15 Million Degrees

by Lucie Green

  Our experience of electricity is as old as our exposure to light, from lightning in a stormy sky to static electric charges on the ground. In the 1800s, over a century after we first began to develop a fundamental understanding of light, it was electricity’s turn to be scrutinized. It was a substantial effort, and the names of those who carried out the experimental theoretical work live on today, in the terms for scientific units that may be familiar to you: Ampère, Gauss, Ohm, Faraday and Coulomb. Their work laid the foundation for a theory that united electricity with light. The theory was developed by 1862 and was the work of the great Scottish mathematician James Clerk Maxwell.

  At the heart of electricity are electric charges, which are either ‘positive’ or ‘negative’ – arbitrary labels that have become established over the years but which reflect that there are two distinct types. Particles with the same electric charge repel each other, but particles with ‘opposite’ charges are attracted. It is this force that is acting within every atom, keeping the negatively charged electrons in place around the positively charged nucleus, which contains protons and neutral neutrons, at the centre of the atom.

  We all make use of moving electrically charged particles every day: your home is full of wires carrying electrical currents of slowly moving electrons. But something important happens when electrically charged particles are moving, and it can be investigated using a compass. Place a small compass (or even the compass app on a smartphone) next to the cord of your kettle. As you flick the electric current on and off you will see the needle move back and forth slightly. The reason for this is that when a charged particle moves, another force springs to life: magnetism. And if understanding light needs an understanding of electric currents, it must also involve magnetism.

  Magnetism is another ghostly force, like electricity, which seems to act at a distance. Electrically charged particles repel or attract each other without ever coming into contact. In both cases the effect can be thought of as a field of influence, visualized as a series of field lines. Many of us are used to diagrams of magnetic field lines from school science lessons: the field lines close in on themselves to make continuous loops like an elastic band. If the circles are bunched close together, the field is stronger, and if they are more spread out the field is weaker. But the same applies to the less familiar electric fields. To picture the electric field of a charged particle, imagine a series of lines emanating radially out from the particle, a bit like the spokes of a bicycle wheel that stretch out from the hub. The field lines are close together near the centre, where the particle is, indicating that the force is strong there, and spread apart the farther away they stretch, showing that the greater the distance from the particle, the weaker the force. But, unlike electricity, there are no particles that have a ‘magnetic’ charge. Instead a magnetic field can appear whenever there is a moving electric charge. This is why one appears when you turn on your kettle and the electric current starts to flow.

  1.1 Schematics of the electric field of a stationary positively charged particle (left) and magnetic field lines of a bar magnet (right).

  Don’t worry if you find magnetic and electric fields somewhat mysterious; it is not your fault but rather that of physics. It turns out they are two sides of the same coin, which can lead to confusing overlap.

  So far we have stationary charged particles that produce an electric field and moving charged particles that produce a magnetic field (the electrons in a bar magnet are moving within their atoms, hidden from sight). But there is a different way to produce an electric field, and that is with a moving magnetic field, which is what we get when a charged particle is accelerating. But when changing its speed, the magnetic field produced by an electrically charged particle is also always in a state of flux and this in turns produces a new, secondary, electric field – an electric field which is also moving …

  1.2 Magnetic and electric fields inducing each other in a never-ending cycle. This schematic shows that the magnetic field and electric field oscillate at right angles to each other.

  Magnetic and electric fields are more intimately linked than anyone had ever expected. It was Maxwell who realized that a changing electric field, producing a changing magnetic field, producing a changing electric field, and so on ad infinitum, would produce a kind of self-propagating electromagnetic pulse that would, if left to its own devices, ripple out through space indefinitely: a self-sustaining wave not requiring any medium to move through. In 1862 Maxwell calculated the exact rate this propagation would occur at as 193,088 miles per second – almost exactly the same as the speed of light. The conclusion was unavoidable: light is an electromagnetic wave. This was the first ever meaningful answer to the question: what is light?

  The conclusion that light is an electromagnetic wave solves a lot of the problems Newton was having. Waves can pass through each other without any disturbance. Electromagnetic waves also don’t need a material to convey them, which is why a light wave can travel through the vacuum of space at 300,000 kilometres per second. At this speed, it takes sunlight only around 8 minutes and 20 seconds to travel the 150 million kilometres from the Sun to us. But that is only the speed it travels at in a vacuum – light will slow down when it has to pass through something: light moves through water at three quarters of its normal speed in air. This can be used to explain refraction.

  The rate at which the waves in the electric and magnetic fields that make up the rainbow of colours oscillate is not the same, and our eyes perceive this variation as different colours. The oscillation rate of the wave is also known as its frequency and it is the different frequencies which together give sunlight the distinct colours we see in a rainbow (but all the colours that comprise sunlight move along at the same speed). Some light oscillates rapidly, and this is what we see as blue light, whereas red light swings back and forth much more slowly. The frequency of red light is 390 terahertz, which means 390 million million wave crests pass any given point in one second, whereas blue is up at 700 terahertz. This also means that the different colours have different wavelengths. If the waves are moving at the same speed, yet the number of wave crests passing a particular point in one second varies, the distance between the crests must vary too.

  When light moves from air to water it slows down, but importantly the frequency of each wave does not change. This is compensated for by a change in wavelength. This makes no difference to our eyes, though, because it is the frequency that they use to distinguish colour. Now, if the beam of light hits the water at exactly 90 degrees, all of the light in the beam changes speed simultaneously. But if the sunbeam hits it at an angle, different parts of the cross-section of the beam will hit the water at fractionally different times. The light that hits the water earlier will slow down before the region of light next to it in the cross-section of the beam. The result is that the light beam bends and changes its direction. Think of a group of children in line abreast and holding hands. Initially they all walk at the same speed and proceed together in a straight line. Now imagine that at one end the children walk more slowly than the others. They start to lag behind and the line of children begins to bend. They can no longer continue walking in their original direction if they keep their new speeds. When light changes direction because of this effect it is called ‘refraction’ – a phenomenon we met earlier with Huygens’ theory of light as a wave.

  1.3 A 2D illustration of two waves with different wavelengths used to show that red light (top) has a longer wavelength than blue light (bottom)

  Moreover, as the light passes into the water, the amount that its speed is reduced by differs according to wavelength: shorter-wa
velength, blue light is bent more than the longer-wavelength, red light. Then, because sunlight consists of a continuous spectrum of colours that correspond to a continuous range of wavelengths, hitting water at certain angles will split it into a rainbow, with blue light always at one end of the rainbow and red at the other.

  Even that’s not the whole story. When we think of light, we think of what we can see with our eyes. But there is literally more to sunlight than meets the eye: we cannot rely on our intuitive understanding of the world, mediated by what our brains perceive, if we are going to understand the Sun. Like a detective we must be open to all possibilities, not just the ones we have been taught to expect. ‘Expect the unexpected’ could be the unofficial motto of modern physics.

  The Sun produces light in all sorts of ‘colours’ we cannot even imagine; they are beyond what our visual system can perceive. We call the frequencies of light we can see ‘colours’, but for frequencies well outside that range we abandon the notion of colour and start giving them names like ‘microwaves’ and ‘radio waves’. In the last seven decades of studies of the Sun we have extended our perception of sunlight into these frequencies as we have developed ways to ‘see’ the Sun. Telescopes and detectors on the ground and in space have given us new and different kinds of eyes. Using these we have seen that the Sun emits very low-frequency and long-wavelength light. Whereas the wavelengths of visible light are in the region of hundreds of billionths of a metre, the low-frequency waves can have wavelengths of metres. Beyond the violet light of the visible spectrum the Sun also emits high-energy ultraviolet radiation, X-rays and gamma rays that have high frequencies and wavelengths as small as atoms. This broad range of wavelengths together make what is known as the ‘electromagnetic spectrum’. We need now to introduce a term that can be used to refer to any of these waves across the spectrum, whether they are visible to the eye or not. For this, the term electromagnetic radiation will be used, or radiation for short.

  However, what we have found is that the Sun emits some frequencies constantly whilst others are produced in sporadic bursts. The Sun doesn’t emit all frequencies of the electromagnetic spectrum in equal measure: less than half is emitted in the visible range, about half in the infrared and less than one tenth in the ultraviolet, with all other frequencies making up a small fraction of sunlight. And there’s a further complication: the frequencies of radiation that arrive on Earth are not an accurate representation of what the Sun produces. The reason for this is that our atmosphere acts as a filter, and its effect is stronger on some frequencies than on others. Gamma rays, X-rays and most of the ultraviolet radiation are absorbed by our atmosphere, as is much of the infrared. Some, but not all, of the radio radiation makes its way to us. In the end, by far the biggest part of the solar spectrum that reaches us on the surface of the Earth is the Sun’s visible radiation. This is a key reason why we have evolved only to detect these frequencies with our eyes: Nature is an efficient mistress and she uses the parts of sunlight that are most abundant on the ground.

  There are other good reasons why Nature doesn’t bother with the low-and high-frequency radiation as a means for humans to visualize the world around them. You may be wearing sunglasses as you read this book so that the intensity of the visible light reflecting off the page is reduced. When you bought the glasses I hope you chose a pair that filters out the Sun’s ultraviolet radiation as well as a decent amount of the visible range: this high-frequency radiation causes eye damage and, over time, is thought to lead to cataracts.

  Another excellent reason for seeing only the visible radiation becomes apparent if we consider what it would be like if our eyes were able to detect radio waves. In order to form a clear, crisp image of the world – in order to distinguish the words ‘kerning’ and ‘keming’, for example – we rely on light entering our eye through the pupil and on our eye being able to resolve the detail. Variations in the wavelength of the light and the diameter of the pupil affect the level of detail that can be achieved in this way: increasing the pupil size gives us the ability to see finer and finer detail, whereas increasing the wavelength of light has the opposite effect. An average human pupil with a diameter of, say, 3 millimetres does well for light in the visible range of the spectrum, with wavelengths between 400 billionths and 700 billionths of a metre. Consider now that the radio waves which reach us from the Sun have a wavelength of one metre – a million times greater than the wavelength of radiation used by our eyes. So, to be able to see the same level of detail as we do normally, we would need a pupil a million times larger – 3000 metres in diameter. It doesn’t take eyes three kilometres big to immediately see the problem here.

  Perhaps the most important thing that we can infer from sunlight is the simplest thing of all. And we can observe this without using our eyes at all. If you are reading this book outside, take a moment now to run your fingers over the page. If the sunlight is strong enough, the paper will feel warm to your touch. Not only is the sunlight that reaches us full of different colours, but it also exudes warmth. In fact, the warmth that you feel in sunlight is the result of a wavelength of radiation that is longer than that in the red end of the visible spectrum: infrared. We experience this wavelength of radiation not through our eyes but through the sensation of heat.

  This is what is fundamentally important about the electromagnetic radiation coming from the Sun and the reason why we cannot live without it – it carries energy to us in its electromagnetic waves. Energy can come in many forms but what unites them all is the capability they have to be used to do something – such as move an object or accelerate particles. The ability of charged particles to move as they feel a force in an electromagnetic field means that the field contains energy. Infrared radiation is merely the form that is most obviously detectable by us because it heats our bodies by causing molecules in our skin to vibrate, but whether visible or invisible there is energy in electromagnetic waves. This is what gives them the potential to heat materials, move charged particles, drive photosynthesis and much, much more. In fact, plants have adapted to absorb light specifically at the red and blue wavelengths to power the synthesizing of nutrients; the remaining green wavelengths are simply reflected, which is why plants are pretty much always that colour.

  RETURN OF THE PARTICLE

  By the end of the nineteenth century, it looked like humans’ understanding of light was finally in order. The observation of how light behaves, the investigation of electricity and magnetism, and the resulting theory of electromagnetism provided us with an explanation of light as a wave. There was just one small outstanding problem about how light actually transfers all that energy it seems to be carrying around. Explaining how the Sun’s infrared radiation is heating up the page in your book was not quite as simple as scientists had hoped.

  If instead of hitting your book and warming it up, the light beaming from the Sun hits a special sheet of metal instead, it can be made to bump some electrons loose within that metal and an electric current starts to flow. This process is at the heart of all modern solar panels. But the electric current does not behave in a logical fashion. If you produce a low-energy current and then dramatically turn up the brightness of the light hitting it you suddenly get … no change. More electrons are produced, but the energy of each one stays put. Yet a dimmer light, of a larger frequency, will produce a higher energy current. This problem was solved with some clever mathematics.

  A German scientist, Max Planck, had shown at the turn of the nineteenth century that radiation emitted by a hot and glowing object could only be described by assuming that it is made of individual packets of energy, not a continuous stream of waves
. He saw that if you did the calculations for light as a wave, the results did not match what actually happened in the real world. The only way to get the theory to match observations was to use a mathematical model based on light being made up of tiny discrete particles. We are back in Newton territory.

  At the time, Planck dismissed the interpretation of radiation coming in packets of energy as nothing more than a mathematical manoeuvre to make the equations fit the observations – a convenient mathematical approximation and not a description of reality. But someone else did take the particle theory of light seriously: Albert Einstein.

  In 1905 Einstein demonstrated that when radiation is absorbed, it acts as if made of individual particles, or photons. This was an important contribution to the Nobel Prize that was awarded to Einstein in 1921. The energy carried by each individual photon was related to its frequency – the higher the frequency the higher the energy, and two photons of the same frequency will always carry the same amount of energy. This explains the photo-electric effect: more light would not mean more energetic electrons as each photon is a discrete particle with an energy set by its frequency, and they all only knock out one electron each. Photons of higher frequency, which carry more energy, are needed for more energetic electrons.

  It seems slightly unfair that, just as we began to understand light as a propagating wave, we should discover that light behaves as if it were being transmitted by particles. Thank goodness Hooke wasn’t alive to see this. Newton, however, would have loved it. The wave and particle descriptions of light may seem counterintuitive but light is what it is, it behaves in its own way. It is up to us to find a description that best fits its behaviour and, for now, we need both. Part of the problem comes from our conceptual approach as we try to describe light in familiar and simple terms. Throughout this book both wave and particle descriptions will be used and I hope you’ll feel light’s seemingly fickle character starting to have purpose.