by Harry Cliff
*5 Non–quantum mechanically speaking, angular momentum depends upon the size, shape, and mass of an object and how fast it’s rotating. Subatomic particles can also possess angular momentum in the form of spin.
*6 If you’d like to know more of the history of who did what, and who may or may not deserve the credit, I can highly recommend The Infinity Puzzle by Frank Close.
*7 One important qualification of all this is that the Higgs field only gives mass to fundamental matter particles, including electrons and quarks. However, most of the mass of protons and neutrons does not come from their constituent quarks but from the energy stored in the gluon fields that bind the quarks together. That means that most of the mass of an atom actually comes from the strong force, not the Higgs.
*8 That stands for Anderson, Brout, Englert, Guralnik, Hagen, Higgs, Kibble, ’t Hooft.
WARNING
Science Under Construction
The discovery of the Higgs marks a turning point in our quest to find the ultimate apple pie recipe. The Higgs completes the standard model of particle physics, a theory that has been staggeringly successful in describing the basic ingredients of our universe and the laws that govern their behavior. However, despite its success, the standard model cannot explain a critical detail—namely, where the matter in our apple pie came from. There must be more to the story.
The discovery of the Higgs at the Large Hadron Collider tells us about the physics that was going on in the universe around a trillionth of a second after the big bang. We now have fairly solid evidence that about this time the Higgs field switched on, giving mass to the fundamental particles and setting up the basic ingredients of the universe as we know them today. However, what happened before this moment is still shrouded in uncertainty.
How did the particles in our apple pie come to be? Why does the universe contain the quantum fields that it does? Are there ingredients that we’re still missing? How did the universe begin? To answer these questions, we must now push back even farther into that first trillionth of a second. It was in that short but crucial epoch that the matter of which we, and everything in the universe, is made came into being. Almost all the great questions of modern physics and cosmology turn on what happened in that first instant after the universe burst into existence.
So here I must give a disclaimer, like a tour guide taking you off the well-trodden paths into uncertain terrain. The farther we go from here, the less sure of our footing we become. We are entering a world of speculation, where sometimes even the questions aren’t clearly formed, let alone the answers. But that’s where Carl Sagan’s challenge leads us. It’s time to invent the universe.
CHAPTER 11
The Recipe for Everything
Around a millionth of a second after the big bang everything almost ended.
During the first microsecond, the universe had been so incredibly hot that particles and antiparticles were constantly being created and destroyed. Quarks and antiquarks, electrons and antielectrons flashed in and out of existence, emerging from the seething plasma in particle-antiparticle pairs only to annihilate again an instant later.
Meanwhile the universe had been rapidly expanding and cooling. Around a millionth of a second in, there was no longer enough heat in the plasma to create new protons and antiprotons and the apocalypse began. Particles and antiparticles destroyed each other in a great annihilation, wiping out almost all the matter in the universe in an almighty blast of radiation. This cataclysm should have spelled the end of all matter and antimatter, leaving a vast, dark, empty void with only a few lonely photons coasting through the endless nothingness.
But somehow, around 1 particle in 10 billion survived. We don’t know how this happened. But it is only thanks to this 1 in 10 billion imbalance between matter and antimatter that the material universe—galaxies, stars, planets, human beings, apple pies—exists.
For all its success in describing the behavior of the fundamental particles that make up our world, the standard model of particle physics predicts that the material universe should not exist. Now any theory that predicts the nonexistence of its own authors is in fairly serious trouble, which is one reason why physicists are convinced there must be something new still to discover.
The problem can be traced back to a time long before the standard model was first assembled, to 1928, when a young Paul Dirac saw antielectrons emerging from his famous equation. Even back then, Dirac knew that if antiparticles existed then they should always be created together with ordinary particles. Make an electron, said Dirac, and you must also make an antielectron. Every experiment performed since has proved Dirac right. It is true that the Large Hadron Collider makes matter out of energy, but add up all the particles that are created in a collision and you will always find an equal number of antiparticles. It seems to be impossible to make or destroy a particle without doing the same to an antiparticle.
This perfect balance between matter and antimatter should have led to an empty universe, and yet here we are. This is one of the biggest mysteries in modern physics, and attempts to explain it generally involve new, hitherto undiscovered quantum fields.
That said, it is possible to imagine a way around this problem that doesn’t involve any new particle physics. What if, instead of particles totally annihilating one another, random motion in the churning primordial plasma randomly led to some regions where there was more matter and some where there was more antimatter? Fast-forward to the present day, and these regions would have been blown up by the expansion of space to cover vast tracts of the cosmos, some containing ordinary gas, dust, stars, and galaxies and others anti-gas, anti-dust, anti-stars, and anti-galaxies. From here on Earth, a distant anti-galaxy would look no different from an ordinary one, so perhaps some of the galaxies in the night sky are made of antimatter.
It’s a neat idea; the trouble is that if there were really regions of the universe made of antimatter, then there would inevitably be boundaries where they pushed up against ordinary matter regions. Even the huge, empty spaces between galaxies contain small amounts of hydrogen and helium gas, so wherever such a boundary occurred you’d expect to see telltale gamma rays being produced by the annihilation of gas and anti-gas. The fact that we don’t see any signals from such annihilations anywhere in the night sky suggests that the entire observable universe is made only from ordinary matter.
So the only explanation left to us is that sometime in the first moments of the universe’s existence, something happened that allowed a tiny bit more matter to form than antimatter. That tiny imbalance—just 10 billion and 1 protons for every 10 billion antiprotons—allowed enough matter to survive the great annihilation to create everything we see around us today. However, finding a way to even create an imbalance this small proves to be incredibly difficult.
One of the first people to have a go was the Russian theoretical physicist Andrei Sakharov, who laid out three conditions that had to be satisfied in order for matter to be made in the early universe. They’re known as the Sakharov conditions:
A process must exist that allows you to make more quarks than antiquarks.
The symmetry that relates matter to antimatter has to be imperfect.
When this matter-making process happened, the universe needed to be out of thermal equilibrium.
Condition 1 is probably the most straightforward to understand; clearly if we want to be able to make more matter than antimatter, we need a process that can do this. However, this isn’t enough on its own, because even if such a process exists, then the symmetry between matter and antimatter would imply a mirror image process that makes more antimatter than matter. Hence, we need condition 2, which insists that the symmetry between matter and antimatter is broken, allowing the matter-making process to run faster than the antimatter-making process.
Finally, we have condition 3: the universe needs
to have been out of thermal equilibrium when these processes were running. By definition, a system that’s in thermal equilibrium isn’t changing, usually because all processes are running forward and backward at the same rate. Therefore, we need to find a time in the universe’s history when things were out of balance, allowing the matter-making process to run forward faster than it ran backward.
One of the great missions of theoretical and experimental physics over the past few decades has been to find a recipe that satisfies all three of Sakharov’s conditions at the same time. There are several speculative ideas on the market, but we’ll focus on what are generally regarded as the two most promising candidates. Although we don’t know which one is right yet, physicists around the world are working hard to bring the pieces of the puzzle together so that one day, perhaps, we might learn the recipe for everything.
THE MIRROR WORLD
When you look in a mirror, in all likelihood the person you see is subtly different from the one your friends, colleagues, and lovers know and, presumably, love. Perhaps your nose bends slightly to the left, or your smile is a little lopsided, charmingly so of course. You shouldn’t feel bad about this. Even Hollywood actors and supermodels are never totally symmetrical. We are all at least a little bit wonky.
Unlike us imperfect humans, for a very long time the laws of physics were thought to be endowed with perfect symmetry. Reflect the universe in a mirror and it was assumed that its mirror image would be indistinguishable, with every process carrying on exactly as before. The idea that nature should have a left- or right-handed bias seemed nonsensical. This was such a basic assumption that no one ever really gave it much thought, that is until a stunning experiment carried out by the Chinese American physicist Chien-Shiung Wu.
Wu’s famous experiment, which she performed at the U.S. National Bureau of Standards in 1956, produced a truly earth-shattering result: the weak force seemed to be wonky. Or, more precisely, the weak force seemed to prefer left-handed particles over right-handed ones.
It may seem strange that a particle can be left- or right-handed, but it all comes down to the fact that particles behave as if they are rotating, as described by the quantum mechanical property of spin. If you hold out both hands with your thumbs pointing upward then the curl of the fingers on your left hand defines a left-handed rotation, while the fingers of your right hand define a right-handed rotation. In a similar way, the direction that a particle is spinning compared to the direction it’s traveling determines whether it is right- or left-handed.
Wu discovered that electrons emitted by radioactive atoms of cobalt-60 tended to be left-handed more often than they were right-handed. This was a truly shocking result. When the famous quantum physicist Wolfgang Pauli heard about Wu’s experiment he exclaimed, “That’s total nonsense!” However, it wasn’t nonsense;*1 the weak force really does violate mirror symmetry, which physicists refer to as “parity violation.”
RIGHT-HANDED ELECTRON
LEFT-HANDED ELECTRON
The ultimate reason for parity violation is that the weak force interacts more strongly with left-handed particles than right-handed ones—in other words it “prefers” left-handed particles. In fact, if the particles involved are massless, the weak force only interacts with left-handed particles. This isn’t true for the electromagnetic or strong forces, both of which have no preference for left or right.
Faced with the loss of mirror symmetry, physicists suggested that perhaps order could be restored by adding another symmetry into the mix: charge symmetry. Take the universe and reflect it in a mirror and flip the sign of all charges, so that positive becomes negative, negative becomes positive, and this new mirror universe should now look the same as the original one. Crucially, flipping charges around transforms particles, like electrons and protons, into their antiparticles, so in such a universe, left-handed particles would become right-handed antiparticles. In other words, you get a mirror universe made of antimatter!
If this combined charge-parity (CP) symmetry is exact, then it implies that just as the weak force prefers left-handed particles over right-handed ones, it ought also to prefer right-handed antiparticles over left-handed ones. This is indeed true as later experiments showed. If Wu had been able to get her hands on some anti-cobalt-60 atoms*2 and watched the antielectrons come whizzing out, she would have found more righties than lefties.
CP symmetry promised to restore order to the particle world. However, it also posed a problem. If CP symmetry is exact, then it would have been impossible to make more matter than antimatter during the big bang and we would not exist.
Fortunately for us all, in 1964, an experiment performed at Brookhaven shattered the restored charge-parity symmetry. A small team led by James Cronin and Val Fitch were using Brookhaven’s most powerful particle accelerator to study beams of particles called “neutral kaons.” These exotic beasts come in two types, one made of a strange quark and a down antiquark, and its antiparticle made of a down quark paired with a strange antiquark. When Cronin and Fitch analyzed the results of their experiments, they were stunned to discover that these particles were decaying in a way that broke the sacred principle of CP symmetry.
If Wu’s discovery of parity violation sent tremors through physics, the discovery of CP violation caused an earthquake. Cronin and Fitch’s findings were so surprising that many theorists went to great lengths to explain them away, but before long, hard experimental evidence proved the case beyond doubt: CP symmetry is not an exact symmetry of nature. Reflect the universe in a mirror and flip the charges of all the particles, and the mirror anti-universe you find will look ever so slightly different from the one we live in. Nature’s mirror is warped.
The discovery of CP violation makes it at least possible to imagine a recipe for making more matter than antimatter, but it’s not enough on its own. For one, it is still far from clear whether there is enough CP violation in nature to account for the preponderance of matter that we see in the world around us. We’ll come back to this thorny issue shortly. But more to the point, we’ve only satisfied one of the three Sakharov conditions. We still need to find a way to actually make more particles than antiparticles, something that we have never seen happening in the real world. However, such a process has been at least imagined, and remarkably, it doesn’t require any new particles or forces beyond the ones we know about. Unfortunately, what it does require is some very, very hard math….
ENTER THE SPHALERON
“I remember this flash of inspiration. I was walking home from the Maths Institute in Oxford, where I was visiting for three months in eighty-three, back to my apartment along Banbury Road, I remember almost exactly where it was and suddenly, I realized, Wow! I’ve got it!”
I met Nick Manton over a cup of tea at Cambridge’s Department of Applied Mathematics and Theoretical Physics on a damp October morning. We chatted surrounded by a couple of dozen theoretical physicists enjoying their midmorning coffees, watched over by a bronze bust of their late colleague, Stephen Hawking. When Nick noticed me gazing enviously at the impressive spread of cakes and biscuits on offer (at the Cavendish we have to bring in our own), he told me that the largesse was thanks to Hawking, who had set aside a legacy to fund the group’s eleven o’clock coffee break in perpetuity. That’s one sure-fire way to make certain you’re remembered fondly by your colleagues.
I was there to try to get my head around a strange set of objects that Nick, as a young researcher almost forty years earlier, had discovered hiding in the equations of the standard model. What had begun as a bit of a theoretical curiosity opened up one of the only viable ways we know of making more particles than antiparticles. These strange objects are called “sphalerons” and they just might be the reason that everything in the universe exists.
“You know, I’d been sort of mulling over this thought, ‘What is this possible solution in the electroweak theory?’ And it was based on som
eone else’s work, someone else had found an unstable solution and I was thinking, ‘Is that idea relevant? How can it be applied to what I’m interested in?’ And then suddenly in a flash of inspiration, I saw it.”
What Nick saw is almost impossible to describe to someone without advanced training in quantum field theory, but back in his office, he nonetheless patiently took me through the logic of the idea, covering a blackboard with intersecting spheres and circles, symbols representing the Higgs field, and towers of particle energy levels in a valiant attempt to convey the core of the idea. His explanation was so clear and methodical that while he was speaking, I really did think I was following, but as soon as I left his office, I could feel my tenuous understanding evaporating like the memory of a dream.
Sphalerons are features of the same electroweak theory that describes the origin of the electromagnetic and weak forces and the Higgs field. When Nick was walking through Oxford in 1983, the W and Z bosons had just been discovered at CERN, putting electroweak theory on solid experimental ground for the first time. He had been thinking deeply about the electroweak equations, and about a particular way to solve them that gave rise to an unstable arrangement of many fields, moving together collectively. Since this collective motion of several fields was highly unstable, Nick coined the term “sphaleron,” from the Greek sphaleros, meaning “ready to fall.”
The first thing to say about a sphaleron is that it is not a particle. A particle, like an electron or a Higgs boson, is a single quantum field wobbling backward and forward around its mean value, like a single note played on a guitar string. A sphaleron, on the other hand, is something more subtle. It is still made of quantum fields, but instead of being made of one field, it is a baroque mixture of the W, Z, and Higgs fields all moving together as one, an orchestra of quantum fields playing in melodic unison.