Farewell to Reality

by Jim Baggott

  In addition to these there are force particles. These include the photon. These are bosons, characterized by integral spins. They are not subject to Pauli’s exclusion principle. Bosons with zero spin are also possible, but these are not force particles. Mesons are examples.

  The taxonomy was a little like organizing the chemical elements into a periodic table. It helped to establish the patterns among the different particle classes but gave no real clue to the underlying explanation.

  The left hand of the electron

  Things were about to get even more complicated. A wavefunction, such as a sine wave, moves up and down as it oscillates between peak and trough. Parts of the wavefunction have positive amplitude (as it rises to the peak and falls back) and parts have negative amplitude (as it dips below the axis heading for the trough and comes back up again).

  The parity of the wavefunction is determined by its behaviour as we change the signs of the spatial co-ordinates in which the wave propagates. Think of this as changing left for right or up for down or front for back. Changing the signs of all three co-ordinates simultaneously is then a bit like reflecting the wavefunction in a special kind of mirror that also inverts the image and its perspective. The image is inverted left-to-right and up-to-down, and the front goes to the back as the back is brought forward to the front.

  If reflecting the wavefunction in such a ‘parity mirror’ doesn’t change the sign of the wavefunction’s amplitude, then the wavefunction is said to possess even parity. However, if the wavefunction amplitude does change sign (from positive to negative or negative to positive), then the wavefunction is said to have odd parity.

  Parity, like spin, is a property without many analogies in classical physics that are not thoroughly misleading. It is closely connected with and governs angular momentum in elementary particle interactions. As far as the physicists could tell, in all electromagnetic and nuclear interactions, parity is something that is conserved, like angular momentum itself. In other words, if we start with particles which when combined together have even parity, then we would expect that the particles that result from some physical process would also combine to give even parity. Likewise for particles with overall odd parity.

  This seemed consistent with the physicists’ instincts. How could it be possible for the immutable laws of nature to favour such seemingly human conventions of left vs right, up vs down, front vs back? Surely no natural force could be expected to display such ‘handedness’?

  As reasonable as this seems, in fact it is not consistent with what we observe. Parity is conserved in all electromagnetic interactions and processes involving gravity and the strong nuclear force. But nature exhibits a peculiar ‘handedness’ in interactions involving the weak force.

  The first definitive example of such parity violation came from a series of extremely careful experiments conducted towards the end of 1959 by Chien-Shiung Wu, Eric Ambler and their colleagues at the US National Bureau of Standards laboratories in Washington DC. These involved the measurement of the direction of emission of beta-electrons from atoms of radioactive cobalt-60, cooled to near absolute zero temperature, their nuclei aligned by application of a magnetic field. A symmetrical pattern of beta-electron emission would have suggested that no direction is specially favoured, and that parity is conserved. The asymmetrical pattern that was actually observed indicated that parity is not conserved.

  The experiments were unequivocal, and similar results have been observed in many other weak force interactions. Parity is not conserved in processes governed by the weak nuclear force. In fact, by convention, only ‘left-handed’ particles and ‘right-handed’ anti-particles actually undergo weak force interactions.

  Nobody really understands why.

  Unifying the electromagnetic and weak nuclear forces

  The ranges and strengths of electromagnetism and the weak nuclear force are so very different that it appears at first sight impossible to reconcile them. But what if, reasoned Schwinger in 1941, the carrier of the weak nuclear force is actually a massive particle equal in size to a couple of hundred times the proton mass? If a force is carried by such a massive particle then its range becomes very limited, as (unlike photons) massive particles are very sluggish. The force would also become considerably weaker.

  Schwinger realized that if the mass of such a weak force carrier could be somehow ‘switched off’, then the weak force would have a range and strength similar in magnitude to electromagnetism. This was the first hint that it might be possible to unify the weak and electromagnetic forces into a single ‘electro-weak’ force.

  The logic runs something like this. Despite the fact that they appear so very different, the electromagnetic and weak nuclear forces are in some strange way manifestations of the same ‘electro-weak’ force. They appear very different because something has happened to the carrier of what we now recognize as the weak force. Unlike the photon, it somehow gained a lot of mass, restricting the range of the force and greatly diminishing its strength relative to electromagnetism.

  Now, the key question was this. What happened to the carrier of the weak force to make it so heavy?

  The challenge was taken up in the 1950s by Schwinger’s Harvard graduate student, Sheldon Glashow. After some false starts, Glashow developed a quantum field theory of electro-weak interactions in which the weak force is carried by three particles. Two of these particles — now called the W+ and W- — are necessary to account for the fact that, unlike the case of electromagnetism, electrical charge is transferred in weak force interactions (a neutral neutron decays into a positively charged proton, for example). In effect, these particles are electrically charged, heavy versions of the photon. A third, neutral force carrier is also demanded by the theory. This was subsequently called the Z0.

  In this scheme beta-radioactivity could be explained this way. A neutron emits a massive W- particle and turns into a proton. The shortlived W- particle then decays into a high-speed electron (the beta-particle) and what is now understood to be an anti-neutrino.

  But there were more problems. The quantum field theory that Glashow developed predicted that the force carriers should be massless. And if the masses of the force carriers were added to the theory ‘by hand’, the equations couldn’t be renormalized.

  So, precisely how did the W+, W- and Z0 particles gain their mass?

  The ‘God particle’ and the origin of mass

  The solutions to these puzzles were found in the seven-year period 1964–71. The answer to the mass question was to invoke something called spontaneous symmetry-breaking.

  This is a rather grand phrase for what is a relatively simple phenomenon. There are many examples of spontaneous symmetry-breaking we can find in ‘everyday’ life. If we had enough patience, we could imagine that we could somehow balance a pencil finely on its tip. We would discover that this is a very symmetric, but very unstable, situation. The vertical pencil looks the same from all directions.

  But tiny disturbances in our immediate environment (such as small currents of air) are enough to cause it to topple over. When this happens, the pencil topples over in a specific, though apparently random, direction. The horizontal pencil no longer looks the same from all directions, and the symmetry is said to be spontaneously broken.

  We don’t need a PhD to work out that the less symmetrical state with the pencil lying on the table, pointing in a specific direction, has a lower energy than the more symmetrical state with the pencil balanced on its tip. Physicists call this more stable state the ground state of the system.

  They reserve the special term ‘vacuum state’ for the quantum state of lowest possible energy — the ground state with everything removed (the pencil, the table, me, you and every last electron and photon). Now, let’s set aside for a moment everything we learned in the last chapter about quantum fluctuations in the vacuum and think of it as just ‘empty’ space, what the philosophers of Ancient Greece used to call ‘void’. Of course, such an empty space would be hig
hly symmetrical — like the pencil, it would look the same from all possible directions.

  But aside from random quantum fluctuations, what if empty space isn’t actually empty? What if it contains a quantum field that, like the air currents that tip the pencil, spontaneously breaks the symmetry, giving a state of even lower energy?

  When applying this idea to a particular problem in the quantum field theory of superconducting materials, American physicist Yoichiro Nambu realized that spontaneous symmetry-breaking can result in the formation of particles with mass. Some years later he wrote:

  What would happen if a kind of superconducting material occupied all of the universe, and we were living in it? Since we cannot observe the true vacuum, the [lowest-energy] ground state of this medium would become the vacuum, in fact. Then even particles which were massless … in the true vacuum would acquire mass in the real world.9

  Physicists call this lower-energy, more stable vacuum state a ‘false’ vacuum. False, because although it contains nothing of obvious substance, it isn’t empty. It contains a quantum field that breaks the symmetry.

  It was now possible to put two and two together, although the path to a formal solution was still rather tortuous. In 1964 there appeared a series of papers detailing a mechanism for spontaneous symmetry-breaking applied to quantum field theory. These were published independently by Belgian physicists Robert Brout and François Englert, English physicist Peter Higgs at Edinburgh University, and Gerald Guralnik, Carl Hagen and Tom Kibble at Imperial College in London. The mechanism is commonly referred to as the Higgs mechanism.

  It works like this. Prior to breaking the symmetry, the electro-weak force is carried by four massless particles which, for the sake of simplicity, we will call the W+, W0, W- and B0. A massless field particle has two ‘degrees of freedom’ and moves at the speed of light. For the photon, these two degrees of freedom are related to the particle’s spin orientations. We perceive these different spin states as left-circular and right-circular polarization or, when combined in the right way, vertical (up/down) and horizontal (left/right) polarization. Although space is three-dimensional, special relativity forbids the photon from having polarization in a third (forward/back) direction.

  In a conventional quantum field theory of the kind that Glashow developed, there is nothing to change this situation. Massless particles continue to be massless.

  But what if we now assume that the vacuum isn’t actually empty? What happens if we introduce a false vacuum by adding a background quantum field (often called a Higgs field) to break the symmetry? In this situation, massless particles interact with the Higgs field and acquire a third degree of freedom. The W+ and W- particles acquire ‘depth’ and get ‘fat’. This act of gaining three-dimensionality is like applying a brake: the particles slow down to an extent which depends on the strength of their interaction with the field. The field drags on them like molasses.

  In other words, the interactions of each particle with the Higgs field are manifested as a resistance to the particle’s acceleration.*

  Now, we tend to think of an object’s resistance to acceleration as the result of its inertial mass. Our instinct is to assume that mass is a primary or intrinsic quality, and we identify inertial mass with the amount of ‘stuff’ that the object possesses. The more stuff it has, the harder it is to accelerate.

  But the Higgs mechanism turns this logic on its head. The extent to which an otherwise massless particle’s acceleration is resisted by the Higgs field is now interpreted as the particle’s (inertial) mass. Mass has suddenly become a secondary quality. It is the result of an interaction, rather than something that is intrinsic to matter.

  The W0 and B0 particles of the electro-weak force mix together to produce the massive Z0 particle and the massless photon. We associate the massive W+, W- and Z0 particles with the (now broken) weak force and the massless photon with electromagnetism.

  In their publications, Brout, Englert, Higgs, Guralnik, Hagen and Kibble had not sought to apply this mechanism to the problem of the carriers of the electro-weak force. This task fell to American physicist Steven Weinberg. Weinberg had been struggling to apply the Higgs mechanism to a quantum field theory of the strong nuclear force, when he was suddenly struck by another idea: ‘At some point in the fall of 1967, I think while driving to my office at MIT, it occurred to me that I had been applying the right ideas to the wrong problem.’10

  ‘My God,’ he exclaimed to himself, ‘this is the answer to the weak interaction!’11

  In November 1967, Weinberg published a paper detailing a unified electro-weak quantum field theory. In this theory spontaneous symmetry-breaking using the Higgs mechanism is responsible for the differences between electromagnetism and the weak nuclear force in terms of strength and range. These differences can be traced to the properties of the W+, W- and Z0 particles, which gain mass, and the photon, which remains massless. Weinberg estimated that the W particles would each have a mass about 85 times that of the proton, and the Z0 would be slightly heavier, with a mass about 96 times the proton mass.

  A quantum field must have an associated field particle. In 1964, Higgs had referred to the possibility of the existence of what would later become known as a ‘Higgs boson’, the elementary particle of the Higgs field. Three years later, Weinberg had found it necessary to introduce a Higgs field with four components. Three of these give mass to the W+, W- and Z0 particles. The fourth appears as a physical particle — a Higgs boson with a spin quantum number of 0. If the Higgs mechanism really is responsible for the masses of the W+, W- and Z0 particles, then not only should these particles be found with the predicted masses, but the Higgs boson should be found, too.

  In Britain, Tom Kibble introduced the idea of spontaneous symmetry-breaking to one of his colleagues at Imperial College, Pakistan-born theorist Abdus Salam. Salam independently developed a unified electro-weak theory at around the same time. Both Weinberg and Salam believed that the theory should be renormalizable, but neither was able to prove this.

  The proof followed in 1971. By sheer coincidence, Dutch theorists Martinus Veltman and Gerard ’t Hooft rediscovered the field theory that Weinberg had first developed four years earlier, but they could now show how it could be renormalized. ’t Hooft had initially thought to apply the theory to the strong nuclear force, but when Veltman asked a colleague about other possible applications, he was pointed in the direction of Weinberg’s 1967 paper. Veltman and ’t Hooft now realized that they had developed a fully renormalizable quantum field theory of electro-weak interactions.

  This was all fine in theory, but what of experiment?

  The electro-weak theory makes three principal predictions. First, if the weak nuclear force really does require three force carriers, then the exchange of one of these — the Z0 — should result in weak force interactions involving no change in charge. To all intents and purposes, these interactions look just like interactions involving the exchange of a photon. The physicists call such interactions ‘weak neutral currents’ — they involve the weak force and result in no exchange of electrical charge (they are neutral).

  Such currents were identified in particle accelerator experiments performed at CERN in Geneva in 1973, and subsequently at the US National Accelerator Laboratory (which was renamed Fermilab in 1974).

  Second, Weinberg had predicted the masses for all the weak force carriers. At the time he made these predictions there was no particle accelerator large enough to observe them. But in the years that followed, a new generation of particle colliders was constructed in America and at CERN. The discovery of the W particles at CERN was announced in January 1983, with masses 85 times that of the proton, just as Weinberg had predicted. The discovery of the Z0 was announced in June that year, with a mass about 101 times that of a proton.12

  The third prediction concerns the existence of the Higgs boson. Given that the Higgs mechanism allows the masses of the weak force carriers to be predicted with such confidence, the existence of a H
iggs field — or something very like it — seems a ‘sure thing’. However, there are alternative theories of symmetry-breaking that do not require a Higgs field, and there remain problems with the electro-weak theory which erode our confidence somewhat and suggest that we might not yet have the full story.

  The question of whether or not the Higgs boson exists in nature is therefore of fundamental importance.

  On 4 July 2012, scientists at CERN’s Large Hadron Collider declared that they had discovered a new particle ‘consistent’ with the standard model Higgs boson. After hearing presentations from the two detector collaborations, ATLAS and CMS, CERN director-general Rolf Heuer declared: ‘As a layman I would say that I think we have it. Do you agree?’13

  The new boson was found to have a mass around 133 times that of a proton14 and interacts with other standard model particles in precisely the way expected of the Higgs. Apart from some slight anomalies, notably an observed enhancement in the decay into two photons (H → γγ), the new boson’s decay modes to other particles have the ratios expected of a standard model Higgs. Whilst the ATLAS and CMS experiments were clear that this is a boson, neither could be clear on the precise value of its spin quantum number, which on the basis of the experimental results could be 0 or 2. However, the only particle anticipated to have spin-2 is the graviton, the purported carrier of the force of gravity. Spin-0 is therefore much more likely.

  Although further research is required to characterize the new particle fully, the default assumption is that this is indeed a Higgs boson. But which Higgs boson? The standard model needs just one to break the electro-weak symmetry, though there are theories that extend beyond the standard model which demand rather more. The only way to find out precisely what kind of particle has been discovered is to explore its properties and behaviour in further experiments.

  CERN commented:

  Positive identification of the new particle’s characteristics will take considerable time and data. But whatever form the Higgs particle takes, our knowledge of the fundamental structure of matter is about to take a major step forward.15