Farewell to Reality (12 page)

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 Z
⁰
.

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 Z
⁰
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 highly 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
⁺
, W
⁰
, W
^-
and B
⁰
. 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 W
⁰
and B
⁰
particles of the electro-weak force mix together to produce the massive Z
⁰
particle and the massless photon. We associate the massive W
⁺
, W
^-
and Z
⁰
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 Z
⁰
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 Z
⁰
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 Z
⁰
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 Z
⁰
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.