by Harry Cliff
The protons collide at the center of this huge barrel, sending particles flying out through concentric subdetectors, like the layers of an onion, each of which provides different information about the particles: their momentum, energies, directions, and so on. My specific project involved helping to get one of these layers, known as the “electromagnetic calorimeter” (ECAL), ready for data collecting.
The ECAL is one of the star features of CMS, a gleaming crystal cylinder made up of more than 75,000 transparent blocks of lead tungstate, a compound of lead, tungsten, and oxygen that looks like glass but has the heft of a block of lead. When an electron or photon smacks into one of these crystal blocks, it releases a burst of light, which is recorded by a sensor glued to one end, allowing the energies of the photon or electron to be measured.
The challenges of building the ECAL were immense. Each crystal had to be grown slowly over a period of two days in specially designed platinum-lined crucibles, and the number needed was so huge that a former Soviet military factory had to be recommissioned for the purpose, which along with a second facility in China spent ten years churning out crystals, day in, day out. What’s more, the Chinese facility didn’t have access to the quantities of platinum required to line the crucibles, and so the CMS management team had to go to the vaults of UBS in Zurich and borrow $10 million worth of platinum on the promise that it would be returned once the crystals were finished.
You might wonder why you would go to such great lengths to build just one component of the detector. Well, the ECAL has an absolutely critical role in the experiment: its job is to measure the energies of photons and electrons, and it needs to be able to do this fantastically precisely. Why? Well, it all comes down to the raison d’être of the Large Hadron Collider: to find the last missing piece of the standard model of particle physics, a particle whose existence would finally explain the origin of two of the forces of nature and why fundamental particles have mass. In fact, it was so important to our understanding of the laws of nature that it became, rather hyperbolically (and unhelpfully), known as the “God particle.” I am speaking, of course, of the Higgs boson.
Back in the 1990s, the physicists planning CMS realized that one of the best ways to spot signs of the Higgs would be via its decay into two high-energy photons. As is the case with most new particles discovered at colliders, you could never hope to detect a Higgs boson directly. If one got produced by a collision at the LHC, it would decay into other particles almost as soon as it came into being, living far too short a time to reach the sensitive parts of the detector. Instead, all you would detect would be the particles it decays into. Physicists would then have to wade through huge quantities of data in search of particles that might have been produced by the decay of a Higgs, and its decay into two photons would be the easiest to spot. Easy being a relative term of course.
Difficult to build as CMS was, the physicists knew their crystal electromagnetic calorimeter would give them the best possible chance of snaring the Higgs’s telltale decay into two photons. As I stood in that hangar in July 2007, the gargantuan construction project was almost at an end. In just a few short months, the last mighty slab of CMS would be hoisted by the giant crane attached to the roof of the hangar and slowly and delicately lowered into position.
My small role in all this was to write some computer code to convert the amount of light detected by the sensors that were glued to the back of each of these crystal blocks into a measurement of energy. Before I saw CMS, it had seemed like a pretty unstimulating task, but after that visit, I realized how fortunate I was to be able to contribute in even a small way to such a herculean effort.
There was a palpable tension in the air over those hot summer months. As we students got on with our little projects, sought out what scant nightlife was available in Geneva on a student budget, and sat bleary-eyed in lectures the next morning, thousands of physicists, engineers, and computer scientists were working determinedly to prepare for the start of the greatest experiment ever attempted by the human race.
The first major target of this colossal machine would be the Higgs boson, a particle originally predicted almost half a century earlier and one that is the keystone of our modern understanding of the makeup of matter. It is also the last known ingredient that we’ve yet to include in our apple pie recipe. To understand why the Higgs boson is so important and why so many decades of work and billions of dollars were spent in finding it, we are going to need to go even deeper into the strange world of quantum fields. A health warning: what follows includes some truly mind-melting stuff, but, if you persevere, I will try to show you, as best I can, some of the most profound and beautiful ideas in modern science.
HIDDEN SYMMETRY, UNIFICATION, AND THE BIRTH OF A BOSON
To understand why the Higgs is so darn important, we need to go right back to basics and think about the structure of matter. Everything is made of atoms, and an atom is made of negatively charged electrons orbiting a tiny positively charged nucleus. Probe deep inside the nucleus and you find protons and neutrons, go deeper still and you discover that protons and neutrons are made of up and down quarks. Thus, all matter is made from just three fundamental particles: electrons, up quarks, and down quarks. So far so familiar.
Of course, matter is not just the sum of its parts. The structure of an atom is as much determined by the forces that hold it together as it is by its building blocks. We have already encountered two of these forces: the electromagnetic force that binds electrons to the nucleus, and the strong force that holds quarks together inside protons and neutrons. Both of these forces are communicated by quantum fields—the electromagnetic field and the gluon fields—and if you put a discrete packet of energy into one of these quantum fields you create a little quantized ripple (aka a particle), known as a photon or a gluon.
However, there is a third force that we haven’t discussed in detail, arguably the weirdest of all the fundamental forces: the weak force. The weak force is unique among the known forces as the only one that allows one type of fundamental particle to transform into another. The first evidence for the weak force’s influence was Henri Becquerel’s discovery of radioactivity back in 1896. As Ernest Rutherford described a couple of years later, one type of radioactivity known as beta decay involved an unstable nucleus spitting out an electron. This led to no end of confusion for many years, as physicists not unreasonably assumed that if an electron came out of a nucleus, then it must have existed in the nucleus to start with. However, by the 1930s it was realized that this was wrong. There are no electrons in the nucleus; instead during beta decay a neutron transforms into a proton, an electron, and an antineutrino, and it does this via a new fundamental force, the weak force.*3
However, in the 1930s the true nature of the weak force was far from understood. A successful theory had been written down by the Italian-American superstar Enrico Fermi, who described beta decay in terms of a neutron decaying directly into a proton, electron, and antineutrino without the need for any extra force fields to help the decay along. It became clear though that Fermi’s theory was only an approximate description. When you calculated its consequences at higher and higher energies eventually the theory broke down and gave nonsensical answers, spitting out probabilities that were bigger than 100 percent.
Clearly, a more fundamental theory was needed, and by the 1950s physicists had found what seemed like the perfect candidate: quantum field theory. The first successful quantum field theory described the electromagnetic force. Known as “quantum electrodynamics,” it was assembled over a period of years by a stellar cast of physicists including Hans Bethe, Freeman Dyson, Richard Feynman, Julian Schwinger, and Shin’ichirō Tomonaga. Quantum electrodynamics, or QED for short, is the most precise scientific theory ever written down, describing the way charged particles interact with the electromagnetic field with dazzling precision, in some cases making predictions that agree with experiments to better than 1 pa
rt in 10 billion.
At the heart of this stonkingly successful theory was a truly beautiful principle, the principle of “local gauge symmetry.” First introduced by Julian Schwinger, this principle implied something utterly magical—that the fundamental forces arise because of deep symmetries in the laws of nature.
That’s quite a claim, and it requires a bit of unpacking. First, we need to take one step back and consider the wider role of symmetry in physics. The first person to truly understand the power of symmetry in shaping the physical word was the brilliant German mathematician Emmy Noether. Her greatest gift to physics was Noether’s theorem, which shows that if the universe is symmetric in a particular way, then there must be a corresponding quantity that is always conserved. What do we mean by symmetric? Well, as we’ve already seen, a symmetry exists if there is something you can do to a system, be it a physical object or the entire universe, that leaves it unchanged. Take a square and turn it by 90, 180, 270, or 360 degrees and it will look exactly the same as before you rotated it—a square has rotational symmetry.
The same is true for the laws of nature themselves. Imagine that you are a scientist on board an interstellar spaceship, way out in deep space, far beyond the gravitational influence of the Earth or the Sun. You could ask a question: Does the direction that my spaceship is pointing make any difference to the results of any experiment I could think of doing on board? If the answer to this question is that it makes no difference, then we can say that the laws of nature are symmetric under rotations in space. Or put another way, the universe doesn’t care which way you are pointing.*4
Noether’s theorem tells us that this rotational symmetry implies the existence of a conserved quantity—one that never gets bigger or smaller—which turns out to be angular momentum, the amount of rotational oomph possessed by a system.*5 Countless experiments have shown that it is always conserved; it cannot increase or decrease, it can only be redistributed among the component parts of a system. This means that if you set a rigid object spinning in the vacuum of space, it will keep on spinning forever at exactly the same rate, so long as nothing comes along and bumps into it. This is why Earth keeps turning so reliably—day always follows night because of the rotational symmetry of the laws of nature.
The same symmetry principle explains why energy and momentum are always conserved. Energy conservation is due to the fact that the laws of nature don’t change with time, while the conservation of momentum is due to the fact that the laws of nature are the same everywhere in space. However, there is an even more remarkable consequence of symmetry: symmetries seem to be responsible for the forces of nature.
The symmetries connected to the conservation laws that I just described are called “global symmetries,” which means they involve transformations that are the same at every point in time and space. For instance, a global transformation could involve rotating the whole universe by 90 degrees or shifting the entire universe 1 foot to the right. If the universe looks the same after you’ve done this, then it possesses a global symmetry.
However, the symmetries connected to the fundamental forces are local symmetries, meaning that they involve transformations that vary in time and space. The sorts of local transformations that play a role in particle physics are rather harder to visualize, so let’s start with an analogy.
Consider two teams playing a game of football on a flat, well-manicured field. Now imagine that we had the godlike power to raise the level of the field by an arbitrary amount, it could be a meter or a mile. Apart from the fact that the players might struggle to breathe if we lifted the field too high, as long as we raised the whole field by the same amount, this should have absolutely no effect on how the game is played. As a result, we can say that football is symmetric under a global change of field height.
Now let’s imagine that instead of raising the entire field by the same amount, we somehow conspired to tip it at an angle so that one team found themselves playing uphill and the other downhill. This would count as a local transformation since the change of ground level depends on where you are on the field. Clearly, such a transformation would have a big impact on the game; I imagine (though as my friends will tell you I know absolutely f-all about football) it would be far easier to reach the goal at the bottom of the field than the one at the top, giving one team a big advantage. In other words, this local transformation does not result in a symmetry.
However, what if we were being really stubborn and insisted that we somehow wanted to restore fairness to the game? Well, one way to do this would be to use our aforementioned godlike powers to create a wind that blew constantly uphill, making it harder for the team playing downhill to reach the goal and easier for the team playing uphill. In other words, symmetry is restored by introducing a force.
Amazingly, this is not a million miles from how the electromagnetic force arises in QED, except that instead of a game of football we are now considering the rules governing the way electrons and other charged particles behave. As we’ve discussed over the last couple of chapters, an electron is a wave or vibration in the electron field. Just like a wave on the ocean, this wave changes with time. If you look at one point in space, sometimes the vibration in the electron field will be big, at other times it will be small, following a characteristic cycle as it wobbles up and down. Where you are in this cycle is known as the “phase” of the wave. You can think of the phase as like a little clock that tells you how far through a wobble in the electron field you are.
Just like with the level of our imaginary football field, it is possible to ask what happens if we perform transformations to the electron field’s phase. First, let’s say we make a global transformation, shifting the electron’s internal clock by a uniform amount, say a half cycle, everywhere in space and time. According to Noether’s theorem, if this global transformation has no effect on how the electron field behaves, then a conserved quantity exists, which, rather incredibly, turns out to be none other than electric charge. Or to put it another way, electric charge is conserved because of a global symmetry.
Now for the really amazing part. Let’s say we introduce a phase shift that varies in space and time. Imagine, if you will, a vast array of tiny clocks describing the phase of the electron field, one for each point in space and time. A local transformation could mean that over here the hand of the clock is shifted forward a quarter turn, while over there it’s shifted back by a half. If we want to be able to introduce different phase shifts at different places and times without affecting the way the electron field behaves then we discover that we have no choice but to introduce a new quantum field. And most remarkably of all, this new field has the precise properties of the electromagnetic field. The electromagnetic field acts like the wind on our sloped football field, correcting the effect of shifting the phase of the electron field unevenly through space and time.
It’s worth pausing for a moment to appreciate how tremendous an insight this is. According to QED, your fridge magnet sticks to your fridge, electric currents flow through wires, and atoms have the structure that they do ultimately because of deep symmetries in the laws of nature. When I first learned this fact as an undergraduate, it left me in awe. Years later it still feels a little bit like magic.
In QED, the collection of phase transformations that gives rise to the electromagnetic field is described by a mathematical object known as the U(1) symmetry group. What this group is in detail doesn’t really matter for our purposes, but the important point is that if you demand that the laws of nature don’t change when you perform a local U(1) phase transformation, then the electromagnetic field must exist. Even better, the mathematical structure of U(1) completely determines the rules of electromagnetism and all the phenomena that depend on them, from the way sunlight reflects off the surface of a lake to the awesome power of a lightning storm. Importantly, it also means that the photon, the particle of light, has to be massless. The equiv
alent in our football analogy would be to discover a deep symmetry principle that automatically generates the complete rulebook for the game of football, including the offside rule and specifying the size of the ball.
This idea of symmetry now leads us back to where we started: the Higgs and the problem of the weak force. Once QED was discovered, physicists naturally tried to see if other quantum field theories describing the weak and strong force could be found based on similar symmetry principles. A class of such theories was discovered by Chen Ning Yang and Robert Mills in 1954, but they all suffered from what seemed to be a terminal problem—they predicted the existence of new massless particles. These particles would be similar to photons—the particles of the electromagnetic field—in that they would have no mass, but different in that they carried a charge. The problem was that if such particles existed then they ought to be flying about all over the place, meaning they should have been discovered long ago. As a result, most physicists believed that so called Yang-Mills theories, based on similar symmetry principles to electromagnetism, were nonstarters.
Now, as we already saw in the case of the strong force, such massless particles do exist—they’re called gluons—but they hadn’t been discovered in 1954 because gluons are inexorably locked inside protons and neutrons, thanks to the tremendous strength of the strong force.
However, the absence of massless particles can’t be explained away like this for the weak force. The symmetry group that was identified as being the most promising candidate for a quantum field theory of the weak force is known as SU(2), and it predicts three new force fields, along with their corresponding massless particles: the W+, W−, and the Z0 bosons.
In case you were wondering what this boson business is about, a brief aside. Particles are divided into two categories depending on their spins. As we’ve seen, quantum mechanical spin comes in lumps of ¹/₂ and particles with so-called half-integer spins—those in the sequence ¹/₂, ³/₂, ⁵/₂, etc.—are known as fermions. The matter particles, including electrons and quarks, are all spin ¹/₂ fermions. Bosons, on the other hand, have integer spins in the sequence 0, 1, 2, etc. and include the force particles like the photon, gluons, and W and Z bosons, which all have spin 1.