by Jim Baggott
Although the Higgs mechanism was invoked to explain how the carriers of the weak force acquire their mass, it is now understood that this is the mechanism by which all elementary particles gain mass. In a book published in 1993, American physicist Leon Lederman emphasized* the fundamental role played by the Higgs boson and called it the God particle.
Not many practising physicists like it, but it is a name that has stuck.
Three (actually, six) quarks for Muster Mark!
The flurry of experimental activity that established the ‘zoo’ of particles in the late 1950s demanded some simplifying theoretical scheme. Significant advances were made in the early 1960s. Further patterns identified by American theorist Murray Gell-Mann and Israeli Yuval Ne’eman called attention to the possibility that the hadrons might actually all be composite particles made of three even more elementary particles then unknown to experimental science.
The patterns suggested that hadrons such as the proton and neutron should no longer be considered to be elementary particles, but are instead composed of smaller constituents. But there was a big problem.
When Gell-Mann’s colleague Robert Serber broached this idea over lunch at Columbia University in New York in 1963, Gell-Mann was initially dismissive.
It was a crazy idea. I grabbed the back of a napkin and did the necessary calculations to show that to do this would mean that the particles would have to have fractional electric charges — -⅓, +⅔, like so — in order to add up to a proton or neutron with a charge of plus or zero.16
By this time, more than fifty years had elapsed since the idea of a fundamental unit of electrical charge had been established, and there had been no hints that there might be exceptions. But despite these worrying implications, there was no doubting that a system of smaller elementary particles did provide a potentially powerful explanation for the pattern of hadrons. Gell-Mann called these odd new particles ‘quarks’.*
At that time the pattern of particles demanded three quarks, which were called ‘up’, with a charge of +⅔, ‘down’, with a charge of -⅓, and ‘strange’, a heavier version of the down quark, also with a charge of -⅓. The baryons known at that time could then be formed from various permutations of these three quarks and the mesons from combinations of quarks and anti-quarks.
In this scheme the proton consists of two up quarks and a down quark, with a total charge of +1. The neutron consists of an up quark and two down quarks, with a total charge of zero. Beta radioactivity could now be understood to involve the conversion of a down quark in a neutron into an up quark, turning the neutron into a proton, with the emission of a W- particle.
Hints that there might be a fourth quark emerged in 1970. This was a heavy version of the up quark with a charge of +⅔, and was called ‘charm’. It was now understood that the neutrino was paired with the electron (thus it is now called the electron neutrino). The muon neutrino was discovered in 1962. It seemed possible that the elementary building blocks of material substance consisted of two ‘generations’ of matter particles. The up and down quarks, the electron and electron neutrino formed the first generation. The charm and strange quarks, muon and muon neutrino formed a heavier second generation.
Most physicists were generally sceptical that a fourth quark was needed. But when another new particle, called the J/ψ, was discovered in 1974 simultaneously at Brookhaven National Laboratory in New York and the Stanford Linear Accelerator Center (SLAC) in California, it was realized that this must be a meson formed from charm and anti-charm quarks. Here was physical evidence that the charm quark exists. The scepticism vanished.
Such was the physicists’ commitment to the emerging standard model of particle physics that when the discovery of yet another, even heavier, version of the electron — called the tau — was announced in 1977, it was quickly accommodated in a third generation of matter particles. American physicist Leon Lederman found the upsilon at Fermilab in August 1977, a meson consisting of what had by then come to be known as a bottom quark and its anti-quark. The bottom quark is a heavier, third-generation version of the down and strange quarks with a charge of -⅔.
The discoveries of the top quark and the tau neutrino were announced at Fermilab in March 1995 and July 2000 respectively. Together they complete the heavier third generation of matter particles, which consists of the top and bottom quarks, the tau and tau neutrino. Although further generations of particles are not impossible, there is some reasonably compelling experimental evidence to suggest that three generations is all there is.
Asymptotic freedom and the colour force
The quark model was a great idea, but at the time these particles were proposed there was simply no experimental evidence for their existence. Gell-Mann was himself rather cagey about the status of his invention. He had argued that the quarks were somehow ‘confined’ inside their larger hosts and, wishing to avoid getting bogged down in philosophical debates about the reality or otherwise of particles that could never be seen, he referred to them as ‘mathematical’.
But experiments carried out at SLAC in 1968 provided strong hints that the proton is indeed a composite particle, made up of even smaller, more elementary constituents. It was not clear that these constituents were necessarily quarks, and the experimental results suggested that, far from being held together tightly, they were actually rattling around inside the proton as though they were entirely free. How could this be squared with the notion of quark confinement?
This puzzle was cleared up in 1973 by Princeton theorists David Gross and Frank Wilczek, and independently by David Politzer at Harvard. When we imagine a force acting between two particles, we tend to think of examples such as gravity or electromagnetism, in which the force grows stronger as the particles move closer together. But the strong nuclear force doesn’t behave this way. The force exhibits what is known as asymptotic freedom. In the asymptotic limit of zero separation between two quarks, the particles feel no force and are completely ‘free’. As the separation between them increases beyond the boundary of the proton or neutron, however, the strong force tightens its grip.
It is as if the quarks are fastened to each end of a piece of strong elastic. When they are close together, the elastic is loose. There is little or no force between them. But as we try to pull the quarks apart, we begin to stretch the elastic. The force increases the harder we pull.
Building on earlier work, Gell-Mann, German theorist Harald Fritzsch and Swiss theorist Heinrich Leutwyler now developed a quantum field theory of the strong nuclear force. In addition to the quark ‘flavours’ — up, down, strange, etc. — they introduced a new variable which they called ‘colour’. Each quark can possess one of three different colour ‘charges’ — red, green or blue.
Baryons are formed from three quarks each of a different colour, such that their total ‘colour charge’ is zero and the resulting particle is ‘white’. For example, a proton may consist of a blue up quark, a red up quark and a green down quark. A neutron may consist of a blue up quark, a red down quark and a green down quark. The mesons, such as pions and kaons, consist of coloured quarks and their anti-coloured anti-quarks, such that the total colour charge is zero and the particles are also ‘white’.
In this model, quarks are bound together by a ‘colour force’, carried by eight massless particles called gluons, which also carry colour charge and, like the quarks, are confined inside the hadrons. Gell-Mann called the theory quantum chromodynamics, or QCD.
In essence, this completes the standard model of particle physics. The model consists of three generations of matter particles, a collection of force particles and the Higgs boson (Figure 2). The interactions of these particles are described by a combination of electro-weak field theory and QCD. The electro-weak theory is itself a combination of weak force theory (sometimes referred to as quantum flavour dynamics, or QFD)* and QED, their distinction forced as a result of the Higgs mechanism. We can therefore think of the standard model as the combination QCD × QFD × QED.
There is, at the time of writing, no observation or experimental result in particle physics that cannot be accommodated within this framework.** It is not the end, however, as we will see.
The construction of mass
I have a heavy glass paperweight on the desk in front of me. Where, exactly, does the mass of this paperweight reside?
The paperweight is made of glass. It has a complex molecular structure consisting primarily of a network of silicon and oxygen atoms bonded together. Obviously, we can trace its mass to the protons and neutrons which account for 99 per cent of the mass of every silicon and oxygen atom in the structure. Not so very long ago, we might have stopped here, satisfied with our answer.
Figure 2 The standard model of particle physics describes the interactions of three generations of matter particles through three kinds of force, mediated by a collection of field particles or ‘force carriers’. Note that only ‘left-handed’ leptons and quarks experience the weak nuclear force. The masses of the matter and force particles are determined by their interactions with the Higgs field.
But we now know that protons and neutrons are made of quarks. So, we conclude that the mass of the paperweight resides in the cumulative masses of the quarks from which they are composed. Right?
Wrong. Because the quarks are confined, it’s quite difficult to determine their masses, but it is known that they are substantially smaller and lighter than the protons and neutrons that they comprise. For example, the Particle Data Group quotes mass ranges for both up and down quarks. If we pick masses at the higher end of these ranges and add the masses of two up quarks and a down quark, we get a result that represents about 1 per cent of the mass of a proton.
Hang on a minute. If 99 per cent of the mass of a proton is not to be found in its constituent quarks, where is it?
The answer to this question demands an understanding of colour charge. The Ancient Greeks used to claim that nature abhors a vacuum. A contemporary version of this aphorism might read: ‘nature abhors a naked colour charge’.
In principle, the energy of a single isolated quark is infinite, which is why individual quarks have never been observed. It is much less expensive in energy terms to mask the colour charge that would be exposed by an individual quark either by pairing it with an anti-quark of the corresponding anti-colour or combining it with two other quarks of different colour such that the net colour charge is zero.
However, even within the confines of a proton or neutron, it is not possible to mask the exposed colour charges completely. This would require that nature somehow pile the quarks directly on top of one another, so that they all occupy the same location in space and time. But quarks are quantum wave particles, and they can’t be pinned down this way — Heisenberg’s uncertainty principle forbids it.
Nature settles for a compromise. Inside a proton or neutron the colour charges are exposed and the energy — manifested in the associated gluons that are exchanged between them — increases. The increase is manageable, but it is also substantial. The energy of the gluons inside the proton or neutron builds up, and although the gluons are massless, through m = E/c2 their energy accounts for the other 99 per cent of the particle’s mass.
And there you have it. For centuries we believed that it would one day be possible to identify the ultimate constituents of material substance, the ultimate ‘atoms’ of matter from which everything is constructed. This was Dirac’s dream. We assumed that such constituents would possess certain characteristic physical properties, such as the primary quality of mass.
What the standard model of particle physics tells us is far stranger and, consequently, far more interesting. There do appear to be ultimate constituents (at least for now), and they do have characteristic physical properties, but mass is not really one of them. Instead of mass we have interactions between constituents that would otherwise be massless and the Higgs field. These interactions slow the particles down, giving rise to behaviour that we interpret as mass. As the constituents combine, the energy of the massless force particles passing between them builds, adding to the impression of solidity and substance.
Nobody said that science would deliver a description of empirical reality that was guaranteed to be easily comprehensible. But it is nevertheless rather disconcerting to have the rug of our common experience of light and matter pulled from beneath our feet in this way.
* At first sight this might seem an odd thing to demand, but it ensures that the ‘laws’ of nature that we deal with in our theories are genuine laws, independent of any specific point of view.
* On 23 September 2011, physicists at CERN’s OPERA experiment reported results that suggested that neutrinos travelling the 730 kilometres from Geneva to Italy’s Gran Sasso laboratory do so with a speed slightly greater than that of light. Data collected from over 16,000 events recorded over a three-year period suggested that the particles were arriving about 61 billionths of a second earlier than expected. Such faster-than-light neutrinos would have represented a fundamental unravelling of Einstein’s special theory of relativity and thus the current authorizsed version of reality. Many scientists were sceptical of the results and some argued that they couldn’t be correct. On 22 February 2012, the OPERA results were shown to be erroneous, and a loose fibre-optic cable was blamed. The claims were withdrawn, and a couple of high-profile members of the collaboration resigned their positions.
* Note that it is accelerated motion which is impeded. Panicles moving at a constant velocity are not affected by the Higgs field. For this reason the Higgs field is not in conflict with the demands of Einstein’s special theory of relativity.
* Or over-emphasized, depending on your point of view.
* At around the same time, American physicist George Zweig developed an entirely equivalent scheme based on a fundamental triplet of particles that he called ‘aces’. Zweig struggled to get his papers published, but Gell-Mann subsequently made strenuous efforts to ensure Zweig’s contributions were recognized.
* This might suggest that the theory applies only to quarks, but the different kinds of leptons (electron, muon, tau and their corresponding neutrinos) are also sometimes referred to as ‘flavours’.
** Provided, that is, that the particle recently discovered at CERN proves to be the standard model Higgs boson.
4
Beautiful Beyond Comparison
Space, Time and the Special and General Theories of Relativity
The theory is beautiful beyond comparison. However, only one colleague has really been able to understand it …
Albert Einstein1
When Newton published his classic work Philosophiœ Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy) in 1687, he defined an authorized version of reality that was to prevail for more than two hundred years. Newton’s mechanics became the basis on which we sought to understand almost everything in the physical world. There appeared to be no limits to its scope, from the familiar objects of everyday experience here on earth to objects in the furthest reaches of the visible universe.
But Newton had been obliged to sweep at least two fundamental problems under the carpet. The first of these appeared to be largely philosophical, and therefore (it could be argued) a matter of personal preference. The second seemed no less philosophical but was more visibly physical, and disconcerting. It would fall to Einstein, and those physicists and philosophers who inspired him and on whose work he built, to resolve these problems from within his special and general theories of relativity.
Einstein’s theories of relativity were radically to transform how we seek to comprehend space and time, and the ways in which space and time respond to the presence of material substance.
After Einstein, reality would never be quite the same again.
Newton’s bucket
The first problem Newton had to confront concerned the very nature of space and time. Are these things aspects of an independent physical reality? Do they exist independentl
y of objects and of perception or measurement? In other words, are they ‘absolute’ things-in-themselves?
Take your eyes away from this book and look around you. What do you see? That’s easy. You see objects in your immediate environment — perhaps chairs, a table, a TV in the corner of the room. These, you conclude, are objects in space.
But what, precisely, is space? Can you see it? Can you touch it? Well, no, you can’t. Space is not something that we perceive directly. We perceive objects, and these objects have certain relations with one another which we might be tempted to call spatial relations, but space itself does not form part of the content of our direct experience. Our interpretation of the objects as existing in a three-dimensional space is the result of a synthesis of sense impressions in our brains translated by our minds.*
Similarly, you can’t reach out and touch time. Time is not a tangible object. Your sense of time would seem to be derived from your sense of yourself and the objects around you changing their relative positions, or changing their nature, from one type of thing into another.
The pragmatists among us shrug their shoulders (again). So what? Just because we can’t perceive these things directly doesn’t mean they aren’t ‘real’. Newton was inclined to agree, although he was willing to acknowledge the essential relativity of space and time in our ‘vulgar’ experience. Objects move towards or away from each other, changing their relative positions in space and in time. This is relative motion, occurring in a space and time defined only by their relationships to the objects of reality.
But Newton’s mechanics demanded an absolute motion. He argued that, although we can’t directly perceive them, absolute space and time really do exist, forming a ‘container’ within which matter and energy can interact. Take all the matter and energy out of the universe, he decreed, and the empty container would remain: there would still be ‘something’.