15. Outer Space, The Scientists

Our understanding of the Universe at large rests upon two foundations – being able to measure the distances to the stars, and being able to measure the compositions of the stars. As we have seen, the first real understanding of the distances to the stars emerged in the eighteenth century, when Edmond Halley realized that some of the ‘fixed’ stars had moved since the time they were observed by his predecessors in Ancient Greece. By this time, astronomers had begun to make accurate measurements of distances across the Solar System, using the same process of triangulation that is the basis of surveying. To measure the distance to an object without actually going there, you need to be able to see the object from both ends of a baseline of known length. From the angles made by the lines of sight to the object from each end of the baseline, you can then work out the distance from the geometry of triangles. This technique had already been used to measure the distance to the Moon, our nearest neighbour in space, just 384,400 km away; but for more distant objects you need longer baselines to be able to make accurate measurements. In 1671 the French astronomer Jean Richer (1630–1696) travelled to Cayenne, in French Guiana, where he made observations of the position of Mars against the background of ‘fixed’ stars at the same time that his colleague in Paris, the Italian-born Giovanni Cassini (1625–1712), made similar observations. This made it possible to work out the distance to Mars, and, by combining this with Kepler’s laws of planetary motion, to calculate the distance from the Earth (or any other planet in the Solar System) to the Sun. The figure Cassini came up with for the Sun–Earth distance, 140 million km, was only 7 per cent less than the accepted modern value (149.6 million km), and gave the first accurate indication of the scale of the Solar System. Similar studies of Venus during the transits of 1761 and 1769 (predicted by Halley) led to an improved estimate of the Sun–Earth distance (known as the Astronomical Unit, or AU) of 153 million km, close enough to the modern value for us to leave the later improvements in the measurements as fine tuning, and accept that by the end of the eighteenth century astronomers had a very good idea of the scale of the Solar System.

What was highly worrying about this at the time was that it implied almost unimaginable distances to the stars. During any interval of six months, the Earth moves from one side of the Sun to the other, at opposite ends of a baseline 300 million km (or 2 AU) long. Yet the positions of the stars on the night sky do not change when viewed from either end of this enormous baseline. You would expect the nearer stars to seem to move against the background of more distant stars, in the same way that if you hold a finger out at arm’s length and close each of your eyes in turn, the position of the finger seems to move against the background of more distant objects (an example of the effect known as parallax). It is easy to calculate how much a star ought to be seen to move when viewed from different places in the Earth’s orbit. Astronomers define one parallax second of arc, or parsec, as the distance to a star which would show a displacement of one second of arc on the sky from opposite ends of a baseline 1 AU long.¹ So a star 1 parsec away would show a displacement of 2 seconds of arc from opposite ends of the 300 million km baseline represented by the diameter of the Earth’s orbit. From simple geometry, such a star would be 3.26 light years away, 206,265 times as far away from us as the Sun. And yet, no star is close enough to us to show this much parallax displacement on the sky as the Earth moves around the Sun.

There were already hints that stars must be at the kinds of distances this simple calculation implied. Christiaan Huygens, for example, tried to estimate the distance to Sirius, the brightest star in the night sky, by comparing its brightness to that of the Sun. To do this, he let sunlight into a darkened room through a pinhole in a screen, adjusting the size of the hole until the pinprick of light looked about the same as the brightness of Sirius – not easy, since obviously he had to look at the Sun in daytime and Sirius at night. Nevertheless, by showing how small a fraction of the Sun’s light corresponded to the observed brightness of Sirius, and knowing that the brightness of an object is inversely proportional to the square of its distance, he argued that if Sirius were actually as bright as the Sun it must be 27,664 times further away. The Scot James Gregory (1638–1675) improved on this technique by comparing the brightness of Sirius with the brightness of the planets, which could be seen in the sky at the same time. The calculation was a little more complicated, since it involved working out how the sunlight became attenuated on its way out to the planets, estimating how much of the light was reflected and calculating how the reflected light was attenuated on its way to Earth. But in 1668, Gregory provided an estimate of the distance to Sirius equivalent to 83,190 AU. Isaac Newton updated this calculation, using improved estimates of the distances to the planets, and came up with a distance to Sirius of one million AU, published in his System of the World in 1728, the year after he died. The actual distance to Sirius is 550,000 AU, or 2.67 parsecs; but the apparent accuracy of Newton’s estimate owes as much to luck as judgement, with several of the inevitable errors resulting from the imperfect data available to him cancelling each other out.

Measuring distances to stars using the triangulation, or parallax, technique required the positions of the stars on the sky (which really means their positions relative to each other) to be measured to very high accuracy. Flamsteed’s catalogue, a tremendous achievement in its day, gave positions to an accuracy of only 10 seconds of arc (merely 1/180th of the diameter of the full Moon on the sky). The first distances to stars were only measured in the 1830s, because it was only then that, with improving technology, the measurements became accurate enough to measure the tiny parallax shifts involved – but once the technology was good enough, several astronomers immediately began to make the measurements. The pioneers chose for study stars which they had some reason to think must be relatively close to us – either because they are very bright or because they are seen to move across the sky as the years go by (they have large ‘proper motions’), or both. The first person to announce a stellar parallax determination and the associated distance to a star was the German Friedrich Wilhelm Bessel (1784–1846), in 1838. He chose 61 Cygni, a star with a large proper motion, and found its parallax to be 0.3136 seconds of arc, implying a distance of 10.3 light years (modern measurements give a distance of 11.2 light years, or 3.4 parsecs). In fact, the first person to measure a stellar parallax was the Scot Thomas Henderson (1798–1874), working in South Africa in 1832; he studied Alpha Centauri, the third brightest star in the night sky, and came up with a parallax of 1 second of arc (later reduced to 0.76 arc seconds, implying a distance of 1.3 parsecs (4.3 light years)). Henderson’s results, though, were not published until he returned to England in 1839. Alpha Centauri (which is now known to be a triple system, with three stars in orbit around one another) is the closest star to the Sun, with the largest measured parallax. A year after Henderson’s announcement, the German-born astronomer Friedrich von Struve (1793–1864), working at the Pulkova Observatory near St Petersburg, measured the parallax of Vega (also known as Alpha Lyrae); his figure was a little too high, but modern measurements give a parallax of 0.2613 seconds of arc and a distance of 8.3 parsecs (27 light years). The important thing to take away from these measurements is that they are all for stars which are our near neighbours on the cosmic scale. The nearest star to the Sun is 7000 times further away than Pluto, generally regarded as the most distant planet in the Solar System. And once you know the true distance to a star, you can work out its true brightness (called the absolute magnitude) by reversing the technique which Huygens, Gregory and Newton applied to Sirius. In this way, we now know that Sirius itself, 2.67 parsecs away from us, is actually much brighter than the Sun, something that Newton and his contemporaries had no way of telling. Even these breakthroughs at the end of the 1830s, however, did no more than indicate the vast scale of the Universe. It wasn’t until the end of the nineteenth century that it became possible to measure parallaxes more easily, using photographic plates to record the positions of the stars. Before then, the positions had to be measured by eye, using the crosswires of a telescope, in real time; hardly surprisingly, the rate of new measurements was roughly one a year from 1840 to the end of the century, so that by 1900 only 60 parallaxes were known. By 1950, the distances to some 10,000 stars had been determined (not all of them by parallax²), and towards the end of the twentieth century the satellite Hipparcos measured the parallaxes of nearly 120,000 stars, to an accuracy of 0.002 arc seconds.

In many ways, modern astronomy – astrophysics – only began at the beginning of the twentieth century, precisely because of the application of photographic techniques to preserve images of the stars. As well as giving distances to enough stars for statistical studies of stars to be meaningful, photography also provided a way of recording and preserving images of the spectra of stars, and it was, of course, spectroscopy (developed, as we have seen, only in the 1860s) that enabled astronomers to obtain information about the composition of the stars. One other vital piece of information was needed – the masses of stars. This was supplied by studies of binary systems, in which two stars orbit around one another. For a few nearby binaries, the separation between the stars can be measured in angular terms, and this can be converted into linear distances if the actual distance to the star system is known (as it is for Alpha Centauri). The invaluable Doppler effect³ in the spectrum of light seen from the stars in the binary system tells astronomers how fast the stars are moving around one another, and together with Kepler’s laws (which apply equally as well to stars orbiting one another as they do to planets orbiting around stars), this is enough to enable astronomers to work out the masses of the stars. Once again, by the early 1900s there were just enough observations of this kind for the statistics to be meaningful. So it is no surprise that at just that time two astronomers working on opposite sides of the Atlantic Ocean independently put all of the pieces of the puzzle together and came up with the single most important insight into the nature of stars, a diagram which relates the colours of the stars to their brightnesses. It doesn’t sound all that impressive, but it is as important to astrophysics as the periodic table of the elements is to chemistry. But, as I hope we have made clear, like most developments in science it was not really a revolutionary development but an evolutionary progression from what had gone before, built on the foundations of improved technology.

The Dane Ejnar Hertzsprung was born in Frederiksberg on 8 October 1873. He trained as a chemical engineer, graduating from Copenhagen Polytechnic in 1898, and later studied photochemistry, but from 1902 onwards he worked privately (that is, in an unpaid capacity) at the observatory of the University of Copenhagen, learning how to be an observational astronomer and applying his photographic skills to astronomical observations. It was during this time that he discovered the relationship between the brightness of a star and its colour, but he published these results (in 1905 and 1907) in a photographic journal, where they lay unnoticed by professional astronomers around the world. Even so, Hertzsprung’s local reputation grew to the point where, in 1909, he was offered a post at the Göttingen Observatory by Karl Schwarzschild (1873–1916), with whom he had been corresponding. When Schwarzschild moved to the Potsdam Observatory later that year, Hertzsprung went with him, staying there until 1919 when he moved to The Netherlands, becoming first a professor at Leiden University and then, in 1935, Director of the Leiden Observatory. Although he officially retired in 1944, Hertzsprung carried on astronomical research back home in Denmark well into his eighties, and died on 21 October 1967, just after his ninety-fourth birthday. He made many contributions to observational astronomy, including studies of proper motions and work on the cosmic distance scale, but nothing to rank with the discovery he made while still technically an amateur.

Henry Norris Russell was born in Oyster Bay, New York, on 25 October 1877. He had a more conventional start to his academic career than Hertzsprung, studying at Princeton and visiting the University of Cambridge before taking up a post as professor of astronomy at Princeton in 1911. It was there that he made essentially the same discovery as Hertzsprung about the relationship between the colours of stars and their brightnesses, but he had the good sense to publish (in 1913) in a journal read by astronomers, and the flash of inspiration to plot the relationship on a kind of graph, now known as the Hertzsprung–Russell (or just HR) diagram, which made the importance of the discovery immediately apparent to his readers.⁴ Hertzsprung’s contribution to the discovery was quickly recognized, hence the name given to the diagram. Russell was based at Princeton throughout the rest of his working life, although he also made good use of the new telescopes built in California over the next few years. Apart from the HR diagram, he made important contributions to the study of binary stars, and also investigated the composition of the atmosphere of the Sun, using spectroscopy. He retired in 1947 and died in Princeton on 18 February 1957.

The point about the HR diagram (sometimes called a colour–magnitude diagram, since in astronomy magnitude is another term for brightness) is that the temperature of a star is closely related to its colour. We are not talking just in a qualitative way about the colours of the rainbow here, although it is true that blue and white stars are always intrinsically bright, while some orange and red stars are bright and some are faint⁵ (the key observation made by Hertzsprung in the first decade of the twentieth century). Astronomers can do better than this, and put the measurement of colour on a quantitative footing. They define the colour of a star very precisely in terms of the amount of energy it is radiating at different wavelengths, which tells you the temperature of the surface emitting the light. Using the known properties of black-body radiation, the surface temperature of a star can be determined from measurements at just three wavelengths (at a pinch, and slightly less accurately, from just two). But the intrinsic brightness of a star (its absolute magnitude) tells you how much energy the star is radiating overall, regardless of its temperature. It is possible for some red stars to be both cool and bright because they are very big, so that even though each square metre of the surface only glows red, there are an awful lot of square metres letting energy out into the Universe. Small stars can only be as bright if they are blue or white hot, with a lot of energy crossing each square metre of the smaller surface; and small orange stars (like the Sun) are intrinsically less bright than hot stars the same size or large stars with the same temperature. And the bonus comes when masses of stars are included. When the temperatures (or colours) and brightnesses (or magnitudes) of stars are plotted on the HR diagram, most stars lie on a band running diagonally across the diagram, with hot, massive stars about the same size (diameter) as the Sun at one end of the band, and cool, dim stars with less mass than the Sun at the other end. The Sun itself is an average star, roughly in the middle of this so-called main sequence. The large, cool but bright stars (red giants) lie above the main sequence, and there are also some dim, small but hot stars (white dwarfs) below the main sequence. But it was the main sequence itself which gave astrophysicists their first insight into the internal workings of the stars, an insight developed initially largely by the British astronomer Arthur Eddington, often regarded as the first astrophysicist, who was the person who discovered the relationship between the mass of a star and its position on the main sequence.

Eddington was born in Kendal, in the Lake District of England, on 28 December 1882. His father died in 1884 and the family (Arthur had one sister) moved to Somerset, where he was brought up as a Quaker. Eddington studied at Owens College in Manchester (the forerunner of the University of Manchester), then from 1902 to 1905 at the University of Cambridge. He worked at the Royal Greenwich Observatory until 1913, before returning to Cambridge as Plumian Professor of Astronomy and Experimental Philosophy (succeeding George Darwin), and in 1914 also became director of the university observatories. He held these posts until he died, in Cambridge, on 22 November 1944. Skilled as an observer, a brilliant theorist, an able administrator and with a gift for communicating important scientific ideas in clear language to a wide audience (he was the first popularizer of Einstein’s theories of relativity in English), Eddington made a profound mark on astronomy in the twentieth century, but is best remembered for two key contributions.

The first came about partly because Eddington was a Quaker and a conscientious objector to war. Einstein’s general theory of relativity was first presented by him to the Berlin Academy of Sciences in 1915, and published in Germany the following year, when Britain and Germany were, of course, at war. But a copy of Einstein’s paper went to Willem de Sitter (1872–1934) in the neutral Netherlands, and de Sitter passed a copy on to Eddington, who among his other activities was Secretary of the Royal Astronomical Society at that time. In that capacity, he broke the news about Einstein’s work to the Society; this was the beginning of Eddington’s role as the front man for the general theory in the English-speaking world. Among other things, Einstein’s theory predicted that light from distant stars should be bent by a certain amount as it passed close by the Sun, shifting the apparent positions of those stars on the sky. This could be observed during an eclipse. As it happened, a suitable eclipse was due in 1919, but it would not be visible from Europe. In 1917, the Royal Astronomical Society began to make contingency plans to send a pair of expeditions to observe and photograph this eclipse from Brazil and from the island of Principe, off the west coast of Africa, if the war ended in time.

At that time, though, there was little obvious reason why the war should end quickly, and the losses at the front had become so heavy that the British government introduced conscription, with all able-bodied men eligible for the draft. Although 34, Eddington was able-bodied, but clearly much more valuable to Britain as a scientist than as a soldier in the trenches (although the argument that scientists deserve special treatment is not one that we would endorse; everyone at the front would have been more use to society back at home). The point was put to the Home Office by a group of eminent scientists, and Eddington was advised that he would be exempt from the draft on the grounds of his value to the scientific community. He replied that if he had not been deferred on these grounds he would have claimed exemption on conscientious grounds anyway, which infuriated the bureaucrats in the Home Office. Their first reaction was that if Eddington wanted to be a conscientious objector he could go and join his Quaker friends in agricultural work, which he was quite prepared to do. But some nifty footwork by the Astronomer Royal, Frank Dyson, saved face all round and persuaded the Home Office to defer Eddington’s draft on condition that he would lead an expedition for the government to test Einstein’s light-bending prediction. He would have been the ideal choice anyway, having first-hand experience of eclipse studies from Brazil during his time with the Royal Greenwich Observatory; but these machinations make an intriguing background to the fact that Eddington was indeed ‘the man who proved Einstein was right’. This time, he went to Principe, but a twin expedition was sent to Brazil, with Eddington in overall charge of processing and analysing the results. The importance of these eclipse observations will become clear shortly; but first, Eddington’s other key contribution to science.

As the world returned to normal after the First World War, in the early 1920s Eddington gathered all the data he could find on stellar masses and linked this with data from the HR diagram to show that the brighter stars are the most massive. A main sequence star twenty-five times the mass of the Sun, for example, is 4000 times as bright as the Sun. This made sense. A star holds itself up by the pressure it generates in its interior, counteracting the inward pull of gravity. The more massive it is, the more weight there is pressing inwards and the more pressure it has to generate. It can only do this by burning its fuel – whatever that fuel may be – more quickly, thereby generating more heat, which eventually escapes from the surface of the star as more light for us to see. The physics of what goes on is actually rather simple, for the reasons we mentioned before concerning the fate of complicated structures under conditions of high temperature and pressure, so the temperature at the heart of a star can be calculated from observations of its brightness, mass and size (determined from the brightness if the distance is known, but also, once the relationships were discovered, from its position on the HR diagram). When Eddington put the numbers in, he came up with a profound insight – all main sequence stars have roughly the same central temperature, even though they cover a range in masses from tens of times the mass of the Sun down to a tenth the mass of the Sun. It is as if stars have an inbuilt thermostat; as a ball of gas shrinks under its own weight and gets hotter inside as gravitational energy is converted into heat, nothing happens to halt this process until a critical temperature is reached, when the thermostat switches on an almost inexhaustible (by human standards) supply of energy. And by the 1920s, it was fairly obvious (at least to Eddington) where the energy must be coming from.

In the nineteenth century there had been a sometimes fierce debate between the geologists and evolutionists on one side, and the physicists on the other, about the age of the Earth and the Sun. Quite reasonably, physicists such as William Thomson (Lord Kelvin) pointed out that there was no process known to the science of the time that could keep the Sun shining for the long timescales required to explain the evolution of life on Earth. They were right, but even before the end of the nineteenth century, as we have seen, sources of energy new to science were discovered, in the form of radioactive isotopes. In the early years of the twentieth century this led to speculation that a star like the Sun might be kept hot if it contained radium – just 3.6 grams of pure radium in every cubic metre of the Sun’s volume would be enough to do the job, an idea which was discussed by, among others, Eddington’s predecessor as Plumian Professor, George Darwin. In fact, the half-life of radium, as was soon appreciated, is much too short for this to work, but it was clear that ‘subatomic energy’ must hold the key to the longevity of the Sun and stars. With the developments in subatomic physics over the first two decades of the twentieth century, and armed with Einstein’s special theory of relativity and his equation E = mc², as early as 1920 Eddington was able to spell out the implications to the audience at the annual meeting of the British Association for the Advancement of Science:

A star is drawing on some vast reservoir of energy by means unknown to us. This reservoir can scarcely be other than the sub-atomic energy which, it is known, exists abundantly in all matter; we sometimes dream that man will one day learn to release it and use it for his service. The store is well-nigh inexhaustible, if only it could be tapped. There is sufficient in the Sun to maintain its output of heat for 15 billion years.

[Francis] Aston has further shown conclusively that the mass of the helium atom is even less than the masses of the four hydrogen atoms which enter into it – and in this, at any rate, the chemists agree with him. There is a loss of mass in the synthesis amounting to 1 part in 120, the atomic weight of hydrogen being 1.008 and that of helium just 4. I will not dwell on his beautiful proof of this, as you will no doubt be able to hear it from himself. Now mass cannot be annihilated, and the deficit can only represent the mass of the electrical energy set free in the transmutation. We can therefore at once calculate the quantity of energy liberated when helium is made out of hydrogen. If 5 percent of a star’s mass consists initially of hydrogen atoms, which are gradually being combined to form more complex elements, the total heat liberated will more than suffice for our demands, and we need look no further for the source of a star’s energy.

Eddington was on the right track, but it would take decades for the details of how energy is liberated inside stars to be worked out, partly because of a misunderstanding implicit in that reference to ‘5 percent’ of a star being composed of hydrogen, partly because the full calculations would need quantum mechanics, which was not fully developed until the end of the 1920s. We shall come back to this story in due course; but by the 1920s stellar astronomy had come up with another way to measure distances to at least some of the stars, and a new telescope with which to apply the technique; this combination would soon produce another dramatic change in humankind’s view of our place in the Universe. The evidence of the main sequence was that the Sun is just an ordinary star, nothing special in the Milky Way. The evidence that would eventually emerge from the new distance indicators was that the Milky Way itself is nothing special in the Universe.

The colour–magnitude relationship portrayed in the HR diagram itself gives you a guide to the distances to stars. If you measure the colour of a star, then you know where it belongs on the main sequence, and that tells you its absolute magnitude. So all you have to do is measure its apparent magnitude to work out how far away it is. At least in principle. Things aren’t quite that easy in practice, chiefly because dust in space, along the line of sight to the star, dims its light (causing ‘extinction’) and makes it look redder – a process known as reddening, but nothing to do with the redshift. This interferes with our observations of both colour and brightness, although the effects can often be compensated for, at least approximately, by looking at different stars in roughly the same direction in space. But the key step in developing a cosmic distance scale came from a quite different kind of investigation, also going on at about the time Hertzsprung and Russell were developing their ideas about the colour–magnitude relation.

The discovery came as a result of an investigation of the stars of the southern skies, carried out under the direction of Edward Pickering (1846–1919), who became director of the Harvard University Observatory in 1876. Pickering was an inveterate cataloguer, and the inspiration for the next generation of American astronomers, but his single most important contribution to astronomy resulted from a survey of the southern skies carried out for him from Peru by his brother William Pickering (1858–1938). The actual job of cataloguing – recording neatly, using pen and ink in large ledgers, the positions and brightnesses of all the individual stars on the photographic plates sent to Harvard – was carried out by teams of women, who, in those less enlightened days, were generally cheaper to hire than men, and often not regarded as having the intellectual capacity for any more creative work. To his credit, Pickering encouraged some of these women who showed an aptitude for astronomy to move into research proper, giving a few of them an entry into the almost exclusively male academic world of the time. One of these women was Henrietta Swan Leavitt (1868–1921), who joined the Harvard team in 1895 (initially as an unpaid volunteer, such was her enthusiasm for astronomy, although she later became head of the department of photographic photometry). Pickering gave her the task of identifying variable stars in the southern skies, which could only be done by comparing photographic plates of the same region obtained at different times to see if any of the stars had changed their appearance.

Such variations can happen for two reasons. First, it may be because the ‘star’ is actually a binary system and we are seeing partial eclipses as one star moves in front of the other – and studying binaries, as we have seen, is a key to measuring stellar masses. Second, stars may be intrinsically variable, changing their brightness as a result of some change in their internal structure, and this is interesting in its own right. Some such stars, we now know, swell up and shrink back upon themselves, pulsating in a repeating cycle, with their light output changing regularly as they do so. One such class of pulsating star is known as the Cepheids, after the archetypal example of its kind, a star known as Delta Cephei, which was identified as a variable by the English astronomer John Goodricke in 1784, two years before he died at the age of 21. All Cepheids show a characteristic pattern of repeated brightening and dimming, but some have periods as short as a day or so, while others have periods of more than a hundred days.

The photographic plates from Peru that Leavitt was studying in Harvard covered two clouds of stars, known as the Large and Small Magellanic Clouds, which are now known to be small satellite galaxies associated with the Milky Way Galaxy in which we live. During the course of her painstaking work, Leavitt noticed that the Cepheids in the Small Magellanic Cloud (SMC) showed an overall pattern of behaviour in which the brighter Cepheids (averaging their brightness over a whole cycle) went through their cycle more slowly. The initial discovery was reported in 1908, and by 1912 Leavitt had enough data to pin down this period-luminosity relationship in a mathematical formula, established from her study of twenty-five Cepheids in the SMC. She realized that the reason why the relationship showed up is because the SMC is so far away that the stars in it are all effectively at the same distance from us, so that the light from each of them is dimmed by the same amount en route to our telescopes. Of course, there are differences in the distances to individual stars in the SMC, and these may amount to dozens or hundreds of light years, in absolute terms; but at the distance of the SMC, these differences are only a small percentage of the distance from Earth, so they only affect the apparent brightnesses of the stars by a small fraction of the overall dimming caused by their distance from us. Leavitt found a clear mathematical relationship between the apparent brightness of a Cepheid in the SMC and its period, so that, for example, a Cepheid with a period of three days is only one-sixth the brightness of a Cepheid with a period of 30 days. This could only mean that the absolute magnitudes of Cepheids are related to one another in the same way, since the distance effect is essentially the same for all of the Cepheids in the SMC. All that was needed now was to find the distance to just one or two Cepheids in our neighbourhood so that their absolute magnitudes could be determined, and then the absolute magnitudes of all other Cepheids (and therefore their distances) could be worked out from the period-luminosity law that Leavitt had discovered.

It was, in fact, Hertzsprung who first measured the distances to nearby Cepheids in 1913, providing the calibration that the Cepheid distance scale needed.⁶ As is usually the case in astronomy, however, the observations were beset by difficulties, not least the problems of extinction and reddening. Hertzsprung’s calibration implied a distance to the SMC of 30,000 light years (roughly 10,000 parsecs); the modern figure, taking account of reddening and extinction effects that he was unaware of, is 170,000 light years (52,000 parsecs). At such a distance, even if two Cepheids are 1000 light years apart this represents only 0.6 per cent of their distance from us, with a correspondingly small effect on their relative dimming due to their distance. Even Hertzsprung’s underestimate was the first indication of just how big space really is. The Cepheid distance scale is, of course, no less important in studies of stars within the Milky Way than it is in studies of the Universe at large. Some clusters of stars, grouped together in space, contain dozens or hundreds of stars with different masses, colours and brightnesses, and if there is just one Cepheid in the cluster then the distance to all those stars is known, with all that that implies for understanding the properties of the stars and, for example, removing the effects of reddening and extinction when plotting them on an HR diagram. But it was in probing beyond the Milky Way that Cepheids altered our appreciation of our place in the Universe.

That probing became possible thanks to the development of a new generation of telescopes, largely as a result of the enthusiasm of one man, George Ellery Hale (1868–1938), an astronomer with a gift for persuading benefactors to part with large sums of money and the administrative skills to see the successful application of that money to the construction of new telescopes and observatories, first at the University of Chicago, then at Mount Wilson in California and finally at Mount Palomar, also in California. The key instrument in this particular phase of the exploration of the Universe was the 100-inch diameter reflector known as the Hooker telescope (after the benefactor who paid for it), completed on Mount Wilson in 1918 and still in use today (or rather, tonight). It was the largest telescope on Earth for 30 years, and transformed our understanding of the Universe, largely in the hands of two men, Edwin Hubble (1889–1953) and Milton Humason (1891–1972).

You mustn’t believe everything you read about Hubble, who, to put it politely, exaggerated his own early achievements, making up stories about his prowess as an athlete and pretending that he had once been a successful lawyer. But that doesn’t detract from the importance of his work in astronomy.

The first person to use Cepheids to produce a map of the Milky Way Galaxy which resembles the modern one was Russell’s former student Harlow Shapley (1865–1972), at the end of the second decade of the twentieth century. He used a 60-inch reflector on Mount Wilson, from 1908 to 1918 the biggest telescope in the world, and was one of the first people to use the 100-inch, but moved on to become director of the Harvard College Observatory in 1921, missing the opportunity to take full advantage of the opportunities opened up by the new telescope. Unknown to Shapley, some of the stars he thought were Cepheids were actually members of a different family, now known as RR Lyrae stars. They behave in a similar fashion to Cepheids (making them important distance indicators in their own right), but with a different period–luminosity relationship. Fortunately, some of the errors introduced into Shapley’s calculations by this confusion were cancelled out by the fact that he wasn’t making sufficient allowance for extinction. It was already clear by then (and had been increasingly clear since the time of Galileo and Thomas Wright) that the band of light on the night sky known as the Milky Way is a flattened, disc-shaped system containing vast numbers of stars, and that the Sun is just one star among this multitude. It had been widely thought that the Sun lay at the centre of the disc of stars that makes up the Milky Way. But there are also concentrations of stars, roughly spherical systems known as globular clusters, which lie above and below the plane of the Milky Way, occupying a spherical volume of space in which the disc of the Milky way is embedded. By mapping the distances to the globular clusters, Shapley found where this sphere is centred and established that the Sun is not at the centre of the Milky Way. By 1920, his measurements indicated that the Milky Way itself was about 100,000 parsecs across and that the centre of the Milky Way lay 10,000 parsecs (more than 30,000 light years) away from us. His numbers were still plagued by the extinction problem and the confusion of RR Lyrae stars with Cepheids – we now know that he got the distance to the centre of the Milky Way about right (the modern figure is 8000–9000 parsecs), but that he got the overall diameter of the Galaxy too big (we now estimate it is 28,000 parsecs across). The disc of the Milky Way itself is only a couple of hundred parsecs thick – very thin, actually, compared with its diameter. But the numbers are less important than the fact that Shapley had made yet another reduction in the status of our home in space, removing the Sun to an ordinary location in the suburbs of the disc of the Milky Way Galaxy, an unimportant member of a system estimated to contain several hundred billion stars.

At the beginning of the 1920s, though, it was still widely thought that the Milky Way itself dominated the Universe. Although there were other fuzzy patches of light on the night sky (like the Magellanic Clouds), these were thought to be either smaller systems which were satellites of the Milky Way (a bit like super globular clusters), or glowing clouds of gas within the Milky Way. Only a few astronomers, among whom the American Heber Curtis (1872–1942) was the most vociferous, argued that many of these ‘spiral nebulae’ were actually galaxies in their own right, so far away that individual stars in them could not be resolved even with the best telescopes available,⁷ that the Milky Way was much smaller than Shapley estimated and that it was just one ‘island universe’ among many comparable galaxies scattered across the void.

This is where Hubble comes into the story. In the winter of 1923/4, using the 100-inch Hooker telescope, Hubble was able to resolve individual stars in a large spiral nebula, known as M31, in the direction of the constellation Andromeda (it is sometimes referred to as the Andromeda Nebula or Andromeda Galaxy). Even better, to his surprise he was able to identify several Cepheids in the nebula and calculate its distance, which came out as 300,000 parsecs, almost a million light years; with modern calibration of the Cepheid distance scale and better allowance for problems such as extinction, the Andromeda Galaxy is now known to be even further away, at a distance of 700,000 parsecs. Hot on the heels of this discovery, Hubble found Cepheids in several other similar nebulae, establishing that Curtis was essentially correct. As other techniques were developed to measure distances to galaxies, including observations of exploding stars, supernovae, which all have roughly the same absolute maximum brightness, it eventually became clear that just as there are hundreds of billions of stars in the Milky Way Galaxy, so there are hundreds of billions of galaxies in the visible Universe, which extends for billions of light years in all directions. The Solar System is an insignificant speck within an insignificant speck in all this vastness. But the key step in mapping the Universe is still the magnitude–distance relationship for Cepheids, against which the secondary distance indicators (such as supernovae) are calibrated. And as a result, there was one hangover from the early difficulties posed by problems such as extinction which distorted our view of our place in the Universe right into the 1990s.

As the example of M31 shows, on the distance scale used by Hubble everything seemed to be closer than it really is. For a galaxy of a certain size (say, the same absolute size as the Milky Way itself), the closer it is the bigger the patch of sky it covers. What astronomers actually measure is the angular size of a galaxy on the sky, and if they think it is closer than it really is, they will think that it is smaller than it really is. A child’s toy aeroplane in front of your face or a 747 airliner coming in to land can each look the same angular size; but your guess as to how much bigger a 747 is than the toy will depend on how far away you think the aircraft is. The underestimate of their distances meant that the sizes of all galaxies beyond the Milky Way were at first underestimated, and it seemed that the Milky Way Galaxy was the biggest such object in the Universe. Repeated refinements of the distance scale gradually changed this perception over the decades, but it was only in the late 1990s, using Cepheid data obtained by the Hubble Space Telescope to provide accurate distances to a significant number of spiral galaxies similar to the Milky Way, that it was finally established that our galaxy is just average in size.⁸

Following on from his work of 1923–4, with the aid of Milton Humason in the late 1920s and early 1930s, Hubble extended his measurements of distances to galaxies out into the Universe as far as possible using the 100-inch. Although direct Cepheid distances could only be measured for a handful of relatively nearby galaxies, with the distances to those galaxies known, he could calibrate other features of galaxies in general, such as supernovae or the brightness of particular features in spirals, and use them as secondary indicators to give distances to more remote galaxies in which Cepheids could not be resolved even with the 100-inch. It was while carrying out this survey that Hubble made the discovery with which his name will always be associated – that there is a relationship between the distance to a galaxy and the redshift in the spectrum of light from it.

The preponderance of redshifts in the light from ‘nebulae’ had actually been discovered by Vesto Slipher (1875–1969) in the second decade of the twentieth century, working at the Lowell Observatory (in Flagstaff, Arizona) with a 24-inch refracting telescope. His work in obtaining spectra of such faint objects photographically using this telescope was at the cutting edge of technology at the time, and Slipher was convinced that these diffuse nebulae must be composed of many individual stars because of the similarity between their spectra and the spectra of stars in general. But his equipment was not up to the task of resolving individual stars in these nebulae, so he could not take the step that would be taken by Hubble in the 1920s, and could not measure distances to the nebulae he studied. By 1925, Slipher had measured 39 redshifts in nebulae, but found just two blueshifts. Only four redshifts, and no blueshifts, had been measured by other astronomers in systems that Slipher had not studied first, although many of his results had been confirmed by other observers. The natural interpretation of these data was that they were a result of the Doppler effect, with most nebulae moving rapidly away from us, and just two moving towards us. Hubble and Humason began by measuring distances to nebulae that had first been observed spectroscopically by Slipher, as well as taking their own spectroscopic data (it was Humason who actually did this) to test their own apparatus and confirm Slipher’s results. Then they extended this kind of investigation to other galaxies. Apart from the very few objects already known, no blueshifts were found.⁹ They discovered that the distance of a galaxy is proportional to its redshift, a phenomenon reported in 1929 and now known as Hubble’s law. To Hubble, the value of the discovery was as a distance indicator – now, he (or Humason) only had to measure the redshift of a galaxy and they could infer the distance to it. But the significance of the discovery went far deeper than that, as a few other astronomers were quick to realize.

The explanation for the discovery made by Hubble and Humason came from Einstein’s general theory of relativity, which, as we have seen, had been published in 1916. The feature which makes this theory ‘general’ (as opposed to the restricted nature of the ‘special’ theory of relativity) is that it deals with accelerations, not just with objects moving in straight lines at constant speed. But Einstein’s great insight was to appreciate that there is no distinction between acceleration and gravity. He said that this insight came to him while sitting at his desk in the Patent Office in Bern one day, when he realized that a person falling from a roof would be weightless and would not feel the pull of gravity – the acceleration of their downward motion cancels out the feeling of weight, because the two are exactly equal. We’ve all experienced the equivalence of acceleration and gravity in a lift – as the lift starts to move upward, we are pressed to the floor and feel heavier; when the lift stops, we feel lighter while it is decelerating and, in the case of express lifts, may rise up on our toes as a result. Einstein’s genius was to find a set of equations to describe both acceleration and gravity in one package – as well as all of the special theory of relativity and, indeed, all of Newtonian mechanics, as special cases of the general theory. It is by no means true, in spite of what the newspaper headlines screamed in the wake of Eddington’s eclipse expedition, that Einstein’s theory ‘overturned’ Newton’s work; Newtonian gravity (in particular, the inverse square law) is still a good description of the way the Universe works except under extreme conditions, and any better theory has to reproduce all of the successes of Newtonian theory, plus more besides, just as if a better theory than Einstein’s is ever developed it will have to explain everything that the general theory explains, and more besides.

It took Einstein ten years to develop the general theory from the foundation of the special theory, although he did plenty of other things in those years from 1905 to 1915, leaving the Patent Office in 1909 to become a full-time academic at the University of Zürich, and devoting a lot of his efforts to quantum physics until about 1911, when he worked briefly in Prague before taking up a post at the ETH in Zürich (where he had been such a lazy student) and then settling in Berlin in 1914. The key to the mathematics which underpinned the general theory of relativity was given to him when he was in Zürich in 1912 by an old friend, Marcel Grossmann (1878–1936), who had been a fellow student at the ETH, where he lent Einstein his lecture notes to copy up when Einstein couldn’t be bothered to attend classes. By 1912, Einstein had accepted Hermann Minkowski’s neat representation of the special theory of relativity in terms of the geometry of flat, four-dimensional spacetime. Now, he needed a more general form of geometry to go with his more general form of physics, and it was Grossmann who pointed him towards the work of the nineteenth-century mathematician Bernhard Riemann (1826–1866), who had studied the geometry of curved surfaces and had developed the mathematical tools to describe this kind of geometry (called non-Euclidean geometry, since Euclid dealt with flat surfaces) in as many dimensions as you cared to choose.

This kind of mathematical investigation of non-Euclidean geometry had a long pedigree. Early in the nineteenth century Karl Friedrich Gauss (1777–1855) worked on the properties of geometries in which, for example, parallel lines can cross one another (the surface of the Earth is an example, as shown by lines of longitude, which are parallel at the equator and cross at the poles). Gauss didn’t publish all of his work, much of which only became known after his death, although he did coin the term which translates as ‘non-Euclidean geometry’. Some of his achievements in this area were rediscovered by the Hungarian Janos Bolyai (1802–1860) and the Russian Nikolai Lobachevsky (1793–1856), working independently of one another, in the 1820s and 1830s; but, like the then-unknown work of Gauss, these models dealt only with specific cases of non-Euclidean geometry, such as the geometry of the surface of a sphere. Riemann’s outstanding contribution was to find, and present in a lecture given at the University of Göttingen in 1854, a general mathematical treatment which was the footing for the whole of geometry, allowing a range of different mathematical descriptions of a range of different geometries, which are all equally valid and with the familiar Euclidean geometry of everyday life as just one example. These ideas were introduced to the English-speaking world by the British mathematician William Clifford (1845–1879), who translated Riemann’s work (which had only been published in 1867, a year after Riemann’s early death, from tuberculosis) and used it as the basis for a speculation that the best way to describe the Universe at large is in terms of curved space. In 1870, he read a paper to the Cambridge Philosophical Society in which he talked of ‘variation in the curvature of space’ and made the analogy that ‘small portions of space are in fact of nature analogous to little hills on a surface which is on the average flat; namely, that the ordinary laws of geometry are not valid in them’. Today, following Einstein, the analogy is made the other way around – concentrations of matter, such as the Sun, are seen as making little dimples in the spacetime of an otherwise flat Universe.¹⁰ But it is a salutary reminder of the way science progresses, piece by piece, not through the work of isolated individuals, that Clifford was making his version of this analogy nine years before Einstein was born. Clifford himself died (also of TB) in the year Einstein was born, 1879, and never developed his ideas fully. But when Einstein came on the scene the time was clearly ripe for the general theory, and his contribution, although inspired, is not the isolated act of genius it is often portrayed.

The general theory of relativity describes the relationship between spacetime and matter, with gravity as the interaction that links the two. The presence of matter bends spacetime, and the way material objects (or even light) follow the bends in spacetime is what shows up to us as gravity. The snappiest summary of this is the aphorism ‘matter tells spacetime how to bend; spacetime tells matter how to move’. Naturally, Einstein wanted to apply his equations to the biggest collection of matter, space and time there is – the Universe. He did so as soon as he had completed the general theory, and published the results in 1917. The equations he found had one bizarre and unexpected feature. In their original form, they did not allow for the possibility of a static universe. The equations insisted that space itself must either be stretching as time passed, or shrinking, but could not stand still. At that time, remember, the Milky Way was thought to be essentially the entire Universe, and it showed no signs of either expanding or contracting. The first few redshifts of nebulae had been measured, but nobody knew what that meant, and in any case Einstein was unaware of Slipher’s work. So he added another term to his equations to hold the universe they described still. Usually represented by the Greek letter lambda (λ), this is often referred to as the cosmological constant, and in Einstein’s own words ‘that term is necessary only for the purpose of making possible a quasi-static distribution of matter, as required by the fact of the small velocities of the stars’. In fact, it is wrong to refer to ‘the’ cosmological constant. The equations set up by Einstein allowed you to choose different values of the lambda term, some of which would make the model universe expand faster, at least one of which would hold it still and some of which would make it shrink. But Einstein thought that he had found a unique mathematical description of matter and spacetime which matched the known Universe of 1917.

As soon as the equations of the general theory were made public, however, other mathematicians used them to describe different model universes. Also in 1917, Willem de Sitter, in Holland, found a solution to Einstein’s equations which describes a universe expanding exponentially fast, so that if the distance between two particles doubles after a certain time, it quadruples in the next equal time interval, increases eight times as much in the next time interval, sixteen-fold in the next interval, and so on. In Russia, Aleksandr Friedmann (1888–1925) found a whole family of solutions to the equations, some describing expanding universes and some describing contracting universes, and published the results in 1922 (somewhat to Einstein’s irritation, since he had hoped his equations would provide a unique description of the Universe). And the Belgian astronomer Georges Lemaître (1894–1966), who was also an ordained priest, independently published similar solutions to Einstein’s equations in 1927. There were some contacts between Hubble and Lemaître, who visited the United States in the mid-1920s, and was present at the meeting in 1925 where the discovery of Cepheids in the Andromeda Nebula was announced (on behalf of Hubble, who was not present) by Henry Norris Russell. Lemaître also corresponded with Einstein. One way and another, by the beginning of the 1930s, when Hubble and Humason published redshifts and distances for nearly a hundred galaxies, showing that redshift is proportional to distance, it was not only clear that the Universe is expanding, but there was already a mathematical description – actually, a choice of such cosmological models – to describe the expansion.

It is important to spell out that the cosmological redshift is not caused by galaxies moving through space, and is not, therefore, a Doppler effect. It is caused by the space between the galaxies stretching as time passes, exactly in the way that Einstein’s equations described, but Einstein refused to believe, in 1917. If space stretches while light is en route to us from another galaxy, then the light itself will be stretched to longer wavelengths, which, for visible light, means moving it towards the red end of the spectrum.¹¹ The existence of the observed redshift–distance relation (Hubble’s law) implies that the Universe was smaller in the past, not in the sense that galaxies were crammed together in a lump in a sea of empty space, but because there was no space either between the galaxies or ‘outside’ them – there was no outside. This in turn implies a beginning to the Universe – a concept repugnant to many astronomers in the 1930s, including Eddington, but one which the Roman Catholic priest Lemaître embraced wholeheartedly. Lemaître developed the idea of what he called the Primeval Atom (or sometimes, the Cosmic Egg), in which all of the matter in the Universe was initially in one lump, like a superatomic nucleus, which then exploded and fragmented, like a colossal fission bomb. The idea gained popular attention in the 1930s, but most astronomers went along with Eddington in thinking that there could not really have been a beginning to the Universe, and what is now known as the Big Bang model¹² only became part of mainstream astronomy (and then only a small part) in the 1940s, following the work of the ebullient Russian émigré George Gamow (1904–1968) and his colleagues at George Washington University and Johns Hopkins University, in Washington DC.

Apart from the difficulty many astronomers had at first in accepting the idea that the Universe had a beginning, in the 1930s and 1940s there was another problem with this straightforward interpretation of the observations made by Hubble and Humason (and soon followed up by other astronomers, although the Mount Wilson team retained the technological advantage of the 100-inch telescope). Still plagued by the observational problems we have mentioned, and the confusion between Cepheids and other kinds of variable stars, the distance scale worked out by Hubble at the beginning of the 1930s was, we now know, in error by roughly a factor of ten. This meant that he thought the Universe was expanding ten times faster than we now think. Using the cosmological equations derived from the general theory of relativity (in their simplest form, these solutions correspond to a model of the Universe developed by Einstein and de Sitter, working together in the early 1930s, and known as the Einstein–de Sitter model), it is straightforward to calculate how long it has been since the Big Bang from the redshift–distance relation. Because Hubble’s data implied that the Universe was expanding ten times too fast, such calculations based on those data gave an age of the Universe only one tenth as large as the modern value, as low as 1.2 billion years – and that is scarcely a third of the well-determined age of the Earth. Clearly something was wrong, and until the age question was resolved it was hard for many people to take the idea of the Primeval Atom seriously.

Indeed, this age problem was one of the reasons why Fred Hoyle (1915–2001), Herman Bondi (1919–) and Thomas Gold (1920–), in the 1940s, came up with an alternative to the Big Bang, known as the steady state model. In this picture, the Universe was envisaged as eternal, always expanding, but always looking much the same as it does today because new matter, in the form of atoms of hydrogen, is continuously being created in the gaps left behind as galaxies move apart, at just the right rate to make new galaxies to fill the gaps. This was a sensible and viable alternative to the Big Bang model right through the 1950s and into the 1960s – it is, after all, no more surprising that matter should be created steadily, one atom at a time, than it is to suggest that all the atoms in the Universe were created in one event, the Big Bang. But improving observations, including the new techniques of radio astronomy developed in the second half of the twentieth century, showed that galaxies far away across the Universe, which we see by light (or radio waves) which left them long ago, are different from nearby galaxies, proving that the Universe is changing as time passes and galaxies age. And the age question itself was gradually resolved as better telescopes became available (notably the 200-inch reflector on Mount Palomar, completed in 1947 and named in honour of Hale) and the confusion between Cepheids and other kinds of variable stars was resolved. It took a long time to narrow down the uncertainty in these still-difficult measurements of the expansion rate of the Universe to an uncertainty of 10 per cent – indeed, this was only achieved in the late 1990s, with the aid of the Hubble Space Telescope.¹³ But by the end of the twentieth century the age of the Universe had been determined reasonably accurately, as somewhere between 13 billion and 16 billion years. This is comfortably older than anything whose age we can measure, including the Earth itself and the oldest stars.¹⁴ But all that lay far in the future when Gamow and his colleagues began the scientific investigation of what went on in the Big Bang itself.

Gamow had actually been one of Friedmann’s students in the 1920s, and also visited the University of Göttingen, the Cavendish Laboratory and Niels Bohr’s Institute in Copenhagen, where he made significant contributions to the development of quantum physics. In particular, he showed how quantum uncertainty could enable alpha particles to escape from radioactive atomic nuclei during alpha decay, by a process known as tunnelling. The alpha particles are held in place by the strong nuclear force, and in these nuclei they have nearly enough energy to escape, but not quite, according to classical theory. Quantum theory, however, says that an individual alpha particle can ‘borrow’ enough energy to do the job from quantum uncertainty, since the world is never quite sure how much energy it has. The particle escapes, as if it had tunnelled its way out of the nucleus, and then repays the borrowed energy before the world has time to notice it had ever been borrowed. In one of the many oversights of the Nobel committee, Gamow never received the ultimate prize for this profound contribution to our understanding of nuclear physics.

Gamow’s background in nuclear and quantum physics coloured the way he and his student Ralph Alpher (1921–) and Alpher’s colleague Robert Herman (1922–1997) investigated the nature of the Big Bang. Alongside his post at George Washington University, in the 1940s and early 1950s Gamow was a consultant at the Applied Physics Laboratory of Johns Hopkins University, where Alpher worked from 1944 onwards full time while studying for his bachelor’s degree, master’s and finally PhD (awarded in 1948) in the evenings and at weekends at George Washington University. Herman had a more conventional academic background, with a PhD from Princeton, and joined the Johns Hopkins Laboratory in 1943, initially, like Alpher, involved in war work. Also like Alpher, he did his work on the early Universe in his own time, technically as a hobby. Under Gamow’s supervision, Alpher investigated for his doctorate the way in which more complicated elements could be built up from simple elements under the conditions that they assumed must have existed in the Big Bang, when the entire observable Universe was packed into a volume no bigger across than our Solar System is today. The chemical elements we, and the rest of the visible Universe, are made of have to come from somewhere, and Gamow guessed that the raw material for their manufacture was a hot fireball of neutrons. This was at a time when the first nuclear bombs had recently been exploded, and when the first nuclear reactors were being constructed. Although a great deal of the information on how nuclei interact with one another was classified, there was an expanding data bank of unclassified information about what happens to different kinds of material when irradiated with neutrons from such reactors, with nuclei absorbing neutrons one by one to become the nuclei of heavier elements, and getting rid of excess energy in the form of gamma radiation. Sometimes, unstable nuclei would be created in this way, and would adjust their internal composition by emitting beta radiation (electrons). Although the raw material of the Universe was assumed to be neutrons, neutrons themselves decay in this way to produce electrons and protons, which together make the first element, hydrogen. Adding a neutron to a hydrogen nucleus gives a nucleus of deuterium (heavy hydrogen), adding a further proton makes helium-3, and adding another neutron as well makes helium-4, which can also be made by the fusion of two helium-3 nuclei and the ejection of two protons, and so on. Nearly all the deuterium and helium-3 is converted into helium-4, one way or another. Alpher and Gamow looked at all of the available neutron-capture data for different elements and found that the nuclei formed most easily in this way turned out to be those of the most common elements, while nuclei that did not form readily in this way corresponded to rare elements. In particular, they found that this process would produce an enormous amount of helium compared with other elements, which matched up with observations of the composition of the Sun and stars that were becoming available around that time.

As well as providing Alpher with the material for his PhD dissertation, this work formed the basis of a scientific paper published in the journal Physical Review. When the time came to submit the paper, Gamow, an inveterate joker, decided (overriding Alpher’s objections) to add the name of his old friend Hans Bethe (1906–) as co-author, for the sole reason that he liked the sound of the names Alpher, Bethe, Gamow (alpha, beta, gamma). To his delight, by a coincidence the paper appeared in the issue of Physical Review dated 1 April 1948. That publication marks the beginning of Big Bang cosmology as a quantitative science.

Soon after the alpha-beta-gamma paper (as it is usually referred to) was published, Alpher and Herman came up with a profound insight into the nature of the Big Bang. They realized that the hot radiation which filled the Universe at the time of the Big Bang must still fill the Universe today, but that it would have cooled by a quantifiable amount as it expanded along with the universal expansion of space – you can think of this as an extreme redshift, stretching the wavelengths of the original gamma rays and X-rays far into the radio part of the electromagnetic spectrum. Later in 1948, Alpher and Herman published a paper reporting their calculation of this effect, assuming that this background radiation is black-body radiation at the appropriate temperature. They found that the temperature of the background radiation today should be about 5 K – that is, roughly – 268 °C. At the time, Gamow did not accept the validity of this work, but after about 1950 he became an enthusiastic supporter of the idea and referred to it in several of his popular publications,¹⁵ often getting the details of the calculation wrong (he was never good at sums) and without giving proper credit to Alpher and Herman. The result is that he is often incorrectly given credit for the prediction of the existence of this background radiation, when that credit belongs entirely to Alpher and Herman.

Nobody took much notice of the prediction at the time. People who knew about it mistakenly thought that the available technology of radio astronomy was not good enough to measure such a weak hiss of radio noise coming from all directions in space; people with access to the technology seem to have been unaware of the prediction. In the early 1960s, however, two radio astronomers working with a horn antenna at the Bell Laboratories research station near Holmdel, New Jersey, found that they were plagued by faint radio noise coming from all directions in space, corresponding to black-body radiation with a temperature of about 3 K. Arno Penzias (1933–) and Robert Wilson (1936–) had no idea what they had discovered, but just down the road at Princeton University a team working under Jim Peebles (1935–) was actually building a radio telescope specifically intended to search for this echo of the Big Bang – not because of the pioneering work of Alpher and Herman, but because Peebles had independently carried out similar calculations. When news came to Princeton of what the Bell researchers had found, Peebles was quickly able to explain what was going on. The discovery, published in 1965, marked the moment when most astronomers started to take the Big Bang model seriously as a plausible description of the Universe in which we live, rather than as some kind of abstract theoretical game. In 1978, Penzias and Wilson shared the Nobel prize for the discovery, an honour they perhaps deserved rather less than Alpher and Herman, who did not receive the prize.¹⁶

Since then, the cosmic microwave background radiation has been observed in exquisite detail by many different instruments, including the famous COBE satellite, and has been confirmed to be perfect black-body radiation (the most perfect black-body radiation ever seen) with a temperature of just 2.725 K. This is the most powerful single piece of evidence that there really was a Big Bang – or, to put it in more scientific language, that the visible Universe experienced an extremely hot, dense phase about 13 billion years ago. Cosmologists in the twenty-first century are tackling the puzzle of how this superhot fireball of energy came into existence in the first place, but we shall not describe these still-speculative ideas here, and will end our discussion of the history of cosmology at the point where there is overwhelming evidence that the Universe as we know it did emerge from a Big Bang – if you want to put a date on this, the announcement of the COBE results in the spring of 1992 is as good as any. Indeed, having made predictions that have been proved correct by observation, the Big Bang model is now entitled to be given the name Big Bang theory.

But what exactly was it that emerged from the Big Bang? As Alpher and Herman refined their calculations further, they soon discovered that there was a major problem with their whole scheme of manufacturing elements (nucleosynthesis) by the repeated addition of neutrons, one at a time, to nuclei. It soon turned out that there are no stable nuclei with masses of 5 units or 8 units on the atomic scale. Starting out with a sea of protons and neutrons (now thought to have been manufactured out of pure energy in the Big Bang fireball (in line with E = mc²), it is easy to make hydrogen and helium, and modern versions of the calculations pioneered by Gamow’s team tell us that a mixture of roughly 75 per cent hydrogen and 25 per cent helium could be made in this way in the Big Bang. But if you add a neutron to helium-4, you get an isotope so unstable that it spits out the extra neutron before it has time to interact further and make a stable nucleus. A very little lithium-7 can be made by rare interactions in which a helium-3 nucleus and a helium-4 nucleus stick together, but under the conditions existing in the Big Bang fireball the next step is to produce a nucleus of beryllium-8, which immediately breaks into two helium-4 nuclei. If you could only make hydrogen and helium (and tiny traces of lithium-7 and deuterium) in the Big Bang, then all the other elements must have been manufactured somewhere else. That ‘somewhere’ – the only possible alternative place – is the insides of stars. But an understanding of just how this happens emerged only gradually, starting with the realization, in the late 1920s and 1930s, that the Sun and stars are not made of the same mixture of elements as the Earth.

The idea that the Sun is basically made of the same kind of stuff as the Earth, but hotter, had a long pedigree, and represented the fruits of the first known attempt to describe heavenly bodies in what we would now call scientific terms, rather than treating them as gods. It goes back to the Greek philosopher Anaxagoras of Athens, who lived in the fifth century BC. Anaxagoras got his ideas about the composition of the Sun when a meteorite fell near Aegospotami. The meteorite was red hot when it reached the ground, and it had come from the sky, so Anaxagoras reasoned that it came from the Sun. It was made largely of iron, so he concluded that the Sun was made of iron. Since he knew nothing about the age of the Earth, or how long it would take a large ball of red-hot iron to cool down, or whether there might be a form of energy keeping the Sun shining, the idea that the Sun was a ball of red-hot iron was a good working hypothesis in those days (not that many people took Anaxagoras seriously at the time). When people started thinking about nuclear energy as the source of the Sun’s heat at the beginning of the twentieth century, the realization that the radioactive decay of a relatively small amount of radium could keep the Sun shining (if only for a relatively short time) encouraged the idea that most of the Sun’s mass might consist of heavy elements. As a result, when a few astronomers and physicists started to investigate how nuclear fusion might provide the energy that keeps the Sun and stars hot, they started out by investigating processes in which protons (nuclei of hydrogen) fuse with nuclei of heavy elements, on the assumption that heavy elements were common and protons were rare inside the stars. Even Eddington, with his prescient comments in 1920 about converting hydrogen into helium, was still only suggesting that 5 per cent of a star’s mass might start out in the form of hydrogen.

The process by which protons penetrate heavy nuclei is the opposite of the process of alpha decay, in which an alpha particle (helium nucleus) escapes from a heavy nucleus, and it is governed by the same rules of quantum tunnelling discovered by Gamow. Gamow’s calculations of the tunnel effect were published in 1928, and just a year later the Welsh astrophysicist Robert Atkinson (1889–1982) and his German colleague Fritz Houtermans (1903–1966), who had previously worked with Gamow, published a paper describing the kind of nuclear reactions that might occur inside stars as protons fused with heavy nuclei. Their paper began with the words ‘Recently Gamow demonstrated that positively charged particles can penetrate the atomic nucleus even if traditional belief holds their energy to be inadequate.’ This is the key point. Eddington, in particular, had used the laws of physics to calculate the temperature at the heart of the Sun from its mass, radius and the rate at which it is releasing energy into space. Without the tunnel effect, this temperature – about 15 million K – is too low to allow nuclei to come together with sufficient force that they overcome their mutual electrical repulsion and stick together. In the early 1920s, when physicists first calculated the conditions of temperature and pressure required for protons to fuse together to make helium, this seemed to many an insuperable problem. In his book The Internal Constitution of the Stars, published in 1926 just as the quantum revolution was taking place, Eddington replied that ‘we do not argue with the critic who urges that the stars are not hot enough for this process; we tell him to go and find a hotter place’. This is usually interpreted as Eddington telling his critics to go to Hell. It was the quantum revolution, and tunnelling in particular, which soon showed that Eddington was right to stick to his guns, and nothing indicates more clearly the interdependence of different scientific disciplines. Progress in understanding the internal workings of the stars could only be made once the quantum properties of entities such as protons were beginning to be understood.

But even Atkinson and Houtermans, as we have seen, were still assuming in 1928 that the Sun was rich in heavy elements. Just around the time they were carrying out their calculations, however, spectroscopy became sophisticated enough to cast doubt on this assumption. In 1928, the British-born astronomer Cecilia Payne (later Cecilia Payne Gaposchkin; 1900–1979) was working for her PhD at Radcliffe College, under the supervision of Henry Norris Russell. Using spectroscopy, she discovered that the composition of stellar atmospheres is dominated by hydrogen, a result so surprising that when she published her results, Russell insisted that she include a caveat to the effect that the observed spectroscopic features could not really be taken as implying that stars are made of hydrogen, but must be due to some peculiar behaviour of hydrogen under stellar conditions, enhancing its appearance in the spectra. But at about the same time, the German Albrecht Unsöld (1905–1995) and the young Irish astronomer William McCrea (1904–1999) independently established that the prominence of hydrogen lines in stellar spectra indicates that there are a million times more hydrogen atoms present in the atmospheres of stars than there are atoms of everything else put together.

All of these pieces of work, coming together at the end of the 1920s, marked the beginning of the development of an understanding of what keeps the stars shining. It still took some years for astrophysicists to pin down the most likely nuclear interactions to explain the process, and slightly longer for them to appreciate fully just how much hydrogen dominates the composition of the visible Universe. This was partly because of an unfortunate coincidence. As astrophysicists developed mathematical models to describe the internal structure of the stars in more detail in the 1930s, they found that these models worked – in the sense that they predicted the existence of balls of hot gas with the same sort of size, temperature and mass as the stars – either if the composition of the hot objects is roughly two-thirds heavy elements and one-third hydrogen (or a mixture of hydrogen and helium), or if their composition is at least 95 per cent hydrogen and helium, with just a trace of heavy elements. With either mixture, but no other, the properties of the hot balls of gas predicted by the equations would match up with those of real stars. Having only just realized that there is more than a trace of hydrogen inside the stars, at first the astrophysicists naturally plumped for the option with two-thirds heavy elements, and this meant that for a almost a decade they concentrated on investigating interactions in which protons tunnel into heavy nuclei. It was only after they discovered the detailed processes which can turn hydrogen into helium that they realized that heavy elements are rare in stars, and that hydrogen and helium together make up 99 per cent of star stuff.

As is so often the case with scientific ideas whose time has come, the key interactions involved in the nuclear fusion processes which keep the stars shining were identified independently by different researchers at about the same time. The principal contributions came from the German-born Hans Bethe, then working at Cornell University, and Carl von Weizsäcker (1912–), working in Berlin, in the final years of the 1930s. They identified two processes which could operate at the temperatures known to exist inside stars, making allowance for quantum processes such as tunnelling, to convert hydrogen into helium, with the appropriate release of energy. One of these, known as the proton–proton chain, turns out to be the dominant interaction in stars like the Sun. It involves two protons coming together, with a positron being ejected, to make a nucleus of deuterium (heavy hydrogen).¹⁷ When another proton fuses with this nucleus, it forms helium-3 (two protons plus one neutron), and when two helium-3 nuclei come together and eject two protons, the result is a nucleus of helium-4 (two protons plus two neutrons). The second process operates more effectively at the slightly higher temperatures found in the hearts of stars at least one and a half times as massive as the Sun, and in many stars both processes are at work. This second process, the carbon cycle, operates in a loop, and it requires the presence of a few nuclei of carbon, involving protons tunnelling into these nuclei in the way Atkinson and Houtermans suggested. Because the process operates in a loop, these heavy nuclei emerge at the end of the cycle unchanged, effectively acting as catalysts. Starting with a nucleus of carbon-12, the addition of a proton makes unstable nitrogen-13, which spits out a positron to become carbon-13.¹⁸ Adding a second proton makes nitrogen-14, while adding a third proton to the nitrogen-14 nucleus makes unstable oxygen-15, which ejects a positron to become nitrogen-15. Now comes the finale – with the addition of a fourth proton the nucleus ejects a whole alpha particle and reverts to being carbon-12, the starting ingredient. But an alpha particle is simply a nucleus of helium-4. Once again, the net effect is that four protons have been converted into a single nucleus of helium, with a couple of positrons and a lot of energy ejected along the way.

These processes were identified shortly before the beginning of the Second World War, and further progress in understanding the internal workings of the stars had to await the return of normal conditions in the late 1940s. But these studies then benefited enormously from the wartime effort to understand nuclear interactions in connection with research into nuclear weapons and the development of the first nuclear reactors. As the appropriate information was declassified, it helped astrophysicists to work out the rates at which interactions like the ones we have just described could go on inside the stars. And, as the work by Alpher, Herman and Gamow highlighted, the problem of the ‘mass gaps’ for the manufacture of heavier elements step by step from hydrogen and helium, in the 1950s several astronomers looked at the problem of how the heavy elements (which, after all, had to come from somewhere) might be manufactured inside stars. One idea that was aired was the possibility that three helium-4 nuclei (three alpha particles) could come together essentially simultaneously, forming a stable nucleus of carbon-12 without having to manufacture the highly unstable beryllium-8 as an intermediate step. The key insight came from the British astronomer Fred Hoyle in 1953. Rather in the way that ‘classical’ physics said that two protons could not fuse under the conditions inside a star like the Sun, the simplest understanding of nuclear physics said that such ‘triple-alpha’ interactions could occur, but would be far too rare to make sufficient amounts of carbon during the lifetime of a star. In most cases, such triple collisions ought to smash the particles apart, not combine them in a single nucleus.

The proton fusion puzzle was solved by quantum tunnelling; Hoyle suggested, on the basis of no other evidence than the fact that carbon exists, a comparably profound solution to the triple alpha puzzle – that the nucleus of carbon-12 must possess a property known as a resonance, which greatly increased the probability of three alpha particles fusing. Such resonances are states of higher-than-usual energy. If the base energy of the nucleus is likened to the fundamental note played on a guitar string, resonances can be likened to higher notes played on the same string, with only certain notes (certain harmonics) being possible. There was nothing mysterious about the idea of resonances when Hoyle made his suggestion – but there was no way to calculate in advance what resonances carbon-12 ought to have, and in order for the trick to work, carbon-12 had to have a resonance with a certain very precise energy, corresponding to a very pure note. Hoyle persuaded Willy Fowler (1911–1995), an experimental physicist working at Caltech, to carry out experiments to test for the existence of such a resonance in the carbon-12 nucleus. It turned up exactly where Hoyle had predicted. The existence of this resonance allows three alpha particles to merge smoothly together, instead of colliding in an impact which smashes them apart. This creates an energetic nucleus of carbon-12 which then radiates away its excess energy and settles into the basic energy level (known as the ground state). This was the key discovery which explained how elements heavier than helium can be manufactured inside stars.¹⁹ Once you have carbon nuclei to work with, you can make heavier elements still by adding more alpha particles (going from carbon-12 to oxygen-16 to neon-20, and so on) or by the kind of drip-feed addition of protons discussed by people such as Atkinson and Houtermans and, in a different context, by Alpher and Herman (this kind of process is also at work in the carbon cycle). Hoyle, Fowler and their British-born colleagues Geoffrey Burbidge (1925–) and Margaret Burbidge (1922–) produced the definitive account of how the elements are built up in this way inside stars in a paper published in 1957.²⁰ Following this work, astrophysicists were able to model in detail the internal workings of the stars, and by comparing these models with observations of real stars, to determine the life cycles of stars and work out, among other things, the ages of the oldest stars in our Galaxy.

This understanding of nuclear fusion processes operating inside stars explained how all the elements up to iron can be manufactured from the hydrogen and helium produced in the Big Bang. Even better, the proportions of the different elements predicted to be produced in this way match the proportions seen in the Universe at large – the amount of carbon relative to oxygen, or neon relative to calcium, or whatever. But it cannot explain the existence of elements heavier than iron, because iron nuclei represent the most stable form of everyday matter, with the least energy. To make nuclei of even heavier elements – such as gold, or uranium, or lead – energy has to be put in to force the nuclei to fuse together. This happens when stars rather more massive than the Sun reach the end of their lives and run out of nuclear fuel which can generate heat (by the kind of interactions we have just described) to hold them up. When their fuel runs out, such stars collapse dramatically in upon themselves, and as they do so, enormous amounts of gravitational energy are released and converted into heat. One effect of this is to make the single star shine, for a few weeks, as brightly as a whole galaxy of ordinary stars, as it becomes a supernova; another is to provide the energy which fuses nuclei together to make the heaviest elements. And a third effect is to power a huge explosion in which most of the material of the star, including those heavy elements, is scattered through interstellar space, to form part of the raw material of new stars, planets and possibly people. The theoretical models describing all this were developed by many people in the 1960s and 1970s, drawing on observations of supernovae (which are rather rare events) in other galaxies. Then, in 1987, a supernova was seen to explode in our near neighbour, the Large Magellanic Cloud – the closest supernova to us to have been seen since the invention of the astronomical telescope. With a battery of modern telescopes turned upon the event for months, analysing it in every detail with observations at all possible wavelengths, the processes unfolding in this supernova were seen to match closely the predictions of those models, effectively slotting into place the last piece in our understanding of the basics of how stars work. They were, to astronomers who had seen this understanding develop during the span of a single human lifetime, the most important and exciting discoveries concerned with the origin of the elements, confirming that the theoretical model is broadly correct.

This leads us to what is, in my view, the most profound discovery of the whole scientific endeavour. Astronomers are able to calculate with great accuracy how much material of different kinds is manufactured inside stars and scattered into space by supernovae and lesser stellar outbursts. They can confirm these calculations by measuring the amount of different kinds of material in clouds of gas and dust in space, the raw material from which new stars and planetary systems form, using spectroscopy. What they find is that apart from helium, which is an inert gas that does not take part in chemical reactions, the four most common elements in the Universe are hydrogen, carbon, oxygen and nitrogen, collectively known by the acronym CHON. This is an ultimate truth revealed by a process of enquiry that began when Galileo first turned his telescope towards the sky, and ended with those observations of the supernova of 1987. Another line of investigation, which for centuries seemed to have nothing to do with the scientific study of the stars, began a little earlier, when Vesalius started to put the study of the human body on a scientific footing. The ultimate truth revealed by this line of enquiry, culminating with the investigation of DNA in the 1950s, is that there is no evidence of a special life force, but that all of life on Earth, including ourselves, is based on chemical processes. And the four most common elements involved in the chemistry of life are hydrogen, carbon, oxygen and nitrogen. We are made out of exactly the raw materials which are most easily available in the Universe. The implication is that the Earth is not a special place, and that life forms based on CHON are likely to be found across the Universe, not just in our Galaxy but in others. It is the ultimate removal of humankind from any special place in the cosmos, the completion of the process that began with Copernicus and De Revolutionibus. The Earth is an ordinary planet orbiting an ordinary star in the suburbs of an average galaxy. Our Galaxy contains hundreds of billions of stars, and there are hundreds of billions of galaxies in the visible Universe, all of them full of stars like the Sun and laced with clouds of gas and dust rich in CHON. Nothing could be further removed from the pre-Renaissance idea that the Earth was at the centre of the Universe, with the Sun and stars orbiting around it, and humankind as the unique pinnacle of creation, qualitatively different from the ‘lesser’ forms of life.

But do these discoveries mean, as some have suggested, that science is about to come to an end? Now that we know how life and the Universe work, is there anything left except to fill in the details? I believe that there is. Even filling in the details will be a long job, but science itself is now undergoing a qualitative change. The analogy I have used before, but which I cannot improve upon, is with the game of chess. A small child can learn the rules of the game – even the complicated rules like the knight’s move. But that does not make the child a grandmaster, and even the greatest grandmaster who ever lived would not claim to know everything there is to know about the game of chess. Four and a half centuries after the publication of De Revolutionibus, we are in the situation of that small child who has just learned the rules of the game. We are just beginning to make our first attempts to play the game, with developments such as genetic engineering and artificial intelligence. Who knows what the next five centuries, let alone the next five millennia, might bring.

^1.To give you a feel for these angular sizes, the full Moon covers 31 minutes of arc, just over half a degree; so one second of arc is roughly one sixtieth of one thirtieth, or 1/1800, of the apparent width of the Moon on the sky.

^2.For example, distances to groups of stars that move together through space in a cluster can be approximately determined geometrically, by measuring the way in which the proper motions of the stars seem to converge at a point on the sky, just as parallel railway lines seem to converge at a point in the distance. There are other statistical techniques that helped indicate the distances to stars, but the details need not concern us here.

^3.This squashes light waves from objects moving towards us, shifting features in the spectrum towards the blue end of the spectrum, and stretches waves of light from objects moving away from us, producing a redshift, with the size of the shift in either case indicating the relative speed of the object.

^4.By then, Hertzsprung had also published his results in a graphical form, in 1911, but yet again in a journal that was rather obscure (to astronomers).

^5.Intrinsically bright or faint, we emphasize. This is not about the apparent brightness of a star on the sky, but how bright it really is, close up, which we know from its distance.

^6.And it was Russell, with his student Harlow Shapley, of whom more shortly, who first improved these distance estimates by allowing for extinction, in 1914.

^7.Just as the stars of the Milky Way cannot be resolved by the unaided human eye, and were only ‘discovered’ when Galileo turned his telescope upon them.

^8.I was a member of the team that finally established that the Milky Way is just an ordinary galaxy; my colleagues were Simon Goodwin, now at the University of Cardiff, and Martin Hendry, now at the University of Glasgow.

^9.The couple of blueshifted galaxies, one of which is Andromeda, are very close to us on a cosmic scale and moving our way under the influence of gravity; this overwhelms the universal expansion on such relatively local scales.

^10.Einstein’s theory predicts the exact size of the dimples, and therefore to what degree light is bent as it follows a line of least resistance passing near an object like the Sun, which is why Eddington’s eclipse expedition of 1919 was so important.

^11.You can picture this by drawing a wavy line on a fat elastic band and then stretching the elastic band.

^12.A term actually coined by the astronomer Fred Hoyle in the 1940s as a term of derision for a model he abhorred.

^13.The very latest data suggest that the Universe may now have begun to expand more rapidly, presumably because there is, after all, a cosmological constant. This does not affect these calculations of the age of the Universe significantly, and discussion of this work in progress lies outside the scope of the present book.

^14.This is actually a very profound discovery. The age of the Universe is essentially calculated from the general theory of relativity, and deals with the laws of physics on the very large scale; the ages of stars are, as we shall see below, essentially calculated from the laws of quantum mechanics, physics on the very small scale. Yet the age of the Universe comes out to be just enough older than the ages of the oldest stars to allow the time required for the first stars to form after the Big Bang. This agreement between physics on the largest and smallest scales is an important indication that the whole of science is built on solid foundations.

^15.Such as his book The Creation of the Universe.

^16.I’ve always suspected that the Nobel committee, like many other people, thought that the prediction had been made by Gamow, who was dead by 1978, and Nobel prizes are never awarded posthumously. There is no other obvious reason why Alpher and Herman were ignored.

^17.Many of these interactions also involve the ejection of neutrinos, but for simplicity we shall not go into such detail.

^18.Ejecting a positron converts one of the protons in the nucleus into a neutron.

^19.And it’s worth noting that it was made less than half a century after Rutherford had identified alpha radiation as helium nuclei.

^20.With the name of the authors listed alphabetically as Burbidge, Burbidge, Fowler and Hoyle, this paper is known to all astronomers as ‘B²FH’.