Forces of Nature

by Professor Brian Cox

  That said, let us continue down the particular tangled path we’ve chosen. The investigation of the rainbow has served as an introduction to and raised a series of questions about light that we should now seek to answer. The origin of the light that shines into the water droplets is a good place to start. As we’ve seen, there was vigorous debate in Alhazen’s time about whether vision was an active or passive process, and the study of rainbows played a part in establishing that the light that creates them has its origin in the Sun.

  Why does the Sun shine?

  Why does the Sun emit light? The answer would seem to be obvious: the Sun is hot, and all hot things shine. But why do hot things shine? This is a deeper question. There is also the question of the energy source that powers the Sun and heats it up in the first place. The energy output of the Sun was well known in the nineteenth century because it is an easy thing to measure if you know the distance to the Sun. One way is to take a known volume of water with a known surface area, place it in direct sunlight and see how long it takes for the water temperature to rise by one degree. This will tell you how much energy has entered the water during the measured time. A more accurate measurement would take account of the loss of solar energy as the light travels through the atmosphere.

  Observations at high altitude can help. The first measurement of the solar constant – the power output of the Sun – was made in 1838 by a Frenchman, Claude Pouillet. He estimated that around 1.2 kW of power per square metre falls on the Earth, 93 million miles away from the Sun. The modern measurement for the power delivered by the Sun at the top of the Earth’s atmosphere per square metre is 1.41 kW in January, when the Earth is closest to the Sun, and 1.32 kW in July, when the Earth is furthest away; the Earth’s orbit is an ellipse with the Sun at one focus. This is a colossal amount of energy. Imagine a sphere 93 million miles in radius, with enough energy to power a bright floodlight, falling on every square metre of the inside of the sphere every second. Sometimes numbers are so large that they are not helpful, but we may as well quote the total solar power output; it is 3.8 x 1023 kW. The total power-generating capacity of our civilisation today is around 16 x 109 kW; twenty million million times smaller. Here we go again, down a tangled path suggested by a simple question. This is a vast amount of energy. What could the source possibly be?

  NASA’s space shuttle Atlantis stands out in sharp relief against the vast backdrop of the Sun during a solar transit on 12 May 2009.

  The origin of the Sun’s energy was highly controversial during the late nineteenth and early twentieth centuries, because there was no known physical process capable of sustaining such a vast energy output for more than a few thousand years, notwithstanding the enormous size and mass of our star. Again, it’s very hard to picture the enormity of the Sun; a hundred Earths would line up along its diameter. It would take the average passenger jet six months to fly around it. It is traditional to say something about the size of Wales at this point; it would take 289 million countries the size of Wales to tile the surface of the Sun. But even with these vast resources of matter, the power output is difficult to explain. In 1862, Lord Kelvin, one of the greatest and most respected scientific voices of the day, declared that the Sun could be no more than 30 million years old, given its colossal power output, in direct contradiction with estimates of the age of the Earth from geological and biological evidence, which pointed to an age in excess of 300 million years.

  It’s very hard to picture the enormity of the Sun; a hundred Earths would line up along its diameter. It would take the average passenger jet six months to fly around it.

  Kelvin was over-confident and wrong, because he did not admit to the possibility of new physics providing an explanation for the source of solar energy. ‘He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency’; Kelvin would have done well in this instance to read Alhazen. The new discovery was nuclear physics. Physicists like to do back-of-the-envelope calculations, and we can use one to see how nuclear physics helps. Kelvin calculated that, if the Sun were made of coal, then this vast burning repository, papered by 289 million countries the size of Wales, would contain enough ‘coal’ to shine with the measured brightness for 3000 years. This gives some indication of the power stored in a star. Chemical reactions such as coal burning typically proceed at energy scales a million times smaller than nuclear reactions. This is a reflection of the fact that the strong nuclear force, which binds the nucleus of atoms together, is much stronger than the electromagnetic force, which binds atoms together. Chemistry is about rearranging atoms, and nuclear physics is about rearranging nuclei. Ernest Rutherford discovered the atomic nucleus in May 1911 in Manchester, and so Kelvin knew nothing of this hidden, higher-energy layer of physics. Because nuclear reactions typically operate at energies of the order of a million times those of chemical reactions, they will increase the energy available to the Sun by a factor of around a million, give or take. This suggests an age of at least 3 billion years – much closer to the modern estimate of a 10-billion-year solar lifetime. The current best estimates of the age of the Sun from computer modelling are around 4.57 billion years, which agree nicely with the radioactive dating of meteorites in the Solar System.

  In solar plants across the world, like this one in Germany, we are harnessing the energy of the Sun to create our own natural energy source.

  The nuclear physics of the Sun

  All of the four fundamental forces of nature that we met in Chapter One are involved in the energy-releasing nuclear reactions inside the Sun’s core. Stars begin their lives as clouds of hydrogen and helium, the atomic nuclei of which were formed in the first three minutes after the Big Bang. Under the action of gravity, the clouds collapse in on themselves, and the collapse heats them up. When the temperature reaches around 100,000 degrees Celsius, the hydrogen and helium nuclei can no longer hold on to their electrons and the cloud becomes a plasma – a hot gas of free electrically charged particles. As the collapse continues, the temperature rises further, and for sufficiently massive clouds the naked hydrogen nuclei approach each other with such speed that, despite their mutual electromagnetic repulsion – recall that a hydrogen nucleus is a single proton, which carries a positive electric charge – they can get very close. When this happens, a transformation takes place under the influence of the weak nuclear force. We met this transformation in passing in Chapter One as I reminisced about my time doing particle physics in Hamburg. There was a point there beyond gentle biography; we explored the constituents of matter using a particle accelerator and by consuming red wine and fine cheeses and attempting to get gout. Physics should be joyous. But I digress... Recall that a proton is made of two up quarks and one down quark and a neutron is made of two down quarks and an up quark. The weak nuclear force can turn an up quark into a down quark, so a proton can be transformed into a neutron, along with the creation of a positron and a neutrino. Neutrons are electrically neutral, and shorn of their positive electric charge carried off by the positron, they are free to approach the proton closely enough for the strong nuclear force to take over and bind them together tightly. The resulting atomic nucleus, made up of one proton and one neutron, is called a deuteron.

  Coronal mass ejections and solar flares demonstrate the sheer energy of the Sun – one such explosion has the power of one billion hydrogen bombs.

  The white dwarf Sirius B shines bright while the Sun gradually radiates its heat away until it is left as a darkening ember, a black dwarf.

  Uncovered by NASA’s Hubble Space Telescope, these ancient white dwarfs are some of the oldest burnt-out stars in the galaxy, at around 12–13 billion years old.

  The formation of a deuteron from two protons is known as nuclear fusion. It releases a vast amount of energy because the deuteron is less massive than two free protons. Einstein discovered that mass can be transformed into energy according to the equation E=mc2 (by taking Maxwell’s equations describing
the nature of light seriously – the tangled path), and it is the energy of fusion which is the power source of all the twinkling stars in the night sky.

  The numbers involved are absolutely huge; if we could take a cubic centimetre of the Sun’s interior and convert all the protons into deuterons, we could power an average-sized town for a year. Inside the Sun the fusion process doesn’t stop with the creation of deuterons. Another proton quickly fuses with the deuteron to form a helium-3 nucleus, and two helium-3 nuclei then fuse together to form a helium-4 nucleus, with the release of two protons. At each stage, mass is transformed into energy, which heats up the star. This energy also halts the gravitational collapse, because the super-heated plasma exerts an outward pressure that balances the inward pull of gravity. This is why stars are long-lived structures – they exist in a delicate yet stable equilibrium, as long as they have nuclear fuel to burn in their cores. Our Sun burns six hundred million tonnes of hydrogen fuel every second into helium, with the loss of four million tonnes of mass, which is released as energy. To get a sense of how many individual fusion reactions this corresponds to, consider that there are sixty billion neutrinos per square centimetre per second passing through your head from the Sun as you read this book, and only one is released every time a proton turns into a neutron. We’ll have more to say about these neutrinos later on, because they are very interesting. At this rate, the Sun has enough nuclear fuel to last another five billion years, at which point it will begin to fuse helium into carbon and oxygen before running out of options to release more fusion energy and collapsing into a fading ember known as a white dwarf.

  White dwarfs are dense, exotic objects held up against the crushing force of gravity by a quantum mechanical effect known as the Pauli exclusion principle. They are planetary-sized spheres of stellar mass; a sugar-cubed piece would weigh a tonne. The Sun’s exposed carbon-oxygen core will gradually radiate its heat away, leaving a darkening ember known as a black dwarf; it will last, if not for eternity, then for a very long time. In a thousand billion years the stellar remnant will fade from view as its temperature continues to fall. Its eventual fate is dependent on physics that we have yet to understand. It is thought that matter itself is unstable over very long timescales, and if this is the case then black dwarfs will evaporate, given enough time – of which there is likely to be an infinite amount. Lower limits on the lifetime of black dwarves suggest they should be around for at least 1032 years, which is ten thousand billion billion times the current age of the Universe.

  Nuclear fusion is the origin of the Sun’s energy, and ultimately the source of its light. The physical processes that produce the light that arrives at the Earth are different, however. It is the glowing surface of the Sun that we see in the sky, not its hidden nuclear-fired core. The surface of the Sun has a temperature of only 5500 degrees Celsius, and the light it emits is characteristic of this temperature, and not the 15 billion degrees at which the fusion reactions take place.

  If we could take a cubic centimetre of the Sun’s interior and convert all the protons into deuterons, we could power an average-sized town for a year.

  The idea that objects emit light according to their temperature is a familiar one. We speak of things as being ‘white hot’, and are familiar with the cooling red embers of a dying fire. The temperature of something is related to the colour of light it emits, and this is a clue to the origin of that light. Simple questions lead to deep answers, and the question of how hot things emit light is the classic example. The first thing to say is that it’s an old question; Isaac Newton considered it in his treatise on light, Opticks, published in 1704, and his suggested answer is correct in broad outline. ‘Do not all fix’d Bodies, when heated beyond a certain degree, emit Light and shine; and is not this Emission perform’d by the vibrating motion of its parts?’ It is the motion of the building blocks of matter that produces light, but it was not until the mid-nineteenth century that we began to understand the mechanism for this emission, and the quest for answers ultimately led to quantum theory and the construction of the technological foundations upon which our modern society rests.

  Why do hot things shine?

  Part 1: James Clerk Maxwell and the Golden Age of Wireless

  Through his work with electrical currents and magnetism Michael Faraday (1791–1867) laid the foundations for the work of James Clerk Maxwell.

  Matter is constructed of electrically charged particles, and when charged particles are shaken around, they emit light. More precisely, they emit electromagnetic radiation. The discovery that light is an electromagnetic phenomenon was made by the Scottish physicist James Clerk Maxwell in a series of papers published between 1861 and 1862.

  We’ve already met Maxwell’s equations in Chapter Two, as the inspiration for Einstein’s Theory of Special Relativity. To recap, Maxwell discovered a unified description of the experimental and theoretical work of a generation of physicists, including some of the great names commemorated today in the units we use to describe electricity: Volt, Ampère, Faraday, Gauss. If Maxwell’s only achievement were simplification, however, Einstein wouldn’t have described his work as ‘the most profound and the most fruitful that physics has experienced since the time of Newton’.

  Through a series of experiments, Michael Faraday came to the important conclusion that electricity and magnetism are related.

  Maxwell’s ‘profound’ achievement was not merely to unify, but to discover something quite new. He discovered that light is intimately connected to electricity and magnetism in a piece of work representing one of the most vivid examples of what physicist Eugene Wigner termed the unreasonable effectiveness of mathematics in the physical sciences; the notion that mathematical beauty, occasionally alone, can lead to a deeper understanding of the physical world.

  By the mid-1800s Faraday and others had discovered that electricity and magnetism are related. If an electric current is pulsed through a wire, a compass needle close to the wire is deflected in time with the pulse. If a magnet is moved in and out of a coil of wire, an electrical current flows through the wire whilst the magnet is moving. This is the basis of the electric motor and generator. Faraday thought deeply about the connection between the wires and the magnets. He reasoned that there must be some sort of physical link between the electrical current in a wire and the compass needle in order to deflect the needle; things don’t just move of their own accord. He pictured this physical link as a ‘field’, which might be visualised as the pattern formed when iron filings are scattered onto a piece of paper above a magnet.

  Maxwell discovered a unified description of the experimental and theoretical work of a generation of physicists, including some of the great names commemorated today in the units we use to describe electricity: Volt, Ampère, Faraday, Gauss.

  Faraday’s rather mechanical idea of electric and magnetic fields was not widely accepted at the time, primarily because it didn’t appear to be necessary. The mathematical equations that described electric and magnetic phenomena were written in terms of things that can be directly measured – volts and amps and forces that cause compass needle deflections. The deeper level of abstraction represented by the fields appeared to add unnecessary complication.

  Maxwell’s wave equations for the electric and magnetic fields.

  Maxwell discovered that this was emphatically not the case. He embraced the deeper description and rewrote all the equations describing electrical and magnetic phenomena in terms of electric and magnetic fields, rather than currents, voltages and forces. In doing so, he was forced to add an extra term into one of the equations for reasons of mathematical consistency. That term, which is called Maxwell’s displacement current, had a remarkable consequence. Once present, Maxwell saw that he could rewrite his equations in a different form, known as wave equations. In this form, the equations are able to describe a self-propelling disturbance in the electric and magnetic fields.

  Maxwell’s wave equations can be pictured as describing energy sloshi
ng backwards and forwards between the electric and magnetic fields, radiating outwards from an electromagnetic disturbance in the way ripples radiate outwards on a pond in response to a splashing stone. The difference is that there is no water or any other medium needed to support the disturbance – the fields themselves are sufficient to carry the energy away, one rising as the other falls. This is a fascinating observation in itself, but there was a great and most marvellous denouement. I cannot imagine how Maxwell reacted; he must have felt he was allowed a brief glimpse beyond the shadows at one of Nature’s clean foundations. This self-propelling disturbance has a speed, according to Maxwell’s wave equations – in the equation on here it is represented by the symbol c. Perhaps unsurprisingly, the speed has to do with the strengths of the electric and magnetic forces – the amount by which a change in one field induces a change in the other. The speed is predicted to be the ratio of the strengths of the two forces, and Maxwell knew these quantities because Faraday and others had measured them in experiments in their laboratories. If you’re familiar with a bit of electromagnetism from school, you may recognise their names and symbols; the permittivity of free space, εο, and the permeability of free space, μ0. When Maxwell put the numbers in, he discovered that the speed of the disturbance came out as the speed of light! Immediately, he would have known that he had found a deeper description of the nature of light itself: light is a travelling disturbance in the electromagnetic field that drives itself along at precisely 299,792,458 metres per second.