by Frank Close
What we can now do in experiments is in effect reverse the process and observe matter change back into its original primaeval forms. Heat matter to a few thousand degrees and its atoms ionise – electrons are separated from the central nuclei. That is how it is inside the Sun. The Sun is a plasma, that is gases of electrically charged electrons and protons swirling independently. At even higher temperatures, typical of the conditions that can be reached in relatively small high-energy accelerators, the nuclei are disrupted into their constituent protons and neutrons. At yet higher energies, these in turn ‘melt’ into a plasma of freely flowing quarks.
How this all happened, how we know, and what we’ve discovered are the themes of this Very Short Introduction.
Chapter 2
How big and small are big and small?
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Atoms are very small; the cosmos is very big. How do they compare with everyday things? The universe isn’t the same everywhere – the Sun and stars are much hotter than the Earth and matter takes on different forms, but it is ultimately made of the same stuff. The universe hasn’t been the same throughout time. Formed 15 billion years ago in a hot Big Bang, it was then that the seeds of matter were formed.
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From quarks to quasars
Stars are huge, and visible to the naked eye over vast distances. This is in stark contrast to their basic components, the particles that eventually make up atoms. It would take about a billion atoms placed on top of one another to reach your head; it would take a similar number of people head to toe to give the diameter of the Sun. So this places the human measuring scale roughly in the middle between those of the Sun and an atom. The particles that make up atoms – the electrons that form the outer regions, and the quarks, which are the ultimate seeds of the central nucleus – are themselves a further factor of about a billion smaller than the atomic whole.
A fully grown human is a bit less than two metres tall. For much of what we will meet in this book, orders of magnitude are more important than precise values. So to set the scale I will take humans to be about 1 metre in ‘order of magnitude’ (this means we are much bigger than 1/10 metre, or 10–1m, and correspondingly smaller than 10 m). Then, going to the large scales of astronomy, we have the radius of the Earth, some 107 m (that is, 1 followed by 7 zeroes); that of the Sun is 109 m; our orbit around the Sun is 1011 m (or in more readable units, 100 million km). For later reference, note that the relative sizes of the Earth, Sun, and our orbit are factors of about 100.
Distances greater than this become increasingly hard to visualize, with large numbers of zeroes when expressed in metres, so a new unit is used: the light year. Light travels at 300,000 metres per second. This is fast but not infinite: it takes light a nanosecond, that is 10–9 s, to travel 30 cm, which is about the size of your foot. Modern computers operate on such timescales, and such microtimes will become central when we enter the world within the atom. For the moment, we are heading to the other extreme – the very large distances of the cosmos, and the long times that it takes for light to travel from remote galaxies to our eyes here.
It takes light 8 minutes to travel the 150 million km from the Sun; so we say the Sun is 8 light minutes away. It takes a year for light to travel 1016 m, and so this distance is referred to as a light year. Our Milky Way galaxy extends for 1021 m, or some 100,000 light years. Galaxies cluster together in groups, extending over 10 million light years. These clusters are themselves grouped into superclusters, about 100 million light years in extent (or 1024 m). The extent of the visible universe is some 10 billion light years, or 1026 m. These actual numbers are not too important, but notice how the universe is not homogeneous, and instead is clustered into distinct structures: superclusters, clusters of galaxies, and individual galaxies such as our own, with each being roughly 1/100 smaller than its predecessor. When we enter the microworld, we will once again experience such layers of structure, but on a much emptier scale; not 1/100 but more like 1/10,000.
Having made a voyage out into the large scales of space, let’s now take the opposite direction into the microworld of atoms, and their internal structure. With our unaided naked eye, we can resolve individual pieces of dust, say, that are as small as a tenth to a hundredth of a millimetre: 10–4 to 10–5 m. This is at the upper end of the size of bacteria. Light is a form of electromagnetic wave, and the wavelength of visible light that we see as the rainbow spans 10–6 to 10–7 m. Atoms are a thousand times smaller than this: some 10–10 m. It is the fact that atoms are so much smaller than the wavelength of visible light that puts them beyond the reach of our normal vision.
Everything on Earth is made from atoms. Every element has its smallest piece, far too small to see by eye but real nonetheless, as special instruments can show.
To recap from Chapter 1: atoms are made of smaller particles. Electrons whirl in their remote reaches: at their heart is the compact massive atomic nucleus. The nucleus has a structure of its own, consisting of protons and neutrons, which in turn are made of yet smaller particles: the ‘quarks’. Quarks and electrons are the seeds of matter as we find it on Earth.
Whereas the atom is typically 10–10 m across, its central nucleus measures only about 10–14 to 10–15 m. So beware the oft-quoted analogy that atoms are like miniature solar systems with the ‘planetary electrons’ encircling the ‘nuclear sun’. The real solar system has a factor 1/100 between our orbit and the size of the central Sun; the atom is far emptier, with 1/10,000 as the corresponding ratio between the extent of its central nucleus and the radius of the atom. And this emptiness continues. Individual protons and neutrons are about 10–15 m in diameter and are in turn made of yet smaller particles known as quarks. If quarks and electrons have any intrinsic size, it is too small for us to measure. All that we can say for sure is that it is no bigger than 10–18 m. So here again we see that the relative size of quark to proton is some 1/10,000 (at most!). The same is true for the ‘planetary’ electron relative to the proton ‘sun’: 1/10,000 rather than the ‘mere’ 1/100 of the real solar system. So the world within the atom is incredibly empty.
3. Comparisons with the human scale and beyond normal vision. In the small scale, 10–6 metres is known as 1 micron, 10–9 metres is 1 nanometre, and 10–15 metres is 1 fermi.
To gain some sort of feel for this, imagine the longest hole that you are likely to find on a golf course, say 500 m. The relative length of this fairway to the size of the tiny hole into which you will eventually pot the ball is some 10,000:1 and hence similar to that of the radius of the hydrogen atom to its central nucleus, the proton.
Just as large distances become unwieldy when expressed in metres, so do the submicroscopic dimensions of atomic and nuclear structures. In the former case we introduced the light year, 1016 m; in the latter it is customary to use the angstrom, A, where 1 angstrom = 10–10 m (typically the size of a simple atom) and the fermi, fm, where 1 fm = 10–15 m. Thus angstroms are useful units to measure the sizes of atoms and molecules, while fermis are natural for nuclei and particles. (Ångström and Fermi were famous atomic and nuclear scientists of the 19th and 20th centuries, respectively.)
Our eyes see things on a human scale; our ancestors developed senses that would protect them from predators and had no need for eyes that could see galaxies that emit radio waves, or the atoms of our DNA. Today we can use instruments to extend our senses: telescopes that study the depths of space and microscopes to reveal bacteria and molecules. We have special ‘microscopes’ to reveal distances smaller than atoms: this is the role of high-energy particle accelerators. By such tools we can reveal nature over a vast range of distance scales. How this is done for particles will be the theme of Chapters 5 and 6.
The universe in temperature and time
That is how things are now, but it hasn’t always been that way. The universe, as we know it, began in a hot Big Bang where atoms could not survive. Today, about 14 billion years later, the universe at large is very cold and atoms can survive.
There are local hot spots, such as stars like our Sun, and matter there differs from that found here on our relatively cool Earth. We can even simulate the extreme conditions of the moments immediately following the Big Bang, in experiments at particle accelerators, and see how the basic seeds of matter originally must have emerged. However, although the forms that matter takes vary through space and time, the basic pieces are common. How matter appears in the cold (now), in the hot (such as in the Sun and stars), and in the ultra-hot (like the aftermath of the original Big Bang), is the theme of this section.
In macroscopic physics we keep our energy accounts in joules, or in large-scale industries, mega- or terajoules. In atomic, nuclear, and particle physics, the energies involved are trifling in comparison. If an electron, which is electrically charged, is accelerated by the electric field of a one-volt battery, it will gain an energy of 1.6 × 10–19 J. Even when rushing at near to the speed of light, as in accelerators at CERN in Geneva, the energy still only reaches the order of 10–8 J, one hundredth of a millionth of a joule. Such small numbers get messy and so it is traditional to use a different measure, known as the ‘electronvolt’, or eV. We said above that when accelerated by the electric field of a one-volt battery, it will gain an energy of 1.6 × 10–19 J, and it is this that we define as one electronvolt.
Now the energies involved in subatomic physics become manageable. We call 103 eV a kilo-eV or keV; a million (mega), 106 eV is 1 MeV; a billion (giga), 109 eV is 1 GeV; and the latest experiments are entering the ‘tera’ or 1012 eV, 1 TeV, region.
Einstein’s famous equation E = mc2 tells us that energy can be exchanged for mass, and vice versa, the ‘exchange rate’ being c2, the square of the velocity of light. The electron has a mass of 9 × 10–31 kg. Once again such numbers are messy and so we use E = mc2 to quantify mass and energy which gives about 0.5 MeV for the energy of a single electron at rest; we traditionally state its mass as 0.5 MeV/c2. The mass of a proton in these units is 938 MeV/c2, which is nearly 1 GeV/c2.
Energy is profoundly linked to temperature also. If you have a vast number of particles bumping into one another, transferring energy from one to the next so that the whole is at some fixed temperature, the average energy of the individual particles can be expressed in eV (or keV and so on). Room temperature corresponds to about 1/40 eV, or 0.025 eV. Perhaps easier will be to use the measure of 1 eV 104 K (where K refers to Kelvin, the absolute measure of temperature; absolute zero 0K = –273 Celsius, and room temperature is about 300 K).
Fire a rocket upwards with enough energy and it can escape the gravitational pull of the Earth; give an electron in an atom enough energy and it can escape the electrical pull of the atomic nucleus. In many molecules, the electrons will be liberated by an energy of fractions of an eV; so room temperature can be sufficient to do this, which is the source of chemistry, biology, and life. Atoms of hydrogen will survive at energies below 1 eV, which in temperature terms is of the order of 104 K. Such temperatures do not occur normally on Earth (other than specific examples such as some industrial furnaces, carbon arc lights, and scientific apparatus) and so atoms are the norm here. However, in the centre of the Sun, the temperature is some 107 K, or in energy terms 1 keV; atoms cannot survive such conditions.
At temperatures above 1010 K there is enough energy available that it can be converted into particles, such as electrons. An individual electron has a mass of 0.5 MeV/c2, and so it requires 0.5 MeV of energy to ‘congeal’ into an electron. As we shall see later, this cannot happen spontaneously; an electron and its antimatter counterpart – the positron – must be created as a pair. So 1 MeV energy is needed for ‘electron positron creation’ to occur. Analogously, 2 GeV energy is needed to create a proton and its antiproton. Such energies are easy to generate in nuclear laboratories and particle accelerators today; they were the norm in the very early universe and it was in those first moments that the basic particles of matter (and antimatter) were formed. The details of this will be given in Chapter 9, but some outline will be useful for orientation now.
4. The correspondence between scales of temperature and energy in electronvolts (eV).
The galaxies are observed to be rushing apart from one another such that the universe is expanding. From the rate of the expansion we can play the scenario back in time and deduce that about 14 billion years ago the universe would have been compacted in on itself. It is the explosive eruption from that dense state that we call the Big Bang. (It is not the primary purpose of this book to review the Big Bang; to learn more read Peter Coles’ Cosmology in the Very Short Introduction series). In that original state, the universe would have been much hotter than it is now. The universe today is bathed in microwave radiation with a temperature of about 3 K. Combining this with the picture of the post-Big Bang expansion gives a measure of temperature of the universe as a function of time.
Within a billionth of a second of the original Big Bang, the temperature of the universe would have exceeded 1016 K, or in energy terms 1 TeV. At such energies particles and antiparticles were created, including exotic forms no longer common today. Most of these died out almost immediately, producing radiation and more of the basic particles such as electrons and the surviving quarks that make up matter today.
As the universe aged, it cooled, at first very quickly. Within a millionth of a second quarks clustered together in threes, where they have remained ever since. So protons and neutrons were born. After about three minutes the temperature had fallen to about 1010 K, or in energy 1 MeV. This is ‘cool’ enough for protons and neutrons to stick together and build up the nuclear seeds of the (yet to be completed) atomic elements. A few light nuclei were formed, such as helium and traces of beryllium and boron. Protons, being stable and the simplest, were most common and clustered under gravity into spherical balls that we call stars. It was here that the nuclei of heavy elements would be cooked over the next billions of years. In Chapter 9 I shall describe how the protons in these stars bumped into one another, clustering together and by a series of processes made the nuclear seeds of heavier elements: first helium, and eventually the heavier ones such as oxygen, carbon, and iron. When such stars explode and die they spew these nuclear seeds out into the cosmos, which is where the carbon in your skin and the oxygen in our air originated.
The Sun is going through the first part of this story now. It has been converting protons into the nuclei of helium for 5 billion years and has used up about half of its fuel so far. The temperatures involved in its heart that do this are similar to those of the whole universe when it was a few minutes old. So the Sun is carrying on today what the universe did at large long ago.
Atoms cannot survive inside the depths of the Sun, and nor could they in the early universe. It was not until some 300,000 years had elapsed that the universe had cooled enough for these nuclei to entrap passing electrons and make atoms. That is how things are here on Earth today.
Chapter 3
How we learn what things are made of, and what we found
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Instruments such as microscopes and particle accelerators enable us to extend our vision beyond the rainbow of visible light, and see into the subatomic microworld. This has revealed the inner structure of the atom – electrons, nuclear particles, and quarks.
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Energy and waves
To find out what something is made of you might (a) look at it; (b) heat it and see what happens; or (c) smash it by brute force. There is a common misconception that it is the latter that high-energy, or ‘particle’, physicists do. This is a term left from the days when particle accelerators were known as ‘atom smashers’. And indeed, historically that was what took place, but today the aims and methods are more sophisticated. We will come to the details later, but to start, let’s focus on the three options just mentioned. Each of them shares a common feature: they all use energy.
In the case of heating, we have already seen how temperature and energy are correlated (104 K 1eV). Even in looking
at things, energy will turn out to play a role.
You are seeing these words because light is shining on the page and then being transmitted to your eyes; the general idea here is that there is a source of radiation (the light), an object under investigation (the page), and a detector (your eye). Inside a full stop are millions of carbon atoms and you will never be able to see the individual atoms even with the most powerful magnifying glass. They are smaller than the wavelength of ‘visible’ light and so cannot be resolved in an ordinary magnifying glass or microscope.
Light is a form of electromagnetic radiation. Our eyes respond only to a very small part of the whole electromagnetic spectrum; but the whole of it can be accessed by special instruments. Visible light is the strongest radiation given out by the Sun, and humans have evolved eyes that register only this particular range. The whole spread of the electromagnetic spectrum is there, as we can illustrate by an analogy with sound. A single octave of sound involves a halving of the wavelength (or a doubling of the frequency) from one note (say the A at 440 Hz) to that of an octave above (the A at 880 Hz). Similarly for the rainbow: it is an ‘octave’ in the electromagnetic spectrum. As you go from red light to blue, the wavelength halves, the wavelength of blue light being half that of red (or equivalently, the frequency with which the electric and magnetic fields oscillate back and forth is twice as fast for blue light as red). The electromagnetic spectrum extends further in both directions. Beyond the blue horizon – where we find ultraviolet, X-rays, and gamma rays – the wavelengths are smaller than in the visible rainbow; by contrast, at longer wavelengths and in the opposite direction, beyond the red, we have infrared, microwaves, and radio waves.
