How to Make an Apple Pie from Scratch

by Harry Cliff

  This SU(2) theory had lots of attractive features; for instance, it could explain what was really going on in beta decay. Instead of a neutron decaying directly into a proton, electron, and antineutrino all in one go, as in Fermi’s theory, the neutron now decayed into a proton by giving off a W− boson, which then converted into an electron and an antineutrino.

  For force fields like the electromagnetic field or the weak fields, the mass of the particle that goes with the field can be thought of as a kind of energy toll for using that field, a bit like the toll you might pay for crossing a bridge. Since photons have zero mass, the cost of crossing the electromagnetic field is zero, which means two things. First, if you have two electrically charged particles, they will exert a force on each other via the electromagnetic field no matter how far apart they are. Of course, the force gets weaker the bigger the distance between them, but nonetheless, a force is still exerted. In physics parlance we therefore say that the electromagnetic force is “long ranged.” The second consequence of the fact that the toll for using the electromagnetic field is zero is that the electromagnetic force is a relatively strong force.

  However, there is a big problem with this theory. Since it predicts that the W+, W−, and Z0 bosons should be massless, it should be incredibly easy to make them, for instance when two particles bang into each other. So just like light, which is made up of photons, we ought to see them flying about all over the place in the real world. The fact that no one had ever seen a W or Z boson meant that the theory had to be wrong. Worse still, massless particles would turn the weak force into a strong force.

  Fermi theory: Neutron (n0) turns straight into a proton (p+), electron (e-), and an antineutrino. (vˉ)

  SU(2) theory: Neutron (n0) turns into a proton (p+) and a W− boson, which then turns into an electron (e-) and an antineutrino (vˉ).

  If the weak particles were also massless the same would be true of the weak force—it would be long ranged and strong. However, as the name suggests, the weak force is weak and extremely short ranged; its effects only become apparent at distances smaller than an atomic nucleus, which is why we don’t notice the weak force in our everyday lives.

  One way to keep the weak force weak would be to give the W and Z particles very large masses—in other words, introduce a large energy toll for using the weak fields. This would be like charging a thousand dollars for every meter you drive across a bridge, which would mean only the richest drivers (that is, those with the most energy) would use it, and the journeys would tend to be very short. Consequently, large masses would make the weak force weak and short ranged and also neatly explain why no one had seen a W or a Z particle in the 1950s and 60s—if their masses were sufficiently large, they would be too heavy to have been created in any experiment at the time.

  However, there was a serious problem with this fix. Giving mass to the W and Z particles broke the beautiful SU(2) symmetry that was used to determine the form of the weak force in the first place. Even worse, the theory became plagued by infinities— calculations of probabilities that gave infinite answers—rendering it effectively useless.

  Theorists had run into similar infinities when QED was being put together during the 1930s and 40s, but these had eventually been overcome, turning QED into a theory that gave sensible answers. This technique, known as “renormalization,” was so crucial to the success of QED that it won Schwinger, Feynman, and Tomonaga the 1965 Nobel Prize. However, renormalization didn’t seem to work for a weak force that assumed massive particles. The way to a quantum field theory of the weak force seemed well and truly blocked.

  It would take a decade for the solution to be found, and yet more time for that solution to be incorporated into a fully functioning theory of the real world. The story of its discovery is long and tangled and was a group effort featuring many star players. Julian Schwinger, Yoichiro Nambu, Jeffrey Goldstone, and Philip Anderson laid the foundations; Robert Brout, François Englert, Peter Higgs, Gerald Guralnik, Carl Hagen, and Tom Kibble hit upon a potential solution; Abdus Salam, Sheldon Glashow, and Steven Weinberg applied this solution to the weak force; and, finally, Gerard ’t Hooft and Martin Veltman proved the resulting theory was free of infinities. This complex history behind this theory could fill a book in its own right,*6 so instead I will simply focus on the physics. The final theory is like a cathedral, towering, beautiful, the work of many hands over many years. It is the heart of the standard model of particle physics.

  Physicists were facing a paradox: they knew that the particles of the weak force must have large masses, or else the weak force would be strong and long ranged like electromagnetism, which it isn’t. However, massive particles resulted in a theory that gave infinite results and destroyed the jewel-like symmetry that determined the form of the weak force in the first place.

  But what if the symmetry wasn’t destroyed? What if it was just hidden? Or to put it another way, what if the weak particles were fundamentally massless but got their masses from somewhere else? Enter the Higgs field.

  The Higgs field is a brand-new type of quantum field that’s unlike anything that we’ve seen so far. All the fields we’ve met are either matter fields with spin ¹/₂, like the electron, or spin 1 force fields, like the photon. This new field, uniquely, needed to have a spin of 0.

  It is also unique in another crucial respect: it needed to have a non-zero value everywhere in space. This is very different from, say, the electromagnetic field. If you go to a really empty bit of space and remove all the photons so that there are no ripples sloshing about in the electromagnetic field, then the value of the field is pretty much zero, apart from some gentle jittering due to quantum uncertainty. However, even when you remove all the particles from the Higgs field, it still has a large nonzero value, effectively filling the entire universe with a uniform Higgs field soup.

  The key insight was that such a Higgs soup could give masses to the weak particles. The story goes something like this. Way, way back in the very first moments of the universe’s history the Higgs field’s value was zero and as a result the three weak particles, the W+, W−, and Z0, all had zero mass and symmetry reigned. However, after around a trillionth of a second, the Higgs field “switched on,” going from zero to a fixed value, filling the universe with a Higgs field soup and making the weak particles suddenly appear massive. When this happened, the perfect symmetry that was manifest at the beginning of time became hidden, and what we think of today as the weak force changed: from strong and long ranged to weak and short ranged.

  At the same time, the particles of matter that would go on to make our apple pie, including electrons and quarks, which had previously been zipping through the universe at the speed of light, suddenly found themselves plowing through this thick Higgs soup. As they interacted with the Higgs field, they too transformed from zippy massless particles into ponderous massive ones. If it helps, an imperfect analogy is to imagine the Higgs field as a gloopy substance that sticks to particles like electrons and quarks, slowing them down and imbuing them with the property of mass. Meanwhile, particles like photons and gluons remain massless because they don’t interact directly with the Higgs field.

  So the Higgs field isn’t just responsible for giving mass to the particles of the weak force, it gives mass to the fundamental matter particles as well.*7 This makes it an absolutely essential ingredient of our apple pie and, by extension, our universe. Without the Higgs field, the world as we know it could not exist. Particles like electrons would have no mass, meaning that they would zip around at the speed of light and never bind to make atoms. At the same time the forces of nature that we know and love would be utterly transformed. Precisely what this Higgsless universe would look like is hard to say, but it would certainly not be a place where we could live.

  The basic principles of this mechanism were first published in 1964 by three independent groups: first into print were Ro
bert Brout and François Englert in Brussels, next Peter Higgs in Edinburgh, and finally Gerald Guralnik, Carl Hagen, and Tom Kibble in London. Why then, you might ask, is Peter Higgs the only one whose name got attached to the idea? Well, in essence it’s down to an unfair quirk of history. Higgs himself, who is unfailingly self-effacing, refers to it as the ABEGHHK’tH*8 mechanism, in credit to the many theorists who contributed to the idea. Sadly, saying that out loud tends to make people think that you’re trying to regurgitate a hairball.

  There is one thing that marked Higgs out from the rest of the pack. When the first draft of his paper was rejected by the journal, Higgs decided to beef it up by adding some experimental consequences of his idea. Inventing a new cosmic energy field is all well and good, but how do you know if such a thing exists? Higgs knew that like all other quantum fields it should be possible to create a ripple in this new field, which would show up in experiments as a new particle. Now, to anyone with training in quantum field theory, the fact that a particle should come along with the Higgs field was pretty obvious, but since no one else had thought to mention it explicitly, Higgs’s name became forever associated with that particle—the famous Higgs boson.

  What the gang of six had outlined was the basic principle of giving mass to particles using a new quantum field. However, it had yet to be fully adapted to describe the weak force. In 1968, Sheldon Glashow, Abdus Salam, and Steven Weinberg used it to create a fully consistent theory of the real world. In doing so, they discovered that the only way to make the mass-giving mechanism work was to include the electromagnetic force in the theory as well, which led to one of the most profound discoveries of the twentieth century: the electromagnetic and weak forces, which appear utterly different in our ordinary world, are in truth different aspects of one unified electroweak force. The only reason we see two separate forces today is that early in the universe, the Higgs field gave mass to the W and Z bosons but left the photon massless.

  This truly incredible revelation marked the greatest unification in physics since Faraday and Maxwell had shown that electricity and magnetism were one and the same phenomenon, aspects of a single, unified electromagnetic field. Now the electromagnetic field had been united with the weak force through the application of deep symmetry principles. The resulting electroweak theory predicted the existence of three new massive force particles, the W+, W−, and Z0 bosons, which were spectacularly discovered at CERN’s Super Proton Synchrotron collider in 1983. At long last, the weak force was understood and the electroweak theory became the core of the modern standard model of particle physics.

  However, one piece of the puzzle had yet to be found: the Higgs boson itself. Without the Higgs, the cornerstone of the beautiful theoretical cathedral built in the 1960s and 70s was missing. It was the Higgs that explained the strength of the weak force, unified it with electromagnetism, and gave mass to the particles that make up every atom in the universe. That is why finding it was so crucial, and that is why, in the late 1970s, some farsighted physicists at CERN began to plan the most audacious scientific experiment ever attempted.

  THE BIG BANG MACHINE

  On Tuesday, March 30, 2010, just before lunchtime, two unsuspecting protons are about to make history. Their day began ordinarily enough, bouncing around contentedly in a canister of hydrogen gas in a nondescript surface building at CERN, a few miles from downtown Geneva. It is a day that should have been utterly forgettable. After all, they have both lived unimaginably long and varied lives by human standards, born as they were 13.8 billion years ago in the furious heat of the big bang.

  The things they’ve seen! They witnessed the searing light of creation and the endless dark before the first stars. They danced in the shining atmospheres of blue hypergiants and surfed the cosmos on the shockwaves of supernovae. One of them had even spent some time in a skin cell on the tip of Paul McCartney’s left middle finger, albeit during his time in Wings.

  However, unbeknownst to them, their long lives are about to be cut brutally short. But for the misfortune of ending up in that particular bottle of hydrogen gas, they might have lived to see the passing of the human race, the death of the Sun, and perhaps even the coming of the second great darkness at the end of the universe. Unfortunately, that particular canister has been chosen to act as the proton source for the most powerful particle collider on planet Earth. They are about to become martyrs to the cause of science.

  Without warning, the opening of a valve sucks them unceremoniously from their gas bottle into an adjacent metal box, where a fierce jolt of electrical energy rips them rudely from their hydrogen molecules. Bidding farewell to their companion electrons, the protons find themselves naked and alone, hurtling down an evacuated pipe running through the center of the first accelerator in a long chain that will lead them, inexorably, to their doom. When they exit the prosaically named Linear Accelerator 2 after a short trip of just 30 meters, they are already traveling at a third of the speed of light. Neither of our two protons has traveled this fast for billions of years, but still, a third of the speed of light is nothing to get too worried about. Many of their companions rained down on the Earth as cosmic rays at far higher speeds.

  However, as they pass through a series of increasingly large circular accelerators, their alarm begins to grow. With each turn, powerful electric fields give them a kick in energy, while stronger and stronger magnetic fields hold them ever-more tightly on their orbits. Before long they find themselves racing around a huge 7-kilometer-circumference ring, the Super Proton Synchrotron (SPS), once CERN’s mightiest accelerator. Each proton is now flying in a tightly packed swarm with billions of its former canistermates as they are gradually accelerated to ever-more terrifying speeds. When the SPS maxes out at 99.9998 percent of the speed of light, they hope their ordeal might nearly be over.

  It is not. A sudden magnetic jolt kicks the protons out of the SPS and along a transfer line leading to an even larger ring, the largest of all in fact, the Large Hadron Collider. Ominously, our two protons now find themselves moving around the 27-kilometer ring in opposite directions. That can’t be good. They get some brief comfort from the fact that the gentler curve of the larger machine means they are being yanked on less fiercely by the LHC’s magnets. Alas it is not to last.

  At 11:40 a.m., with two fully loaded beams circling in opposite directions, the LHC begins to push the protons into uncharted territory. On each orbit of the ring, they pass through a short stretch of metal cavities where they are subjected to a cascade of violent smacks from a 2-million-volt electric field, pushing them ever closer to the speed of light. At the same time, more than a thousand superconducting magnets that make up the bulk of the collider begin to generate increasingly powerful magnetic fields, pulling the protons toward the center of the ring with ever-more terrible force.

  For an hour the protons endure this electromagnetic torture. Mercifully, thanks to their tremendous speeds and the time-warping effects of relativity, this hour passes in little over a second from the protons’ point of view. At 12:38 p.m., after around 40 million orbits of the 27-kilometer ring, they reach their final, dizzying speed: 99.999996 percent of the speed of light.

  Each proton has been transformed into a projectile of unrivaled potency, carrying 3.5 trillion electron volts (TeV) of energy, approximately 3,700 times its own rest mass. As they flash around the ring once every 90 microseconds, they repeatedly pass through the hearts of each of the four vast detectors—ATLAS, ALICE, CMS, and LHCb—which wait patiently to record their demise. For now, the two oppositely rotating beams are kept apart, coming within a few millimeters each time they pass through the detectors, but not yet meeting.

  A few short minutes later, at 12:56 p.m., the protons find themselves slowly shifting in their orbits as sets of magnets positioned on either side of the four detectors begin to guide the two counter-rotating beams closer and closer together. With each orbit, the gap between them narrow
s, until there is less than a whisker between them.

  12:58 p.m. Our two protons, now moving faster than they have since the beginning of the universe, pass each other one last time and begin their final approach from a distance of 27 kilometers. A mere 22.5 microseconds later the distance between them has halved. Another 22.5 microseconds and they enter one of the detector caverns from opposite ends. The only mercy is that they can’t see each other coming, being protons and not having eyes, and also because the inside of the LHC is pitch-black.

  As the two mighty beams of the LHC cross paths inside all four detectors, our hapless protons run headlong into each other with a violence not seen since the big bang. The world record for the highest energy collision ever produced by science is smashed.

  The force of the impact utterly obliterates the protons, spraying their innards outward in a firework of quarks and gluons. At the same time, their vast energy sends ripples cascading through the quantum fields of nature, creating new particles from the force of the impact: electrons, muons, photons, gluons, quarks, and many more besides. As our two protons die, new particles are born. Their deaths make new matter from energy. E = mc2.

  A hundred meters aboveground, as images of the first collisions flash up on screens in control rooms around the LHC ring, engineers and physicists erupt in jubilation. After more than thirty years of dreaming, planning, construction, testing, setbacks, and recoveries, the most ambitious scientific experiment ever conceived has finally begun. The achievement is all the sweeter for the engineers in charge of the LHC in the CERN Control Centre, many of whom have spent the last year working tirelessly down in the 27-kilometer tunnel repairing the collider after it literally blew itself apart shortly after it first switched on in September 2008. As champagne bottles are uncorked across CERN, Mirko Pojer, one of the two engineers operating the LHC that day, simply notes in the log, “First collisions at 3.5TeV per beam!”