by Marcus Chown
To Manjit,
With love, Marcus
There are two kinds of geniuses: the ‘ordinary’ and the ‘magicians’. An ordinary genius is a fellow whom you and I would be just as good as, if we were only many times better. There is no mystery as to how his mind works. Once we understand what they’ve done, we feel certain that we, too, could have done it. It is different with the magicians. Even after we understand what they have done it is completely dark.
MARK KAC
Genius: Feynman and Modern Physics
BY JAMES GLEICK
Contents
Title Page
Dedication
Epigraph
Introduction:
The central magic of science
1 Map of the invisible world
2 Voices in the sky
3 Mirror, mirror on the wall
4 Goldilocks universe
5 Ghost busters
6 The day without a yesterday
7 The holes in the sky
8 The god of small things
9 The voice of space
10 The poetry of logical ideas
Further Reading
Acknowledgements
Index
About the Author
By the Same Author
Copyright
Introduction
The central magic of science
The universe is full of magical things patiently waiting for our wits to grow sharper.
EDEN PHILLPOTTS1
Nothing is too wonderful to be true.
MICHAEL FARADAY
About 3.6 million years ago, three hominins walked across a volcanic landscape and left footprints in the recently fallen ash. The impressions of those footprints, which are visible today at Laetoli in Tanzania, are intensely evocative. As the biologist Richard Dawkins remarked, ‘Who does not wonder what these individuals were to each other, whether they held hands or even talked, and what forgotten errand they shared in a Pliocene dawn?’2
We will, of course, never know the answers to these questions, but we can hazard a guess at some of the things the three hominins, probably Australopithecus afarensis, saw and wondered about on that distant day, long before the dawn of our own species. Much of the natural world is chaotic and unpredictable, but some things are regular and reliable: the rising and setting of the Sun; the march of the seasons; the changing phases of the Moon; the gradual drift of star patterns across the night sky. Such natural rhythms would almost certainly have left a deep impression on even our earliest ancestors.
There was no progress made in understanding these rhythms for tens of thousands of centuries after the footprints at Laetoli were made. Everything changed, however, with a critical invention in the Middle East around 3000 bc: writing provided the means to record events in the sky and to recognise ever more subtle patterns in the movement of the heavenly bodies. In Babylon in modern-day Iraq, it became possible to predict astronomical spectacles such as eclipses of the Moon and the Sun. And those who made such predictions and controlled the dissemination of such information were able to strike awe in the minds of the population. Even if they were not tempted to pass themselves off as gods, they gained immense power over the masses.
That power, however, was nothing compared with the power of science. Science, which was born in the seventeenth century, found the ultimate reason for the world’s patterns – the general ‘laws’ that underpin the rhythms of nature. And those laws are portable. So, although Isaac Newton famously deduced his law of gravity from the fall of an apple and the motion of the Moon around the Earth, he was also able to apply it in another, entirely different domain to explain why there are two tides in the oceans every twenty-five hours.3
Recognising a pattern in, for instance, eclipses permitted only the prediction of future eclipses. But science, by exploiting general-purpose laws, could predict the existence of phenomena that nobody had ever suspected. The first, and most striking, example of this was the prediction of an unknown planet by Urbain Le Verrier. When Neptune was found in 1846 – within a whisker of where in the night sky the French astronomer’s calculations revealed it should be – it created an international sensation and made Le Verrier a superstar. ‘Science has made gods of men,’ the French biologist Jean Rostand would later write.4
The discovery of Neptune was a dramatic demonstration of the central magic of science: its ability to predict the existence of things previously undreamt of which, when people went out and looked for them, turned out to actually exist in the real universe. This ability is so magical that even the exponents of science can often scarcely believe it. Famously, Albert Einstein did not believe two predictions of his own theory of gravity: black holes and the Big Bang. And when it came to a third prediction – gravitational waves – he vacillated, predicting their existence in 1916 and unpredicting them a year later, before predicting them again in 1936. They would eventually be discovered on 14 September 2015.
The central magic of science appears miraculous because nobody knows why it works. The predictions made by physicists arise from mathematical formulae, or ‘equations’, which are found to describe aspects of the universe. But nobody knows why such equations so perfectly describe the physical world or, to paraphrase the twentieth-century Austrian physicist Eugene Wigner, why mathematics is unreasonably effective in the natural sciences. Put simply, the universe has a mathematical twin that can be written on a piece of paper or scrawled across a whiteboard. But why it has such a twin is a huge mystery.
The importance of the central magic of science is that it is at the crux of why physics works. Physicists naturally want to understand why the principal tool they use in their working lives is so effective, and understanding why it works will conceivably tell us something very profound about our universe and why it is constructed the way it is.
In this book I will tell the stories of some of the people who have demonstrated the central magic of science. One striking thing is the difference in their approaches. The Scot James Clerk Maxwell was arguably the greatest physicist between Newton and Einstein. His thought processes were essentially like those of a normal human being, though of course a souped-up version; in his mind, he concocted mechanical models of phenomena such as electricity and magnetism using everyday objects like cogs and wheels. Only when he was satisfied that he had captured the essence of reality did he express his model in mathematical terms. In the case of electricity and magnetism, this yielded his famous ‘equations of electromagnetism’, which revealed that light is an ‘electromagnetic wave’ and predicted the existence of radio waves, making possible the ultra-connected world of the twenty-first century. The approach of the English physicist Paul Dirac, however, was very different: the hyper-literal ‘Mr Spock of physics’ simply plucked the formula which describes an electron travelling at close to the speed of light out of thin air. The ‘Dirac equation’, which predicted a hitherto unsuspected universe of ‘antimatter’ and is one of only two equations inscribed on the stone floor of Westminster Abbey, was the result of Dirac playing with equations on a piece of paper and insisting on mathematical consistency.
The stories I tell here of Maxwell, Dirac and many others who demonstrated the central magic of science are as factual as I can make them. If the scientists are alive and it was possible to interview them, I did so; for those that are dead, I used the facts at my disposal and dramatised the events around them. For instance, my description of the day that Maxwell came to the stunning realisation that light is a wave of electricity and magnetism is pieced together from the available facts. On his return from a summer holiday at his Glenlair estate in Scotland, he did indeed go to the library at London’s King’s College to look in a reference book for the measured values of the permittivity and
permeability of air, which had been obtained by Wilhelm Weber and Rudolf Kohlrausch. He did walk or catch the horse-drawn bus from his home in Kensington to the Strand and back each day, a route that took him along Piccadilly and past the Albemarle Street turn-off to the Royal Institution, where he would sometimes stop. And he and his wife did ride regularly in Hyde Park and Kensington Gardens, Katherine’s pony Charlie having been brought down to London by train from Glenlair.
My hope is that, by dramatising such stories of scientific prediction and discovery, I will not only bring the events alive but also provide some idea of what the moment of discovery must be like and how exhilarating it must be to realise a profound truth about the world that no one has known before. For those interested in the history of science, I have provided copious references.
This is the story of the magicians who, with pen and paper, not only predicted the existence of unknown worlds, black holes and subatomic particles but antimatter, invisible waves that course through the air, ripples in the fabric of space–time and many more things besides. This is the story of the central magic of science and how it made gods of men.
Notes
1 A Shadow Passes by Eden Phillpotts (cited in The Strange Death of Fiona Griffiths by Harry Bingham).
2 The Ancestor’s Tale: A Pilgrimage to the Dawn of Evolution by Richard Dawkins (Weidenfeld & Nicolson, London, 2005).
3 The Ascent of Gravity: The Quest to Understand the Force that Explains Everything by Marcus Chown (Weidenfeld & Nicolson, London, 2017).
4 Pensée d’un biologiste by Jean Rostand (1939).
1
Map of the invisible world
The hypotheses which we accept ought to explain phenomena which we have observed. But they ought to do more than this: our hypotheses ought to foretell phenomena which have not yet been observed.
WILLIAM WHEWELL1
I grew up believing my sister was from the planet Neptune and had been sent down to Earth to kill me.
ZOOEY DESCHANEL
Berlin, 23 September 1846
They had been searching for almost an hour and had already slipped into an automatic rhythm. Johann Galle squinted through the giant brass refractor at the clear night sky, adjusted the controls of the telescope until a star appeared in the cross hairs and barked out its co-ordinates. His young assistant Heinrich d’Arrest was seated at a wooden table across the stone floor of the observatory dome. He ran his finger over a star map by the light of an oil lamp and shouted back, ‘Known star.’ Galle twiddled the brass knobs again, lining up another star. Then another. In the chilly night air, he was already getting a crick in his neck and was beginning to wonder whether they were wasting their time.
The director of the Berlin Observatory, Johann Franz Encke, had certainly thought so that afternoon when Galle had appeared at his office door with his unusual request. But because Encke planned to be at home that night celebrating his fifty-fifth birthday rather than at the 22-centimetre refractor, he had given Galle permission to use the instrument.
The exchange between Galle and Encke had been overheard by d’Arrest, an astronomy student who was lodging in one of the observatory’s outbuildings so he could gain more practical experience; he immediately begged Galle to let him help. And so here the pair of them were, on the crystal-clear night of 23 September 1846, scanning the skies with the great, clock-driven Fraunhofer telescope, one of the most advanced instruments of its kind in the world.
They had started their search when the gaslights of Berlin sputtered off, plunging the city into blackness, and it was now approaching midnight. Galle manoeuvred the cross hairs to the next star and called out its co-ordinates. His mind wandered to thoughts of the warm bed he would soon be sharing with his wife and he began to think how ridiculous he would seem in the morning when he told Encke of their failure. He waited for a response from d’Arrest. And waited. What in the world, he wondered, was his assistant doing?
The crash of a chair hitting the floor shocked Galle back to reality. Leaping back from the eyepiece, he saw his assistant silhouetted against the oil lamp, rushing towards him, flapping his star map like a demented bird. It was too dark to make out the expression on d’Arrest’s face, but Galle would remember his words for the rest of his life: ‘The star is not on the map! It is not on the map!’
Paris, 18 September 1846
The man who had suggested looking for a star that was not on any star chart, in a letter that had arrived at the Berlin Observatory on 23 September, was Urbain Le Verrier. An astronomer at the École Polytechnique in Paris, Le Verrier was interested not in observing celestial bodies from draughty telescope domes but in sitting at his desk and using Newton’s law of gravity to calculate the orbits of such bodies and compare them with existing observations. In the course of this work, he had become obsessed by a planet which seemed to break all the rules: Uranus.
Uranus had been discovered by a musician from Hanover in Germany. In 1757, William Herschel, aged just nineteen, had moved with his sister Caroline to Bath in the west of England, a pretty spa town which had been developed by the Romans because of its hot springs. He found work as a church organist, but his real passion was astronomy, and in the garden of his house he built one of the best telescopes of his day. It was on 13 March 1781, while scanning the night sky with this instrument, that a fuzzy star popped into his eyepiece. At first Herschel thought it was a comet, but unlike a comet it did not have a gossamer tail. Not only that but, as it crept across the constellation of Gemini over the subsequent nights, it did not follow the highly elongated orbit of a comet but the near-circular orbit of a planet.
Herschel had discovered the first new planet in the age of the telescope, the first world entirely unknown to ancient astronomers. Throughout all of recorded history, the number of planets had stood at six. Now, incredibly, there were seven. Herschel’s discovery created an international sensation and elevated him to the status of a scientific superstar.
Herschel’s greatest desire, as an immigrant, was to be accepted by his adopted country, and he therefore christened the new planet ‘George’, after King George III (actually, he named it ‘George’s star’). Not surprisingly, French astronomers objected to having a planet named after an English king and instead referred to it as ‘Herschel’. In an attempt to make the peace, the astronomer Johann Bode suggested it be named after Uranus, father of the Roman god Saturn, and the name stuck. (If it had not stuck, the planets, in increasing distance from the Sun, would have been Mercury, Venus, Earth, Mars, Jupiter, Saturn … and George.)
Actually, Uranus had been seen almost a century earlier, in 1690, by the English astronomer John Flamsteed, but he had mistakenly believed it to be a star and catalogued it as 34 Tauri, the thirty-fourth star in the constellation of Taurus. Historical records of the planet’s position were able to supplement new observations of the planet; consequently, by the early nineteenth century, its orbit was known precisely enough that it could be compared with that predicted by Newton’s law of gravity. But the comparison threw up an anomaly.
Whenever an orbit was predicted for Uranus, the planet would stray from it over the following months. No one seriously believed there was anything wrong with Newton’s law of gravity. Its successes had been so overwhelming and so comprehensive that it had a status akin to the word of God. Instead, the suspicion arose that Uranus was constantly veering from its calculated orbit because it was being tugged by the gravity of another world even further from the Sun. It was a tantalising possibility, and Le Verrier could not resist the challenge of pursuing it. Seated at his desk at the École Polytechnique in Paris, he set out to deduce, from the observed effect of the hypothetical planet on Uranus, exactly where in the night sky it must be.
The Sun accounts for a whopping 99.8 per cent of the mass of the solar system, so, to a very good approximation, a planet can be assumed to be moving under the influence of the Sun alone. However, Newton’s law of gravity is a ‘universal’ law, which means there is a force of
attraction between every chunk of matter and every other chunk of matter; consequently, a planet is influenced not only by the gravitational tug of the Sun, but of all the other planets as well. To be sure he was seeing the effect of an unknown planet in the outer solar system on Uranus, Le Verrier needed to first subtract the effect of the known planets, and especially of the two most massive ones: Jupiter and Saturn.
The calculations were complex and time-consuming. Each one had to be checked and re-checked, since a single small error might be magnified and bring the whole mathematical edifice crashing down. But that was not the only problem Le Verrier faced: the gravitational pull of a lightweight planet close to Uranus would be indistinguishable from that of a massive planet far away. Therefore, in order to make any progress in pinning down the orbit of the hypothetical planet, Le Verrier had to guess its mass and distance from the Sun.* It was a gargantuan task that took up all of his working days and some of his nights as well. But, eventually, Le Verrier succeeded. He deduced not only an orbit for the hypothetical planet but, most importantly, where in the night sky a telescope should be pointed to look for it: between the constellations of Capricorn, the goat, and Aquarius, the water carrier.
Le Verrier was a confident man but, as his quill hovered above the dense formulae that covered the pages spread across his desk, he felt a buzz of nervous excitement. To know something that no one else in the world knew or understood was a most exhilarating feeling of power, but could he be wrong? Was he a god, or merely a fool? And how was it possible that the equations before him described reality? Before he could be overwhelmed by doubts, he pulled himself together. There was only one thing for him to do: inform the observational astronomers.
