The cosmic rainbow

In chapter 1, we did a rapid survey of the universe, listing its contents, and in chapter 4, we plan to discuss these objects in more detail. You may wonder how such a detailed picture about the universe has been put together. This has been possible because we can now observe the universe in a wide variety of wavebands of the electromagnetic spectrum, and virtually every cosmic object emits radiation in one band or another. In this brief chapter, we shall have a rapid overview of how these observations are made. While describing the observational techniques, we will also mention briefly the astronomical objects which are relevant to these observations. These objects are described in detail in the next chapter, and you could refer back to this cha46 pter after reading chapter 4.

It is rather difficult to ascertain when the first astronomical observation was made. Right from the days of pre-history, human beings have been wondering about the heavens and making note of the phenomena in the skies. The earliest observations, needless to say, were made with the naked eye. With the advent of the optical telescope, one could probe the sky much better and detect objects which were too faint to be seen with the naked eye. As the telescopes improved, the quality of these observations increased.

There is, however, an inherent limitation in these early observations. All these observations were based on visible light. We now know that visible light is an electromagnetic wave whose wavelength is in a particular range.

The subject of cosmology – and our understanding of how structures like galaxies, etc., have formed – have developed considerably in the last two decades or so. Along with this development came an increase in awareness about astronomy and cosmology among the general public, no doubt partly due to the popular press. Given this background, it is certainly desirable to have a book which presents current thinking in the subject of cosmology in a manner understandable to the common reader. This book is intended to provide such a nonmathematical description of this subject to the general reader, at the level of articles in New Scientist or Scientific American. An average reader of these magazines should have no difficulty with this book.

The book is structured as follows: chapter 1 is a gentle introduction to the panorama in our universe, various structures and length scales. Chapter 2 is a rapid overview of the basic physical concepts needed to understand the rest of the book. I have tried to design this chapter in such a manner as to provide the reader with a solid foundation in various concepts, which (s)he will find useful even while reading any other popular article in physical sciences. Chapter 3, I must confess, is a bit of a digression.

Probing the past

The discussion in the last chapter shows that most of the prominent structures in the universe have formed rather recently. In terms of redshifts we may say that galaxy formation probably took place at z < 10. Our understanding of galaxy formation could be vastly improved if we could directly observe structures during their formative phases. Remember that in the case of stars we can directly probe every feature of a stellar life cycle from birth to death; this has helped us to understand stellar evolution quite well. Can we do the same as regards galaxies?

Unfortunately, this task turns out to be very difficult. The life span of a typical star — though large by human standards — is small compared to the age of the universe. This allows one to catch the stars at different stages of their evolution. For galaxies, the timescale is much longer and so we cannot hope to find clear signals for galaxies of different ages. Secondly, the distance scales involved in extragalactic astronomy are enormously large compared to stellar physics. This introduces several observational uncertainties into the study.

In spite of all these difficulties, astronomers have made significant progress in probing the universe during its earlier phases. We saw in chapter 5 that the farther an object is the higher its redshift will be. But since light takes a finite time to travel the distance between a given object and us, what we see today in a distant object is a fossilized record of the past. Consider, for example, a galaxy which is at a distance of one billion light years.

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.