This book is an introduction to the physics of the solar wind and magnetosphere. These regions of space are filled with charged particle gases called plasmas. The study of solar system plasmas is commonly called space physics. This book started as lecture notes for courses that I have taught at the University of Michigan and the University of Kansas. The book is an introductory textbook aimed at advanced undergraduate and graduate students who possess an undergraduate physics background but have not taken any plasma physics courses. An introduction to plasma physics, including the topic of magnetohydrodynamics, is included in order to make the book self-contained. Undergraduate-level electromagnetic theory and mechanics are extensively used, and the Appendix provides a very brief review of the first topic.

The book can be divided into three parts. The first part, consisting of Chapters 1 through 4, provides an introduction to plasma physics. In particular, Chapter 1 gives a brief introduction to space plasma physics, kinetic theory is discussed in Chapter 2, and Chapter 3 is concerned with single particle motion in electric and magnetic fields. Chapter 3 also contains material on energetic particle motion in the radiation belts. Magnetohydrodynamics (MHD) is introduced in Chapter 4. Examples dealing with phenomena in the solar wind and magnetosphere are provided. Students who have already taken a standard plasma physics course can skip over much of the first part of the book.

The beginnings

The term ‘science fiction’ was first used by one of the founders of the modern genre, Hugo Gernsback. Gernsback, after whom the annual science fiction 'Hugo’ awards are named, was the founder of the Amazing Stories magazine in April, 1gz6.The slogan on the title page proclaimed its mission: 'Extravagant Fiction Today … Cold Fact Tomorrow'. Of course, few of the stories published in Amazing Stories lived up to this claim, but science fiction does have some notable successes to its credit over its relatively brief history. Two of the founding fathers of science fiction – H. G. Wells and Isaac Asimov – have already been mentioned in earlier chapters. In this final chapter, we shall examine the interplay between relativity and science fiction. We begin with Johannes Kepler, arguably the first writer of the genre.

Kepler was born in south-west Germany in a small town called Weil-der-Stadt. Kepler's first great work, A New Astronomy, was published in I 609, and it remains a landmark in the history of science. In it, Kepler formulated the first ‘natural laws’ – precise, verifiable statements about natural phenomena expressed in terms of mathematical equations. Arthur Koestler, in his marvellous book The Sleepwalkers, claims that it was Kepler's laws that 'divorced astronomy from theology and married astronomy to physics'. Unlike Copernicus, Galileo or Newton, Kepler did not attempt to disguise the way in which he arrived at his conclusions -all his errors and sidetracks are faithfully recorded along with his final revelation.

Geometry and gravity

The discovery of ‘non-Euclidean’ geometry in the nineteenth century came as a great surprise and was greeted by disbelief. One of the pioneers of this new geometry, Janos Bolyai, a Hungarian army officer, expressed his joy with the words:

'Euclidean’ geometry is the geometry we learn in school, with its familiar apparatus of points, straight lines, circles, ellipses and triangles. In particular, we are all brought up to believe that the three angles of a triangle add up to 180 degrees and that parallel lines never meet. Such Euclidean geometry is the geometry of the plane – technically called a ‘flat’ space. By contrast, non- Euclidean geometry describes a ‘curved’ space. What do we mean by these terms?

Some idea of a curved space can be gained by considering geometry on the surface of the Earth. The Earth is approximately spherical, and on its surface it is easy to construct triangles whose angles add up to more than I 80 degrees (Figure 9. I). Similarly, lines of longitude start out parallel at the equator but converge and cross at the poles. The surface as a whole does not obey Euclid's rules. Since such a familiar example of a surface is non- Euclidean, why are such geometries so unfamiliar to most of us?

The momentous day in May

In May of 1905, Einstein was twenty-six years old, and his ten-year struggle with the problems of relativity was about to come to a triumphant climax. About a year before this, he had begun to feel that the velocity of light must be universal – independent of the motion of the source. If this were true, then there was no need to worry about motion relative to any mythical aether, and the null result of Michelson and Morley became obvious: the speed of light is the same in both arms of the apparatus, whatever direction they are pointing relative to the Earth's motion. But the Earth does move round the Sun – so something was wrong with the ‘relativity’ of Galileo and Newton and their familiar addition of velocities, at least where light is concerned. As we asserted in chapter 2, and as we shall show in the next chapter, in Einstein's relativity speeds do not add up in the expected way. We are also forced to re-think our notions of space and time. This new vision of space and time is what we shall look at in this chapter. Let us start by recalling what Galileo and Newton believed, before looking at Einstein's version of the relativity principle.

In the sixteenth century, it seemed natural to believe that, if the Earth was moving, neither an arrow shot straight up nor a stone dropped from a tower would follow the same straight-line path.

Einstein's revolution

The famous Russian scientist Lev Landau used to keep a list of names, in wich he graded, physicists into ‘leagues’. The first division contained the names of physicists such as Niels Bohr, Werner Heisenberg and Erwin Schroedinger, the founding fathers of modern quantum physics, as well as historical ‘giants’ such as Isaac Newton. He was rather modest about his own classification, grading himself 2½, although he later promoted himself to a 2. Most working physicists would be happy even to make it into Landau's fourth division: David Mermin, a well-known and perceptive American physicist, once wrote an article entitled ‘My life with Landau: homage of a 4½ to a 2’. What is the point of this story? The point is that any book about relativity is inevitably also about Albert Einstein, and Einstein was a remarkable physicist by any standard. Landau, in fact, created a special ‘superleague’ containing only one physicist, Einstein, whom he classified uniquely as a½. Thus, the popular opinion that Einstein was the greatest physicist since Newton is widely shared among professional physicists.

When Einstein wrote about ‘The wonderful events which the great Newton experienced in his younger days…’, and commented that, to Newton, Nature was ‘an open book’, he could well have been writing about himself.

The weight of light

In 1913, Max Planck visited Einstein in Zurich with the aim of persuading him to move to Berlin. In conversation, Einstein remarked to Planck that he was working on a new theory of gravity. Planck's response was forthright, but concerned:

Planck was only partly right. Einstein succeeded and his theory of ‘general relativity’ was believed, but, for the most part, his theory had little relevance to mainstream physics. It was not until after Einstein's death in 1955 that the new technological advances of the 1960s rekindled interest in general relativity. Whereas most advances in understanding Nature could have been made by several scientists working at the time instead of the actual discoverer, this is probably not true of general relativity.

Fields of force

Three pictures hung on the wall of Einstein's study – portraits of Isaac Newton, Michael Faraday and James Clerk Maxwell. These three physicists provided the inspiration for Einstein's great works. With the tools provided by Faraday and Maxwell, Einstein eventually overturned Newton's conception of the universe and the very fabric of space and time which had proved itself so successful for over 200 years.

Newton pictured atoms of matter as having various powers of attraction and repulsion, gravity being the most famous such property. In Newton's scheme of things, the Earth attracts the Moon and all other bodies – such as the famous apple -by virtue of its mass. Newton discovered how this attractive force diminished with distance and, by applying his force law to the Sun and the planets of the solar system, he was able to explain the orbits of the planets.

Encouraged by the success of The Quantum Universe, we have tried to adopt a similarly pragmatic approach in this sister volume on Albert Einstein's relativity. Our goal is not only to present the essential ideas of both special and general relativity as simply as possible, but also to demonstrate how the predictions of these theories are verified by the results of experiments. Special relativity is concerned with uniform motion, and does away with Isaac Newton's notion of 'absolute time': it makes startling predictions for objects and observers moving at very high speeds. General relativity, on the other hand, is concerned with accelerations: it turns out to be a theory of gravity which has had a profound impact on our modem view of the universe.

Since our aim is to introduce as many people as possible to the strange world of relativity we have deliberately used a minimal amount of mathematics in the text. Some simple derivations requiring no more than high school maths have been relegated to an appendix for the curious. Needless to say, any book about both special and general relativity must also be to some extent about the physicist who almost single-handedly created these theories. Einstein's legacy is truly remarkable – both inside and outside of physics – and we hope to have captured some flavour of the man through the quotations and stories that accompany the text.

Time dilation

In chapter 3, we promised more details on the derivation of relativistic ‘time dilation'. We considered a thought experiment with a simple clock and two 'observers’ – one at rest relative to the clock and one in motion. We shall now see that the stationary observer sees the moving clock running slow.

Our ‘clock’ consists of a box with a mirror at either end. A light pulse bounces back and forth between the two mirrors, and the time taken for one round trip is taken to be one ‘tick’ of the clock. For an observer at rest relative to this clock, all is fine. Consider how things look for an observer moving in a direction at right angles to the length of the clock (Figure AI). She will see the light pulse start out, and she will see the clock with its two mirrors move away from her with a constant speed. According to her, the light must travel further than just twice the distance between the mirrors. The argument is very similar to that used in the Michelson and Morley experiment. If the distance between the mirrors is denoted by L, and the speed at which the clock moves away from our observer is written as v, we can relate the times measured by the two observers: TR for the observer at rest with respect to the mirrors, and TM for the observer in motion.

The strange behaviour of the velocity of light

As we have seen, Roemer showed as long ago as I 676 that the velocity of light was not infinite. Subsequent measurements by Michelson and others now agree on a value for the speed of light of some 299 792 kilometres/second. This applies not only to the visible part of the electromagnetic spectrum but also to much longer-wavelength radio waves and much shorter-wavelength gamma rays, as expected from Maxwell's equations. Now, according to Newton's laws of motion, there is nothing special about the speed of light. There is nothing, in principle, to stop one accelerating an object – or indeed oneself – to any speed whatsoever. It was the problem of what one would see in a mirror if both observer and mirror were moving at the speed of light that set Einstein on his path to relativity.

It is sometimes said that Einstein showed little exceptional talent when he was at school. This may be true, but it is certain that few schoolboys could have formulated the key paradox of the mirror at the age of sixteen.

The expanding universe

After his stunning success with general relativity, Einstein began to think about the implications of his theory for the universe as a whole. In 1917, he wrote a paper that began a new field of physics, that would be called ‘relativistic cosmology’. He wrote to his friend Paul Ehrenfest:

Although Einstein had the nerve to provide the first mathematical model of the universe, he had also, in a sense, lost his nerve at the crucial moment. Instead of predicting Hubble's discovery of the expansion of the universe, a solution that followed naturally from his own field equations, Einstein chose to modify gravity and introduce a new repulsive force.