The Ascent of Gravity
Page 15
The LIGO physicists knew they had detected a burst of gravitational waves from space because the two detectors, separated by about 2,500 kilometres, picked up precisely the same signal, ruling out the possibility of a mundane local effect like someone slamming a car door 10 kilometres away. But the LIGO physicists were also sure they had detected gravitational waves from space because of the way in which the frequency of the waves rose to a peak then dropped off rapidly as the new-born black hole settled down. It matched precisely the prediction of Einstein’s general theory of relativity.
What is so extraordinary about this is that Einstein’s theory had previously been tested only in circumstances in which gravity is very weak such as the Solar System, never in the ultra-strong regime that exists in the vicinity of black holes. Yet general relativity passed this test with flying colours. The world’s media was quick to declare that Einstein had been proved right. The irony is that he had been proved both right and wrong. Right for predicting gravitational waves. But wrong for not believing in another prediction of his theory of gravity: black holes.
A black hole is surrounded by an imaginary membrane which marks the point of no-return for in-falling light or matter. Just as the sound of a bell ringing is a unique signature of the bell, the sound of this ‘event horizon’ ringing is the unique signature of a new-born black hole. Because it was heard on 14 September 2015, we now know for sure that black holes exist.19
Three men, more than any others, are responsible for LIGO. The first is Kip Thorne of the California Institute of Technology, the hippie-dressing theorist famous for his black hole wagers with Stephen Hawking, most of which he has won. The second is Rainer ‘Rai’ Weiss, an experimentalist at the Massachusetts Institute of Technology who graduated from building hi-fi sound systems in New York in the 1940s to building sound systems for listening to the cosmos. Weiss has walked every inch of the LIGO tunnels, personally evicting wasps, rats and other intruders. But the most complex and tragic member of the LIGO ‘troika’ is Scottish physicist Ronald Drever.
A short, dumpy man who carried his papers in supermarket carrier bags and whose overhead projector transparencies were covered with greasy fingerprints and tea stains, Drever was an experimental genius.20 While Thorne would get an answer to a technical question after pages of careful calculation, Drever would reach the same conclusion with a simple diagram. Unfortunately, the Scottish physicist was constitutionally incapable of sharing control of the project and, in 1997, was fired. He remained in Pasadena, close to Caltech, confused and saddened by events. An unworldly man who never married and had no real friends in the US, he finally succumbed to dementia. In Black Hole Blues, Levin relates the heartbreaking tale of Caltech faculty member Peter Goldreich taking the bewildered Drever to New York’s JFK airport and putting him on a plane back to his brother in Glasgow. Drever now lives in a care home in Scotland, which means the Nobel committee does not have much time to honour him.
LIGO is a technological marvel. At each site there are actually two tubes 1.2 metres in diameter, which form an L-shape down which a megawatt of laser light travels in a vacuum better than space. At each end the light bounces off 42-kilogram mirrors, suspended by glass fibres just twice the thickness of a human hair and so perfect they reflect 99.999 per cent of the light. It is the Lilliputian movement of these suspended mirrors that signals a passing gravitational wave. So sensitive is the machine that it was knocked off kilter by an earthquake in China. ‘It whirs with the tidal pull of the celestial bodies, the grumbling of a stillsettling earth, the remnants of heat in the elements, the quantum vibrations and the pressure of the laser,’ writes Levin.
A technological marvel LIGO may be, but not everyone thinks it is what it seems. Levin tells of a man on a flight into Baton Rouge, Louisiana, who informed the LIGO scientist in the seat beside him that the secret government facility below them was designed for time travel. ‘One of the arms brings you to the future,’ he said knowingly, ‘the other sends you to the past.’
With the success of LIGO in 2016, we stand at the dawn of a new era in astronomy. It is as if a deaf person has gained a sense of hearing but, at present, that sense is crude and rudimentary. At the very edge of audibility they have heard a distant rumble of thunder. But they are yet to hear birdsong or a piece of music or a baby crying. As LIGO and other gravitational wave experiments around the world ramp up their abilities, who knows what wonders they will soon hear?
Although the announcement of LIGO’s direct detection of gravitational waves on 11 February 2016 created huge excitement in the scientific world, compelling indirect evidence of the existence of gravitational waves already existed from the ‘binary pulsar’ known as PSR B1913+16. In this system, two supercompact ‘neutron stars’ are spiralling together and so losing orbital energy.
A neutron star is formed in the explosion of a massive star at the end of its life. Paradoxically, while the outer layers of such a star explode into space as a ‘supernova’, the core of the star implodes, forming a super-dense neutron star relic which typically has the mass of our sun compressed into a volume no bigger than that of Mount Everest. (See page 158 for further information about neutron stars.)
One of the neutron stars in PSR B1913+16 is a ‘pulsar’ which, as it spins rapidly, sweeps a lighthouse beam of radio waves across the sky. By carefully observing the system, the American astronomers Russell Hulse and Joseph Taylor found that the stars are losing orbital energy at exactly the rate expected if they are radiating gravitational waves. For their discovery, Hulse and Taylor won the 1993 Nobel Prize for Physics.
The mathematics of curved space
In order to turn his basic insight that matter warps space-time, and warped space-time is gravity, into a theory of gravity, Einstein had to wrestle with the complex mathematics of curved space. Unfortunately, he had skipped mathematics lectures while a student at the Swiss Federal Polytechnic in Zurich, preferring instead to get his hands dirty among the batteries and condensers and galvanometers of the Polytechnic’s Electrotechnical Laboratory. ‘It was a mistake I realised only later, with regret,’ said Einstein.21
Fortunately, Einstein had made a lifelong friend in Marcel Grossman, a mathematics student a year his senior at the Polytechnic. Grossman’s father had used his contacts to help secure Einstein his dream job at the Swiss Federal Patent Office in Bern. And Grossman, crucially, knew about the geometry of curved spaces. He was therefore able to teach Einstein the mathematics he needed in order to express in rigorous terms his revolutionary ideas about gravity and the warpage of space-time.
This field of mathematics had been developed by a number of mathematicians, most importantly Carl Friedrich Gauss and Bernhard Riemann in the nineteenth century. Until that time, geometry was the flat-paper geometry of the Greek mathematician Euclid (who inspired the best-ever title of a popular-science book, Here’s Looking at Euclid!).22 In his Elements, written in the third century BC, Euclid listed five self-evident statements about straight lines and angles. Using these ‘axioms’ as foundations, using logic alone he constructed a great edifice of ‘theorems’ such as ‘the internal angles of a triangle always add up to 180 degrees’.
Euclid’s fifth postulate states that parallel lines never meet. Gauss and Riemann relaxed this postulate, which immediately admitted geometries of curved surfaces such as spheres. On a sphere, for instance, two parallel lines which extend northward from the equator do not stay parallel but meet at the North Pole.
Einstein in Berlin
The struggle to describe gravity as warped space-time – or, more generally, to generalise relativity – would take Einstein eight long years. During that time, he moved from Zurich to Berlin.
Einstein had actually been born in Germany in the southern city of Ulm. But his dismay at the country’s militarism had caused him to renounce his German citizenship in 1896, aged twenty. Despite this, he accepted a university post in Berlin, a city he would call home from 1914 until Hitler’s seizure of power in 1933
made it impossible for Jews like him to remain without endangering their lives, and he emigrated to the United States.
Einstein was lured to Berlin by Max Planck and Walther Nernst. The two giants of German and world science had arrived at the train station in Zurich with an offer Einstein could not refuse: a lucrative professorship at the University of Berlin with no teaching responsibilities. Berlin was fast becoming the epicentre of the scientific world and the possibility of conversing on a daily basis with some of the best scientists on the planet proved a mouth-watering prospect to a man who had spent years in the intellectual wilderness of the Swiss Federal Patent Office. Berlin also offered the possibility of breaking free from the shackles of his by now broken and dysfunctional marriage.
Einstein’s ascent into the scientific stratosphere had been paralleled by Mileva’s descent into a world of childcare and household drudgery. If this was not enough to drive a wedge between husband and wife, Einstein proved himself fundamentally unsuited to marriage. He found it impossible to apply the degree of concentration needed to make profound scientific discoveries and simultaneously occupy his mind with anything else, be it the trivia of everyday life or a meaningful personal relationship.
Newton had solved this problem by never marrying and, as far as anyone knows, never having any close personal relationships. Einstein, though priding himself on his unconventionality, had succumbed to convention, and out of duty married Mileva, though some time after she had become pregnant and given birth to a baby that had been spirited away to Serbia and Mileva’s family. Grief for the loss of a child, whose existence was largely kept a secret from friends, must have put significant strain on the marriage. But the truth is that it had not been the happy and fulfilling union between equals that the two had imagined while naive students at the Swiss Federal Polytechnic.
Einstein travelled from Zurich to Berlin on a circuitous route that involved him visiting physicist friends around Europe. At last he arrived in the Prussian capital in April 1914 and his family soon joined him there. But, by early July, things had gone badly wrong between him and Mileva, and she returned to Zurich with the children. Though the Einsteins did not divorce until 1919, their marriage was effectively over.
In Berlin, Einstein rekindled an affair with his cousin Elsa, which had begun and ended a few years earlier. A divorcee with few prospects, Elsa cooked and cleaned for Einstein and was willing to accept what Mileva could not: that in exchange for the prestige of being with such a renowned man, she was otherwise to place no demands on him or his time.
Einstein treated Mileva abominably. Nevertheless, he was tearful as his wife and two sons boarded the train to return to Zurich. But back at his empty apartment in the suburb of Dahlem, he sat down at his desk and began to work. He had achieved what he most wanted in the world: a bachelor life free of domestic distraction and family responsibility. His friend Janos Plesch described it this way: ‘He sleeps until he is awakened; he stays awake until he is told to go to bed; he will go hungry until he is given something to eat; and then he eats until he is stopped.’
Einstein believed he was at last at peace. He was sadly mistaken.
Within weeks, Germany and its allies were at war with Russia, the British Empire and France. Einstein was in a state of shock. And his shock was magnified by the overnight transformation of his fellow physicists into a war-drunk mob. ‘Our whole, highly prized technological progress and civilisation can be likened to an axe in the hand of a pathological criminal,’ said Einstein.23
Most distressing of all was the behaviour of the chemist Fritz Haber, his closest friend in Berlin. Haber had tried to be a marriage guidance counsellor for Einstein and Mileva, and had accompanied Einstein and his departing family to the train station in Berlin. Now Haber turned his laboratory into a military factory and began concocting ever more horrible poison gases with which to dispense agony to the young men of Europe.24
In the midst of a catastrophic war, Einstein’s monumental detachment – which had wrecked his marriage — served him incredibly well. Locked away in his office in Haber’s institute, surrounded by chemists-turned-killers, he lost himself in the world of physics and, in particular, his theory of gravity.
Einstein delivered his first lectures on the new theory to the Prussian Academy in October 1914. It was not yet complete. But Einstein was confident enough not only to declare that the great Isaac Newton was wrong but that the geometry of warped space-time was crucial for understanding gravity. He might as well have been talking in Martian. Despite being a supernova in the firmament of physics, nobody in his audience took much notice of him. Einstein, being Einstein, was utterly unperturbed. He went back to his office, shut the door, and went back to work.
A year later, at the end of 1915, everything came to a head.
November 1915: Hilbert
Einstein had been invited to give a series of lectures at the University of Göttingen by the foremost German mathematician of his day. David Hilbert had achieved enduring fame in 1900 by highlighting what he considered to be the twenty-three outstanding problems in the field – setting out a road map for mathematical research in the twentieth century.
Ignored by his colleagues in Berlin, Einstein jumped at the chance of being listened to in Göttingen. He travelled to the university town and, at the end of June and the beginning of July 1915, delivered six lectures on his theory of gravity. He informed his audience that the transformation of gravity into geometry was largely correct — though it was still not 100 per cent right. In particular, his theory of gravity was incompatible with one of the key elements of his special theory of relativity of 1905: that observers in uniform motion relative to each other should see the same laws of physics. It also had the problem that it did not predict the correct orbit for Mercury.
Hilbert was sure Einstein was on the right track, so Einstein was in high spirits when he returned to Berlin. But, by late September, his joy had turned to horror.
Unusually for a mathematician, Hilbert was also deeply interested in physics. It was the reason he had invited Einstein to Göttingen in the first place. And it was his interest in physics that prompted him to try and fix the problems Einstein had highlighted in his lectures. Dropping what he was doing, he began looking for a theory of gravity that was compatible with the special theory of relativity. After eight years working entirely alone, Einstein had a competitor. And not any competitor but a man of exceptional mathematical ability.
Still worse, by the end of September, it dawned on Einstein that the incompatibility of his theory with special relativity and its inability to predict the orbit of Mercury were not mere details, as he had naively imagined. They were fundamental. In particular, observers rotating relative to each other would see different laws of physics, which was incorrect. His theory of gravity was in deep trouble.
Einstein, understandably, was depressed. And he could easily have succumbed to the pressure. But, his depression quickly turned to rage. There was no way in the world that he was going to let someone else take the credit for his eight long years of toil. Not without a fight.
By the first week of October, a miracle had occurred. Einstein saw how to proceed. ‘A good scientist is someone who works hard enough to make every possible mistake before coming to the right answer,’ said the American physicist Richard Feynman.25 Einstein was that scientist. He made every possible mistake in his long struggle to obtain his theory of gravity. But the mark of his genius was that every time he found himself hopelessly lost in the forest of the night, he somehow found a path out again.
Out of the woods and back on the right trail, Einstein worked in a frenzy for the next six weeks, often forgetting to eat or sleep. It was, he would later maintain, the most intense mental struggle of his life.
By the beginning of November, he was almost, but not quite, there. He still did not have the correct equation for describing the gravitational ‘field’. But he could not afford to delay going public a moment longer.
Einste
in had agreed months before to present his theory in a series of lectures at the Prussian Academy. At the time, he had thought his theory was in good shape. Now, of course, he knew that it was incomplete. Nevertheless, he had to go ahead. It was a race against time. He simply had to get to the finishing post before Hilbert.
Einstein was to a give one lecture a week for four weeks. He managed to get together enough material to give the first lecture. From then on, it was seat-of-the-pants stuff. During each succeeding week, he spent his time furiously trying to solve the problem that he had struggled with for eight years. At the end of each week, he stood before his audience at the Prussian Academy and lectured on what he had just figured out.
All the while, his rival was breathing down his neck. The letters from Hilbert showed that the great mathematician was more or less on the right track. They spurred Einstein to ever more frantic activity.
In his first lecture, delivered on 4 November, Einstein made no prediction. But now the theory was internally consistent and compatible with the special theory of relativity. As if to underline the fact, Einstein was able to show that Newton’s theory of gravity emerged as an approximation of his theory when the curvature of space-time is small.26 For the first time the theory had the smell of something that was right.
Two weeks later, on 18 November 1915, Einstein at last announced some predictions of his theory. He had calculated the gravitational field close to the Sun. This enabled him not only to calculate the light bending by the Sun but, most importantly, to predict the precession of the perihelion of Mercury.