The Magic of Reality

IN VICTORIAN TIMES, a favourite book for children was Edward Lear’s Book of Nonsense. As well as the poems about the Owl and the Pussycat (which you may know because it is still famous), The Jumblies and The Pobble Who Has No Toes, I love the Recipes at the end of the book. The one for Crumboblious Cutlets begins like this: ‘Procure some strips of beef, and having cut them into the smallest possible slices, proceed to cut them still smaller, eight or perhaps nine times.’

What do you get if you keep on cutting stuff into smaller and smaller pieces?

Suppose you take a piece of anything and cut it in half, using the thinnest and sharpest razor blade you can find.

Then you cut that in half, then cut that half in half, and so on, over and over again.

Do the pieces eventually get so small that they can’t get any smaller? How thin is the edge of a razor blade? How small is the sharp end of a needle?

What are the smallest bits that things are made of?

The ancient civilizations of Greece, China and India all seem to have arrived at the same idea that everything is made from four ‘elements’: air, water, fire and earth. But one ancient Greek, Democritus, came a bit closer to the truth. Democritus thought that, if you cut anything up into sufficiently small pieces, you would eventually reach a piece so small that it couldn’t be cut any further. The Greek for ‘cut’ is tomos, and if you stick an ‘a’ in front of a Greek word it means ‘not’ or ‘you can’t’. So ‘a-tomic’ means something too small to be cut any smaller, and that is where our word ‘atom’ comes from. An atom of gold is the smallest possible bit of gold. Even if it were possible to cut it any smaller, it would cease to be gold. An atom of iron is the smallest possible bit of iron. And so on.

We now know that there are about 100 different kinds of atoms, of which only about 90 occur in nature. The few others have been concocted by scientists in the lab, but only in tiny quantities.

Pure substances that consist of one kind of atom only are called elements (same word as was once used for earth, air, fire and water, but with a very different meaning). Examples of elements are hydrogen, oxygen, iron, chlorine, copper, sodium, gold, carbon, mercury and nitrogen. Some elements, such as molybdenum, are rare on Earth (which is why you may not have heard of molybdenum) but commoner elsewhere in the universe (if you wonder how we know this, wait for Chapter 8).

Metals such as iron, lead, copper, zinc, tin and mercury are elements. So are gases such as oxygen, hydrogen, nitrogen and neon. But most of the substances that we see around us are not elements but compounds. A compound is what you get when two or more different atoms join together in a particular way. You’ve probably heard water referred to as ‘H₂O’. This is its chemical formula, and means it is a compound of one oxygen atom joined to two hydrogen atoms. A group of atoms joined together to make a compound is called a molecule. Some molecules are very simple: a molecule of water, for example, has just those three atoms. Other molecules, especially those in living bodies, have hundreds of atoms, all joined together in a very particular way. Indeed, it is the way they are joined together, as well as the type and number of atoms, that makes any particular molecule one compound and not another.

You can also use the word ‘molecule’ to describe what you get when two or more of the same kind of atom join together. A molecule of oxygen, the gas we need in order to breathe, consists of two oxygen atoms joined together. Sometimes three oxygen atoms join together to form a different kind of molecule called ozone. The number of atoms in a molecule really makes a difference, even if the atoms are all the same.

Ozone is harmful to breathe, but we benefit from a layer of it in the Earth’s upper atmosphere, which protects us from the most damaging of the sun’s rays. One of the reasons Australians have to be especially careful when sunbathing is that there is a ‘hole’ in the ozone layer in the far south.

Crystals – atoms on parade

A diamond crystal is a huge molecule, of no fixed size, consisting of millions of atoms of the element carbon stuck together, all lined up in a very particular way. They are so regularly spaced inside the crystal, you could think of them as being like soldiers on parade, except that they are parading in three dimensions, like a shoal of fish. But the number of ‘fish’ in the shoal – the number of carbon atoms in even the smallest diamond crystal – is gigantic, more than all the fish (plus all the people) in the world. And ‘stuck together’ is a misleading way to describe them if it makes you think of the atoms as solid lumps of carbon closely packed with no space in between. In fact, as we shall see, most ‘solid’ matter consists of empty space. That will take some explaining! I’ll come back to it.

All crystals are built up in the same ‘soldiers-on-parade’ way, with atoms regularly spaced in a fixed pattern that gives the whole crystal its shape. Indeed, that is what we mean by a crystal. Some ‘soldiers’ are capable of ‘parading’ in more than one way, producing very different crystals. Carbon atoms, if they parade in one way, make the legendarily hard diamond crystals. But if they adopt a different formation they make crystals of graphite, so soft it is used as a lubricant.

We think of crystals as beautiful transparent objects, and we even describe other things like pure water as ‘crystal clear’. But actually, most solid stuff is made of crystals, and most solid stuff is not transparent. A lump of iron is made of lots of tiny crystals packed together, each crystal consisting of millions of iron atoms, spaced out ‘on parade’ like the carbon atoms in a diamond crystal. Lead, aluminium, gold, copper – all are made of crystals of their different kinds of atoms. So are rocks, like granite or sandstone – but they are often mixtures of lots of different kinds of tiny crystals all packed together.

Sand is crystalline, too. In fact, many sand grains are just little bits of rock, ground down by water and wind. The same is true of mud, with the addition of water or other liquids. Often, sand grains and mud grains get packed together again to make new rocks, called ‘sedimentary’ rocks because they are hardened sediments of sand and mud. (A ‘sediment’ is the bits of solid stuff that settle in the bottom of a liquid, for example in a river or lake or sea.) The sand in sandstone is mostly made of quartz and feldspar, two common crystals in the Earth’s crust. Limestone is different. Like chalk it is calcium carbonate, and it comes from ground-down coral skeletons and sea shells, including the shells of tiny single-celled creatures called forams. If you see a very white beach, the sand is most likely calcium carbonate from the same shelly source.

Sometimes crystals are made entirely of the same kind of atoms ‘on parade’ – all of the same element. Diamond, gold, copper and iron are examples. But other crystals are made of two different kinds of atoms, again on parade in strict order: alternating, for example. Salt (common salt, table salt) is not an element but a compound of two elements, sodium and chlorine. In a crystal of salt, the sodium and chlorine atoms parade together alternately. Actually, in this case they are called not atoms but ‘ions’, but I’m not going to go into why that is. Every sodium ion has six chlorines for neighbours, at right angles to each other: in front, behind, to left, to right, above, and below. And every chlorine ion is surrounded by sodiums, in just the same way. The whole arrangement is composed of squares, and this is why salt crystals, if you look at them carefully with a strong lens, are cubic – the three-dimensional form of a square – or at least have squared-off edges. Lots of other crystals are made of more than one kind of atom ‘on parade’, and many of them are found in rocks, sand and soil.

Solid, liquid, gas – how molecules move

Crystals are solid, but not everything is solid. We also have liquids and gases. In a gas, the molecules don’t stick together as they do in a crystal, but rush freely about within whatever space is available, travelling in straight lines like billiard balls (but in three dimensions, not two as on a flat table). They rush about until they hit something, such as another molecule or the walls of a container, in which case they bounce off, again like billiard balls. Gases can be compressed, which shows there is a lot of space between the atoms and molecules. When you compress a gas, it feels ‘springy’. Put your finger over the end of a bicycle pump and feel the springiness as you push the plunger in. If you keep your finger there, when you let the plunger go it shoots back out. The springiness that you are feeling is called ‘pressure’. The pressure is the effect of all the millions of molecules of air (a mixture of nitrogen and oxygen and a few other gases) in the pump bombarding the plunger (and everything else, but the plunger is the only part that can move in response). At high pressure the bombardment happens at a higher rate. This will happen if the same number of gas molecules are confined in a smaller volume (for instance, when you push the plunger of a bicycle pump). Or it will happen if you raise the temperature, which makes the gas molecules charge about faster.

A liquid is like a gas in that its molecules move around or ‘flow’ (that’s why both are called ‘fluids’, while solids aren’t). But the molecules in a liquid are much closer to each other than the molecules in a gas. If you put a gas into a sealed tank, it fills every nook and cranny of the tank up to the top. The volume of gas rapidly expands to fill the whole tank. A liquid also fills every nook and cranny, but only up to a certain level. A given amount of liquid, unlike the same amount of gas, keeps a fixed volume, and gravity pulls it downwards, so it fills only as much as it needs of the tank, from the bottom upwards. That’s because the molecules of a liquid stay close to each other. But, unlike those of a solid, they do slide around over each other, which is why a liquid behaves as a fluid.

A solid doesn’t even try to fill the tank – it just retains its shape. That’s because the molecules of a solid don’t slide around over each other like those of a liquid, but stay in (roughly) the same positions relative to their neighbours. ‘Roughly’ because even in a solid the molecules do sort of jiggle about (faster at higher temperatures): they just don’t move far enough from their position in the crystal ‘parade’ to affect its shape.

Sometimes a liquid is ‘viscous’, like treacle. A viscous liquid flows, but so slowly that, although a very viscous liquid eventually fills the bottom part of the tank, it takes a long time to do so. Some liquids are so viscous – flow so slowly – that they might as well be solid. Substances of this kind behave like solids, even though they’re not made of crystals.

Solid, liquid and gas are the names we give to the three common ‘phases’ of matter. Many substances are capable of being all three, at different temperatures. On Earth, methane is a gas (it’s often called ‘marsh gas’, because it bubbles up from marshes, and sometimes it catches fire and we see it lit up as eerie ‘will o’ the wisps’). But on a large, very cold moon of the planet Saturn called Titan there are lakes of liquid methane. If a planet were colder still, it might have ‘rocks’ of frozen methane. We think of mercury as a liquid, but that just means it’s liquid at ordinary temperatures on Earth. Mercury is a solid metal if you leave it outside in the Arctic winter. Iron is a liquid if you heat it to a high enough temperature. Indeed, around the deep centre of the Earth is a sea of liquid iron mixed with liquid nickel. For all I know, there may be very hot planets with oceans of liquid iron at the surface, and perhaps strange creatures swimming in them, although I doubt that. By our standards, the freezing point of iron is rather hot, so at the surface of the Earth we usually encounter it as ‘iron – cold iron’ (Google it. It’s from the poet Rudyard Kipling), and the freezing point of mercury is rather cold, so we usually encounter it as ‘quicksilver’. At the other end of the temperature scale, both mercury and iron become gases if you heat them enough.

Inside the atom

When we were imagining cutting matter into the smallest possible pieces at the beginning of this chapter, we stopped at the atom. An atom of lead is the smallest object that still deserves to be called lead. But can you really not cut an atom any further? And would an atom of lead actually look like a tiny little chip of lead? No, it wouldn’t look like a tiny piece of lead. It wouldn’t look like anything. That’s because an atom is too small to be seen, even with a powerful microscope. And yes, you can cut an atom into even smaller pieces – but what you then get is no longer the same element, for reasons we shall soon see. What is more, this is very difficult to do, and it releases an alarming quantity of energy. That is why, for some people, the phrase ‘splitting the atom’ has such an ominous ring to it. It was first done by the great New Zealand scientist Ernest Rutherford in 1919.

Although we can’t see an atom, and although we can’t split it without turning it into something else, that doesn’t mean we can’t work out what it is like inside. As I explained in Chapter 1, when scientists can’t see something directly, they propose a ‘model’ of what it might be like, and then they test that model. A scientific model is a way of thinking about how things might be. So a model of the atom is a kind of mental picture of what the inside of an atom might be like. A scientific model can seem like a flight of fancy, but it is not just a flight of fancy. Scientists don’t stop at proposing a model: they then go on to test it. They say, ‘If this model that I am imagining were true, we would expect to see such-and-such in the real world.’ They predict what you’ll find if you do a particular experiment and make certain measurements. A successful model is one whose predictions come out right, especially if they survive the test of experiment. And if the predictions come out right, we hope it means that the model probably represents the truth, or at least a part of the truth.

Sometimes the predictions don’t come out right, and so scientists go back and adjust the model, or think up a new one, and then go on to test that. Either way, this process of proposing a model and then testing it – what we call the ‘scientific method’ – has a much better chance of getting at the way things really are than even the most imaginative and beautiful myth invented to explain what people didn’t – and often, at the time, couldn’t – understand.

An early model of the atom was the so called ‘currant bun’ model proposed by the great English physicist J. J. Thomson at the end of the nineteenth century. I won’t describe it because it was replaced by the more successful Rutherford model, first proposed by the same Ernest Rutherford who split the atom, who came from New Zealand to England to work as Thomson’s pupil and who succeeded Thomson as Cambridge’s Professor of Physics. The Rutherford model, later refined in turn by Rutherford’s pupil, the celebrated Danish physicist Niels Bohr, treats the atom as a tiny, miniaturized solar system. There is a nucleus in the middle of the atom, which contains the bulk of its material. And there are tiny particles called electrons whizzing around the nucleus in ‘orbit’ (though ‘orbit’ may be misleading if you think of it as just like a planet orbiting the sun, because an electron is not a little round thing in a definite place).

One surprising thing about the Rutherford / Bohr model, which probably reflects a real truth, is that the distance between each nucleus and the next is very large compared with the size of the nuclei, even in a hard chunk of solid matter like a diamond. The nuclei are hugely spaced out. This is the point I promised to return to.

Remember I said that a diamond crystal is a giant molecule made of carbon atoms like soldiers on parade, but a parade in three dimensions? Well, we can now improve our ‘model’ of the diamond crystal by giving it a scale – that is, a sense of how sizes and distances in it relate to one another. Suppose we represent the nucleus of each carbon atom in the crystal not by a soldier but by a football, with electrons in orbit around it. On this scale, the neighbouring footballs in the diamond would be more than 15 kilometres away.

The 15 kilometres between the footballs would contain the electrons in orbit around the nuclei. But each electron, on our ‘football’ scale, is much smaller than a gnat, and these miniature gnats are themselves several kilometres away from the footballs they are flying around. So you can see that – amazingly – even the legendarily hard diamond is almost entirely empty space!

The same is true of all rocks, no matter how hard and solid. It is true of iron and lead. It is also true of even the hardest wood. And it is true of you and me. I’ve said that solid matter is made of atoms ‘packed’ together, but ‘packed’ means something rather odd here because the atoms themselves are mostly empty space. The nuclei of the atoms are spaced out so far apart that, if they were scaled up to footballs, any pair of them would be 15 kilometres apart with only a few gnats in between.

How can this be? If a rock is almost entirely empty space, with the actual matter dotted about like footballs separated by kilometres from their neighbours, how come it feels so hard and solid? Why doesn’t it collapse like a house of cards when you sit on it? Why can’t we see right through it? If both a wall and I are mostly empty space, why can’t I walk straight through the wall? Why do rocks and walls feel hard, and why can’t we merge our spaces with theirs?

We have to realize that what we feel and see as solid matter is more than just nuclei and electrons – the ‘footballs’ and the ‘gnats’. Scientists talk about ‘forces’ and ‘bonds’ and ‘fields’, which act in their different ways both to keep the ‘footballs’ apart and to keep the components of each ‘football’ together. And it is those forces and fields that make things feel solid.

When you get down to really small things like atoms and nuclei, the distinction between ‘matter’ and ‘empty space’ starts to lose its meaning. It isn’t really right to say that the nucleus is ‘matter’ like a football, and that there is ‘empty space’ until the next nucleus.

We define solid matter as ‘what you can’t walk through’. You can’t walk through a wall because of these mysterious forces that link the nuclei to their neighbours in a fixed position. That’s what solid means.

Liquid means something similar, except that the mysterious fields and forces hold the atoms together less tightly, so they slide over each other, which means that you can walk through water, although not so fast as you can walk through air. Air, being a gas (a mixture of gases, actually), is easy to walk through because the atoms in a gas whizz about freely, rather than being tied to each other. A gas becomes difficult to walk through only if most of the atoms are whizzing in the same direction, and it is the opposite direction to the one in which you are trying to walk. This is what happens when you are trying to walk against the wind (that’s what ‘wind’ means). It can be difficult to walk against a strong gale, and impossible against a hurricane or against the artificial gale hurled out behind a jet engine.

We can’t walk through solid matter, but some very small particles such as the ones called photons can. Light beams are streams of photons, and they can go right through some kinds of solid matter – the kinds we call ‘transparent’. Something about the way the ‘footballs’ are arranged in glass or in water or in certain gemstones means that photons can pass right between them, although they are slowed down a bit, just as you are slowed down when you try to walk through water.

With a few exceptions like quartz crystals, rocks aren’t transparent, and photons can’t pass through them. Instead, depending on the rock’s colour, they are either absorbed by the rock or reflected from its surface, and the same is true of most other solid things. A few solid things reflect photons in a very special straight-line way, and we call them mirrors. But most solid things absorb many of the photons (they aren’t transparent), and scatter even the ones that they reflect (they don’t behave like mirrors). We just see them as ‘opaque’, and we also see them as having a colour, which depends on which kinds of photons they absorb and which kinds they reflect. I’ll return to the important subject of colour in Chapter 7, ‘What is a Rainbow?’ Meanwhile, we need to shrink our vision to the very small indeed, and look right inside the nucleus – the football – itself.

The tiniest things of all

The nucleus isn’t really like a football. That was just a crude model. It certainly isn’t round like a football. It isn’t even clear whether we should speak of it as having a ‘shape’ at all.

Maybe the very word ‘shape’, like the word ‘solid’, loses all meaning down at these very tiny sizes. And we are talking very very tiny indeed: the full stop at the end of this sentence contains about a million million atoms of printing ink.

Each nucleus contains smaller particles called protons and neutrons. You can think of them as balls too, if you wish, but like the nuclei they are not really balls. Protons and neutrons are approximately the same size as each other. They are very very tiny indeed, but even so they are still 1,000 times bigger than the electrons (‘gnats’) in orbit around the nucleus. The main difference between a proton and a neutron is that the proton has an electric charge. Electrons, too, have an electric charge, opposite to that of protons. We needn’t bother with exactly what ‘electric charge’ means here. Neutrons have no charge.

Because electrons are so very very very tiny (while protons and neutrons are only very very tiny!) the mass of an atom is, to all intents and purposes, just its protons and neutrons. What does ‘mass’ mean? Well, you can think of mass as rather like weight, and you can measure it using the same units as weight (grams or pounds). Weight is not the same as mass, however, and I’ll need to explain the difference, but I’m postponing that to the next chapter. For the moment just think of ‘mass’ as something like ‘weight’.

The mass of an object depends almost entirely on how many protons and neutrons it has in all its atoms added together. The number of protons in the nucleus of any atom of a particular element is always the same, and is equal to the number of electrons in orbit around the nucleus, although the electrons don’t contribute noticeably to the mass because they are too small. A hydrogen atom has only one proton (and one electron). A uranium atom has 92 protons. Lead has 82. Carbon has 6. For every possible number from 1 to 100 (and a few more), there is one and only one element that has that number of protons (and the same number of electrons). I won’t list them all, but it would be easy to do so.

The number of protons (or electrons) that an element possesses is called the ‘atomic number’ of that element. So you can define an element not just by its name but by its own unique atomic number. For example, element number 6 is carbon; element number 82 is lead. The elements are conveniently set out in a table called the periodic table – I won’t go into why it’s called that, although it is interesting. But now is the moment to return, as I promised I would, to the question of why, when you cut a piece of, say, lead into smaller and smaller pieces, you eventually reach a point where, if you cut it again, it is no longer lead. An atom of lead has 82 protons. If you split the atom so that it no longer has 82 protons it ceases to be lead.

The number of neutrons in an atom’s nucleus is less fixed than the number of protons: many elements have different versions, called isotopes, with different numbers of neutrons. For example, there are three isotopes of carbon, called Carbon-12, Carbon-13 and Carbon-14. The numbers refer to the mass of the atom, which is the sum of the protons and neutrons. Each of the three has six protons. Carbon-12 has six neutrons, Carbon-13 has seven neutrons and Carbon-14 has eight neutrons. Some isotopes, for example Carbon-14, are radioactive, which means they change into other elements at a predictable rate, although at unpredictable moments. Scientists can use this feature to help them calculate the age of fossils. Carbon-14 is used to date things younger than most fossils, for example ancient wooden ships.

Well then, does our quest to cut things ever smaller and smaller end with these three particles: electrons, protons and neutrons? No – even protons and neutrons have an inside. Even they contain yet smaller things, called quarks. But that is something I’m not going to talk about in this book. That’s not because I think you wouldn’t understand it. It is because I know I don’t understand it! We are here moving into a wonderland of the mysterious. And it is important to recognize when we reach the limits of what we understand. It is not that we shall never understand these things. Probably we shall, and scientists are working on them with every hope of success. But we have to know what we don’t understand, and admit it to ourselves, before we can begin to work on it. There are scientists who understand at least something of this wonderland of the very small, but I am not one of them. I know my limitations.

Carbon – the scaffolding of life

All the elements are special in their different ways. But one element, carbon, is so special that we will end the chapter by talking briefly about that. Carbon chemistry even has its own name, separating it from the whole of the rest of chemistry: ‘organic’ chemistry. All the rest of chemistry is ‘inorganic’ chemistry. So what is so special about carbon?

The answer is that carbon atoms link up with other carbon atoms to form chains. The chemical compound octane, which, as you may know, is an ingredient of petrol (gasoline), is a rather short chain of eight carbon atoms with hydrogen atoms sticking out to the sides. The wonderful thing about carbon is that it can make chains of any length, some literally hundreds of carbon atoms long. Sometimes the chains come around in a loop. For example, molecules of naphthalene (the substance that mothballs are made of) are also made of carbon with hydrogen attached, this time in two loops.

Carbon chemistry is rather like the toy construction kit called Tinkertoy. In the laboratory, chemists have succeeded in making carbon atoms join up with each other, not just in simple loops but in wonderfully shaped Tinkertoy-like molecules nicknamed Buckyballs and Buckytubes. ‘Bucky’ was the nickname of Buckminster Fuller, the great American architect who invented the geodesic dome. The Buckyballs and Buckytubes scientists have made are artificial molecules. But they show the Tinkertoyish way in which carbon atoms can be joined together into scaffolding-like structures that can be indefinitely large. (Just recently the exciting news was announced that Buckyballs have been detected in outer space, in the dust drifting near to a distant star.) Carbon chemistry offers a near-infinite number of possible molecules, all of different shapes, and thousands of different ones are found in living bodies.

One very large molecule called myoglobin, for example, is found, in millions of copies, in all our muscles. Not all the atoms in myoglobin are carbon atoms, but it is the carbon atoms that join together in these fascinating Tinkertoy-like scaffolding structures. And that is really what makes life possible. When you think that myoglobin is only one example among thousands of equally complicated molecules in living cells, you can perhaps imagine that, just as you can build pretty much anything you like if you have a large enough Tinkertoy set, so the chemistry of carbon provides the vast range of possible forms required to put together anything so complicated as a living organism.

What, no myths?

This chapter has been unusual in that it didn’t begin with a list of myths. This was only because it was so hard to find any myths on this subject. Unlike, say, the sun, or the rainbow, or earthquakes, the fascinating world of the very small never came to the notice of primitive peoples. If you think about this for a minute, it’s not really surprising. They had no way of even knowing it was there, and so of course they didn’t invent any myths to explain it! It wasn’t until the microscope was invented in the sixteenth century that people discovered that ponds and lakes, soil and dust, even our own bodies, teem with tiny living creatures, too small to see, yet complicated and, in their own way, beautiful – or perhaps frightening, depending on how you think about them.

Dust mites are distantly related to spiders but too small to see except as tiny specks. There are thousands of them in every home, crawling through every carpet and every bed, quite probably including yours. If primitive peoples had known about them, you can imagine what myths and legends they might have invented to explain them! But before the invention of the microscope, their existence was not even dreamed of – and so there are no myths about them. And, small as it is, even a dust mite contains more than a hundred trillion atoms.

Dust mites are too small for us to see, but the cells of which they are made are smaller still. The bacteria that live inside them – and us – in vast numbers are smaller even than that.

And atoms are far far smaller even than bacteria. The whole world is made of incredibly tiny things, much too small to be visible to the naked eye – and yet none of the myths or so-called holy books that some people, even now, think were given to us by an all-knowing god, mentions them at all! In fact, when you look at those myths and stories, you can see that they don’t contain any of the knowledge that science has patiently worked out. They don’t tell us how big or how old the universe is; they don’t tell us how to treat cancer; they don’t explain gravity or the internal combustion engine; they don’t tell us about germs, or nuclear fusion, or electricity, or anaesthetics. In fact, unsurprisingly, the stories in holy books don’t contain any more information about the world than was known to the primitive peoples who first started telling them! If these ‘holy books’ really were written, or dictated, or inspired, by all-knowing gods, don’t you think it’s odd that those gods said nothing about any of these important and useful things?