The Ascent of Gravity

by Marcus Chown

  ‘Aside from Velcro, time is the most mysterious substance in the Universe,’ says American humorist Dave Berry. ‘You can’t see it or touch it, yet a plumber can charge you upwards of seventy-five dollars per hour for it, without necessarily fixing anything.’

  No absolute space, no absolute time

  The realisation that moving clocks slow – an effect known as ‘time dilation’ – and moving rulers shrink – known as ‘Lorentz-FitzGerald contraction’ – represents a seismic shift in our picture of reality.22 It explains perhaps why all the great physicists of Einstein’s time, despite being in possession of exactly the same facts, did not go where Einstein went. But then nobody except Einstein had the sheer bare-faced nerve to doubt Newton.

  Newton, largely for pragmatic reasons, believed in ‘absolute space’, which existed as a backdrop to the Universe, like a great canvas on which the great cosmic drama was played out. Everyone would measure the same separation of two points in such space just as everyone would measure the same distance between two pins stuck in an artist’s canvas.

  But Einstein showed there is no such thing as absolute space.

  Newton, in addition to absolute space, also believed in ‘absolute time’, which ticked away as if somewhere in the Universe there is a great master clock. Because of the existence of absolute time, everyone would agree on the same interval of time passing between any two events.

  But Einstein showed that, just as there is no such thing as absolute space, neither is there is any such thing as absolute time. ‘I can’t talk to you in terms of time,’ said the novelist Graham Greene, ‘your time and my time are different.’

  Exactly right. One person’s interval of time is not the same as another person’s interval of time, and one person’s interval of space is not the same as another person’s interval of space. Time and space are like shifting sand. The rock on which the Universe is built is the speed of light.

  If all this seems a little imprecise, that is because it is. Einstein started his journey of discovery, aged sixteen, simply by imagining what it would be like to catch up with a light beam. This had revealed to him the shortcomings of the Newtonian view of motion and also hinted at what was needed to supplant it. But Einstein needed to construct a self-consistent theory, one founded on a minimum of assumptions, from which all the consequences for space and time would follow as inevitably as night follows day. How to do this was worked on by Einstein in the weeks following his pivotal meeting with Besso in May 1905.

  The two foundation stones of relativity

  Einstein built what would become known as the ‘special theory of relativity’ on two foundation stones.23 The first is the assertion that the speed of light is independent of the speed of its source or the speed of an observer. And the second is the ‘principle of relativity’.

  Galileo, back in the seventeenth century, had realised that there was something odd about motion at constant speed in a straight line. It does not change anything. Say you throw a ball to a friend. It does not matter whether you are standing twenty paces away from them in a field or twenty paces away on the deck of a ship (providing the ship is moving smoothly and uniformly through the waves). In both cases, the ball loops through the air in precisely the same way.

  From this common observation, Galileo concluded that the laws of motion are the same for all people who are moving at constant speed relative to each other. In other words, if you were to be beamed by a Star Trek matter transporter to a blacked-out cabin on-board a ship, you would not be able to tell from the flight of a ball through the air whether you were on-board a ship ploughing through the waves or stationary on dry land. In technical language, the laws of motion – distilled down to three basic edicts by Newton after Galileo’s death – are ‘invariant’ with respect to motion at constant speed in a straight line. They will not reveal to you whether you are in such ‘uniform motion’. And that is because the very idea of absolute motion — that is, motion with respect to absolute space à la Isaac Newton – is utterly meaningless.

  Einstein extended ‘Galilean relativity’. According to his principle of relativity, it is not just the laws of motion that are invariant with respect to uniform motion but all the laws of physics. In other words, there is no experiment you can do, including those involving the propagation of light, which can reveal whether you are moving or not.

  As already mentioned, the aether was the hypothetical medium through which light rippled and against which it was possible to measure motion. Einstein’s principle of relativity dispenses with the aether entirely.24 The aether is revealed for what it is. A fantasy. An unfortunate cul-de-sac into which physicists had mistakenly wandered. No more than the nineteenth-century incarnation of Newton’s ‘absolute space’. Light needs no medium in which to propagate. It is a self-sustaining wave in the electromagnetic field.

  With no fixed backdrop of absolute space with which to measure absolute velocity, the only meaningful concept is ‘relative velocity’. When you see a person flying past you and their space shrinking and their time slowing compared to your own, you may wonder what you look like to them. The answer is exactly the same as they look to you. To them, you shrink in the direction of your motion and appear to be moving as if through treacle. There is complete symmetry because only relative motion matters. You are moving relative to them and they are also moving relative to you at the same speed (though in the opposite direction, of course). As the joke goes: ‘When does Zurich stop at this train?’ – Albert Einstein.

  In summary, Einstein needed only two principles to build his revolutionary theory of space and time: the principle of relativity and the principle of the constancy of the speed of light.25 And armed with these deceptively simple ideas, he was able to deduce absolutely everything else.

  A fundamental basis for relativity

  Einstein began by trying to define time pragmatically. ‘Time’, he said with child’s simplicity and directness, ‘is what a clock measures’.26 The question then is: what is a clock?

  Einstein imagined the simplest possible ‘clock’. It consisted of a light source with a flat mirror some distance above it. The ‘tick’ of the clock was simply the time taken for the light to travel from the source up to the mirror, bounce off it and return to the source.

  Think of such a clock in a train racing past you. In order to see the clock, of course, you would have to have X-ray eyes or the train would have to be transparent! But forget the details. This is just a ‘thought experiment’, designed to lay bare the fundamentals. The point is that, while the light is travelling up to the mirror, both it and the mirror move relative to you because the train is moving. So, instead of seeing the light travel vertically upwards to the mirror, you see it travel at a slant towards the mirror. And, similarly, when the light bounces off the mirror, you see it travel back down to its source at a slant. From your point of view beside the train track, the light does not simply travel up and down, it travels along two sides of an isosceles triangle. Since it has to cover a larger distance, the tick of the moving clock takes longer, demonstrating in a nuts-and-bolts way that moving clocks do indeed run slow.

  A similar geometrical argument can be used to show that, from your point of view standing beside the train track, a ruler on the moving train shrinks in the direction of motion.

  If you think all this reasoning concerns rather artificial abstract clocks and rulers, it turns out that the very atoms you are made of function as tiny clocks and rulers. Einstein’s logic is inescapable. There is absolutely no way of sidestepping it. All clocks – which in the final analysis have to be read by means of light bouncing off them – ultimately boil down to the simple clock just described.27

  Time slows and space shrinks everywhere, depending on your state of relative motion. One person’s time is not another person’s time.28 One person’s space is not another person’s space. The measurement of time and space are inextricably bound up with signal velocity – the speed of light. And, because they are,
reality is profoundly affected by its dogged constancy.

  It took Einstein five weeks to write his paper. In the process he overthrew the Newtonian world view and replaced it with his own. To his colleague Josef Sauter at the Patent Office, he said: ‘My joy is indescribable.’29

  ‘On the electrodynamics of moving bodies’ was published on 28 September 1905. Usually, at the end a scientific paper, the author lists the papers of other scientists which have influenced the work. Einstein acknowledged no other papers. In fact, the only other scientists he mentioned were the greats such as Newton and Galileo, Clerk-Maxwell and Hertz, and he used their names merely as labels for their theories. But then no one had influenced Einstein’s thinking. Not fundamentally. Many had seen fragments of the new picture of reality. But no one else had seen it in its entirety – the fundamental unifying principles that tied everything together.

  It was rather like Halley, Wren and Hooke all guessing the inverse-square law of gravity. But, without the vision — the bird’s-eye view afforded Newton by his precise definitions of mass and force, and by his fundamental ‘laws of motion’ – the insight amounted to nothing. Newton alone had the vision. And that was why he, like Einstein, was the one to change our fundamental worldview.

  But Einstein’s paper did not simply lack a reference list of other scientific work. Usually, an author thanks all the people who have helped with advice or in discussing the author’s work. But Einstein was the ultimate outsider, working in splendid isolation at the Swiss Patent Office in Bern, unknown in scientific circles. At the end of his paper, he thanked just one person: ‘My friend and colleague Michele Besso steadfastly stood by me in my work on the problem here discussed,’ he wrote. ‘I am indebted to him for many a valuable suggestion.’

  Space-time

  The consequences of the speed of light being the rock on which the Universe is founded are more than simply that one person’s time is not the same as another’s time, and one person’s space is not the same as another’s space. It is worse than this. It turns out that one person’s space is another person’s space and time, and one person’s time is another person’s time and space.

  None of this is apparent in the cosmic slow lane of the everyday world. But it would be glaringly obvious if you could travel at close to the speed of light. Space and time are not only like elastic, able to stretch without limit, but they can morph one into another. Ultimately, the reason for this is that they are aspects of the same thing: space-time.

  We are used to thinking of there being three dimensions of space — east-west, north—south, up-down — and one dimension of time – past-future. But, actually, the dimensions of space and time intermingle to create four dimensions of space-time. Being denizens of a 3D world, we cannot perceive 4D space-time in its entirety. Instead, living in nature’s slow lane, we perceive only ‘shadows’ of the 4D reality cast on our 3D world: one shadow being time, the other three being space.

  Einstein, while a student at the Swiss Federal Polytechnic in Zurich, was taught by a mathematics professor called Hermann Minkowski. He famously referred to his student as a ‘lazy dog’. Later, much to his credit, Minkowski recognised the genius of Einstein, and in fact recognised something that his student had not spotted in his own theory: that it unifies space and time. ‘From now on, space of itself and time of itself will sink into mere shadows and only a kind of union between them will survive,’ said Minkowski.

  ‘The most important single lesson of relativity theory,’ said Stephen Hawking’s collaborator, the British mathematician Roger Penrose, ‘is, perhaps, that space and time are not concepts that can be considered independently of one another but must be combined together to give a 4-dimensional picture of phenomena: the description in terms of space-time.’30

  That there is such a thing as space-time, so that time shares some of the properties of space, means that the events of the Universe can be imagined spread out across a 4D map exactly like geographical features on a standard 2D map. From our perspective, within the map, time appears to flow. But, from an Einsteinian, ‘bird’s-eye’ perspective, time does not flow. All events – from the big bang to the end of the Universe — exist simultaneously, laid out on the 4D map of space-time. Each person’s life is a chain of events, referred to by physicists as a ‘world line’, which stretches like a snake across the map.

  ‘The objective world does not happen, it simply is,’ wrote the German physicist Hermann Weyl in 1949. ‘Only to the gaze of my consciousness, crawling upward along the world line of my body, does a section of this world come to life as a fleeting image in space which continuously changes in time.’ Weyl implicitly recognised that our experience of time flowing has no explanation in physics but only in biology, and in the way the human brain processes reality.31 ‘Reality is merely an illusion, albeit a very persistent one,’ said Einstein.

  The idea of all events existing simultaneously on the 4D map of space-time proved a source of comfort to Einstein when his good friend Besso died in 1955. ‘Now he has departed from this strange world a little ahead of me,’ he wrote to his bereaved family. ‘That means nothing. People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion.’

  Mass and energy

  Space and time are the foundation stones of pretty much all other physical concepts. So, when they are shown to be nothing but shifting sand, so too are lots of other things in physics. Take electric and magnetic fields. Just as space and time are aspects of the same thing – space-time – electric and magnetic fields turn out to be aspects of the same entity – the electromagnetic field. In fact, this insight of Einstein’s resolves a paradox in Maxwell’s theory.

  According to Maxwell, if you travel alongside an electric charge such as an electron, so that it is not moving relative to you, you feel an electric force field. If the electric charge is moving relative to you, however, you feel an electric field and a magnetic field. Similarly, if you travel alongside a magnet, you feel a magnetic field. But, if the magnet is moving relative to you, you feel a magnetic field and an electric field.

  How is it possible that, from one perspective, there is an electric field and, from another, no electric field? How is it possible that, from one perspective, there is a magnetic field and, from another, no magnetic field? The answer, Einstein realised, is that an electric field and a magnetic field are simply different facets of the same thing – an electromagnetic field – and how much of each facet you see depends on your speed relative to the source of the electromagnetic field.

  But Einstein showed not only that electric and magnetic fields are two sides of the same coin, and that space and time are facets of the same basic entity, he also showed that mass and energy are aspects of the same thing.32 And this last unification was maybe the greatest of all the consequences of the special theory of relativity.

  E = mc2

  By the time Einstein’s paper on the foundation of relativity was announced to the world in the 28 September 1905 issue of Annalen der Physik, its editor had received a three-page supplement from Einstein. It contained perhaps the most famous equation in all of physics: E = mc2.33

  It was an extraordinary and unexpected result. Mass, it turns out, is merely another form of energy, like sound energy or heat energy or electrical energy Its distinguishing feature is merely that it is the most compact form of energy. In fact Einstein’s formula, which multiplies the mass, m, of a body by the square of a very big number – the speed of light, universally referred to by physicists by the letter c - reveals that even the tiniest of masses contains a mind-bogglingly huge amount of energy, E.

  It is a fundamental feature of the world that one form of energy can be converted into another form – for instance, electrical energy can be transformed into light energy in a light bulb and the chemical energy of food can be converted into the energy of motion of your muscles. Mass-energy is no exception. It too can be converted into other forms of
energy such as heat and light. The appalling reality of that would be demonstrated to the world in August 1945 over the Japanese cities of Hiroshima and Nagasaki.

  But Einstein’s E = mc2 formula can be read both ways. Not only is mass a form of energy but energy has an effective mass. Any type of energy. So sound energy has a mass, heat energy has a mass, chemical energy has a mass, and, crucially, so does energy of motion.

  So a body has an intrinsic mass – universally known as its ‘rest mass’ – but it also possesses mass due to its motion. In other words, as a body is boosted in speed, it becomes more massive. You weigh more if you are running for a bus than if you are standing still at a bus stop. A mug of coffee weighs more when it is hot than when it is cold because ‘temperature’ is a measure of microscopic motion, and the molecules in the coffee jiggle about more rapidly when it is hot than when it is cold. Of course, such increases in mass become appreciable only when a body is close to the speed of light, making them too small to notice in everyday circumstances.

  But, as a body is boosted in speed and becomes more massive, it becomes harder to push. In fact, if a material body were ever to attain the speed of light it would become infinitely massive, which is impossible. There is simply not enough energy in the Universe. This then is an explanation for why a light beam is un-catchable.34 Everything hangs together. Einstein’s special theory of relativity is a beautiful, seamless whole.

  For light, which has no rest mass and which can travel at the cosmic speed limit, time slows to a standstill, and its birth at the beginning of the Universe and its death at the end of the Universe are simultaneous events. ‘What binds us to space-time is our rest mass, which prevents us from flying at the speed of light, when time stops and space loses meaning,’ says the Ukrainian mathematician Yuri Ivanovitch Manin. ‘In a world of light there are neither points nor moments of time; beings woven from light would live “nowhere” and “nowhen”; only poetry and mathematics are capable of speaking meaningfully about such things.’