The Ascent of Gravity: The Quest to Understand the Force that Explains Everything

the ascent of

gravity

THE QUEST TO UNDERSTAND THE

FORCE THAT EXPLAINS EVERYTHING

MARCUS CHOWN

To Mike & Claire, Val & Pat, Maureen & Pete With love, Marcus

It’s embarrassing that we’re in the twenty-first century and we don’t even know what makes gravity work.

Woody Norris

Contents

Foreword: Six things you may not know about gravity

Author’s note

PART ONE: NEWTON

1  The Moon is falling

How Newton found the first universal law – one that applies in all places and at all times

2  The last of the magicians

How Newton created a system of the world and found the key to understanding the Universe

3  Beware the tides of March

How Newton’s theory of gravity is rich in consequences and can explain not only the motion of the planets but also the tides in the oceans

4  Map of the invisible world

How Newton’s law of gravity not only explains what we see but also reveals what we cannot see

PART TWO: EINSTEIN

5  Catch me if you can

How Einstein realised that nothing can travel faster than light and that this is incompatible with Newton’s law of gravity

6  Ode to a falling man

How Einstein realised that the ‘force’ of gravity is an illusion and all there really is is warped space-time

7  Where God divided by zero

How Einstein’s theory of gravity predicts daft things at the ‘singularity’ of a black hole and how a deeper theory is needed that doesn’t

PART THREE: BEYOND EINSTEIN

8  A quantum of space-time

How quantum theory implies that space and time are doomed and must somehow emerge from something more fundamental

9  The undiscovered country

The struggle to find a deeper theory than Einstein’s theory of gravity that will tell us why there is a Universe and where it came from

Notes

Acknowledgements

Index

Foreword

Six things you may not know about gravity

1

Gravity creates a force of attraction between you and the coins in your pocket and between you and a person passing you on the street

2

It is so weak that, if you hold your hand out, the gravity of the whole Earth cannot overcome the strength of your muscles

3

Despite its weakness, gravity is so irresistible on the large scale that it controls the evolution and fate of the entire Universe

4

Everyone thinks it sucks but in most of the Universe it blows

5

If it had not ‘switched on’ after the big bang time would not have a direction

6

Only by figuring it out will we be able to answer the biggest question of all: Where did the Universe come from?

At Livingston in Louisiana and Hanford in Washington State there are 4-kilometre-long rulers made of laser light. At 05.51 Eastern Daylight Time on 14 September 2015, a shudder went through first the Livingston ruler, then 6.9 milliseconds later, the one at Hanford. It was the unmistakable calling card of a passing gravitational wave – a ripple in the very fabric of spacetime – predicted to exist by Einstein almost exactly 100 years ago.

In a galaxy far, far away, at a time when the Earth hosted nothing bigger than a simple bacterium, two monster black holes, locked in a death-spiral, swung around each other one last time. As they kissed and coalesced, three whole solar masses vanished, reappearing instantly as a tsunami of a warped space-time, which raced outwards at the speed of light. For an instant its power was fifty times greater than that of all the stars in the Universe put together.

The detection of gravitational waves by the twin detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) on 14 September 2015 was an epoch-making moment in the history of science. Imagine you have been deaf since birth, then, suddenly, overnight, you are able to hear. This is the way it is for physicists and astronomers. For all of history we have been able to ‘see’ the Universe. Now, at last, we can ‘hear’ it. Gravitational waves are the voice of space. It is not too much of an exaggeration to say that their detection is the most important development in astronomy since the invention of the telescope in 1608.

Gravitational waves confirm that space-time is a ‘thing’ in its own right, which can quiver and shudder, sending undulations propagating outwards like ripples spreading on a pond. They are the ultimate proof of Einstein’s contention that gravity is warped space-time. Whereas Newton imagined a ‘force’ of gravity reaching out from the Sun and ensnaring the Earth like a piece of invisible elastic, Einstein recognised that the Sun creates a valley in space-time in its vicinity around which the Earth circles endlessly like a planet-sized roulette ball in an oversized roulette wheel.

Although Newton’s theory of gravity was hugely successful, explaining the motion of the planets and the ocean tides and even predicting the existence of an unknown world – Neptune – Einstein’s theory of gravity was just as successful, explaining the anomalous motion of Mercury and predicting the existence of black holes and the big bang in which the Universe was born. But Einstein’s theory of gravity, like Newton’s before it, contains the seeds of its own destruction. At the hearts of black holes and at the birth of the Universe, it predicts the existence of nonsensical ‘singularities’ where the parameters of physics skyrocket to infinity.

The irony is that the first force to be described by science and the one everyone thinks was understood long ago is actually the least understood. Gravity, to steal the words of Winston Churchill, is ‘a riddle, wrapped in a mystery, inside an enigma’.

Now, at the outset of the twenty-first century, we stand on the verge of a new revolution. The search for a deeper theory than Einstein’s – a quantum theory of gravity – is the greatest endeavour ever embarked upon by physics. Already, there are tantalising glimpses of a new world view. Perhaps another Newton or Einstein is at this moment waiting in the wings, assembling the fragmentary pieces of the puzzle into a coherent whole. Or perhaps — a more likely scenario – it will take the efforts of dozens of people working in concert. Many physicists believe we are on the verge of a seismic shift in our view of reality, one more far-reaching in its consequences than any that has gone before.

Will the deeper theory than Einstein’s give us warp drives and time machines, the ability to manipulate space and access parallel universes? No one can predict, just as no one in the preelectrical era could have predicted televisions and mobile phones and the World Wide Web. What we do know is that when at last we have the elusive theory in our possession, we will be able to answer the biggest scientific questions of all. What is space? What is time? What is the Universe? And where did it come from?

But I am getting ahead of myself. How did we get to where we are today, standing on the brink of a vast undiscovered landscape of physics? The story began with a twenty-two-year-old named Isaac Newton in the plague year of 1666 . . .

Author’s note

A word on endnotes, which readers will find after the final chapter of the book: some contain asides that, if included in the text, would have broken its flow. Some amplify the explanations in the text, occasionally using technical language. And some are references to books and articles, where you can find out more information about the subject in the text.

PART ONE

Newton

1

The Moon is falling

How Newton found the first universal law — one that applies in all places and at all times

For in those days I was in the prime of my age for invention and minded Mathematicks & Philosophy more than at any time since.

Isaac Newton¹

You fainted and I caught you. It was the first time I’d supported a human. You had such heavy bones. I put myself between you and gravity. Impossible.

Elizabeth Knox, The Vintner’s Luck²

‘So, Mr Newton, how did the idea of universal gravity come to you?’

They are in the garden of Woolsthorpe Manor, half a century after the event: the elderly natural philosopher, now the most famous personage of his day, sitting across the table from William Stukeley, the young clergyman and archaeologist who has set himself the formidable task of writing the first biography of Isaac Newton. A stream burbles at the bottom of the garden and lambs bleat at random intervals in the field beyond. A raven lands on the lush orchard grass before them, pecks at nothing in particular and takes wing again.

The old man ponders the question, sweeps his long white hair back from his face, then says: ‘Mr Stukeley, you see that tree yonder?’

‘I do.’

‘In the spring of 1666, on a warm day not unlike this, I was seated in this very spot, jotting in my notebook, when an apple fell from the tree. . .

But great men are apt to concoct their own legends. The story of the apple was indeed told by Newton, close to the end of his life, in the garden of Woolsthorpe Manor, Linconshire. ‘After dinner, the weather being warm, we went into the garden and drank tea, under the shade of some apple trees,’ wrote Stukeley in Memoirs of Sir Isaac Newton’s Life, published in 1752. ‘He told me, he was just in the same situation as when formerly the notion of gravitation came into his mind. It was occasion’d by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself . . .?’³

The truth, however, is that Newton never once mentioned the tale of the falling apple in the half century after his discovery of the universal law of gravity. Was it true? Or did Newton, his creative days far behind him and his mind now occupied by his legacy, simply see the potential of the story to burn itself into the popular imagination and ensure his immortality? ‘Three apples changed the world,’ someone tweeted on the death of Steve Jobs, co-founder of Apple computers. ‘Adam’s apple, Newton’s apple, and Steve’s apple.’⁴

Nobody knows what led Newton to make his critical connection between heaven and earth, between the force of gravity pulling on the Moon and the force of gravity pulling on an apple. All we know is that the genesis of Newton’s universal law of gravity came at a truly horrific time, described so vividly by Daniel Defoe in Journal of the Plague Year.⁵

In August 1665, bubonic plague was raging in London. So great was the dread of contamination that in Cambridge, 55 miles to the north-east, the university was closed. Newton, twenty-two years old, unremarkable, unknown, made the trek, by foot, by horse-drawn cart, back to his family farm in Woolsthorpe. There he remained secluded for eighteen months, during which time he not only discovered the universal law of gravity but changed the face of science.

The special one

Isaac Newton was born on Christmas Day 1643. Despite this auspicious date, the ‘special one’ was so small at birth, reportedly he would fit in a quart mug, and so weak he was expected to die within days.⁶

Newton was a ‘posthumous child’. His father had died three months before his birth. His mother was left with little means of support and, when Newton was three, accepted a proposal of marriage from a wealthy rector, almost twice her age. Because he wanted a wife not a stepson, when she moved to his rectory in a nearby village, she had no choice but to abandon Newton to be brought up by his maternal grandparents. Newton despised his substitute parents and later in his notebook confessed to the sin of ‘threatening my father and mother Smith to burne them and the house over them’.

On the death of her husband eight years later, Newton’s mother returned to Woolsthorpe Manor, bringing with her a half-brother and two half-sisters for Newton. But by this time Newton’s sense of rejection by his mother had stoked in him a blind fury that would never be assuaged.

As heir to the family farm, Newton was prohibited from playing with the ‘common’ children of the agricultural workers. Forced to make his own entertainment, he cut a lonely figure, lost in his imagination, forever building things and investigating things about the world around him. He constructed model windmills and bridges. He cut sundials in stone and, hour by hour, day by day, season by season, recorded the movement of their shadows.

It was because of Newton’s singular ability that, when he was twelve, money was found to send him to Kings School in Grantham. The eight miles to the market town was too far to walk each day so he lodged with a local apothecary. Cut off even from family members, he was further isolated. But he fell under the wing of the headmaster, who had a special interest in mathematics and, recognising Newton’s exceptional talent, taught the boy everything he knew.

In 1659, when Newton was sixteen, his mother summoned him home to Woolsthorpe to be a farmer and run the family estate, with its woods and streams, barley fields and grazing sheep. But Newton spent his time gathering herbs and reading books.⁷ He built water wheels in the stream while the sheep trampled the neighbouring farmer’s barley. He let his pigs trespass on others’ land, left the fences in disrepair, and was fined in the manor court on both counts.⁸ To everyone’s relief, including Newton’s, he was returned to school in Grantham the following year.

Newton’s uncle on his mother’s side was another who recognised Newton’s unusual abilities. A rector who had studied for the clergy at Cambridge, he helped the eighteen-year-old find a place at the university in 1661. At the time the institution was situated in little more than a dirty and scruffy village. Newton paid his way as a ‘sub-sizar’, surviving by waiting on wealthier students, running errands for them and eating their leftovers. His undergraduate studies at Cambridge culminated in a Bachelor of Arts degree, awarded to him in January 1665.

Little is known about Newton’s experiences as a student. Like his twentieth-century successor Albert Einstein, he appeared not to have distinguished himself in any way. Nevertheless, he studied mathematics and science with intensity, devouring and absorbing the philosophical work of the Greeks. But, crucially, he was critical of what he read. ‘Plato is my friend – Aristotle is my friend,’ he wrote in his precious notebook, ‘but my greatest friend is truth.’

Voyaging through strange seas of thought alone

In 1665, when Newton settled back into life at Woolsthorpe, it was still summer and the air was abuzz with insects and alive with birdsong. So idyllic was the scene that it must have been difficult to believe that, just 100 miles away in London, people were stumbling and dropping in the streets. They were suffering fever and chills and muscle cramps and aching limbs. They were gasping for breath and sometimes coughing up blood. Their armpits and groins were swollen with black buboes as the plague bacterium multiplied in their lymph glands. Before the outbreak was over, 100,000 souls – a quarter of London’s population -would be carried away on carts and dumped unceremoniously in plague pits.⁹

Woolsthorpe Manor was a slightly dilapidated two-storey dwelling with grey limestone walls, nestling amid apple trees and grazing sheep on the side of the valley of the River Witham. Seated at his desk, Newton shut all the horrors of his time from his mind. Perhaps he was able to do it because he was psycho-pathically detached from human suffering. Or perhaps he knew there was nothing he could do. Why worry about things that cannot be changed? Why agonise about things that are in the hands of the Almighty?

Newton was a pragmatist at heart. And a pragmatic man might use a time of terror as an interlude, as a God-given opportunity to penetrate the mind of the Creator. ‘My greatest friend is truth,’ Newton had written. At Woolsthorpe, while the horror of plague stalked England, Newton began to seek that truth. ‘Voyaging through strange seas of thought alone,’ he would become the pre-eminent mathematician in the world.¹⁰ He would discover the laws of optics and colours, the mathematics of ‘calculus’ and the ‘binomial theorem’. But, most significantly of all, he would find the universal law of gravitation.

The moment was now ripe for such a discovery because there was a realistic model of the Earth’s place in the cosmos. But this had not always been the case.

Mass is the key

Once, it had been thought that the Earth was the centre of the Universe. The mistake was perfectly understandable. After all, the Sun, the Moon and the stars very definitely appear to circle the Earth.

But there are anomalies.

To the ancients, the five naked-eye planets – Mercury, Venus, Mars, Jupiter and Saturn – could not have stood out more prominently if they pulsed on and off like celestial fireflies. They alone crawl snail-like across the backdrop of fixed stars.¹¹ And, crucially, the pace at which they crawl is uneven. Watch one, night after night, week after week, and occasionally and unexpectedly, it can reverse its direction, and reverse again, describing a crazy loop in the night sky. How is this possible if planets are merely circling the Earth?

The answer is it is not.

To explain the anomalous motion of the planets – which comes from the Greek for ‘wanderer’ – there was concocted an ingenious and cunning scheme. The Greeks were wedded to the idea that the heavens, unlike the Earth, were a realm of utter perfection. And the perfect figure to their minds was the circle. Perhaps, as a planet circles the Earth, it also moves in a smaller circle about its average position? A circle within a circle, or an ‘epicycle’. Since motion around the smaller circle allows a planet to travel briefly backwards in its orbit, this would explain why sometimes we see a planet loop back on itself.

This solution to the puzzle of planetary motion is in fact a big con. With enough circles within circles within circles it is possible to mimic absolutely any motion whatsoever. Not only that but the solution is complex and messy. And a key characteristic of modern scientific explanations is that they are simple and economical.

A better explanation of the peculiar planetary motion was proposed by the Polish astronomer Nicolaus Copernicus in 1543. Say the centre of everything is not the Earth but the Sun, and that all of the planets, including the Earth, actually go around the Sun? In this case, Copernicus pointed out in On the Revolutions of the Heavenly Spheres, the motion of planets is easy to explain. As it circles the Sun, the Earth regularly catches up and overtakes a planet like Mars, which is orbiting more slowly in its orbit. From the point of view of the Earth, the planet drops behind, appearing briefly to travel backwards against the fixed stars.¹²

Copernicus’s explanation of the motion of the planets came at a cost. There were now two bodies about which other bodies circle – the Sun, which ensnares the planets, including the Earth, and the Earth, which holds onto the Moon. And things got even worse when the Italian scientist Galileo zoomed in on the heavens with his new-fangled astronomical telescope. Not only did he see stars invisible to the naked eye, mountains on the Moon and the phases of Venus but, in 1610, he was amazed to find that Jupiter is orbited by four moons. There are not two bodies acting as centres in the Solar System: there are at least three.

Ancient ideas were crumbling. According to the Greeks, the most important factor for understanding our world and the Universe was location. Each of the four ‘fundamental elements’ – earth, fire, air and water – seeks out its allotted place. And all are related to the Earth, with earth, not surprisingly, desiring to get as close to the centre of the Earth as possible. But, in the new view, there was nothing at all special about location. How could there be when there are at least three locations about which other celestial bodies revolve?

The lesson from observing our Solar System is that massive bodies orbit other massive bodies. Location is not the important thing.¹³ Mass is the key.

Nature’s lonely hearts club force

The pressing question is: how does one mass enslave another? A clue came from magnetism. Lodestones are naturally magnetised chunks of the mineral magnetite. One lodestone attracts another lodestone with a mysterious ‘force’ that reaches across the empty space between them. As early as the sixth century BC their unusual properties had been remarked upon by the father of Greek philosophy, Thales of Miletus.

In 1600, the English scientist William Gilbert suggested that magnetism might be the force holding together the Solar System. He demonstrated experimentally that the attraction exerted on a piece of iron by a lodestone is bigger the bigger the mass of the lodestone. He also showed that the attraction is mutual – that is, the force of attraction exerted by a lodestone on a piece of iron is exactly as strong as the force of attraction exerted by the iron on the lodestone.

Others such as Robert Hooke, the man who would become Newton’s greatest rival, were much taken by Gilbert’s findings. But the Sun is a hot body and lodestones heated until red hot were known to lose their magnetism. Hooke therefore saw magnetism as merely a model for the force that is orchestrating the motion of the bodies of the Solar System. Like magnetism, gravity reaches out from one mass across empty space and grabs another mass. Like magnetism, the force is bigger the bigger the masses involved. And, like magnetism, it is a mutual force.

Gravity pulls masses together. It attempts to break their terrible isolation. It is truly nature’s lonely hearts club force.

This was the state of play in the plague year of 1666 as Newton sat deep in thought at his desk at Woolsthorpe Manor and began to ponder the nature of the force between massive bodies. He had no more idea what the force of ‘gravity’ is than what the magnetic force of a lodestone is. But not knowing what the force is did not hamper him. In the words of the twentieth-century physicist Niels Bohr: ‘It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.’

Newton knew this truth instinctively. Just because he did not know what gravity is did not mean he could not ask: how does gravity behave?

Reading the book of nature (Kepler’s laws)

The vital clues to gravity’s behaviour had been discovered by the German mathematician Johann Kepler. Between 1609 and 1619, he had built on the work of the Danish astronomer Tycho Brahe, famous among other things for having a prosthetic nose made of brass after his real one was sliced off in a duel. Brahe had made precise naked-eye observations of the planets from his observatory on the island of Hven, now part of Sweden. After poring long and hard over Brahe’s records, Kepler deduced three laws that govern the behaviour of the planets.

Kepler’s first law states that the orbit of a planet is an ellipse, with the Sun at one focus. An ellipse is a very specific closed curve, not simply an oval. It can be drawn by pinning two tacks to a flat surface, stretching a loop of string over them, pulling the loop of string taut with a pencil, and moving the pencil point in a complete circuit around them. The two tacks mark the foci of the ellipse. In mathematical terms, wherever a point is located on the ellipse, the sum of the distances to the two foci is the same.

Kepler’s recognition that the orbit of a planet is an ellipse was a decisive and significant break with the past. The Greek conviction that circles are perfect had caused them to impose circles on the cosmos. But nature is a book to be read not a book to be written. Realising this, Kepler, and the scientists who followed him, demonstrated more humility than their Greek predecessors. They studied nature and looked to see what it was telling them. And what nature was telling Kepler, through the medium of Brahe’s painstaking observations, was that the planets are orbiting the Sun not in circles but in egg-shaped ellipses.

Kepler’s second law says that a planet does not go around the Sun at a uniform speed but moves more quickly when it is nearer the Sun and more slowly when it is further from the Sun. Actually, the law is a bit more precise than this. It states that an imaginary line joining a planet to the Sun sweeps out equal areas in equal times. Take, for instance, a time interval of 10 days. Two points on a planet’s orbit that are 10 days apart can be joined to the Sun to make a triangle. The area of the triangle is always the same irrespective of whether the planet is close to the Sun in its orbit or far from the Sun. It is impossible not to admire the sheer ingenuity of Kepler in teasing out such an odd law from Brahe’s observations.

Newton, ensconced at Woolsthorpe, thought long and hard about Kepler’s second law. And thinking long and hard was the secret of his genius. Yes, he could build complex things and carry out complex experiments, and he could do both of these things far better than most. But what truly set him apart from all others was his phenomenal, almost unearthly power of concentration. This was the secret of his success. This was his thing.

Newton took no exercise, indulged in no amusements, and worked incessantly, often spending eighteen or nineteen hours a day writing.¹⁴ The clockwork of his mind whirred incessantly. Every hour spent not studying he considered an hour lost. While others could hold an abstract problem in their mind’s eye for fleeting minutes, Newton could focus on a problem for hours, weeks, whatever it took, until finally, he burned through to its inner core and it yielded its precious secret. ‘I keep the subject constantly in mind before me and wait ’til the first dawnings open slowly, by little and little, into full and clear light,’ wrote Newton.¹⁵

Newton applied the laser beam of his intellect to Kepler’s second law. And eventually, inevitably, he saw what it was telling him about the force of gravity experienced by a planet. And the thing it was telling him has nothing to do with the strength of that force or the way in which that strength changes with distance from the Sun or any other detail like that. A planet sweeps out equal areas in equal times, Newton realised, on one condition and one condition only: that the force it is experiencing is always directed towards the Sun.¹⁶

Kepler’s third law of planetary motion is subtly different from the first two. Instead of describing the individual orbits of planets, it describes how the orbits of different planets relate to each other. It states that the further a planet is from the Sun, the slower it moves and so the longer it takes to complete an orbit. This is a clear indication that the force of gravity experienced by a planet is weaker the further the planet is from the Sun. But there is more in the law than this. Kepler was a mathematical genius. His third and last law actually says that the square of the orbital periods of the planets goes up in step with the cube of their distances from the Sun. So, for instance, a planet that is 4 (that is, 2²) times as far from the Sun as another takes 8 (that is, 2³) times as long to complete an orbit.

Kepler’s third law is even more esoteric than his