A physicist is just an atom’s way of looking at itself.
NIELS BOHR
To see a World in a Grain of Sand
And a Heaven in a Wild Flower,
Hold Infinity in the palm of your hand
And Eternity in an hour.
WILLIAM BLAKE, ‘Auguries of Innocence’, 1803
Richard Feynman was arguably the most important American physicist of the post-war era. He won the Nobel Prize for devising the theory of quantum electrodynamics, which describes how light interacts with matter and, in doing so, explains pretty much every aspect of the everyday world. In The Feynman Lectures on Physics, Feynman asks, ‘If in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words?’ Feynman answers, ‘All things are made of atoms.’1
The idea of the atom has an ancient history. Around 440 BC, the Greek philosopher Democritus picked up a stick or rock or it might have been a vase, and asked himself, ‘If I could cut this object in half, then in half again, could I go on subdividing like this for ever?’ To Democritus it was inconceivable that he could. Sooner or later, he reasoned, he would come to a grain of matter that could not be cut in half any more. Since the Greek for uncuttable was a tomos, Democritus called such an indivisible grain an ‘atom’.
Democritus further postulated that atoms come in just a handful of different types. And by combining them in different ways it is possible to make a flower or a cloud or a newborn baby. ‘By convention there is colour, by convention sweetness, by convention bitterness, but in reality there are atoms and the void,’ said Democritus.
It was a remarkable leap of the imagination. The world around us looks bewilderingly complex. But this is an illusion, according to Democritus. Beneath the skin of reality things are simple.2 Everything is made of a limited number of types of atom. Everything is in the combinations. Atoms, in short, are the alphabet of nature.
Democritus was led to his idea by the power of thought. But atoms, if they existed, were far too small to see with the naked eye. It took more than two millennia and the rise of science before indirect evidence was found for Democritus’ idea. In a steam engine, for instance, steam pushes with a pressure on its container. If the container is fitted with a movable wall – a piston – this can then drive machinery such as a spinning machine or a train. The movement of the piston can be explained, scientists discovered, if steam consists of countless tiny atoms3 flying about randomly through space. Their ceaseless drumming on a piston like raindrops on a tin roof creates a jittery force, which, smoothed out, we observe as pressure.4
‘So many of the properties of matter, especially when in the gaseous form, can be deduced from the hypothesis that their minute parts are in rapid motion, the velocity increasing with the temperature,’ said the nineteenth-century Scottish physicist James Clerk Maxwell. ‘The relations between pressure, temperature and density in a perfect gas can be explained by supposing the particles move with uniform velocity in straight lines, striking against the sides of the containing vessel and thus producing pressure.’5
The behaviour of gases such as steam provides evidence of Democritus’ idea that reality is composed of tiny grains of matter. But what about his idea that those grains also come in different types? Proof of this came from an unexpected direction.
For a long time, alchemists hoped it might be possible to turn base materials such as lead into precious stuff such as gold. Not only did they fail but they proved the opposite of what they set out to show. Some substances cannot, by any means, be broken down into simpler ones. In the late eighteenth century, the French man Antoine Lavoisier guessed that such elemental materials are large collections of a single type of atom. Gold was an obvious element. But, over the years, chemists – the successors of alchemists – discovered many more. Today, we know of 92 naturally occurring elements, ranging from the lightest, hydrogen, all the way up to the heaviest, uranium – and we have even made heavier, artificial, elements such as plutonium.
By 1815, the English physician William Prout had noticed that most atoms appear to have a mass that is a whole-number multiple of the mass of a hydrogen atom. This led him to propose that atoms are actually made of smaller things – hydrogen atoms. Actually, as the atom was systematically broken apart in the late nineteenth and early twentieth century, it became clear that it was made of not one smaller thing but three smaller things. Protons and neutrons are close in mass to Prout’s hydrogen building block while electrons are about 2,000 times lighter.
The picture that emerged gradually was of an atom as a miniature Solar System. At the centre, like a Sun, is a tiny nucleus, containing pretty much all the mass of the atom in the form of protons and neutrons (the exception being the lightest atom, hydrogen, whose nucleus contains only a proton). Around the nucleus, like planets around the Sun, there orbit electrons. The protons in a nucleus each have a positive electric charge and they are matched by an equal number of electrons with a negative charge. In fact, it is the force of attraction between opposite charges that keeps the electrons bound to the nucleus.
The planetary picture of the atom was deduced by the New Zealand physicist Ernest Rutherford in 1911. Rutherford’s protégés, Hans Geiger and Ernest Marsden, had in 1909 fired subatomic bullets from the world’s smallest machine-gun – a sample of radioactive radium – at a thin foil of gold. The picture of the atom at the time was of a Christmas pudding, with electrons studded like raisins in a sphere of positive charge. This predicted that Geiger’s and Marsden’s subatomic bullets – alpha particles – would fly through the gold atoms as surely as real bullets would fly though a cloud of gnats. To the astonishment of the two young experimenters, however, 1 in 8,000 bounced back. It took Rutherford two years to deduce that, contrary to the plum-pudding model, 99.9 per cent of the mass of the atom must be concentrated in a tiny nucleus, which 1 in 8,000 alpha particles had hit and bounced off.
One of the shocks of the planetary picture was of the incredible emptiness of an atom. A whopping 99.9999999999999 per cent is nothingness. If you could squeeze all the empty space out of all the atoms in all the people in the world, you could fit the human race in the volume of a sugar cube. The best image of the atom comes from the English playwright Tom Stoppard: ‘Now make a fist, and if your fist is as big as the nucleus of an atom, then the atom is as big as St Paul’s, and if it happens to be a hydrogen atom then it has a single electron flitting about like a moth in an empty cathedral, now by the dome, now by the altar.’6
The electrons, whirling far from the nucleus, represent the surface of the atom, where it makes contact with the world of other atoms. Their number – which is matched by the number of protons – therefore determines how an atom behaves; for instance, how it links with other atoms to make molecules. The lightest atom, hydrogen, has one proton in its nucleus and one electron circling; the second lightest, helium, two protons and two electrons; the third lightest, lithium, three protons and three electrons; and so on.
The neutrons in a nucleus carry no electric charge and play no role in determining how an atom presents itself to the world. Instead, they act as nuclear peacemakers, gluing the nucleus together via the strong nuclear force. Without their stabilising presence, the enormous electrical repulsion between protons would blast the nucleus apart.
It may seem that, with the atom turning out to be made of even smaller building blocks – protons, neutrons and electrons – Democritus’ idea has gone out of the window. However, his proposal was merely that matter, ultimately, is made of indivisible grains. And it turns out that Democritus is right. The world is ultimately made of indivisible grains. It is just that they are not what we have chosen to call atoms. That is our mistake. The ultimate elemental building blocks turn out instead to be subatomic particles known as leptons and quarks.
In fact, normal matter appears to be made of just four basic building blocks: two leptons and two quarks. The two leptons are the electron and the electron-neutrino. The electron is well known because most commonly it orbits in atoms, but the neutrino is less familiar, mainly because it is so amazingly unsociable. Although neutrinos are generated in prodigious quantities by the sunlight-generating nuclear reactions at the heart of the Sun, they interact with normal matter so rarely that they fly through the Earth as if it were transparent.7 In fact, about 100 billion solar neutrinos are streaming through your thumbnail every second without you ever noticing. Eight and a half minutes ago, they were in the heart of the Sun.8
In addition to the two leptons, there are two quarks – the up-quark and the down-quark. These clump together in threes to make the proton and the neutron, with the proton consisting of two up-quarks and one down-quark, and the neutron two down-quarks and one up-quark. The existence of quarks was proved by essentially repeating Geiger’s and Marsden’s experiment of 1909 in which they fired alpha particles into atoms and saw that they were deflected by the atomic nucleus deep inside. Physicists instead fired electrons into protons. In experiments carried out in the late 1960s and early 1970s, the ricocheting electrons revealed the existence of three point-like particles deep inside: the quarks.
Although physicists are now certain that protons and neutrons are made of quarks, bizarrely it is impossible to knock one out and create a free quark. This is because of the peculiar behaviour of the strong nuclear force that glues together quarks. Not only is it super strong – Newton was right to say, ‘The smallest particles may cohere by the strongest attractions’ – it gets stronger the further apart are two quarks. It is as if they are joined by elastic that resists more the more it is stretched. Long before two quarks are free of each other, the energy put into stretching the ‘elastic’ is transformed into the mass energy of new particles, as permitted by the law of conservation of energy. Specifically, the laws of particle physics cause a quark–antiquark pair to be conjured into existence.9 Experimenters must now separate two more quarks. But, in attempting to do that, they will create two more quarks, and so on.
But how do we know that the electron, neutrino, up-quark and down-quark are really nature ’s ultimate indivisible grains? The answer is because of the Pauli Exclusion Principle.10 This quantum edict states that certain subatomic particles cannot share the same quantum numbers. In the case of the electron, this means that two electrons in an atom cannot share the same orbit (and spin). This ensures that electrons do not pile on top of each other, which would effectively make possible only one kind of atom rather than the 92 whose combinations create the variety of our world.
The Pauli Principle is a consequence of three things, one of which is that particles such as electrons are indistinguishable.11 If two things are indistinguishable, it implies they have no substructure – otherwise the arrangement of their components could be used to tell them apart. The point is that leptons and quarks both obey the Pauli Principle. And the only way they can do this is if they are indistinguishable – that is, if they have no substructure and are truly nature ’s indivisible grains of matter.
So is that it? Ultimately, the world is made of just four building blocks – the electron, neutrino, up-quark and down-quark? Not quite. There is a twist. Isn’t there always? For some mysterious reason, nature has decided to triplicate its building blocks! Instead of one quartet of particles, there are three quartets, each containing successively more massive versions of essentially the same particles. So, in addition to generation 1, which consists of the electron, electron-neutrino, up-quark and down-quark, there is generation 2, which consists of the heavier muon, muon-neutrino, strange-quark and charm-quark, and generation 3, which consists of the even heavier tau, tau-neutrino, bottom-quark and top-quark.
Bizarrely, neither of the two heavier families plays any role in the everyday world. In fact, since it takes a large amount of energy to create them, they were common only in the super-energetic fireball of the big bang in the first split second of the Universe ’s existence. When the muon – essentially a heavier version of the electron – was discovered in 1936, the American physicist ‘I. I.’ Rabi said, ‘Who ordered that?’ The same could be said of the all the duplicates of nature ’s four basic building blocks: ‘Who ordered them?’
But how do we know there are not many more than three generations of fundamental building blocks? The answer comes from a surprising place: cosmology. Between 1 and 10 minutes after the birth of the Universe, the big-bang fireball was hot enough and dense enough for protons and neutrons to run into each other and stick together to make nuclei of the second heaviest element, helium. Remarkably, this primordial helium has survived until today and it can be observed throughout the Universe. Astronomers find that it accounts for about 10 per cent of all atoms. However, it turns out that, if there are many more generations of neutrinos, the gravity of their extra mass would have braked the expansion of the big-bang fireball, causing the Universe to stay denser and hotter for longer so that it cooked up a different amount of helium. According to calculations, a Universe with 10 per cent helium atoms is possible only if there are at most three or four generations of neutrinos. So there may be a fourth, even heavier, generation of fundamental building blocks still to be found. However, most physicists would bet against it.12
With three generations of particles, it would appear that there are a total of twelve fundamental building blocks – six quarks and six leptons. This is not quite all. There are also the forces that bind together the quarks and leptons – for instance, that glue the up-quarks and down-quarks into triplets to make protons and neutrons.
According to quantum theory, the forces arise from the exchange of force-carrying particles. Think of two tennis players hitting a tennis ball back and forth. As each player returns the ball, he feels the force of his opponent. Currently, physicists know of four fundamental forces: the electromagnetic force, which holds together the atoms in your body; the strong and the weak nuclear forces, which operate only inside the ultra-tiny domain of the atomic nucleus; and the gravitational force, which holds together planets, stars and galaxies. The electromagnetic force is carried by the photon; the weak nuclear by three vector bosons – the W+, W- and Z; the strong nuclear force by eight gluons; and the gravitational force by the graviton (though nobody has ever detected a graviton, and a quantum description of gravity in terms of such an exchange particle continues to elude physicists).
So now we are talking about twelve basic building blocks and thirteen force-carrying particles. Is that it? Well, actually, there is one other particle – the Higgs boson – which was discovered with much fanfare by the Large Hadron Collider near Geneva in Switzerland in 2012. This a localised lump in the Higgs field, a kind of invisible treacle that fills all of space and impedes the passage of the other particles, thereby endowing them with mass. Well, as ever, this is not quite the whole story.
Surprisingly, the quarks inside protons and neutrons are relatively light and account for a mere 1 per cent of the mass of normal matter, including you. This is what the Higgs explains. So where does the rest of their mass come from? The quarks are whirling about at close to the speed of light under the influence of the super-powerful strong nuclear force. It is their tremendous energy of motion that accounts for the missing 99 per cent of your mass since, as Einstein discovered, all energy has an effective mass.13 Ultimately, that energy of motion – and therefore your mass – comes from the gluon fields responsible for the strong nuclear force.
So there you have it. There are twelve basic building blocks glued together by thirteen force-carrying particles with one extra particle connected to the field that gives all the other particles their masses. This quantum description of the fundamental building blocks and fundamental forces is known as the Standard Model and it is arguably the single greatest achievement of physics. Its major deficiency, however, is that it describes only three of the four fundamental forces of nature. Gravity, currently described by Einstein’s general theory of relativity, remains stubbornly outside the fold.14
Twelve basic building blocks + thirteen force-carrying particles + the Higgs are rather a lot of fundamental particles. And, in fact, there are more – yet another twist. Each particle has associated with it an antiparticle, with opposite properties such as electrical charge or spin. A particle and its antiparticle are always born together, so the mystery is why we live in a matter-dominated Universe. The best guess of physicists is that, in the big bang, some lopsidedness in the laws of physics either favoured the creation of matter or preferentially destroyed antimatter. Incidentally, in addition to heavy particles (baryons) such as the proton and neutron, nature permits the existence of middle weight particles (mesons). Instead of being composed of a trio of quarks, these are made of just two quarks – a quark and an anti-quark.
So, to recap, there are twelve basic building blocks + thirteen force carrying particles + the Higgs + all their antiparticles. But physicists are always hoping to reduce the number. Ever since the late nineteenth century, when James Clerk Maxwell showed that the electric and the magnetic force are mere facets of a single electromagnetic force, physicists have been bitten by the unification bug. They are convinced that the four fundamental forces are merely facets of a single superforce, which reigned supreme in the high-energy conditions in the first moments of the big bang and which, as the temperature plummeted thereafter, repeatedly split into the forces we see today. In fact, in high-energy-particle collisions in the early 1980s, physicists actually witnessed the electromagnetic and weak nuclear forces merge back together into a single electro weak force.
In this spirit of unification, some physicists have suggested that the building-block particles, which are known as fermions, are merely different facets of the force-carrying particles, which are known as bosons.15 A serious drawback of this elegant idea, known as supersymmetry, is that none of the known fermions seems to be the flipside of any of the known bosons! Undeterred, physicists have postulated that the supersymmetric partners of the known particles have very large masses and that current particle accelerators have insufficient oomph to create them in particle collisions.
If supersymmetry is right, it will show that fermions are the flipside of bosons. Unfortunately, it will do so only at the expense of generating a whole host of new particles! The hypothetical supersymmetric partner of the electron, for instance, is the selectron, and of the photon the photino. It might seem a high price to pay for unification. However, there could be a huge pay-off. The reason is that there is yet another twist to the story of the ultimate constituents of matter: dark matter.
Embarrassingly, the stuff made of atoms – the material you, me and the stars are made of and that science has focused exclusively on for 350 years – turns out to account for a mere 4.6 per cent of the mass energy of the Universe.16 A whopping 71.4 per cent is invisible dark energy – but that is not important here. The key thing is that 24 per cent of the mass energy of the Universe is in the form of dark matter, material that gives out no discernible light and whose existence is inferred only from the tug its gravity exerts on the visible stars and galaxies. The identity of the dark matter, which outweighs the Universe ’s visible stuff by a factor of more than five, is a mystery. However, one possibility is that it is made of hitherto undiscovered supersymmetric particles.
Supersymmetry is just a modern attempt to show that a range of phenomena is merely a presentation of different faces of a single, unified, phenomenon. The desire for such unifications, however, is on an inevitable collision course with Democritus’ reductionist desire to show that reality is ultimately created by the permutations of a small number of basic building blocks. After all, if the reductionist programme ever succeeded in whittling down the fundamental building blocks to a single point-like fundamental particle, how could it have different faces? A point-like particle, by definition, looks the same from every viewpoint. There is, however, one way to avoid the conflict between unification and reductionism: if the fundamental building block is not a point-like particle. This is the proposal of string theory.
According to string theory, the fundamental building blocks of matter are one-dimensional strings of mass energy. These can oscillate like ultra-tiny violin strings, with ever more rapid, and therefore more energetic, vibrations manifesting themselves as heavier and heavier particles. One such vibration, for instance, would be the electron.
The strings are hypothesised to be fantastically small, typically a million billion times smaller than an atom. Probing such a tiny scale is way, way beyond our technological capabilities. It would require a particle accelerator to boost subatomic particles to an extraordinary energy since, according to quantum theory, the quantum wave associated with a particle is smaller the greater its momentum (or energy). Ultra-high energy is therefore synonymous with probing ultra-tiny scales – which is why the ultra-high-energy big bang echoed with the roar of things extremely small.
String theory has gained popularity because one particular string – a vibrating loop – has the properties of a graviton, the hypothetical carrier of the gravitational force. Thus string theory automatically incorporates gravity, which has proved the most difficult of the four forces of nature to unite with the others. The major drawback of the theory, however, is that, in order to reproduce the behaviour of all the fundamental forces, a total of ten dimensions is required – that is, six in addition to the four familiar ones. Proponents of string theory claim that the extra dimensions are not apparent because they are rolled up, or compactified, far smaller than an atom.
String theory is a possible candidate for a ‘Theory of Everything’. Such a theory would explain all the fundamental building blocks and how they interact with each other via the fundamental forces in a single neat set of equations that could be scrawled on the back of a stamp – or at least on a postcard. It would, according to physicists such as Stephen Hawking, bring physics to a final and triumphant end. However, a Theory of Everything would not be what it is cracked up to be – and for two crucial reasons.
The first reason is that the Universe cannot simply be the inevitable consequence of a Theory of Everything. This is because a Theory of Everything, by its very nature, would be a quantum theory. In other words, such a theory would predict not what happens but merely the chances, or probabilities, of different things happening. Every time an electron is faced with the choice of going to the left of an obstacle or to the right of it, every time an atom is faced with the choice of spitting out a photon of light or not spitting one out, what it actually chooses is random. And this kind of thing has happened a myriad times since the big bang. The Universe we see around us today is not simply a consequence of a Theory of Everything but the consequence of a Theory of Everything plus a mind-blowingly large sequence of frozen accidents. Billions upon billions of other possible universes could have arisen – all from the same Theory of Everything. Ours is merely one – selected at random. ‘Any entity in the world around us, such as an individual human being, owes its existence not only to the simple fundamental law of physics …’ says American physicist Murray Gell-Mann, ‘but also to the outcomes of an inconceivably long sequence of probabilistic events, each of which could have turned out differently.’17
The Theory of Everything, if we find it, will be a triumph of the human imagination. No doubt about that. But it will also reveal the limitations of the reductionist approach begun by Democritus two and a half millennia ago. We shall know the basic ingredients for a universe and the recipe. And that will be a fantastic achievement. But at the bottom of the recipe will be an instruction crucial to the success of the venture: cook for 13.77 billion years.18
The Theory of Everything has another limitation as well. The set of equations scrawled on the back of that stamp, or postcard, will describe how nature’s fundamental building blocks of matter interact with each other via nature ’s fundamental forces. But it will not explain a newborn baby or a Shakespeare sonnet or why two people fall in love. How do these things arise? According to physicists, these phenomena emerge.
A characteristic of the Universe – or at least our particular corner, the Earth – is that the fundamental building blocks combine together to make bigger building blocks, and these in turn link together to make even bigger building blocks, and so on. So, for instance, quarks and leptons combine with each other to make atoms. Atoms combine with each other to make molecules, including the mega-molecules of DNA. Molecules combine with each other to make gases and liquids and solids – and biological cells. Cells combine with each other to make plants and animals and human beings – and brains. And human brains combine with each other to make a global technological civilisation.
It is characteristic of this hierarchy, which spawns ever more novelty and complexity, that the laws that orchestrate how the building blocks at one level interact with each other give no hint of the laws that govern the behaviour of the building blocks at the next highest level, and so on. ‘Life is not found in atoms or molecules or genes as such, but in organization,’ according to American biologist Edwin Grant Conklin, ‘not in symbiosis but in synthesis.’19
The whole is greater than the sum of its parts. For instance, a knowledge of how quarks glue themselves together to make the nuclei of atoms tells a chemist nothing about the behaviour of how atoms link together to make molecules. And a knowledge of how a single cell works tells a neuroscientist nothing about how 100 billion cells work in concert to make a human brain that can laugh, conceive a plan to send a man to the Moon or paint the Mona Lisa.
This is why, despite the fundamental status of physics, sitting at the bottom of the explanatory hierarchy of the world, it has not made redundant chemists or biologists or sociologists. At each level of complexity, new phenomena, described by new laws, emerge from the interaction of the building blocks at the level beneath. So, for instance, when large numbers of water molecules come together to make a water droplet, there emerges a property called wetness, which makes no sense for a single molecule of H2O. And, when large numbers of atoms come together to make a pot of paint, there emerges a property called colour, which makes no sense for a single molecule of paint pigment.
Emergence might seem like magic but, really, it is not. Nothing is being added. It is more that information is being thrown away. Although it might be perfectly possible to predict the motion of a single molecule of gas flying through space, it is impossible to keep track of the countless quadrillions of gas atoms that make up the entire gas. So physicists ignore a vast amount of information. They approximate. They clear out some of those irrelevant details so that they can zoom out and see the big picture. This involves them inventing quantities such as pressure and temperature, which are averages of the behaviour of vast numbers of microscopic constituents. It is only when they zoom out intelligently in this way that they are able to spot correlations between the averaged-out parameters – new laws that govern their behaviour.
‘The world of the quark has everything to do with a jaguar circling in the night,’ wrote the Chinese-American poet Arthur Sze. But, in practice, connecting the two in a single explanatory framework is way beyond our twenty-first-century capabilities. We approximate because we do not have the mathematical ability to explain everything in terms of the behaviour of the most fundamental building blocks.
And we pile approximation upon approximation. And out of this process there emerge new laws. Ever more approximate laws. This is how we understand the Universe. This is how we make sense of a world that is far too complicated to be perceived in its entirety by the 3-pound lump of jelly and water that constitutes our puny ape brain. As Thomas Carlyle said, ‘I don’t pretend to understand the Universe – it’s a great deal bigger than I am … People ought to be modester.’
What all this means is that a Theory of Everything, if it is ever discovered, will not supplant all of science. Though it will explain the interaction the fundamental building blocks of the world, it will have nothing to say about flowers or sonnets or the chuckle of a newborn baby.
1 See Chapter 16, ‘The discovery of slowness: Special relativity’.
2 If something accelerates at 9.8 metres per second per second it merely means that, every second, it gets faster by 9.8 metres per second.
3 James Chin-Wen Chou et al., ‘Optical Clocks and Relativity’, Science, 24 September 2010, vol. 329, p. 1630.
4 A black hole is a region of space–time where gravity is so strong that nothing, not even light, can escape. Such a region is left when a very massive star reaches the end of its life and its core shrinks catastrophically under its own gravity. See Chapter 22, ‘Masters of the Universe: Black holes’.
5 Photons have no intrinsic, or rest, mass. Their effective mass is entirely due to their energy, or momentum.
6 If gravity is not quite the same as acceleration, it might appear to undermine the whole basis of general relativity. However, gravity and acceleration are always indistinguishable locally – that is, in a small enough region of space. And this, it turns out, is enough of a foundation on which to build Einstein’s theory of gravity.
7 Total eclipses of the Sun by the Moon are possible because of a very fortunate coincidence. Although the Sun is about 400 times further away than the Moon, it is also about 400 times bigger. Consequently, the Sun and the Moon have the same apparent size in the sky. The Moon is moving away from the Earth at about 4 centimetres a year. This means that total eclipses will not be visible in 100 million years’ time. Nor were they visible at the time of the dinosaurs 100 million years ago.
8 Einstein’s fields equations (1915) are: Gmn = -(8pG/c2)Tmn. In words, they say that the warpage, or geometry, of space–time (Gmn) is generated by matter and energy (Tmn). Each superscript represents 1 of the 4 coordinates of space–time so there are actually 4 ¥ 4 = 16 equations. But, since some are repeated, this reduces to 10. This is still 10 times as many as are required for Newton’s law of gravity.
9 According to Newton, gravity is a force of attraction between all bodies. So not only is there a force between the Sun and the Earth, there is a force between you and a person standing next to you, between you and the coins in your pocket. The force is extremely weak but grows with mass, which is why people passing each other in the street are not snapped together, whereas the Earth is trapped by the Sun. The force is mutual – in other words, the Earth exerts the same gravitational force on you as you do on the Earth. The reason you are affected by the Earth more than the Earth is affected by you is simply that you are smaller and easier to move. (‘Is that why I am attracted to big women but big women are not attracted to me?’ asked the English comedy writer Andy Hamilton on the pilot of the BBC4 comedy-science series It’s Only a Theory. He was highlighting a profound truth!)
10 Strictly speaking, a body moving under the influence of the inver-sesquare-force of another body traces out a conic section – an ellipse, parabola or hyperbola. The path is an ellipse if the body has insufficient energy to escape its gravitational entrapment; a hyperbola if it has; and a parabola if the body is teetering on the knife edge between being trapped and escaping to infinity.
11 A spectrum is formed when light is fanned out, or separated, into its constituent colours. In the past half a century, our vision, sensitive to a mere handful of rainbow hues, has been artificially enhanced to reveal a billion new colours arrayed along the electromagnetic spectrum – from gamma rays to radio waves. See Chapter 8, ‘Thank goodness opposites attract: Electricity’.
12 A neutron star is the super-dense relic of a supernova explosion. Paradoxically, when a massive star at the end of its life blows off its outer layers, its core implodes. A neutron star contains about the mass of the Sun compressed into only the volume of Mount Everest. Consequently, a sugar cube of neutron-star stuff weighs about as much as the entire human race. See Chapter 18, ‘The roar of things extremely small: Atoms’.
13 See Chapter 22, ‘Masters of the Universe: Black holes’.
14 A handul of neutrinos have also been detected from beyond the Sun. So too have cosmic rays, atomic nuclei possibly sprayed into space by supernova explosions. But, essentially, all we know about the Universe comes via light we pick up with our telescopes.