Straight talking on curved space
There can’t be too many book chapters that come with a government health warning. This one does—but I’ll try to deliver it as gently as I can. If you suffer from arachnophobia, it might not be a bad idea to skip the first few paragraphs. In fact, don’t even peep.
Australia is famous for its spiders, of course—although in reality you don’t see that many more here than you do anywhere else. It’s just that, here, they tend to be a bit bigger, are often meaner-looking and are sometimes vaguely poisonous. Very occasionally, they are lethal. But in Australia, as elsewhere, you’re far more likely to die in a road accident than from a spider bite.
So, what prompted this excursion along the byways of Australian spider lore in a chapter supposedly exploring the byways of gravity? It comes from an event that occurred several years ago, when my decidedly arachnophobic twelve-year-old son awoke one summer morning to find a large and extremely handsome huntsman spider on the wall opposite his bed. These sleek-looking creatures have a smallish body sprouting what seem like dozens of long, hairy legs—which, on this one, measured a healthy 10 centimetres across their widest span. Huntsmen aren’t venomous, although they can give you a painful nip if, for example, they’ve taken up residence inside one of your gumboots and you innocently attempt a spot of double occupancy with your foot. They spend most of their working lives spread-eagled against whatever surface they happen to be on, and feed by simply grabbing passing insects. When disturbed, they can move with astonishing speed on those long legs, but they do tend to ignore anything that’s happening away from the surface on which they’re sitting.
Given James’ arachnophobia—and the fact that he was on the brink of his attitude years—I have to give him great credit for not leaping out of bed shouting ‘Oh my God, there’s a huge —ing spider in my room!’ at his usual waking time of 6 am. Instead, he waited until a more reasonable hour before calmly alerting his morning-challenged father. Assisted by James’ non-arachnophobic younger brother, Will, I then removed the spider by the time-honoured method of gently covering it with a large transparent kitchen bowl, sliding a sheet of thin card between it and the wall, and delivering it somewhere more distant than the bedroom—to wit, the farmer’s field over the garden fence.
But the spider looked far from happy about this. In fact, it appeared to be shaken rigid—and that is when it occurred to me that we had just committed a horrendous crime against the natural order of spiderhood. Huntsmen normally inhabit the purely two-dimensional world of a surface—a comfortable bedroom wall, for example—and we had just propelled this one into a three-dimensional nightmare of coarse grass in Fred Swanson’s back paddock. No wonder it was peeved. Suddenly having an extra dimension to deal with would be enough to give any huntsman spider a hefty dose of agoraphobia.
SPECIAL CIRCUMSTANCES
If it’s any consolation to the spider, something similar happened to humankind rather more than a century ago. For over 200 years, since the time of Isaac Newton, we had assumed that we occupied a universe of three dimensions, and then along came a fellow called Albert Einstein who said no, there’s actually another one. Einstein was not the first to suggest that time might somehow behave like a fourth dimension, but the idea is so deeply associated with his Special Theory of Relativity of 1905, that we tend to give him the credit. Special relativity is Einstein’s theory of motion, which extends the ideas from Newton’s Principia into a new realm—one in which objects are moving close to the speed of light. It was, in fact, Hermann Minkowski, a young professor at the University of Göttingen, in Germany, who finally gave us the full-blown four-dimensional Universe in elegant mathematical form, three years later. Far from being independent, said Minkowski, space and time were intertwined in a four-dimensional entity called ‘space-time’. Sadly, within months of this coup, Minkowski died from a burst appendix, at the age of only 44.
A key difference between Newton’s Universe and Einstein’s is that Newton thought of time as an absolute—something that was meted out at the same rate everywhere and against which everything else was measured. There were no awkward questions about simultaneity, for example; if two events happened at the same time anywhere in the Universe, they were simultaneous. But Einstein asked what would happen when simultaneous events were seen by two observers, one of whom was moving with respect to the other. He found that, because of the finite speed of light, the notion of simultaneity gets rather vague. Things that happen together for one observer are separated in time for another.
If that seems hard to visualise, try swapping the concept of time for that of space—because another feature of Einstein’s brave new world is that the four dimensions are subtly interchangeable. Let’s imagine you’re sitting on the upper deck of a Qantas super-jumbo en route from Sydney to London to join a Fred Watson study tour of spider habitats around historic European observatories. You’ve finished reading the latest issue of Australasian Arachnid Fanciers Monthly, and dinner is about to be served. Half an hour later, as you take your last sip of lukewarm coffee and digest your Qantas-issue Tim-Tam, you reflect on the fact that two events—the beginning and end of your meal—have occurred in exactly the same place, since you haven’t moved from your seat. But to an observer on the ground, those events are separated by nearly 500 kilometres.
The occurrence of events in space and time is therefore relative rather than absolute—hence the name of Einstein’s theory. And it’s ‘special’ because it refers to the special case of things moving with respect to one another at a constant speed, as in an airliner at its cruising altitude. It has to be said that the discovery that we live in a four-dimensional Universe was nowhere near as traumatic for us as it would be for a huntsman spider suddenly finding itself transferred from a two- to a three-dimensional world. Our extra dimension is not populated with swooping magpies looking for a quick meal. But space-time did take some getting used to—especially when people realised what it could lead to.
Einstein’s Special Theory of Relativity is based on two surprisingly simple postulates. The first is that the laws of physics are the same whether you’re moving or not. You can reflect on this, too, as you finish your airline meal. Unless there’s turbulence over Australia’s top end, your coffee stays in its cup, even though you’re moving at nearly 1000 kilometres per hour over the ground. The other postulate, while still simple, is a little harder to get your head around. It is that the speed of light in a vacuum is always the same, no matter how fast the source of the light is moving. This completely unexpected result was demonstrated in the 1880s in a famous piece of work called the Michelson-Morley experiment. Performed, not surprisingly, by physicists Albert Abraham Michelson and Edward Williams Morley, the experiment was successively refined by those gentlemen over the next 40 years, but with no change in the outcome. No matter how fast the light source is moving, the light it emits always travels through space at 299 792.458 kilometres per second (or 300 000 kilometres per second as near as makes no difference).
When Einstein wove his mathematical magic around these ideas, he arrived at some unusual results about time and space that take on real significance for objects moving at close to the speed of light. To a stationary observer, for example, an object whizzing by at high speed will appear slightly shortened along its direction of travel, a phenomenon called Lorentz-FitzGerald contraction (after—you’ve guessed it—physicists Hendrik Antoon Lorentz and George Francis FitzGerald). If you’re thinking of using this trick to impress your friends with a new slimline you, however, forget it—it only works if you’re travelling close to that 300 000 kilometres per second. And another, less welcome effect of special relativity will also kick in—your mass will increase as you approach the speed of light.
Perhaps more unexpected than the changes in geometry and mass is that time is also affected by your speed. To the stationary observer (who clearly has extraordinarily good eyesight), your watch will appear to slow down as you approach the speed of light. This phenomenon of time dilation immediately dispels the notion of a universal timescale. The fact is that all of us take our individual clocks with us, and the rate at which they tick depends on our state of motion. Of course, most of the human race is moving at roughly the same speed, certainly in comparison with the speed of light, so, for most practical purposes, we all experience time passing at the same rate. But today’s most accurate clocks can easily detect the tiny effect of time dilation in spacecraft, and even in aircraft.
Dramatic and unexpected though these consequences of special relativity were, they were eclipsed by its most significant prediction—certainly as far as everyday life was concerned. Almost as an afterthought in his work on the Special Theory, Einstein arrived at perhaps the most famous equation of all time, linking the mass of an object with its value in energy. You know the one I mean. It is this equation that allows us to understand the prodigious energy output of stars and to contemplate the generation of atomic energy—as well as predicting the devastating power of nuclear weapons. These energetic processes involve reactions between the nuclei of atoms, and result in matter being converted directly into energy. But Einstein’s equation takes the quantity of mass and multiplies it by the square of the speed of light—a truly enormous number—to get the equivalent energy. Hence their prodigious output.
In 1905, those particular discoveries were in the future. In fact, for Einstein, almost everything was in the future. Having had a rather undistinguished academic career, he was, at the age of 26, working as a patent clerk in the Swiss capital of Bern. He had acquired the job, in 1902, on the recommendation of a friend’s father, having relinquished his German nationality for Swiss citizenship the previous year. And his job had just been upgraded from a temporary to a permanent position—a boost for a young family man seeking financial security. What was more unusual about this technical expert (third-class) was that in his spare time he tinkered around with theoretical physics. And he was simply brilliant at it.
Today, the city of Bern relishes its connection with this highly productive period of Einstein’s life. Crowds flock to see his house at 49 Kramgasse—or perhaps it’s to visit the coffee shop in the arcade below, though they can’t fail to notice the life-sized portrait of the great man in one of the first-floor windows. But if you have any interest whatever in the life and work of this most remarkable scientist, you can do no better than visit the superb Einstein Museum, located in Bern’s Historical Museum, just across the Aare River from the minster. There, you can experience every detail of Einstein’s life—his strong Jewish roots, his education and early work, his famously philandering love life, his pacifism, and the progress of his career until his death, in 1955, at the age of 76. The exhibition is stunningly presented and includes hallowed artefacts of Einstein’s life and work, many of which are moving in their intimacy.
It’s not without reason that we tend to refer to 1905 as Einstein’s annus mirabilis—his miraculous year. In fact, special relativity was just one aspect of what amounted to a single-handed revolution in physics. Here’s the timeline:
On 17 March, Einstein submits a research paper on the photoelectric effect and the quantum nature of light, suggesting that light comes in the bullets of energy we now call photons (he won the 1921 Nobel Prize for this work). On 30 April, he completes a paper on the size of molecules (for which he receives his PhD from the University of Zürich). On 11 May, he submits a paper on the motion of small particles suspended in a liquid, leading eventually to the proof that atoms exist. On 30 June, he submits the paper on his new theory of motion, the Special Theory of Relativity. And on 27 September, he submits a short supplementary note on some consequences of special relativity—including that equation.
Given such a breathtaking performance, there is little wonder that the world celebrated the centenary of Einstein’s annus mirabilis with an International Year of Physics. A worldwide program of events in both science and the arts included conferences, lectures, displays, exhibitions, concerts and plays. It was also the year in which the exhibition now in the Bern Einstein Museum was launched. As a result, 2005 was an outstandingly successful Einstein Year. Its one downside was that many people involved with the celebrations felt completely Einsteined-out by the end of it. And that is a pity, because, in reality, Einstein’s annus mirabilis was just the start.
GRAVITY—OR ITS EQUIVALENT
By 1907, Einstein had a couple more publications under his belt and was beginning to win some recognition in scientific circles, although his application for a post at the University of Bern that year was turned down. He was still at the Patent Office. But it was while he was sitting there at his desk, no doubt musing about life, the Universe and everything, that Einstein had what he later described as ‘der glücklichste Gedanke meines Lebens’ (the happiest thought of my life). Given that this man had some quite spectacular thoughts from time to time, his happiest one would have to be something pretty good.
Einstein had been thinking about how special relativity might modify Isaac Newton’s famous theory of gravitation, which we met back in Chapter 5. Arguably the greatest intellectual feat of all time, Newton’s theory had proved amazingly successful in explaining the motions of objects in the Solar System down to the finest detail. It had been instrumental in French astronomer Urbain Le Verrier’s prediction of the existence of a planet beyond Uranus based on observed irregularities in Uranus’ orbit—calculations that had led to the triumphant discovery of Neptune, in 1846. Newtonian gravity still works satisfactorily today in most of the questions associated with orbital motion and the navigation of spacecraft between planets. One day, it could even save the world from a threatening asteroid, if the offending object could be given a slight sideways tug by the gravitational attraction of a massive (20 tonnes or so) spacecraft.
By the end of the nineteenth century, Newton’s gravity seemed able to explain everything, except one small issue. Back in 1859, the doughty Le Verrier had noticed a minute error in the predicted behaviour of Mercury’s orbit. A tiny fraction of the steady sideways drift of the orbit could not be accounted for by Newtonian mechanics. This highly esoteric problem was enough to send poor Le Verrier off on an entirely understandable tangent, looking for an imaginary planet called Vulcan between the orbit of Mercury and the Sun. He didn’t find it—mainly because it doesn’t exist. Apart from that one minuscule aspect of Mercury’s orbit, however, the Solar System was completely understandable in terms of Newton’s theory of gravitation. But Einstein wondered how relativity might affect it, given that Newtonian gravity took no account of time—and he now knew that time and space were intimately linked.
Perhaps because he was bored to death at the Patent Office, Einstein then imagined himself falling from the roof of a tall building and realised that in this rather inconvenient circumstance he would feel no gravitational force. He would certainly feel something when he hit the ground, but that didn’t matter in his thought experiment. Einstein reasoned that he would be in a state of free fall, and if his pipe fell out of his mouth or coins fell out of his pocket they would appear to float around him as if there were no gravity.
We inhabitants of the 21st century are, of course, used to seeing TV images of orbiting astronauts surrounded by the weightless detritus of their trade—floating pens, cameras, food capsules, scientific instruments, sick bags and so on. They, too, are in a state of free fall, but they never hit the ground because the forward motion of their spacecraft matches the rate at which the ground falls away beneath them—another possibility that had been spotted by good old Newton back in 1687. Incidentally, you can exactly replicate this weightlessness yourself, not by jumping off a tall building—unless you’ve truly had enough—but by jumping onto a trampoline. During the one second or so of each jump that your feet aren’t touching the mat, you’re as weightless as an astronaut, and you can prove it by watching coins or keys float from your open hands as you jump. It’s a lot cheaper than going into space.
Commonplace though weightlessness is to us, it was an entirely novel idea for Einstein, and it quickly led him to the next step in his thinking: the realisation that the effects of a gravitational force and an applied acceleration are identical. In the case of your imaginary high jump from the top of a building, the downward acceleration you experience exactly negates the downward pull of gravity, so you become weightless. Looking at it another way, if you were sitting in a windowless compartment on a rocket deep in space and someone lit the fuse, you would not be able to tell whether the force you felt was due to the acceleration of the rocket or to gravity. Therefore—locally, at least—they must be the same thing.
This happiest thought of Einstein’s life was a major breakthrough and is now called the Principle of Equivalence. In fact, it wasn’t until 1912 that Einstein set out a formal statement of the principle, putting it in terms of the equivalence of the gravitational mass of an object (the way it responds to the pull of gravity) and its inertial mass (the way it responds to a force like the thrust of a rocket).
Einstein then began looking for the mathematical tools he needed to develop a new theory of gravity based upon the idea that it was equivalent to acceleration. In particular, he imagined a reference frame (a system of coordinates like the x, y and z we met in Chapter 7) being accelerated, with the observer inside it—thereby placing the observer within an accelerated reference frame. If you’re not sure whether you know what an accelerated reference frame feels like, imagine yourself back in the Qantas super-jumbo. When it makes its take-off run with those four giant turbofans at full power, you, and everyone else on board, are in an accelerated reference frame. It’s unmistakeable, and quite distinct from the constant-velocity reference frame you’ll experience when drinking your coffee at cruising speed.
It is fairly well known that Einstein’s deep insights into physics were not entirely matched by his abilities in mathematics. He was highly competent, of course, but relied on others to channel his thoughts in appropriate directions. Fortunately, his Special Theory of Relativity had brought his name to the attention of many leaders in the field, so he had a wide circle of friends and colleagues upon whose sharp minds he could call. One of those was a remarkable mathematician and astronomer by the name of Erwin Freundlich, a man whose role in the story of relativity is often underrated. Like Einstein, Freundlich was German born, but, unlike Einstein, he’d already had a spectacular academic career, culminating in receiving a doctorate from the University of Göttingen in 1910 when he was 25. He then worked at the Royal Observatory in Berlin, and it was there that he began collaborating with the great man. To start with, he obtained some accurate observations of Mercury to try to establish whether Einstein’s new ideas had any bearing on the problem of its orbit. But then he unwittingly made an even bigger contribution.
Einstein’s thinking on the equivalence principle and its relevance to gravity had led him to the view that much of it boiled down to a problem of geometry—because the laws of relativity that applied in ordinary, or Euclidean, space didn’t work in an accelerated reference frame. He needed a new kind of geometry in which the shape of space itself was modified by forces—called ‘fields’—acting through it. Musing aloud on this to Freundlich one day, Einstein was astonished to be told that such a complex model of space had been known to mathematicians for over half a century. It had been developed in the 1850s by another gifted German mathematician, called Georg Friedrich Bernhard Riemann, and was known as Riemannian geometry. But it involved some very difficult mathematics. According to Walter Ledermann, a later colleague of Freundlich’s, Einstein was so amazed by this news that he accused Freundlich of lying. But it was soon proved to be true. Poor old Einstein then had no alternative but to grasp the painful nettle of Riemannian geometry and begin slogging his way through the algebra.
RELATIVITY COMES OF AGE
What followed was the General Theory of Relativity, so called because it wasn’t limited to the special case of objects moving at a constant velocity. It amounted to a startling new theory of gravity that made the wildly improbable assertion that space-time itself can bend, warped by the presence of matter—which, in turn, responds to the distorted geometry of space-time by moving within it. In practical terms, what that means to you and me is that the downward pull we feel at the surface of the Earth is not, in fact, due to a force existing between the Earth and ourselves, as Newton had proposed. Rather, the shape of the space around us changes very slightly between our feet and our head due to the presence of the Earth. We feel that change in shape as gravity. Gravity is therefore a property of the Universe itself rather than a property of objects within the Universe.
That bland description gives little hint of the complex mathematics needed to describe the theory. Riemannian geometry requires a tool called ‘tensor calculus’, which, to mathematically challenged individuals like me, spells the utmost in doom and gloom. However, the final step in the argument was rather nicely put into words by the late British astronomer and mathematician Sir Fred Hoyle in a popular article in the 1980s:
Einstein’s remarkable idea was to regard the difference between Riemannian spacetime and [Hermann] Minkowski’s spacetime as the true meaning of the phenomenon of gravitation. To this end he modified Newton’s equations of motion so as to form a comprehensive scheme for calculating not just the motions of particles in a prescribed spacetime like that of Minkowski, but a determination of what the more complex Riemannian spacetime had to be.
Not surprisingly, by the time Einstein submitted his work for publication, on 25 November 1915, his mathematical endeavours had taken him through several versions of the theory. Most of these he had published, which meant that other scientists were fully aware of what he was up to and where his thinking might lead. In particular, another able German mathematician—a man seventeen years Einstein’s senior—was working hard on the same theory. This was David Hilbert, who, some have claimed, was robbed of glory by Einstein, because he had actually submitted the correct version of the general relativity equations for publication five days before Einstein did. It seems more likely, though, that Hilbert and Einstein were bouncing ideas off each other, since they were writing cordially to one another throughout that heady November.
A week before submitting his work, Einstein had a tremendous confidence boost. He realised that the final version of his theory exactly accounted for the observed anomaly in Mercury’s orbit, for so long a thorn in the side of astronomy. ‘For a few days, I was beside myself with joyous excitement,’ he wrote later. And who could blame him?
By the time Einstein completed his General Theory of Relativity, he was once again living in Germany and working at the University of Berlin. He was now close to Freundlich, with whom he had long discussions on how to test the theory. This idea of space-time being warped by solid objects was so outlandish that it risked being laughed out of court by most of the astronomers of the day. Newton’s ideas had stood up extremely well for two centuries and had almost acquired the air of religious dogma. To challenge them was dangerous. Not to life and limb, of course—persecution had come a long way since the seventeenth century—but to one’s career. What was needed was a critical test of the theory, and Freundlich was Einstein’s right-hand man in planning it. One of the predictions of general relativity is that a massive object such as the Sun will distort space enough to bend rays of light passing close to it, rather in the fashion of a glass lens. So, if the Sun were a dark object rather than a bright one, you would be able to see the apparent positions of stars close to the edge of the Sun being deflected very slightly away from it as the Sun slowly moved through the sky in front of them. In practice, there’s only one way to make the Sun dark, and that is to hide its light by having the Moon pass in front of it. Since that is exactly what happens in a total eclipse of the Sun, the supporters of Einstein’s general relativity suddenly became avid eclipse-chasers. For them, astronomy tourism took on a quite different meaning from the leisurely study tours featured in this book.
And the ever-faithful Freundlich was first off the mark. While the General Theory was still in an incomplete form, he secured funding to mount an expedition to Feodosiya, in the Crimea, to observe a total eclipse late in 1914, with the aim of testing the theory. But his timing was awful. Before the eclipse occurred, hostilities were declared, and the First World War lumbered forth on its dreadful course. The eclipse expedition was abandoned, but it was too late. As the holder of a German passport, Freundlich was interned in the Crimea as an enemy alien.
PEACEMAKER
Meanwhile, on the other side of the world, the British Association for the Advancement of Science had been holding the various sessions of its annual meeting across five cities in Australia. With nothing remotely like today’s wide-bodied jets to ferry the participants around, this was a remarkably ambitious step for a scientific organisation. The meeting had gone well but had been marred by the declaration of war, received while the sessions were in progress. Not surprisingly, this had led to the early embarkation of many of the participants on steamers back to the Mother Country. Before they left, however, they had earnestly resolved to maintain business as usual, asserting that ‘science is above all politics’.
Within weeks, though, that assertion counted for nothing. Researchers on both sides of the Anglo– German divide had followed the general public’s slide into unashamed jingoism. When no fewer than 93 prominent German scientists signed a Manifesto to the Civilised World defending Germany’s ‘struggle for existence’, their British counterparts hurled accusations of complicity in barbaric atrocities and set about excluding the Germans from all normal channels of scientific communication.
Nowhere was this unseemly crusade mounted more intensively than in the world of astronomy, where impassioned voices on both sides of the conflict asked whether there could ever again be normal relations between the two communities. The professional astronomy journals of the time, still available today in the libraries of many long-established observatories and university astronomy departments, reported on British astronomy meetings at which strident accusations of war crimes were made against German scientists. Prominent among the accusers was Herbert Hall Turner, uncompromising anti-German professor of astronomy at Oxford University, who we met in a very different light in Chapter 2.
As the war dragged on, attitudes became ever more hardened, and long-established academic ties were discarded like spent shell cases. At the Armistice of 11 November 1918, it seemed as if decades must pass before scientific relations could be normalised. Yet within a year the British press was proclaiming a German-born scientist as the champion of the age—someone, moreover, who had overthrown the hallowed ideas of the local hero Sir Isaac Newton. Soon afterwards, scientific cooperation between the two former enemies began to be re-established.
The German-born scientist was, of course, Albert Einstein. When his General Theory of Relativity had been published, in the dark days of 1916, the shut-down in international communication meant that it was accessible only to German scientists. However, one reader in neutral Holland was convinced that British scientists, too, needed to know about it. This man was an astronomer, Willem de Sitter, who still had scientific contacts in the United Kingdom. In the event, though he was uncertain who might read it, de Sitter sent his own interpretation of general relativity to the United Kingdom. It found its way to perhaps the only British scientist who was both capable of grasping its significance and open-minded enough to read work that had originated in wartime Germany. This was Arthur Stanley Eddington, director of the Cambridge Observatories and an astrophysicist of outstanding ability. More importantly, he was, like his German-born counterpart, an ardent pacifist. In fact, that pacifism came from Eddington’s strong Quaker beliefs, which were, for him, as much a framework for life as Einstein’s Jewish background.
Throughout the latter half of the war, Eddington studied the new theory in great detail and recognised the genius behind it. Like Freundlich, he became a champion of relativity, seeking ways in which the theory could be proved by observation. There is a delightful story of Eddington being congratulated by a colleague for being one of only three people in the world who understood relativity. When Eddington paused, and his colleague commented that there was really no need to be so modest about it, the Cambridge astronomer replied that, no, he was just trying to think who the third person might be.
As is well known, Eddington was instrumental in setting up the eclipse expeditions that became the litmus test of general relativity. On 25 May 1919, a solar eclipse in fortuitous circumstances was predicted. It would take place against the backdrop of the Hyades star cluster—a part of the sky rich in bright stars that were perfect for the measurement of their light’s deflection by the eclipsed Sun. The path of the eclipse was in the southern hemisphere, but two British expeditions were organised to well-separated sites on the path, one on the island of Príncipe, off the west African coast, and the other in Sobral, in Brazil. Eddington led the team in Príncipe.
Einstein’s prediction was that light from the stars near the edge of the Sun’s disc would be displaced by the tiny angle of 1.75 arcseconds. An arcsecond is one 3600th of a degree, but I always find it more instructive to imagine someone holding up a $1 coin at a distance of 5 kilometres. The coin, from the observer’s point of view, is 1 arcsecond in diameter—and completely invisible to the observer’s unaided eye (as is the person holding it). The unlikely sounding feat of measuring 1.75 of those minuscule angles was already standard practice in the photographic astronomy of the day, so promising results were obtained from both eclipse sites. There was then a lengthy process of measurement and calculation, which took place back in the United Kingdom.
At a combined meeting of the Royal Astronomical Society and the Royal Society in London on 6 November 1919, Eddington finally announced the results. Yes, the prediction of a 1.75-arcsecond displacement was correct, and Einstein was nothing short of a genius. Eddington took pains to ensure that this triumph of international collaboration was properly reported in the world’s media. He need not have worried. The Times of 7 November 1919 blared: ‘Revolution in Science—New Theory of the Universe—Newtonian Ideas Overthrown.’ None of which was any exaggeration.
The revolutionary new theory of gravity, in which space and time are warped by the presence of matter, had been proved at a solar eclipse observed in far-off lands. Moreover, a comparatively unknown Englishman, motivated by a deep-seated belief in peaceful international collaboration, had provided the dramatic confirmation of the German-born Einstein’s theory. As a result, Einstein himself immediately shot to world fame, but the consequences went much deeper. It can reasonably be argued that, between them, Einstein and Eddington forged the peace that quickly took hold in the scientific world. The developing entente helped to put relativity in the public spotlight, where it remains firmly to this day as the most important theoretical foundation of our understanding of the Universe.
Despite the starring roles of Einstein and Eddington, there were two other important players in this drama. The first was a brilliant young mathematician by the name of Karl Schwarzschild. Within weeks of the publication of Einstein’s final paper on general relativity, Schwarzschild had solved the equations that represented the gravitational effect of a massive compact spherical object. At the time, this was purely of theoretical value, but when astronomers began taking an interest in such things, in the 1960s, Schwarzschild’s mathematical solutions assumed vital importance. Today, we call these objects black holes. Sadly, no triumphant accolades awaited Schwarzschild; he died as a result of illness contracted on the Eastern Front, in 1916.
And what of our old friend Erwin Freundlich? Fortunately, his internment in 1914 was short lived, and he was soon able to return to Berlin. There, he continued his work on observational methods for demonstrating the validity of relativity, working closely with Einstein. In their spare time, the two played music together, Einstein on violin and Freundlich on cello. Freundlich seems to have shown no resentment whatever when the British eclipse expeditions provided the first proof of general relativity, and he went on to mount several more eclipse expeditions of his own, to improve the accuracy of the determinations. He accompanied Einstein on a visit to the United Kingdom in the early 1920s and was feted alongside the great man.
In 1921, Freundlich was appointed to the newly created Einstein Institute at the Astrophysical Observatory in Potsdam. There, he was able to explore one of the other predictions of general relativity, that to an outside observer clocks in a gravitational field appear to run more slowly. This is nothing to do with faulty clocks; time itself is slowed because of the effect of gravity. It is called ‘gravitational time dilation’, and if it sounds familiar, well spotted—it’s analogous to the speed-related time dilation mentioned a few pages ago. Today’s super-accurate atomic clocks are able to detect the difference in time caused by the change in the Earth’s gravity between the top and bottom floors of a skyscraper. But in Freundlich’s day, that was far in the future. The only possible way of investigating it was via a phenomenon called ‘gravitational redshift’, in which the barcode information in the light leaving a massive object is shifted slightly towards the red end of the spectrum. This is a direct consequence of gravitational time dilation, and if you could explore the spectrum of the Sun in fine enough detail, you would have a chance of measuring it.
Thus, Freundlich was instrumental in creating the Einstein Tower—the Expressionist tower telescope in Potsdam that we visited at the beginning of this book. The idea was that a system of mirrors at the top of the tower would guide a magnified image of the Sun to the bottom, where its light could be dispersed into a detailed spectrum. Unfortunately, this monument to relativity never did what it was built to do—the detection of gravitational redshift is an extremely difficult observation and was not finally achieved until 1976.
The Einstein Tower caused a stir of a quite different kind when it was visited by members of the Stargazer II tour in 2010. When the group was told by our guide, Matthias Steinmetz, that Einstein himself had been a regular participant in discussions around the conference table on the tower’s ground floor, tour members wanted to know in which chair the great man had sat. Smiling, Steinmetz told us it could have been any of them—whereupon two-dozen erudite tour participants became a bunch of school kids, taking it in turns to sit in all the chairs, just to make sure. And, yes, your humble author was one of them.
A RELATIVELY SAFE HAVEN
The dramatic political changes that forced Albert Einstein to forsake Germany for the United States, in 1933, also affected Erwin Freundlich. Though not a practising Jew himself, he and his wife were of Jewish descent, and so they, too, left when the Nazis came to power. Moving first to Istanbul and then to Prague, Freundlich continued his work in astronomy. But with Hitler’s advance on Czechoslovakia, the Freundlichs were forced to move again, finally coming to rest in 1939, in the relative safety of Scotland, at the University of St Andrews.
Famous today as the alma mater of the Duke and Duchess of Cambridge—alias Wills and Kate—St Andrews is the oldest university in Scotland and among the oldest in Europe, having received its papal bull of foundation in 1412. It has a long tradition of mathematical astronomy going back to James Gregory, in the 1670s, as we saw in Chapter 5. But in 1939, when Freundlich arrived, there was no astronomy department. Arthur Eddington recommended to the university authorities that such a department was needed—and that Erwin Freundlich was exactly the right person to create it. Thus, Freundlich embarked on a phase of his career in which he was exceedingly happy. Just like William Herschel, 182 years before, he was quick to integrate into the culture of his adopted country and took on a new name to prove it. Since his mother’s maiden name had been Ellen Elizabeth Finlayson—and there are few names more Scottish than that—he duly became Erwin Finlay Freundlich and was known by that name for the twenty years he lived in Scotland.
Having successfully founded the astronomy department, Finlay Freundlich went on to build a new observatory in open land surrounded by the university’s playing fields, equipping it with the most modern observing facilities. Indeed, his plans in that regard were hardly modest, including a proposal to build the most powerful optical telescope in the United Kingdom. A half-scale model was built first, a 38-centimetre-aperture instrument named the Scott Lang Telescope, after a benefactor to the university. In fact, the full-scale version, the 76-centimetre James Gregory Telescope, was not completed until after Finlay Freundlich left St Andrews in retirement, in 1959. For some years, however, it was indeed the most powerful telescope in the United Kingdom.
Perhaps even more important than equipping the fledgling observatory was Finlay Freundlich’s vision of attracting capable astronomers to its staff. This was considerably enhanced when he was appointed to the newly founded position of Napier professor of astronomy, in 1951. But among his earlier recruits was a young Polish refugee by the name of Tadeusz Boleslaw Slebarski, one of Finlay Freundlich’s protégés in mathematical astronomy, although not himself a specialist in relativity. Like Finlay Freundlich, Slebarski was a well-respected man, gentle in manner and generous in spirit. He was known throughout the university simply as Mr Slebarski, and his lectures were models of clarity because, having a less-than-perfect command of English, he wrote absolutely everything on the blackboard. Someone once unkindly remarked that he had forgotten all his Polish and had never learned anything to replace it—but that vastly underrates his capacity as a teacher of science.
Slebarski has a special place in my own history, because a quarter of a century after his appointment—and a decade after Finlay Freundlich had retired to Wiesbaden—he became my research supervisor when I embarked on a masters degree at St Andrews. We worked not on relativity but on asteroid orbits, and I used the Scott Lang Telescope to make my observations. With his customary good nature, Slebarski tolerated the fact that I was far from a model student. I still remember his delight when, years later, I finally submitted my thesis and graduated with the degree.
Neither Finlay Freundlich nor Slebarski is alive today, but their memories live on. For me, they form a direct academic link with Einstein—something of which I would be very proud if I felt I had any right to be. However, I have to come clean and admit that it’s only in recent years that I’ve properly understood relativity. In my student days, I’m afraid I simply didn’t get it.
THE HUNT FOR NEW PHYSICS
Almost a century after its formulation, general relativity is still the best theory of gravity we have. It has survived all the tests that have been thrown at it and has successfully predicted the existence of black holes, the expanding Universe, gravitational lenses, gravitational waves and many other phenomena dear to the hearts of astronomers. It underpins cosmology—the science of the history and evolution of the Universe as a whole. Many non-scientists are familiar with the idea that space-time is curved, and Einstein is regarded as the greatest genius of the twentieth century—not to mention a few other centuries besides.
The one thing that general relativity can’t cope with is gravity on the smallest scale, since the theory is based on space-time as a continuous medium rather than a succession of distinct steps, or quanta—and we know that this is how the submicroscopic world works. The search for a theory of quantum gravity akin to our understanding of the other fundamental forces of nature on submicroscopic scales is well underway. These forces include electromagnetism and two nuclear forces, and we will meet them again in Chapter 10. As yet, however, there is no clear leader among the many candidates for quantum gravity. In any case, these theories all rely on new physics—exotic underlying realities that are not predicted by relativity, in which physical processes as yet unknown are at work.
In fact, relativity itself offers a means of testing for the possibility of new physics. I mentioned a few pages back that the heart of the equivalence principle—and the heart of general relativity itself—is that the gravitational mass and the inertial mass of an object are the same thing. One of the consequences of the equivalence principle is that objects will fall under gravity with the same acceleration, no matter what their internal structure and composition. This harks back to Galileo’s famous experiment at the Leaning Tower of Pisa, in the 1590s, and most of us have been familiar with the acceleration due to gravity at the Earth’s surface (9.8 metres per second per second) since our schooldays. Sometimes from first-hand experience. But the bottom line is that some of the more exotic theories of gravitation—such as those attempting to unify the fundamental forces of nature—would, if correct, lead to a violation of the equivalence principle. Prominent among these unified theories is string theory, which postulates that forces and particles are manifestations of vibrating strings of energy. Hunting for subtle violations is therefore a great way to discover whether new physics is, in fact, at work.
How can one do this? The laboratory method involves comparing the responses of two differing test bodies to the same gravitational pull. Lumps of copper and aluminium sitting in the Earth’s gravitational field, for example. The technique owes its origin to a gifted Hungarian nobleman, Loránd Eötvös, who performed such experiments with a sophisticated torsion (swinging) balance in the 1890s and early 1900s. His work demonstrated no difference in the acceleration experienced by differing test masses to within one part in 100 million, and it was this result that led to Einstein’s adoption of the equivalence principle. The rather striking Hungarian name Eötvös, by the way, is pronounced a bit like ‘oat-fosh’, which explains the whimsical name of the research collaboration that has taken this work forward into the 21st century. Its members are at the University of Washington, in Seattle, and are called the Eöt-Wash group. Boom boom.
Using extraordinarily sensitive balances, Eöt-Wash scientists have confirmed the equivalence principle to better than one part in a trillion using the gravitational attraction not just of the Earth but also of the Sun and our own Galaxy. In the late 1980s, they famously put paid to a flurry of excitement over the possible existence of a so-called ‘fifth fundamental force’, in addition to the four already known to science. Their experiments (and eventually those of other groups, too) showed no evidence of violation—and hence no fifth force. But even the spectacular accuracy achieved by Eöt-Wash is now being surpassed by more refined experiments, using light bounced off reflectors left on the Moon by Apollo astronauts, for example, and test masses in Earth orbit. The most ambitious are expected to provide answers with a head-spinning accuracy of one part in a billion billion.
Such fastidious explorations of the validity of general relativity via the robustness of the equivalence principle are comparable with the gigantic experiments that are now under way at facilities like the Large Hadron Collider, the famous European particle accelerator that straddles the French–Swiss border near Geneva. They, too, are looking for anomalies in our current model of the Universe. It has to be said that the Collider is the poster child in the search for unknown phenomena. But wouldn’t it be astonishing if a whole era of new physics came from nothing more than the detection of a minuscule deviation from the equivalence principle, measured, perhaps, with an ultra-sensitive balance?
Just to put that into perspective, the probability of finding a deviation so impossibly small is about the same as discovering a solitary huntsman spider in a farmer’s field. A farmer’s field the size of Asia, that is.