What We Cannot Know

For example: ‘The elements of oxygen may combine with a certain portion of nitrous gas or with twice that portion, but with no intermediate quantity.’ It certainly didn’t constitute a proof that matter was discrete, and it was not strong enough to knock the belief of those who favoured a continuous model of matter. But it was highly suggestive. There had to be some explanation for the way these substances were combining.

The notation developed to express these reactions added to the atomistic view. The combination of nitrogen and oxygen could be expressed algebraically as N + O or N + 2O. There was nothing in between. It seemed that all compounds came in proportions that were whole-number ratios. For example, aluminium sulphide was given algebraically as 2Al + 3S = Al2S3, elements combining in a 2-to-3 ratio. Elements never combined in a non-whole-number relationship. It was like musical harmony at the heart of the chemical world. The music of tiny spheres.

The Russian scientist Dmitri Mendeleev is remembered for laying out this growing list of molecular ingredients in such a way that a pattern began to emerge, a pattern based on whole numbers and counting. It seemed that the Pythagorean belief in the power of number was making a comeback. Like several scientists before him, Mendeleev arranged them in increasing relative weight, but he realized that to get the patterns he could see emerging he needed to be flexible.

He’d written the known elements down on cards and was continually placing them on his desk in a game of chemical patience, trying to get them to yield their secrets. But nothing worked. It was driving him crazy. Eventually he collapsed in exhaustion and the secret emerged in a dream that, when he woke, gave him the pattern for laying out the cards. One of the important points that led to his successful arrangement was the realization that he needed to leave some gaps – that some of the cards from the pack were missing.

The key to his arrangement was something called the atomic number, which depended on the number of protons inside the nucleus rather than the combination of protons and neutrons that gave rise to the overall weight. But since no one had any clue yet about these smaller ingredients, Mendeleev was guessing somewhat at the underlying reason for his arrangement.

It was a bit like recognizing that a conventional pack of cards can be laid out in suits, but also that across those suits there are cards that are of equal value. A periodicity of eight seemed to underlie the elements, so that elements eight along seemed to share very similar properties. Eight on from lithium was sodium, followed after another eight by potassium. All soft shiny highly reactive metals. Similar patterns matched up gases with related properties.

This rule of eight had been picked up before Mendeleev’s breakthrough and was called the law of octaves. It was compared to the musical octave: if I play the eight notes of a major scale on my cello, the top and bottom notes sound very similar and are given the same letter names. When this law of atomic octaves was proposed by its originator John Newlands, it was laughed out of the Royal Society. ‘Next you’ll be trying to tell us that the elements can be understood by putting them in alphabetical order,’ joked one Fellow. Mendeleev’s arrangement confirmed to a certain extent the veracity of this law of octaves. It was this idea of repeating or periodic patterns that led to Mendeleev’s arrangement being called the periodic table.

Mendeleev’s genius was to realize that if sometimes the elements didn’t quite match up, it perhaps indicated a missing element. The gaps in his table were probably his most insightful contribution. The fact that there was a hole in the 31st place of his table, for example, led Mendeleev to predict in 1871 the existence and properties of a new substance that would later be called gallium. Four years later French chemist Lecoq de Boisbaudran isolated the first samples of this new atom, predicted thanks to the mathematical patterns discovered by Mendeleev.

RECIPE FOR MAKING A DICE

Here then was a list of the atoms that were meant to make up all of matter. For example, my dice is made from putting together carbon atoms, oxygen atoms and hydrogen atoms into a structure called cellulose acetate. My own body is predominantly made up of combinations of these atoms but with a different structure. The cellulose acetate is a homogeneous structure free from bubbles, which makes it more likely to be fair. The more antique dice were made from a nitrate-based cellulose concocted by John Wesley Hyatt in 1868. His cocktail of nitric acid, sulphuric acid, cotton fibres and camphor produced an impressive substance with great tensile strength that resisted the effects of water, oils and even diluted acids.

Hyatt’s brother named it celluloid and it became a highly cost-effective substitute for objects that had previously been carved out of ivory or horn. Billiard balls and removable collars, piano keys and even my dice were made from this synthetic plastic. The dice that were made from cellulose nitrate were the industry standard in the early twentieth century, but after several decades of use they would almost instantaneously crystallize and decompose, crumbling in on themselves and releasing nitric acid gas.

The real collectors’ dice are those Vegas dice made from cellulose nitrate in the late Forties that avoided this crystallization. My dice won’t suffer the same fate. Here is a picture of how the atoms are put together inside my dice.

The identification of these elements was not a proof of a discrete model of matter. There was no reason that this picture of the ingredients of my dice couldn’t be a formula for the way a continuous structure combines. Although the chemists were tending towards an atomistic view of the universe, this was far from the case in the physics community. Those, like the German physicist Ludwig Boltzmann, who proposed atomic models of matter were laughed out of the lab.

Boltzmann believed that this atomic theory was a powerful way to interpret the concept of heat based on the idea that a gas was made up of tiny molecules bashing around like a huge game of micro-billiards. Heat was just the combined kinetic energy of these tiny moving balls. Using this model, combined with ideas of probability and statistics, he was successfully able to explain the large-scale behaviour of a gas. But most physicists were still committed to a continuous view of matter and were very dismissive of Boltzmann’s ideas.

Boltzmann was so ridiculed that he was forced to retreat from his belief that this billiard-ball theory of matter represented a true picture of reality, and instead was obliged to refer to it as a heuristic model if he wanted to get his ideas in print. As Ernst Mach, his great nemesis in the debate about the reality of atoms, declared mockingly: ‘Have you ever seen an atom?’

Boltzmann was plagued by fits of depression, and there is evidence that he was in fact bipolar. The rejection of his ideas by the scientific community is believed to have contributed to the depression that struck in 1906 and that led to him hanging himself during a holiday with his family near Trieste while his daughter and wife were out swimming.

It was a tragic end, not least because the most convincing evidence that he was right was just emerging. And it was one of the big names of physics who produced ideas that supported the atomistic view and were very hard to ignore. The work that Einstein and others did on Brownian motion would prove extremely difficult to explain for those who, like Mach, believed in a continuous view of the world.

POLLEN PING-PONG

Although conventional microscopes don’t allow one to see individual atoms, they did allow scientists in the nineteenth century to see the effect that these atoms were having on their surroundings. It’s called Brownian motion after Robert Brown, who in 1827 noticed the random behaviour of small particles of pollen floating on the surface of water. Since pollen was organic, Brown’s first thought was that it might be exhibiting signs of life as it jumped around the surface. A similar random behaviour of coal dust floating on alcohol had also been observed by Dutch scientist Jan Ingenhousz in 1785. When Brown saw the pollen’s behaviour replicated by inorganic matter, he was rather stumped as to what was causing the jittery motion.

It’s striking that the idea that it might be invisible atoms bashing into the larger visible material had been suggested by the Roman poet Lucretius in his didactic poem On the Nature of Things:

Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways … their dancing is an actual indication of underlying movements of matter that are hidden from our sight … It originates with the atoms which move of themselves. Then those small compound bodies that are least removed from the impetus of the atoms are set in motion by the impact of their invisible blows and in turn cannon against slightly larger bodies. So the movement mounts up from the atoms and gradually emerges to the level of our senses, so that those bodies are in motion that we see in sunbeams, moved by blows that remain invisible.

This was written in 60 BC, but it would take Einstein’s mathematical analysis of the motion to confirm this atomic explanation of the random movement in Lucretius’ sunbeams and Brown’s pollen.

The goal is to provide some model that will produce the strange motion exhibited by the small pieces of pollen on the surface of the water. If you divide the surface into a grid, there seems to be an equal probability that the pollen will move left–right–up–down. It is similar to the motion of a drunken man who randomly makes steps according to the toss of a four-sided dice. The picture below shows the paths of various particles of pollen as plotted by the French physicist Jean Baptiste Perrin, who took up the challenge of explaining the pollen’s motion in his book Les Atomes.

The proposal emerged at the beginning of the twentieth century that scientists were observing the pollen being buffeted by the motion of much smaller molecules of water.

It was Einstein’s mathematical brilliance that allowed him to analyse this model in which a large object was subjected to the impact of much smaller objects that were moving randomly. He proved that the model predicted precisely the observed behaviour. Think of an ice rink with a large puck sitting in the middle of the rink and then introduce a whole system of tiny pucks that are set off in random directions at particular speeds. Every now and again the tiny pucks will hit the large puck, causing it to move in one direction. The skill was to assess how many small pucks you would need, and their relative size, in order to produce the observed behaviour of the larger puck.

Einstein’s success in producing such a mathematical model that replicated the motion of the pollen was a devastating blow to anyone who believed that a liquid like water was a continuous substance. It was very hard for anyone who still believed in Aristotle’s view of matter to come up with a comparably convincing explanation.

The calculations allowed one to estimate how small the molecules of water were in comparison with the pollen they were knocking around. Although it was convincing evidence that matter came in discrete pieces, it did not answer the question of whether you could still infinitely divide these pieces into ever smaller parts.

Indeed, the indivisible atoms turned out to be far from indivisible with the discovery of smaller constituents that made up atoms of carbon or oxygen. The next layer down revealed that an atom is made up of even tinier pucks called electrons, protons and neutrons, the first of which had already come to light some eight years before Einstein’s theoretical breakthrough.

PULLING APART THE ATOM

The way science works is that you can hang on to your model of the universe until something pops up that doesn’t fit: something new that you can’t seem to explain with the current model. The realization that the atom might be made up of smaller bits emerged out of experiments that revealed something particle-like but much tinier than the atoms that made up the periodic table.

This tiny particle-like object materialized from the British physicist J. J. Thomson’s experiments at the end of the nineteenth century to understand electricity. He had been investigating how electricity was conducted through a gas. Early experiments took a glass tube with two electrodes at either end, and by applying a high voltage between the electrodes an electric current was produced. The strange thing was that he seemed to be able to actually see the current because an arc of light appeared between the two electrodes.

Things became even stranger when he removed the gas completely from the tube and applied the voltage across a vacuum. The arc of light disappeared. But, bizarrely, the glass at the end of one tube was found to fluoresce. Stick a metal cross in the tube and a cross-shaped shadow appeared in the middle of the glowing fluorescent patch.

Electrons emitted from the cathode that hit the opposite wall cause the glass to fluoresce.

The shadow always appeared opposite the negative electrode, otherwise known as the cathode. The best explanation was that the cathode was emitting some sort of ray that interacted with matter and made it glow – either the gas in the tube or, in the case of the vacuum, the glass of the tube itself.

These ‘cathode rays’ were something of a mystery. They were found to pass right through thin sheets of gold when they were placed in the way. Were they some sort of wave-like phenomenon like light? Others thought they were made up of negatively charged particles spat out by the negative electrode and then attracted to the positive electrode. But how could these particles pass through solid gold?

If they were negatively charged particles, then, Thomson believed, he should be able to change their path through the tube by applying a magnetic field. The German physicist Heinrich Hertz had already tried this and failed, but Hertz hadn’t removed enough gas, which interfered with the experiment. With the gas removed, things worked just as Thomson had hoped. Apply a magnetic field to the rays and sure enough the shadow shifted. The rays were being bent by the magnet.

The real surprise came when Thomson made a mathematical calculation of what the mass of these charged particles must be. If you apply a force to a mass then, as Newton’s laws of motion state, the amount you’ll be able to move it will depend on the mass. So the amount of deflection that a magnetic field will cause will have encoded in it information about the mass of this proposed particle.

The calculation also depends on the charge on the particle, and once this was determined in a separate experiment Thomson could work out the mass. The answer was startling. It was nearly 2000 times smaller than the mass of a hydrogen atom, the smallest atom in the periodic table.

That these particles seemed to originate from the metal making up the electrode led to the hunch that these particles were actually smaller constituents of the atom. The atom wasn’t indivisible after all. There were smaller bits. They were called electrons, the name originating from the Greek word for amber, the first substance to exhibit a charge.

The discovery that atoms are made up of even smaller constituents was a shock to many scientists’ view of the world. After Thomson gave a lecture on his findings:

I was told long afterwards by a distinguished physicist who had been present at my lecture that he thought I had been pulling their leg.

THE NEXT LAYER

Even when Thomson used a different metal, the masses of particles emitted by the metal didn’t change. It seemed like every atom had these particles as constituents. The first thought was that a hydrogen atom, given that it is 2000 times heavier than this new electron, might be made up of 2000 or so of these electrons. But a helium atom was roughly four times the mass of a hydrogen atom. Why would the number of electrons jump from 2000 to 4000 with nothing in between? This whole-number ratio between masses of atoms in the periodic table had been one of the reasons for supposing they were truly atomic. So what could account for these discrete steps in mass? Furthermore, atoms were electrically neutral. So were there other particles that cancelled out the charge on the electron? Could you get atoms to emit positive particles to counter these negative electrons?

There was actually evidence in the experiments for a positive ray of particles running in the opposite direction. When a magnetic field was applied, they were much harder to deflect, implying that they were more massive than the electrons. The curious feature this time was that the masses of these particles seemed to vary according to the gas that was being used to fill the tubes. For hydrogen the mass was essentially the mass of the atom you started with. It seemed that the hydrogen atoms in the tube were having their electrons stripped off, leaving a large positive particle that was then attracted to the opposite electrode.

Thomson managed to achieve a similar effect with other gases: helium, nitrogen, oxygen. The masses were all whole-number multiples of the positive particle produced by the hydrogen atom. Atomic harmony yet again. As yet, there was no reason to believe that there weren’t just many sorts of positive particles, just as there were many sorts of atoms. Thomson had suggested a model of the atom known as the plum pudding. The positively charged part of the atom, which was more massive than the negative electron, formed the pudding making up the bulk of the atom, while the electrons were the tiny fruit inside.

Then the age of the bombardment of the atom began which would eventually lead to the ultimate atom smasher: the Large Hadron Collider at CERN. The New Zealand-born British physicist Ernest Rutherford is generally credited with the discovery of the proton, the particle that was the building block for all these positive particles that Thomson had investigated.

Rutherford became fascinated by the new subject of radioactivity. Uranium atoms seemed to be spitting out particles that could be picked up by photographic plates. There appeared to be two types of radiation, and these became known as alpha particles and beta particles. The alpha particles were more easily detected. Rutherford found that using a magnetic field he could deflect these alpha rays in the same way that Thomson had deflected the negative particles. Calculations showed that they had the same mass as the stripped helium atoms. Their hunch that the alpha rays being emitted by the uranium were actually bits of helium atoms was confirmed when the alpha rays were combined with a shower of electrons, which resulted in a stable gas being formed. Chemical analysis soon confirmed that the gas was indeed helium.

TISSUE PAPER BALLISTICS

It was when Rutherford’s student Hans Geiger placed a thin sheet of gold foil between a stream of alpha particles and the plate detecting the particles that the evidence once again contradicted the theoretical model of the atom. In the model of the atom which has positive charge distributed evenly like a pudding, positive alpha particles passing through the metal would be repelled by the positive charge in the atom. Given that the charge is distributed over the full extent of the atom, you wouldn’t expect much deflection.

Alpha particles being deflected by the nuclei of atoms of gold.

Geiger found that, on the contrary, some of the alpha particles were deflected wildly, to the extent that some bounced back off the gold foil in the direction they’d been fired from. Rutherford was staggered: ‘It was as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.’

Again it was mathematical calculations that gave rise to a new model. By counting how many alpha particles were deflected, and by how much, they discovered that the data was consistent with the charge and mass being concentrated in a tiny centre of the atom, which became known as the nucleus. It still wasn’t clear whether this nucleus was indivisible or not.

When Rutherford bombarded lighter atoms with alpha particles evidence emerged that the nucleus wasn’t a single entity but made up of constituent particles. Tracing the paths of the alpha particles in a cloud chamber, he detected paths that were four times longer than they should be. It was as if another particle four times as light was being kicked out of the nucleus by the impact of the alpha particles. Different gases produced the same result. Indeed, Rutherford found that pure nitrogen was being converted into oxygen by the impact. Knock out one of these particles and the element changed.

Here was evidence for a building block from which all nuclei of atoms were built. It behaved just like the hydrogen atom with its electron stripped off. Rutherford had discovered the proton. The nuclei of atoms were built by taking multiples of this proton. The only trouble was that the charge on the atom didn’t make sense. Helium had a nucleus that was four times as heavy as the hydrogen atom, yet the charge was only twice as big. Perhaps there were electrons in the nuclei attached to protons, cancelling out the charge. But the physics being developed to explain the behaviour of these particles precluded electrons and protons in such close proximity, so that couldn’t be the answer.

This led Rutherford in the 1920s to guess that there might be a third constituent, which he called a neutron, with the same ball-park mass as the proton but no charge. Producing evidence for this particle proved very tricky. He used to discuss with his colleague James Chadwick crazy ways by which they might reveal the neutron. Experiments conducted in the 1930s in Germany and France eventually picked up particles being emitted when various nuclei were bombarded with alpha particles, and, unlike the proton, these particles did not seem to possess any charge. But the experimenters mistakenly believed it was some sort of electromagnetic radiation, like the high-frequency gamma rays that had been discovered by French physicist Paul Villard at the beginning of the century.

Chadwick, though, was convinced that these particles must be the neutrons he’d discussed with Rutherford. Further experiments revealed that they had mass just slightly bigger than the proton, and without charge this new particle was the missing ingredient that made sense of the numbers. With Chadwick’s discovery it seemed as if the building blocks of matter had been revealed.

It was a very attractive model. Fire, earth, air and water, the four elements of Aristotle, had been reduced to three particles: the electron, proton and neutron. With these three building blocks scientists believed they could build all matter. Oxygen: 8 protons, 8 neutrons and 8 electrons. Sodium: 11 protons, 12 neutrons and 11 electrons. It was as if the music of the spheres was singing out and the foundations of matter were these notes: protons, electrons and neutrons. All matter seemed to be made up of whole-number combinations of these three particles. Why would you expect these particles to be made up of smaller entities? If they were, you might expect to see fractional pieces between the elements in the periodic table.