The Book of Nothing Read online

  Figure 7.9 The four known fundamental forces of Nature.

  The strong force is more complicated. Originally, it was regarded as acting between particles like protons which undergo nuclear reactions. However, experiments in which these particles were collided at high energies revealed that they did not behave as if they were elementary indivisible pointlike particles at all. Rather, the proton deflected incoming particles as if it contained three internal pointlike scatterers. These internal constituents are known as quarks and they possess an analogue of electric charge that is called colour charge. This has nothing to do with the usual meaning of colour, as a hue determined by the wavelength of light absorbed when we observe it. It is just a particular attribute (like electric charge) which is conserved in all the processes that we have ever observed. The strong force acts on every particle that carries the colour charge and for this reason is sometimes called the ‘colour force’. The colour force is mediated by the exchange of particles called gluons which have masses about 90 times less than the W and Z bosons and so the strong force has a range about 90 times greater. It is equal to the size of the largest atomic nucleus, a reflection of the fact that it is this force that binds it together.

  Quarks possess both colour charge and electric charge. Gluons also possess colour charge and are therefore very different to photons. Photons mediate the electromagnetic interactions between electrically charged particles but do not themselves possess that electric charge – you can’t have electromagnetic interactions of photons alone, they need charged particles like electrons to participate as well. Gluons, by contrast, carry the colour charge and mediate interactions between particles that possess colour charge – you could have strong interactions of gluons alone without any quarks. In this respect the gluons are more akin to the gravitons which mediate the gravitational force. Since gravity acts on everything that has mass or energy it also acts on the gravitons which convey it.

  The most elementary particles of matter are believed to be the families of identical quarks and leptons listed in Figure 7.10. ‘Elementary’ means that they display no evidence of possessing internal structure or constituents.

  The story of how this picture was established and the feats of engineering performed to establish the identities of the particles involved and the roles they play in Nature’s great particle play is one about which whole books have been written.34 Our interest is in a particular chapter of the story which reveals the reality and crucial properties of the quantum vacuum.

  Figure 7.10 The three known ‘families’ of quarks and leptons. Each pair of quarks is related to a charged lepton (either the electron, muon or tau) and an uncharged neutrino.

  This theory appears succinct and appealing. It enables us to explain just about everything that is seen and has enabled a succession of successful predictions to be made. However, there is something unattractively in-complete about it all. Physicists believe deeply in the unity of Nature. A universe that rests upon four fundamental laws governing different populations of particles appears to them like a house divided against itself. The unity of Nature reveals itself in a host of different places and provokes us to show that these forces are not really different. If only we could find the right way of looking at them they would fall into place as different pieces of a single big picture, different parts of just one basic force of Nature from which everything derives. An analogy might be found in the behaviour of water. We see it in three very different forms: liquid water, ice and steam. Their properties are different yet they are all manifestations of a single underlying molecular structure for a combination of two hydrogen atoms and one oxygen atom. Despite appearances there is an underlying unity.

  Any attempt to unify the quartet of basic forces seems doomed from the start. They look too different. They act upon different classes of elementary particles and they have very different strengths. The relative strengths are shown in Figure 7.9. We see that gravity is by far the weakest. The gravitational force between two protons is about 1038 times weaker than the electromagnetic force.35 At laboratory energies, the weak force is about a hundred million times weaker than the electromagnetic force and the strong force is ten times stronger than electromagnetism.

  The fact that the four separate forces have such different strengths and act upon separate sub-populations of elementary particles is deeply perplexing for anyone seeking a hidden unity behind the scenes that would unite them into a single superforce described by one all-encompassing ‘theory of everything’. How can they be united when they are so different? The answer that has emerged reveals the vacuum to be the key player.

  VACUUM POLARISATION

  “Thirty spokes share the wheel’s hub

  It is the centre hole that makes it useful.

  Shape clay into a vessel;

  It is the space within that makes it useful.

  Cut doors and windows for a room;

  It is the holes which make it useful.

  Therefore profit comes from what is there;

  Usefulness from what is not there.”

  Lao-tzu36

  We used to think of the strength of a force of Nature like electro-magnetism as a fixed constant of Nature, one of the defining features of the Universe. It could be described by combining the basic unit of electric charge carried by a single electron, the speed of light in a vacuum, and Planck’s constant, h. These can be organised into a combination that possesses no units of mass, length, time or temperature. Thus, it provides us with a universal measure of the strength of electromagnetic forces of Nature irrespective of the units of measurement that we employ for the pieces that go into it (so long as we use the same units for all of them). The value obtained37 by experiments of great accuracy and ingenuity for this pure number, called the fine structure constant and denoted by the Greek letter alpha, is equal to

  α = 1/137.035989561…

  Usually, it is regarded as being approximately equal to 1/137 and physicists would love to explain why it has the precise numerical value that it does. We say that it is a fundamental constant of Nature. Accordingly, the number 137 is instantly recognised by physicists as significant and I have no doubt that the key codes of the locks on the briefcases of a significant number of physicists around the world involve the number 137. For an example of the type of numerological flights of fancy that this quest can inspire see Figure 7.11.

  The fine structure constant tells the strength of the interaction that occurs when we fire two electrons towards each other. They have the same (negative) electric charge and so they repel one another like two magnetic North poles (see Figure 7.12).

  Figure 7.11 Some numerological flights of fancy involving the number 137, compiled by Gary Adamson.38

  In a world without quantum mechanics this interaction should produce the same degree of deflection regardless of the temperature or energy of the environment. All that counts is the number 1/137. In a nineteenth-century vacuum composed of empty space there would be nothing more to be said.

  The quantum vacuum changes all that. Our two electrons are no longer situated in a completely empty space – the Uncertainty Principle forbids us from entertaining any such notion. They are moving in the quantum vacuum and that is far from empty. It is a hive of activity. You recall that the Uncertainty Principle reveals that there are complementary pairs of properties that we cannot measure at once with unlimited precision. The energy and lifetime of a particle or a collection of particles is one of these so-called ‘complementary’ pairs. If you want to know everything about the energy of a particle you have to sacrifice all knowledge about its lifetime. Heisenberg’s Uncertainty Principle tells us that the product of these uncertainties always exceeds Planck’s constant divide by twice the number pi:

  (uncertainty in energy) × (uncertainty in lifetime) > h/2π (*).

  Figure 7.12 Two electrons deflecting in a world with an empty ‘classical’ vacuum.

  Any observed particle or physical state must obey this inequality. Observabilit
y requires that it be satisfied.

  The quantum vacuum can be viewed as a sea composed of all the elementary particles and their antiparticles continually appearing and disappearing. For example, let us focus attention upon the electromagnetic interactions only for the moment. There will be a ferment of electrons and positrons.39 Pairs of electrons and positrons will appear out of the quantum vacuum and then quickly annihilate each other and disappear. If the electron and the positron each have mass m, then Einstein’s famous formula (E = mc2) tells us their ‘creation’ requires an energy equal to 2mc2 to be borrowed from the vacuum. If the time they exist before annihilating back into the vacuum is so short that the Uncertainty Principle (*) is not obeyed, so

  (uncertainty in energy) × (uncertainty in lifetime)
  then these electron-positron pairs will be unobservable. Hence, they are called virtual pairs. If they live long enough for (*) to be satisfied before they annihilate each other and disappear, then they will become observable and are called real pairs. The creation of virtual pairs seems like a violation of the conservation of energy. Nature allows you to violate this principle so long as no one can see you doing it and this is guaranteed so long as you repay the energy quickly enough. It is useful to think of the virtual condition (**) rather like an ‘energy-loan’ arrangement. The more energy you borrow from the energy bank the quicker you have to pay it back before it is noticed.

  The upshot of this is that we can think of our quantum vacuum as containing a collection of continually appearing and disappearing virtual pairs of electrons and positrons. This sounds a little mystical, for if they are unobservable why not just ignore them and opt for a simpler life? But let us reintroduce our two electrons that are all set to interact. Their presence creates an important change in the quantum vacuum. Opposite electric charges attract and so if we put an electron down in the vacuum of virtual pairs the positively charged virtual positrons will be drawn towards the electron, as shown in Figure 7.13(a).

  The electron has created a segregation of the virtual pairs and the electron finds itself surrounded by a cloud of positive charges. This process is called vacuum polarisation. Its effect is to create a positively charged shield around the bare negative charge of the electron. An approaching electron will not feel the full negative electric charge of the electron sitting in the vacuum. Rather, it will feel the weaker effect of the shielded charge and be scattered away more feebly than if the vacuum polarisation was absent.

  This effect changes if we alter the energy of the environment and the incoming electron. If it comes in rather slowly, then it will not penetrate very far into the shielding cloud of positive charges and will be deflected weakly. But, if it comes in with a higher energy, it will penetrate further through the shield and feel the effect of more of the full negative electron charge within. It will be deflected more strongly than the less energetic particle. Thus we see that the effective strength of the electromagnetic force of repulsion between the two electrons depends upon the energy at which it takes place, as shown in Figure 7.13(b). As the energy increases so the interaction appears to get stronger. It is a little like covering two hard billiard balls with a soft woolly padding. If the balls collide very gently then they will deflect only slightly because the hard surfaces will not hit and rebound. Only the woolly shields will gently rebound. But if they are made to collide at high speed the shields will have little effect and the balls will rebound very strongly. The trend is clear: as the energy of the environment increases so the stronger does the effective electromagnetic interaction become. As the energy rises, the incoming particle gets a closer ‘look’ at the bare point electron charge beneath the cloud of virtual positrons and is deflected more.

  Figure 7.13 (a) An incoming electron (B) with low energy scatters weakly due to the outer shield of virtual positive charges around the central negative charge of the electron (A); (b) an incoming electron with high energy penetrates the cloud of positive virtual charges and feels a strong repulsion from the central negative charge of the second electron.

  The same study can be made of the strong interaction that affects particles, like quarks and gluons, which carry the colour charge. The situation is a little more complicated than that of the electromagnetic interaction. When we considered the effects of the repelling charges of virtual electrons and positrons we could ignore the photons mediating their electromagnetic inter-action because they have no electric charge. However, if we put a quark of fixed colour charge down in the vacuum and fire another coloured quark towards it, there are two vacuum polarisation effects to consider. Just as before, there will be a cloud of quark-antiquark pairs which will tend to surround any quark with a screening cloud of opposite colour charge. As with the electrons, the overall effect will be to make the strong interaction effectively stronger at higher energies. However, the presence of the gluons also affects the pattern of colour charge. Virtual gluons have the opposite effect and tend to smear out the central colour charge. When scattering occurs from a more extended, less pointlike object it tends to be weaker. The winner between these two opposed tendencies depends on how many varieties of quark there are to pop up in virtual pairs. If the number is as low as the six that we observe in Nature, then it is the gluon smearing that wins out and the strong interaction is predicted to get effectively weaker as we go to higher energies.

  This property, called ‘asymptotic freedom’ because it implies that if one continues to extrapolate to indefinitely increasing energies there would be no apparent interaction at all – the particles would be free – was predicted in 1973 and was quite unexpected. It is now confirmed by observations of the interaction strength at different energies. It revolutionised the study of elementary particles and high-energy physics and opened the door to making serious studies of the first moments of the expanding Universe when temperatures would have been high enough for these effects to be very significant. Before 1973, there had been widespread belief that the strong interaction was going to be hopelessly complicated and there was not much chance of understanding interactions at very high energies. It was assumed that they got stronger and stronger at higher and higher energies and so became increasingly intractable. Asymptotic freedom meant that in many ways things got simpler and simpler and it was possible to make real progress.

  These important effects of the quantum vacuum enable us to see how the puzzling obstacle to unification of the forces of Nature posed by their different apparent strengths might be overcome. The force strengths do indeed differ significantly in the low-energy world where life like ours is possible, but if we follow the changes expected in those forces as we go to higher and higher energies, they can become closer and closer in strength until a particular energy is reached where the strengths are the same (Figure 7.14). Unification exists only in the ultra-high-energy environment that would have existed in the early stages of the Universe. Today, things have cooled off, and we are left searching for the remnants of a symmetrical past, disguised by billions of years of history. At the energies of our life-supporting environment these forces look very different and the unity of the forces of Nature is hidden. The deep symmetry of the forces that should be found at high energies is possible only because of the contributions of the quantum vacuum. This sea of virtual particles is really there. Its effects can be observed, as predicted, by the change in strength of natural forces as energies increase. The vacuum is far from empty. Nor is it inert. Its presence can be felt and measured in the elementary-particle world, and without its powerful contribution, the unity of Nature could not be sustained.

  Figure 7.14 Asymptotic freedom. The weakening of the strong force between quarks as the energy of interaction increases predicts that it can have the same strength as the electromagnetic force at very high temperatures.

  BLACK HOLES

  “Confinement to the Black Hole … to be reserved for cases of Drunkenness, Riot, Violence, or Insolence to Superiors.”

  British Army Regulation, 1844
r />   One of the most recurrently fascinating concepts in the whole of science has proved to be that of the ‘black hole’.40 This cosmic cookie monster, relentlessly devouring everything that strays too close, has captured the popular imagination like no other scientific concept, starred in Hollywood movies, and inspired a host of science-fiction stories. Black holes are regions where the gravitational field of matter is too strong for anything, even light, to escape from its grasp. In Einstein’s picture of curved space, the concentration of mass within a small region can grow so great that the geometry curves dramatically and pinches off the region surrounding it, preventing any signals getting out. The mass concentration is surrounded by a surface of no-return, called the event horizon, through which material and light can flow in but not out.

  Despite their popular image, black holes are not necessarily solid objects possessing enormous densities. The huge black holes that seem to be lurking at the centres of many large galaxies have masses about a billion times larger than that of the Sun, but their average density is only about that of air.41 We could be passing through the event horizon of one of these vast black holes at this very moment and nothing would seem strange. No alarms bells would ring as we crossed the horizon and we wouldn’t be torn apart.42 Later on, it would: gradually we would find ourselves drawn inexorably towards conditions of increasing density at the centre. If we ever tried to reverse our path, we would find that there was a definite limit to how far back we could get and none of the signals beamed back to base outside the hole would ever be received.

  Black holes are predicted to form whenever a star that is more than about three times the mass of our Sun exhausts its nuclear fuel. It will then cease to have any means of supporting itself against the inward pull of gravity exerted by its constituents. No known force of Nature is strong enough to resist this catastrophic implosion and it will continue to compress the material of the star into a smaller and smaller region until a horizon surface is created. From the inside, the compression just carries on going but from the outside it ceases to be visible. A distant observer looking at the black hole would see light from just outside the horizon becoming redder and redder as it loses energy climbing out of the very strong gravity field.43 The only trace that remains is its gravitational pull.