by Paul Davies
I set to work on this problem with colleagues William Unruh and Stephen Fulling, and we soon figured out what was happening. No energy emanates from inside the black hole itself – it can’t, because of the one-way nature of the event horizon. What happens is that negative energy flows into the black hole. Negative energy? In quantum physics energy can indeed be less than zero. When the rules of quantum physics are applied to totally empty space, the resulting ‘quantum vacuum’ is a ferment of activity, with half-real ‘virtual’ particles flitting in and out of existence (see Chapter 11). Well, all those ghostly comings and goings get upset by the proximity of the black hole, because the virtual particles are obliged to flit about in a space that is geometrically warped by gravity. And the warping affects their energy, making it less in total than it would be with no spacewarp. Hence negative energy, which streams across the event horizon, conveying negative mass into the belly of the beast. When you do the sums, the books balance nicely: the ingoing negative energy causes the black hole to lose mass and shrink, which exactly pays for the energy of the Hawking radiation that flows away into the depths of the universe.
The energy paradox was relatively easy to solve. But all along there was a tougher riddle lurking, one that Hawking himself wrestled with until the very end. He first discussed it with me in a Boston hotel room in 1978, where we had travelled to an astrophysics conference. The Hawking effect predicts that a black hole should gradually get smaller and smaller, eventually disappearing completely. That raises the question of what happened to all the stuff that fell into the hole in the first place. Is it permanently lost? Or is it a case of what goes in must come out? Can an echo of its identity somehow end up mingled in the accumulated heat radiation, but scrambled beyond recognition? Or does new physics come into play at the event horizon to change the whole scenario? Basically, it all boils down to the nature of information – in this case the information concerning the identity of the material that fell into the black hole in the first place. Quantum mechanics says information is never lost; general relativity says it is. Quantum black holes require both theories, so what gives when a black hole shrinks to a vanishing speck?
Although his black-hole work addressed a well-defined branch of astrophysics, Hawking also tackled some questions of a more general philosophical and even theological nature. He liked to profess his strict atheism, but in his writing he often displayed what Einstein called a ‘cosmic religious feeling’. From within his own scientific framework, Hawking celebrated the beauty and ingenuity of a universe that he felt compelled to understand in all its rational majesty. And central to that vision was a belief that, however baffling and complex the universe may seem, beneath it all lies a harmonious mathematical unity – perhaps even a theory of everything.
18. A Theory of Everything?
In 1980, Hawking was appointed to the Lucasian Chair of Mathematics at the University of Cambridge, a position previously held by Newton and Dirac, and on 29 April he delivered his inaugural lecture: ‘Is the end in sight for theoretical physics?’ Hawking didn’t mean that physics might peter out for lack of money or talent; rather, that it would succeed so brilliantly that the only thing left would be to pick over the minor details. It wasn’t the first time such a prediction had been made. In 1894, the American physicist Albert Michelson had proclaimed: ‘The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote.’ Ironically, seven years earlier, Michelson himself had performed the crucial experiment to measure the speed of the Earth through space (see p. 32), the zero result of which precipitated the crisis in physics that led to Einstein’s theory of relativity. However, Hawking’s grand vision far surpassed that of Michelson and others, for it heralded not merely a completion of physics, but its unification into nothing less than a Theory of Everything: ‘A theory of the physical interactions that would describe all possible observations,’ is the way he put it. This capstone project might, he ventured, be attained by the end of the twentieth century. Alas, forty years on we seem to be very far from the final, all-embracing theory that he envisaged. If anything, the obstacles to unification have multiplied. As Mark Twain might have expressed it, rumours of the death of theoretical physics turned out to be greatly exaggerated.
The quest for a unified theory of the universe dates back over two thousand years and has its origins in an ideological confrontation between ancient Greek philosophers concerning the nature of permanence and change. ‘No man steps in the same river twice,’ wrote Heraclitus of Ephesus, a member of the school that maintained the world was in a continual state of flux. An opposing school, led by Zeno of Elea, argued that change was in fact paradoxical, for how could something transform into that which it was not? A third school was born of a scholarly compromise. Known as Atomism, it was represented by Democritus and Leucippus. They suggested that although matter is very complex, it is ultimately composed of simple indivisible building blocks, which they called atoms (a-tom meaning ‘no cut’). The universe, declared the Atomists, consisted of just two things: atoms and the void. All forms of matter could be explained by different arrangements of atoms, and all change by the movement of atoms. Though rooted purely in philosophical deliberations, Atomism is a basically correct account of the structure and behaviour of matter. But Atomism’s influence extended well beyond a theory of form and transformation, for it suggested that the best way to understand a physical object or system is to smash it apart and see what it’s made of, a viewpoint known as reductionism. And that’s precisely what particle physicists have spent the past few decades doing. Reductionism is a powerful methodology, but, as we shall see, it falls short of giving a complete account of the world.
What we now call atoms are actually misnamed: they aren’t the unbreakable particles that the Greek philosophers had in mind, but are composite bodies consisting of a nucleus orbited by electrons. The nucleus is made of protons and neutrons, which are in turn composed of two varieties of smaller particles called quarks, three apiece. This is not a bottomless pit of complexity. Normal matter is mostly explained by the particles I’ve just mentioned, plus the neutrino. Oddly, however, nature chose to triplicate the inventory – there exist two entire additional sets of quarks and neutrinos and two heavier versions of electrons, known as the muon and the tau. And now you have to double this whole list to include all the anti-particles. Apart from the neutrinos, the particles in these additional families are very short-lived and don’t produce many noticeable effects. They aren’t components of ordinary atoms, but subatomic fragments that fly off and quickly disappear.
The entire field of particle physics is confusingly jargon-ridden. Particle properties go far beyond spin and electric charge. There’s isospin and hypercharge and colour and strangeness, and on and on. Listen to particle physicists talking animatedly in a pub and it’s reminiscent of a bunch of insurance brokers or accountants – incomprehensible verbiage. But the plethora of attributes physicists assign to their beloved particles isn’t just a book keeping exercise; it reflects the elaborate mathematical organization of the subatomic world. To a physicist, the particle zoo is a wonderland. These little particles all have, if not quite their own personalities, at least distinctive properties and behaviour – and charm. (As a matter of fact, one of the properties of quarks is actually known, whimsically, as its ‘charm’.) There are light ones and heavy ones, long-lived and short-lived, charged and uncharged; some of them decay in half a dozen different ways, producing rich cascades of progeny, each with their own intrinsically fascinating qualities. Physicists often have their favourite particle (neutral pion, tau neutrino, sigma minus . . . ) just as a zoologist might feel especially passionate about the naked mole-rat or three-toed sloth. The pinnacle of particle fever comes with the discovery of a new one, which was common fifty years ago but is now a rarity.
A complete under
standing of matter – a theory of everything – requires not just a catalogue of the particles that comprise the universe, but a theory of the fundamental forces that act between them. Physicists have been able to identify four: gravity, electromagnetism and two nuclear forces, called simply weak and strong. Two of these four – electromagnetism and the weak nuclear force – turn out to be locked in a mathematical embrace, forming a hybrid ‘electroweak’ force in which the properties of one force intimately link to those of the other. A lynchpin of this linkage is the existence of a new type of particle, known as the Higgs boson. First predicted by Peter Higgs and others in the 1960s, the Higgs boson was finally produced by the LHC in 2012. This was the last definitive discovery of a fundamental particle. As a result, the four fundamental forces have now convincingly been whittled down to three.
The way the forces operate in the microscopic realm, where quantum effects prevail, is by deploying yet more particles, which act like messengers conveying the force from one particle of matter to another. The photon is responsible for the electromagnetic force, while the strong force requires a whole set of particles called gluons, so named because they glue the quarks together. The weak force particles are simply given uninspiring letters: W and Z. Gravity is transmitted by the graviton, doing for gravity what photons do for electromagnetism. The graviton is far and away my own favourite particle, because nobody has ever detected one. Gravity is such a weak force that there’s no hope of seeing it at work between individual subatomic particles. That makes the search for evidence of gravitons a tantalizing challenge. Quantum theory says gravitons have to be there. But where to look?
Figure 14. Unifying physics. Science is ultimately about finding unexpected connections between things. Newton discovered a few basic laws that link together the orbits of planets and comets to the motion of bodies on Earth. Einstein linked space and time, mass and energy and gravitation and geometry. James Clerk Maxwell in the nineteenth century found a connection between electricity and magnetism, which was extended in the 1960s to include the weak nuclear force. Could everything be connected, deep down? That is the dream of a final unified theory.
Together, this rather long list of particles – the electron and neutrino (times three), two sorts of quarks (also times three), the photon, W and Z, eight species of gluons, and the (celebrated) Higgs boson – make up what is known as the Standard Model of particle physics (see Table 1). It has been enormously successful in describing the subatomic world, but nobody thinks it’s the last word. For a start, the electroweak and strong forces haven’t been unified, so the Standard Model is not a fully integrated theory – more cohabitation than marriage. And some really basic things are left out: the poor old graviton, for a start. Also, the Standard Model has little to say about why neutrinos have a non-zero, albeit tiny, mass, or what produced the matter–antimatter asymmetry in the hot early universe. It’s also inconclusive about the nature of dark matter. These shortcomings mean that when the status of the Standard Model gets discussed, it’s generally in the context of what lies beyond it.*
In his lecture, Hawking envisaged a complete unification, in which all the particles and forces are amalgamated into a single, beautiful, mathematical scheme – perhaps even a formula that would fit on a T-shirt. There have been quite a few imaginative candidates for this Last Word theory over the years, but none that has really nailed it. Full unification needs equations that combine particles of matter with the particles that convey the forces. And therein lies a huge problem. Matter particles all possess the weird ‘double-take’ property called intrinsic spin (explained on p. 66), while the force particles don’t. Amalgamating them in a unified theory is like mixing chalk and cheese. An elegant solution is available, however, care of an esoteric branch of mathematics called supersymmetry; physicists have long been attracted to its economy and beauty. It undeniably does the technical job, but it predicts a whole slew of new and exotic particles which haven’t been found. When the LHC was built, it was thought these supersymmetric particles would show up first, but so far there’s no sign of them. Maybe it’s because the LHC, powerful though it is, still lacks the punch to make them. Or perhaps nature doesn’t share our sense of mathematical elegance.
Table 1. The fundamental particles in the Standard Model of particle physics
The four particles in the left-hand column go to make up normal matter. They consist of two quarks, u and d, the electron e and the neutrino that pairs with it, labelled νe. The next two columns are replications of this scheme with heavier, unstable particles. The column on the right shows the particles that convey the forces: the gluons, collectively represented by the symbol g, the photon γ and the two weak force particles W and Z. Also shown is the Higgs boson, H. The six quarks can combine together in many ways to produce composite particles, of which the proton and neutron are the most familiar.
The most ambitious attempt at complete unification is called string theory (or M theory), and the physics community has become rather fixated by it. The basic idea is that the world is indeed built from fundamental, indecomposable entities as the Greek Atomists maintained, but they are not particles. Rather, they are tiny loops of string. And I mean tiny – about twenty powers of ten smaller than a proton, placing them completely beyond the reach of experiment. The strings have tension, so they vibrate like plucked musical instruments. Different patterns of vibration represent different particles and forces when viewed on the relatively large scale of experimental particle physics.
So far, string theory ticks all the right boxes, and is compelling because it includes both supersymmetry and gravitation in the mix. To get the scheme to work, though, the strings have to inhabit more than three space dimensions. For example, one version uses nine. The reason we don’t see the extra six dimensions is because they are rolled up to a tiny size. What does this mean? Imagine viewing a hosepipe from a distance. It looks like a wiggly line, but on closer inspection each point on the line is seen to be a little circle going around the circumference of the pipe (see Figure 15). By analogy, suppose each point of three-dimensional space is in fact a tiny circle (tiny, as in twenty powers of ten smaller than a proton) going around a fourth space dimension. We would never notice.
You can hide any number of additional dimensions by ‘compactifying’ them in this way, but with more than one dimension there are many choices of how to do it. For example, two dimensions can be rolled up as the surface of a sphere or as a doughnut with a hole in the middle (called a torus). Mathematicians describe these two arrangements as different ‘topologies’. When it comes to six additional dimensions, the number of compact topologies is stupendously huge. Whole new branches of mathematics are needed to classify them and determine their properties. The idea is that the strings thread through these higher-dimensional labyrinths, which serve as byzantine echo chambers. History has, it seems, come full circle. The ancient Greeks built music and harmony into the macrocosm and celebrated the music of the spheres. Today, string theorists are tuned reverentially to the music and harmony of the microcosm.
Figure 15. How to hide a dimension of space. From a distance, the hosepipe looks like a wiggly line. Close up, a ‘point’ P on the line is revealed as a little circle going around the tube.
Initially physicists held out the hope that string theory might describe the actual physical world, incorporating the known list of particles and forces as we observe them, possibly even accounting for the force strengths and particle masses. Nobody believes that now. In fact, it seems likely that the theory is consistent with an almost limitless number of possible worlds. Does that make it useless? Not all theorists despair over this ambiguity. What is regarded as a sin by some has been seized on as a virtue by others. As we shall see, a rich smorgasbord of alternative universes is precisely what some physicists seek in order to explain the universe that is ours.
The dry list of particles that I have introduced in this chapter raises the question of why. Is there a deeper reason for the list to b
e populated in just that way, by just those particles, with just those masses, electric charges and spins? And is there something magical about four (really three) basic forces rather than five, or fifty, or five hundred? Also, what is the point of having not merely an electron, but its two heavier cousins – the muon and the tau – extras that accomplish little more than vanishing in a fraction of a second? Is there an abstract mathematical subtext that threads these subatomic splinters into a coherent unity – string theory perhaps, or some other branch of mathematics awaiting a flash of inspiration by a future generation of theoretical physicists? Or might the universe simply be an arbitrary ragbag of components thrown together, which, merely fortuitously, proves sufficient to coax thinking, bewildered beings into existence?
19. Fossils from the Cosmic Dawn
Cosmology’s golden age began with a picture, and a rather unprepossessing one at that. The blotchy panorama of the sky created by COBE (Figure 1, p. 1) can’t compete with the images from the Hubble Space Telescope, or the high-resolution close-ups of the planets taken by space probes. But what COBE’s output lacked in visual appeal, it more than made up for in significance, for when studying that picture, we are in a very real sense looking directly at the primordial furnace itself. The light from the nascent universe imaged there has travelled to us for over 13.7 billion years, during which time it has remained largely undisturbed. That means the CMB is a type of fossil: fossilized light. To be sure, that light has been stretched in wavelength a thousand times, but it’s still distinctive, the graceful profile and purity of its spectrum immediately recognizable. Contrast the pristine CMB with the corrupted fossil remains collected by palaeontologists, from which they try to reconstruct a plausible narrative. There’s a lot of guesswork involved, because palaeontologists can’t physically see the past in the way astronomers can directly see the birth of the universe.