The Quantum Universe

by Brian Cox

  11. Empty Space Isn’t Empty

  Not everything in the world stems from the interactions between electrically charged particles. QED does not explain the ‘strong nuclear’ processes that bind quarks together inside protons and neutrons or the ‘weak nuclear’ processes that keep our Sun burning. We can’t write a book about the quantum theory of Nature and leave out half of the fundamental forces, so this chapter will make right our omission before delving into empty space itself. As we’ll discover, the vacuum is an interesting place, filled with possibilities and obstacles for particles to navigate.

  The first thing to emphasize is that the weak and strong nuclear forces are described by exactly the same quantum field theoretic approach that we have described for QED. It is in this sense that the work of Feynman, Schwinger and Tomonaga had deep-ploughing consequences. Taken as a whole, the theory of these three forces is known, rather unassumingly, as the Standard Model of particle physics. As we write, the Standard Model is being tested to breaking point by the largest and most sophisticated machine ever assembled: CERN’s Large Hadron Collider (LHC). ‘Breaking point’ is right because, in the absence of something hitherto undiscovered, the Standard Model stops making meaningful predictions at the energies involved in the collisions of almost light-speed protons at the LHC. In the language of this book, the quantum rules start to generate clock faces with hands longer than 1, which means that certain processes involving the weak nuclear force are predicted to occur with a probability greater than 100%. This is clearly nonsense and it implies that the LHC is destined to discover something new. The challenge is to identify it among the hundreds of millions of proton collisions generated every second a hundred metres below the foothills of the Jura Mountains.

  The Standard Model does contain a cure to the malaise of the dysfunctional probabilities and that goes by the name of the ‘Higgs mechanism’. If it is correct, then the LHC should observe one more particle of Nature, the Higgs boson, and with it trigger a profound shift in our view of what constitutes empty space. We’ll get to the Higgs mechanism later in the chapter, but first we should provide a short introduction to the triumphant yet creaking Standard Model.

  The Standard Model of Particle Physics

  In Figure 11.1 we’ve listed all of the known particles. These are the building blocks of our Universe, as far as we know at the time of writing this book, but we expect that there are some more – perhaps we will see a Higgs boson or perhaps a new particle associated with the abundant but enigmatic Dark Matter that seems necessary to explain the Universe at large. Or perhaps the supersymmetric particles anticipated by string theory or maybe the Kaluza-Klein excitations characteristic of extra dimensions in space or techniquarks or leptoquarks or … theoretical speculation is rife and it is the duty of those carrying out experiments at the LHC to narrow down the field, rule out the wrong theories and point the way forward.

  Figure 11.1. The particles of Nature.

  Everything you can see and touch; every inanimate machine, every living thing, every rock and every human being on planet Earth, every planet and every star in every one of the 350 billion galaxies in the observable Universe is built out of the particles in the first column of four. You are an arrangement of just three: the up and down quarks and the electron. The quarks make up your atomic nuclei and, as we’ve seen, the electrons do the chemistry. The remaining particle in the first column, called the electron neutrino, may be less familiar to you but there are around 60 billion of them streaming through every square centimetre of your body every second from the Sun. They mostly sail straight through you and the entire Earth, unimpeded, which is why you’ve never seen or felt one. But they do, as we will see in a moment, play a crucial role in the processes that power the Sun and, because of that, they make your life possible.

  These four particles form a set known as the first generation of matter and, together with the four fundamental forces of Nature, they appear to be all that is needed to build a Universe. For reasons that we do not yet understand, Nature has chosen to provide us with two further generations – clones of the first except that the particles are more massive. They are represented in the second and third columns in Figure 11.1. The top quark in particular is much more massive than the other fundamental particles. It was discovered at the Tevatron accelerator at Fermilab near Chicago in 1995, and its mass has been measured to be over 180 times the mass of a proton. Why the top quark is such a monster, while being point-like in the same way that an electron is point-like, is a mystery. Although these extra generations of matter do not play a direct role in the ordinary affairs of the Universe they do seem to have been crucial players in the moments just after the Big Bang … but that is another story.

  Also shown in Figure 11.1, in the column on the right, are the force-carrying particles. Gravity is not represented in the table because we do not have a quantum theory of gravity that sits comfortably within the framework of the Standard Model. This isn’t to say that there isn’t one; string theory is an attempt to bring gravity into the fold but, to date, it has met with limited success. Because gravity is so feeble it plays no significant role in particle physics experiments and for that pragmatic reason we’ll say no more about it. We learnt in the last chapter how the photon is responsible for mediating the electromagnetic force between electrically charged particles and that its behaviour was determined by specifying a new branching rule. The W and Z particles do the corresponding job for the weak force while the gluons mediate the strong force. The primary differences between the quantum descriptions of the forces arise because the branching rules are different. It is (almost) that simple and we have drawn some of the new branching rules in Figure 11.2. The similarity with QED makes it easy to appreciate the basics of the weak and strong forces; we just need to know what the branching rules are and then we can draw Feynman diagrams like we did for QED in the last chapter. Fortunately, changing the branching rules makes all the difference to the physical world.

  If this were a particle physics textbook, we might proceed to outline the branching rules for each of the processes in Figure 11.2, and many more besides. These rules, known as the Feynman rules, would then allow you, or a computer program, to calculate the probability for some process or other, just as we outlined in the last chapter for QED. The rules capture something essential about the world and it is delightful that they can be summarized in a few simple pictures and rules. But this isn’t a particle physics textbook, so we’ll instead focus on the top-right diagram, because it is a particularly important branching rule for life on Earth. It shows an up quark branching into a down quark by emitting a W particle and this behaviour is exploited to dramatic effect within the core of the Sun.

  The Sun is a gaseous sea of protons, neutrons, electrons and photons with the volume of a million earths, collapsing under its own gravity. The vicious compression heats the solar core to 15 million degrees and at these temperatures the protons begin to fuse together to form helium nuclei. The fusion process releases energy, which increases the pressure on the outer layers of the star, balancing the inward pull of gravity. We’ll dig deeper into this precarious balancing act in the epilogue, but for now we want to understand what it means to say that ‘the protons begin to fuse together’.

  Figure 11.2. Some of the branching rules for the weak and strong forces.

  This sounds simple enough, but the precise mechanism for fusion in the Sun’s core was a source of great scientific debate during the 1920s and 30s. The British scientist Arthur Eddington was the first to propose that the energy source of the Sun is nuclear fusion, but it was quickly pointed out that the temperatures were apparently far too low for the process to occur given the then-known laws of physics. Eddington stuck to his guns, however, issuing the famous retort: ‘The helium which we handle must have been put together at some time and some place. We do not argue with the critic who urges that the stars are not hot enough for this process; we tell him to go and find a hotter place.’

&
nbsp; The problem is that when two fast-moving protons in the core of the Sun get close, they repel each other as a result of the electromagnetic force (or, in the language of QED, by photon exchange). To fuse together they need to get so close that they are effectively overlapping and, as Eddington and his colleagues well knew, the solar protons are not moving fast enough (because the Sun is not hot enough) to overcome their mutual electromagnetic repulsion.

  The answer to this conundrum is that the W particle steps in to save the day. In a stroke, one of the protons in the collision can convert into a neutron by converting one of its up quarks into a down quark, as specified by the branching rule in Figure 11.2. Now the newly formed neutron and remaining proton can get very close, because the neutron carries no electric charge. In the language of quantum field theory, this means there is no photon exchange to push the neutron and proton apart. Freed from the electromagnetic repulsion, the proton and neutron can fuse together (as a result of the strong force) to make a deuteron and this quickly leads to helium formation, releasing life-giving energy for the star. The process is illustrated in Figure 11.3, which also indicates that the W particle does not stick around for very long; instead it branches into a positron and a neutrino – this is the source of those very same neutrinos that pass through your body in such vast numbers. Eddington’s belligerent defence of fusion as the power source of the Sun was correct, although he could have had no inkling of the solution. The all-important W particle, along with its partner the Z, was eventually discovered at CERN in the 1980s.

  To conclude our brief survey of the Standard Model, we turn to the strong force. The branching rules are such that only quarks can branch into gluons. In fact they are much more likely to do that than they are to do anything else. This predisposition to emit gluons is why the strong force is so named and it is the reason why gluon branching is able to defeat the repulsive electromagnetic force that would otherwise cause the positively charged proton to explode. Fortunately, the strong force cannot reach very far. Gluons tend not to travel beyond around 1 femtometre (10−15 m) before they branch again. The reason why gluons are so short-ranging in their influence, whilst photons can reach across the Universe, is down to the fact that gluons can also branch into other gluons, as illustrated in the final two pictures in Figure 11.2. This trick of the gluons makes the strong force very different from the electromagnetic force, and effectively confines its actions to the interior of the atomic nucleus. Photons have no such self-branching and that is very fortunate, for if they did you wouldn’t be able to see the world in front of your eyes because the photons streaming towards you would scatter off those travelling across your line of sight. It is one of the wonders of life that we can see anything at all, and a vivid reminder that photons very rarely interact with each other.

  Figure 11.3. Proton conversion into a neutron by weak decay, with the emission of a positron and a neutrino. Without this, the Sun would not burn.

  We have not explained where all of these new rules come from, nor have we explained why the Universe contains the particles that it does. There is a good reason for this: we don’t really know the answers to either of these questions. The particles that make up our Universe – the electrons, neutrinos and quarks – are the primary actors in the unfolding cosmic drama, but to date we have no compelling way to explain why the cast should line up as it does.

  What is true, however, is that once we have the list of particles then the way they interact with each other, as prescribed by the branching rules, is something we can partially anticipate. The branching rules are not something that physicists have just conjured from nowhere – they are in all cases anticipated on the grounds that the theory describing the particle interactions should be a Quantum Field Theory supplemented with something called gauge symmetry. To discuss the origin of the branching rules would take us too far outside the main line of this book – but we do want to reiterate that the essential rules are very simple: the Universe is built from particles that move around and interact according to a handful of hopping and branching rules. We can take those rules and use them to compute the probability that ‘something’ does happen by adding together a bunch of clocks – there being one clock for each and every way that the ‘something’ can happen.

  The Origin of Mass

  By introducing the idea that particles can branch as well as hop we have entered into the domain of Quantum Field Theory, and hopping and branching is, to a large extent, all there is to it. We have, however, been rather negligent in our discussion of mass, for the good reason that we have been saving the best until last.

  Modern-day particle physics aims to provide an answer to the question ‘what is the origin of mass?’ and it does so with the help of a beautiful and subtle piece of physics and a new particle – new in the sense that we have not yet really encountered it in this book, and new in the sense that nobody on Earth has ever encountered one ‘face to face’. The particle is named the Higgs boson, and the LHC has it firmly in its sights. At the time of writing this book in September 2011, there have been tantalizing glimpses, perhaps, of a Higgs-like object in the LHC data, but there are simply not enough events1 to decide one way or the other. It may well be that, as you read this book, the situation has changed and the Higgs is a reality. Or it may be that the interesting signals have vanished under further scrutiny. The particularly exciting thing about the question of the origin of mass is that the answer is extremely interesting beyond the obvious desire to know what mass is. Let us now explain that rather cryptic and offensively constructed sentence in more detail.

  When we discussed photons and electrons in QED, we introduced the hopping rule for each and said that they are different – we used the symbol P(A,B) for the rule associated with an electron that hops from A to B and the symbol L(A,B) for the corresponding rule for a photon. It is time now to investigate why the rule is different in the two cases. There is a difference because electrons come in two different types (as we know, they ‘spin’ in one of two different ways), whilst photons come in three different types, but that particular difference will not concern us here. There is another difference, however, because the electron has mass while the photon does not – this is what we want to explore.

  Figure 11.4 illustrates one way that we are allowed to think about the propagation of a massive particle. The figure shows a particle hopping from A to B in stages. It goes from A to point 1, from point 1 to point 2 and so on until it finally hops from point 6 to B. What is interesting is that, when written in this way, the rule for each hop is the rule for a particle with zero mass, but with one important caveat: every time the particle changes direction we are to apply a new shrinking rule, with the amount of shrinking inversely proportional to the mass of the particle we are describing. This means that, at each kink, the clocks of heavy particles receive less shrinking than the clocks of lighter particles. It is important to emphasize that this isn’t an ad hoc prescription. Both the zig-zag and the shrink emerge directly from the Feynman rules for the propagation of a massive particle, without any further assumptions.2 Figure 11.4 shows just one way that our heavy particle can get from A to B, i.e. via six kinks and six shrinkage factors. To get the final clock associated with a massive particle hopping from A to B we must, as always, add together the infinity of clocks associated with all of the possible ways that the particle can zig-zag its way from A to B. The simplest route is the direct one, with no kinks, but routes with huge numbers of kinks need to be considered too.

  Figure 11.4. A massive particle travelling from A to B.

  For particles with zero mass the shrinkage factor associated with each kink is a killer, because it is infinite. In other words, we are to shrink the clock to zero after the first kink. The only route that matters for massless particles is therefore the direct route – there is simply no clock associated with any other route. This is exactly what we would expect: it means that we can use the hopping rule for massless particles when the particle is massless. However,
for particles with non-zero mass, kinks are allowed, although if the particle is very light then the shrinking factor imposes a severe penalty on paths with many kinks. The most likely paths are therefore those with very few kinks. Conversely, heavy particles do not get penalized much when they kink, and so they tend to be described by paths with lots of zig-zagging. This seems to suggest that heavy particles really ought to be thought of as massless particles that zigzag their way from A to B. The amount of zig-zagging is what we identify as ‘mass’.

  This is all rather nice, for we have a new way to think about massive particles. Figure 11.5 illustrates the propagation from A to B of three different particles of increasing mass. In each case, the rule associated with each ‘zig’ or ‘zag’ of the path is the same as that for a massless particle, and for every kink we are to pay a ‘the clock must be shrunk’ penalty. We should not get overly excited yet because we have not really explained anything fundamental. All we have done is to replace the word ‘mass’ with the words ‘tendency to zig-zag’. We are allowed to do this because they are mathematically equivalent descriptions of the propagation of a massive particle. But even so, it feels like an interesting thing and, as we shall now discover, it may turn out to be rather more than just a mathematical curiosity.