The Ascent of Gravity

by Marcus Chown

  OK. So the fundamental building blocks of the Universe behave as particles and waves. But the waves are decidedly odd. They are mathematical ‘waves of probability’ that encapsulate the chance of finding a particle anywhere or of it doing something. The probability wave spreads throughout space, bouncing off obstacles and ‘interfering’ with itself.9 And the way in which it spreads is described by the ‘Schrödinger equation’, formulated by the Austrian physicist Erwin Schrödinger in 1925. At locations where the wave is big — or, specifically, has a large ‘amplitude’, there is a high probability of finding a particle, and at places where it is small a small probability.10

  The genius of the Schrödinger equation, which Schrödinger actually guessed while on a weekend skiing trip with an old girlfriend, is that it unites the wave-like and particle-like facets of nature. It is the mathematical machinery that makes the wave–particle duality of the world concrete and permits physicists to calculate things in the real world. The same year Schrödinger guessed his equation, Heisenberg, together with Max Born and Pascual Jordan, invented a superficially different, but entirely equivalent, version of quantum theory called ‘matrix mechanics’.

  Multiple realities

  Wave—particle duality is a two-way street. In 1923, the French physicist Louis de Broglie made the claim that not only can light waves behave like localised particles but particles such as electrons can behave as spread-out waves. It seemed mad. But, in 1927, Clinton Davisson and Lester Germer in the US and George Thomson in Scotland demonstrated that electrons could interfere with each other, their quantum waves reinforcing and cancelling each other out just like ripples overlapping on a pond. The irony is that George Thomson’s father was ‘J. J.’ Thomson, who had discovered the electron. The father won the Nobel Prize for proving that the electron is a particle; the son won the Nobel Prize for showing that it isn’t.

  If the consequence for physics of waves behaving as particles is shocking, the consequence of particles behaving as waves is equally shocking. The reason is that the fundamental building blocks of matter can do all the myriad things that waves can do. Although those things have mundane consequences in the everyday world, they have earth-shattering consequences in the microscopic world.

  Picture big waves at sea whipped up by a storm. Now picture the scene when the storm has passed and the water is merely ruffled by a gentle breeze. Anyone who has seen both types of wave will know that it is possible also to have a combination of the two – a big rolling wave whose surface is gently rippled. And this, it turns out, is typical not only of water waves but of all waves. If two waves exist, then a combination, or ‘superposition’, of those waves can also exist. It seems a trivial observation. But in the submicroscopic world it is far from trivial.

  Say there is a quantum wave that represents an oxygen atom (the technical name for such a probability wave is the ‘wave function’). Say it is highly peaked on the left-hand side of a room. In other words, there is pretty much a 100 per cent chance of finding the atom on the left-hand side. Now imagine a quantum wave for the oxygen atom that is highly peaked on the right-hand side of a room. So there is almost a 100 per cent chance of finding the atom on the right hand side. Nothing remarkable here. But, remember, if two waves are possible, so too is a superposition of the two. However, a superposition of the two quantum waves corresponds to an oxygen atom that is simultaneously on the left-hand side of the room and the right-hand side of the room – in two places at once.

  But nobody ever observes an oxygen atom in two places at once.11 If the oxygen atom is found on the left-hand side of the room, then the wave representing the oxygen atom on the right-hand side of the room instantly ‘collapses’. This is what the Schrödinger equation tells us. Until an observation is made there exists a haze of possibilities, but the moment an observation is made one possibility and one possibility only is actualised so that a particle exists in a particular location with 100 per cent certainty. The triumph of the Schrödinger equation is that it reconciles the apparently irreconcilable, encapsulating both the wave-like and particle-like faces of nature in one mathematical expression.12

  But, if nobody ever observes an oxygen atom — or anything else, for that matter – in two places at once, who cares about the phenomenon of quantum-wave superposition? The answer is that it has consequences. And those consequences lead to all kinds of quantum weirdness.

  Here is a simple example. Two identical bowling balls collide and ricochet. They fly outwards from the collision point in opposite directions. Now say they collide over and over and you note the direction they travel outwards. Say, towards 2 o’clock and 8 o’clock, 4 o’clock and 10 o’clock, and so on. After repeating this hundreds of times it will be obvious that the bowling balls have flown off to every point on a clock face, in every possible direction.

  Picture doing the same thing with two identical quantum objects such as two electrons or two oxygen atoms. After colliding them hundreds of times it will be obvious that there are some directions where the quantum particles never go – say, 3 o’clock and 9 o’clock, and 5 o’clock and 11 o’clock. Why? Because these are the directions in which the peaks of the probability wave for one particle coincide with the troughs of the probability wave for the other. So they cancel each other out, or destructively interfere, leaving a probability of zero of finding the particles.

  The point is that ‘interference’ enables two quantum waves in a superposition to interact before a quantum particle is observed. And this can have unexpected consequences – like colliding particles never scattering off each other in particular directions.

  It also explains why an electron orbiting in an atom does not fall into a nucleus, as Maxwell’s theory indicates it should. There are a myriad possible paths that an electron could take as it heads for the nucleus. It could spiral in, or it could head in a straight line, or it could take a wiggly path, and so on. And associated with each is a quantum wave. But it turns out that, close to the nucleus, all the quantum waves destructively interfere, cancelling each other out, so that there is no probability of finding the electron there.

  This highlights another fundamental difference between quantum physics and pre-quantum physics. In ‘classical’ physics, a body such as the Moon travels along a unique and well-defined trajectory. In quantum theory, there is no such thing as a well-defined trajectory. Between observations, an electron can be thought of as travelling along multiple paths, each of which has a particular probability associated with it.

  But, if quantum properties such as superposition are not weird enough, they can combine to create even weirder quantum phenomena. ‘Non-locality’, or ‘spooky action at a distance’, for instance, was considered so mad by Einstein that he believed it proved quantum theory is not nature’s final word but merely an approximation of a deeper theory. To appreciate it, it is necessary to know about ‘spin’.

  Faster-than-light influence

  Quantum spin is another one of those quantum properties like wave-particle duality and unpredictability which has no analogue in the everyday world. Think of an ice skater spinning on the ice. She possesses a thing called ‘angular momentum’, which is simply her ordinary momentum multiplied by the average distance of her body from the axis she is spinning around. Angular momentum, like ordinary momentum and energy, is one of those quantities that can never be created or destroyed but is ‘conserved’. This is why, if the ice skater pulls in her arms, bringing her body closer on average to the spin axis, she spins faster to compensate.

  The quantum twist is that particles such as electrons behave as if they are spinning even though they aren’t. They have intrinsic spin. And just like everything else in the submicroscopic world, it comes in indivisible quanta. For historical (and confusing) reasons, the fundamental unit of spin is ½ of a certain quantity (the quantity is h/2π). This is the spin carried by an electron. And it turns out there are only two possible ways it can spin. They can be thought of as clockwise and anticlockwise, although
of course an electron is not actually spinning! Physicists prefer to refer to the two possibilities as spin ‘up’ and ‘down’.

  Here is how spin plus a few other quantum properties — superpositions and unpredictability – lead to spooky action at a distance.

  Take two electrons. The first electron can be spin up and the second spin down. Or the first can be spin down and the second spin up. But, crucially, it is possible to have a superposition in which the two electrons are spin up, down and spin down, up.

  Now because the electrons have opposite spin, their spins cancel out – that is, their angular momentum is zero. But remember angular momentum can never change. So it must always remain zero – in other words, the spins of the two electrons must always be opposite.

  Without looking at either electron, put one in a box and take it to a distant part of the globe. Now, open the box. Because of quantum unpredictability, the electron has a 50 per cent chance of spinning up when it is observed and a 50 per cent chance of spinning down. But – and this is the key – if the electron is observed to be up, the stay-at-home electron must instantaneously become down, and vice versa. Notice that word instantaneously. This is in total violation of Einstein’s cosmic speed limit of the speed of light. Which is why Einstein thought this spooky action at a distance had to prove that quantum theory was incorrect.

  Unfortunately for Einstein, laboratory experiments have shown that subatomic particles born together – like these two electrons – can indeed influence each other faster than light. Even if they are on opposite sides of the Universe. In the jargon, they are ‘entangled’. As Niels Bohr said: ‘If anybody says he can think about quantum physics without getting giddy, that only shows he has not understood the first thing about them.’

  Non-locality, also known as ‘entanglement’, is compatible with special relativity as long as special relativity forbids the transmission of ‘information’ at speeds faster than light. In the case of the two electrons, you can never know whether an electron is up or down until you look at it, and then the direction it takes is random. So encoding a message – for instance, making up a ‘1’ and down a ‘0’ – can never work. All that can ever be transmitted is random gobbledygook, useless information, never a true message.

  But, apart from unpredictability, superpositions and entanglement, there is an even more basic property of waves that has implications for reality . . .

  The uncertainty principle

  Think of a wave that undulates up and down with a constant wavelength. Such a ‘sine wave’ marches on for ever, which means its precise location is 100 per cent uncertain. Now think of the momentum carried by the wave. Intuitively, it is related to its wavelength, with a very wiggly wave – that is, one of short wavelength – carrying a lot of momentum, and a sluggish wave — one of long wavelength – carrying little momentum. Because the sine wave is a wave of only a single wavelength, it has a precise momentum. To labour the point, its momentum is 100 per cent known.

  Now, it is always possible to create a wave that is more localised than a sine wave. To create such a ‘wave packet’, simply add another sine wave, with a different wavelength. And another. And another . . . It is also possible to arrange things so that the sine waves cancel out everywhere except in a localised region13 And the more waves that are superposed, the more localised the wave can be made. But – and this is the point – there is a price to pay for pinning down where the wave is. Since the wave is now composed of a number of sine waves, each with its own characteristic wavelength – and, crucially, its own characteristic momentum – the wave’s overall momentum is now uncertain.

  So, the cost of knowing the location of a wave more precisely is knowing its momentum less precisely. And the opposite is also true. Recall that, in the case of the single sine wave, it was possible to know its momentum with 100 per cent certainty but only at the cost of its location being 100 per cent uncertain. There is a trade-off between our knowledge of the location of a wave and of its momentum. And it is a fundamental property of all types of wave. There is no way of getting around it. And since the microscopic building blocks of matter behave like waves, they too are subject to the same trade-off between knowledge of their location and knowledge of their momentum. We have met it before. It is called the Heisenberg Uncertainty Principle.14

  To be more precise, the product of the uncertainty in a particle’s location and the uncertainty in its momentum cannot be smaller than h/2π15 And a similar constraint holds for energy and time. Specifically, the product of the uncertainty in a particle’s energy and the uncertainty in the time for which it exists cannot be smaller than h/2π16.

  It is because h is so very small and your momentum is so large that you do not behave as a spread-out wave with an uncertain location. But, for tiny subatomic particles with low momentum, the uncertainty in their location is great. The building block of everyday matter with the smallest mass, and therefore momentum, is the electron. It consequently exhibits the most marked wave properties with the most uncertainty in its location. In fact, as pointed out in Chapter 7, this is another way of understanding why atoms exist and their electrons do not spiral into their central nuclei. An electron cannot be squeezed into a small volume near the nucleus because, having the biggest quantum wave, it needs loads of elbow room.

  The Heisenberg Uncertainty Principle is actually the protector of the quantum world. If a quantum entity is located too precisely, it no longer has the spread-out waviness which is critical for it to exhibit interference and all the other wave phenomena behind quantum behaviour.

  The disintegration of space and time

  The Heisenberg Uncertainty Principle has profound consequences for the empty space. It means that smaller and smaller regions of the vacuum have larger and larger uncertainties in energy contained within them. The energy pops into existence and pops out again like money stolen from a wallet which is returned before the owner notices its absence. Such ‘quantum fluctuations’ manifest themselves as particle-antiparticle pairs such as electrons and positrons appearing out of nothing like rabbits out of a hat. But they have such a fleeting existence, disappearing in the merest split-second whence they came, that it is actually a stretch to call them real particles. Nevertheless, such ‘virtual’ particles have a real effect on atoms, buffeting their outer electrons and causing a tiny change in the energy of the light those electrons give out as they jump between orbits. For measuring this ‘Lamb shift’ in the light of the hydrogen atom, the American physicist Willis Lamb won the 1955 Nobel Prize for Physics.

  Because of quantum fluctuations, the vacuum is actually seething with energy. And on the smallest scales, where the fluctuations are large enough, that energy is sufficient grossly to warp space-time.17

  Think of the vacuum as like the ocean on a stormy day. From the perspective of a high-flying seagull, the ocean looks perfectly smooth. This is what space-time looks like on the largest scales. But from the perspective of a seagull flying much lower, big rolling waves can be seen on the ocean. Similarly, on smaller scales, space-time begins to convulse. Finally, from the perspective of a seagull on the deck of a trawler, waves can be seen smashing over the bow. All is froth and chaos. And this is what space-time is believed to look like on the smallest possible scales.

  John Wheeler coined the name ‘quantum foam’ for this chaotic space-time. But it should be stressed we currently have no observational evidence that it exists. Although quantum foam should by rights affect the light from distant events in the Universe such as ‘quasars’ and ‘gamma ray bursters’ on its multi-billion-year journey to Earth, no one has yet detected the effect.18

  Most physicists agree with Wheeler that, on the smallest scales, space-time does not exist. ‘Space-time is doomed – that much is pretty universally agreed,’ says Nima Arkani-Hamed of the Institute for Advanced Study in Princeton, New Jersey. ‘It must be replaced by more fundamental building blocks. The question is what exactly?’

  Arkani-Hamed is widely co
nsidered one of the world’s most original and talented theoretical physicists. With his trademark black T-shirt, shorts, sandals and long flowing black hair, he cuts a striking figure at a blackboard, scrawling equations and waving his arms wildly for emphasis. Generous with his time, he will talk physics with absolutely anyone. In fact, he claims he has never turned down a graduate student who wanted to work with him.19

  That Arkani-Hamed is at the epicentre of twenty-first-century physics is somewhat of a miracle. Aged ten, he nearly died of a fever in the mountains between Iran and Turkey as his family fled the Khomeini regime in 1982. As his mother’s horse carried him through the night, she kept him conscious by pointing out the phosphorescent band of the Milky Way and promising him a telescope when they got to safety. He duly got his telescope in Toronto, Canada, and eventually made his way via Berkeley in California and Harvard to the Institute for Advanced Study, famous for being the place where Einstein and logician Kurt Gödel spent their twilight days.

  Arkani-Hamed is using his seemingly boundless energy and enthusiasm to persuade the Chinese to build a particle accelerator to dwarf the LHC and probe nature on a scale ten times smaller and an energy ten times higher than the European machine. If it comes off, the ‘Great Collider’ could be operational by 2042. But Arkani-Hamed’s theoretical focus is firmly on finding a deeper theory than Einstein’s theory of gravity. And because that theory recognises that gravity is nothing more than the curvature of space-time, the quest to understand gravity has been transformed into a quest to understand the origin of space and time.