulated effect of a large number of collisions might. According to kinetic theory, a pollen particle floating in water is surrounded by thousands of water molecules, which are all jittering about thanks to the heat of the water. Because of the inherent randomness of this jittering, sometimes one side of the pollen particle will get hit by more water molecules than the other, creating a net force large enough to make it move.
This cumulative effect causes the pollen particle to follow what is known as a “random walk” through the liquid, a zigzagging path that looks a bit like a drunkard stumbling around in the dark. At one moment the pollen particle will be pushed in one direction, and then a moment later in a different, random direction. Even though each step on this journey is random, over time the particle gradually moves farther and farther away from its starting point. Einstein’s aim was to connect the average distance that a pollen particle moves in some fixed amount of time to the number of molecules in a given volume of water.
After some brilliant physical insights and very clever mathematics, he arrived at a single equation that says that the distance a pollen particle jiggles away from its starting point in some amount of time goes up as the number of water molecules goes down. Now let’s think about the big argument that Einstein was trying to settle: one side said that matter is made of atoms, the other that atoms are just a figment of physicists’ imagination and that matter is continuous. If matter is continuous, then that means you can divide up any object, be it an apple pie or a drop of water, into an infinite number of infinitely small bits. Or to put it another way, there are an infinite number of infinitely small water molecules in a drop of water. If that were true, then according to Einstein’s equation, a pollen particle wouldn’t move at all, which sort of makes sense if you think about it. If the number of water molecules is effectively infinite then there will always be an equal number (that is, infinity) pushing on the pollen particle from any given direction, which means that the forces experienced by the particle are always perfectly balanced and hence the pollen particle stays dead still.
