by Harry Cliff
The source of this catastrophe lies in the fact that even a quantum field with no particles in it is never completely quiet; it is constantly jittering, like the shimmering surface of an almost-still pond. These jitters are due to Heisenberg’s famous uncertainty principle, which forbids us from knowing that a field has precisely zero energy. Instead, an empty field must be constantly fluctuating around its zero value.
In principle, these quantum jitters contain energy. How much energy? Well, bizarrely perhaps, it depends on how closely you look at the field. Thanks to the uncertainty principle, as you zoom in on a quantum field and look at it from shorter and shorter distances, the size of these jitters grow larger and larger. This would mean that if you could zoom in infinitely close, the jitters would become infinitely big, giving the vacuum an infinite amount of energy. Fortunately, we know that we can’t keep zooming in forever because at a certain extremely short distance, gravity comes into play.
This special distance is known as the Planck length, and it is very, very small: approximately sixteen-trillionths of a trillionth of a trillionth of a meter or, if you prefer lots of zeroes in a row, that’s 0.000000000000000000000000000000000016 meters. For scale, the Planck length is roughly to a quark what a quark is to you and me; in other words very, very, very small indeed. This distance is special because it is thought that if you could force two particles to within a Planck length of each other, then gravity would cause them to collapse into a tiny black hole. That means that it doesn’t make sense to think about distances shorter than a Planck length, and so this is where we stop zooming in.
Even so, since the Planck length is stupendously small, the energy of the jitters in a quantum field at this distance is absolutely enormous. A fairly naïve calculation suggests that the energy stored in the quantum jitters of a single quantum field is so large that 1 cubic centimeter of apparently empty space should contain enough energy to blow up every star in the observable universe many, many times over.*2
If you are shocked by this result, you should be! Surely that can’t be right? The idea that every single sugar-cube-sized bit of space is seething with an apocalyptic quantity of energy seems utterly barmy. Indeed, some physicists doubt the validity of this sort of logic, but it seems to be unavoidable if we accept quantum field theory. Fortunately, this vacuum energy cannot hurt us as it is locked up in space itself and can’t be gotten out. However, even if it can’t hurt us, it should have a powerful effect on the Higgs field.
The Higgs field is unique among the fields of the standard model; as we’ve seen, it is the only one with zero spin. The others are either spin ¹/₂ matter fields or spin 1 force fields. This means that unlike the other fields, it feels the effect of these violent vacuum fluctuations like a kite flying in a hurricane.
Imagine releasing a kite in the most powerful hurricane that the world has ever seen. What might you expect to happen? Well, there are probably two likely options: either the wind picks up the kite and drags it high, high into the air or it slams it into the ground, pinning it there. It would be extremely surprising if you found the kite hovering steadily, say, a foot off the ground.
But this is exactly the situation we find ourselves in with the Higgs field. Like the kite, the Higgs field’s value is buffeted by these tremendously powerful vacuum fluctuations, which should either drag it all the way up to the Planck energy (that’s 10,000,000,000,000,000,000 GeV) or smack it into the ground at 0 GeV. However, what we find in our universe is that the Higgs field hovers just above zero at 246 GeV, precisely in the right ballpark to allow atoms, and therefore the universe as we know it, to exist.
This bizarre situation demands an explanation. The only way to account for it in the standard model is for the wild fluctuations in every quantum field we have discovered so far (and even in ones we haven’t discovered) to precisely cancel one another out to an absolutely unbelievable level of accuracy. This is akin to all the swirling, howling gusts of wind in a hurricane miraculously balancing one another so that the air around our kite ends up almost perfectly calm.
Roughly speaking, the chances of the fluctuations in all the different quantum fields canceling one another out to the degree needed to keep the Higgs field steady at 246 GeV are one in a million trillion trillion (1030). Such huge numbers are more or less meaningless, but to put it in some sort of context you’d be significantly more likely to win the lottery jackpot three weeks in a row.
Such an incredible conspiracy between all the different quantum fields is surely totally implausible. We are left with the impression that some great cosmic tinkerer has carefully balanced these fluctuations in just the right way to allow atoms to exist. In other words, the laws of physics look as though they have been fine-tuned for life.
This smells extremely fishy if you’re a physicist, and we’re talking halibut-left-down-the-back-of-the-sofa-for-several-months-over-an-unusually-hot-summer fishy. This so-called hierarchy problem has been the greatest motivator for the search for physics beyond the standard model for the past few decades. The hope is that we can discover some new physical phenomena, be that a new set of quantum fields or something else, that explains why the Higgs field ends up at its perfect Goldilocks value. In our kite analogy, this would be akin to discovering iron rods tethering the kite a foot above the ground, or perhaps realizing that the hurricane’s terrible winds are far weaker than we forecast.
Finding such new phenomena was and remains one of the great goals of the Large Hadron Collider. In fact, along with finding the Higgs, searching for a solution to the hierarchy problem was the main reason the collider was built. The stakes could not be higher. This is more than just another scientific problem; it strikes at the heart of what it means to do physics. Whether we can solve it is intimately bound up with a far deeper issue—namely, whether there are features of our universe that are impossible to explain.
For behind all this lurks a specter that has haunted physics for decades. Reviled by many, embraced enthusiastically by others, this specter is the multiverse. This is the idea that our universe is one of a huge, perhaps even an infinite number, with the laws of physics varying from universe to universe. Admit this possibility, and the apparently impossible value of the Higgs field becomes not only probable but inevitable. If we allow for the possibility of other universes, then in the vast majority of them the Higgs field is either at zero or at the Planck scale, and atoms cannot exist. We find ourselves living in a universe where the Higgs field is around 246 GeV not thanks to any miraculous fine-tuning, but because it is the only sort of universe we can live in.
If this line of thinking is right, then we will never be able to explain why our universe is the way it is. The Higgs field turned out the way it did by dumb luck, like Brian falling into the path of that spaceship. It was dumb luck that allowed atoms to exist and for life to eventually evolve. What stinks about this way of thinking is that we will never know if it’s right or not. There will almost certainly never be a way to detect other universes, as by definition they lie outside our own and out of reach.
To put it another way, if the multiverse is right, then we can never know how to make an apple pie from scratch.
What many physicists hope, though, is that some unknown effects are responsible for stabilizing the Higgs field against catastrophe. If this is right, then there are good reasons to believe that new particles should exist, with masses similar to the Higgs boson itself. So just as the Higgs was emerging from the data at the Large Hadron Collider, hundreds of other physicists were scouring the collisions in search of a chink in the standard model’s armor that might explain why we live in such an impossibly unlikely universe.
INTO THE UNKNOWN
Every Wednesday morning, a group of physicists squeeze into a windowless meeting room on the first floor of the Cavendish Laboratory in Cambridge. Sitting around a large table scattered with coffee cups and lit dimly by
a frosted skylight, the discussion is animated and peppered with strange vocabulary. “Squarks,” “neutralinos,” “gravitons,” “Z primes,” and “micro black holes” fly back and forth across the table. Every so often someone will jump up to scribble something on a whiteboard, hieroglyphs of arrows and wiggles or semidecipherable scrawls of mathematical symbols, while others argue from their seats, watch on pensively, or tap away on their laptops.
The Supersymmetry Working Group has been meeting since before I arrived at the Cavendish in 2008. While there are a hell of a lot of meetings in particle physics,*3 what makes this one unusual is that it is a coming together of experimentalists working on the LHC along with theoretical physicists from the Cavendish and the math department down the road. For more than a decade now, they have trawled through recent results from the LHC and the latest theoretical ideas in pursuit of new schemes to search for exotic phenomena.
Among the regulars are Ben Allanach and Sarah Williams. Ben, a professor of theoretical physics, has spent the past ten years helping to guide experimentalists down promising avenues while figuring out what the latest LHC result means for speculative theories that go beyond the standard model. Meanwhile, Sarah has been on the hunt for signs of something new in the trillions of collisions recorded by the ATLAS experiment.
For years, by far the most promising of these speculative theories was supersymmetry, an idea so seductive that Ben has spent his entire career thinking about it, while Sarah and hundreds of her collaborators on ATLAS have performed dozens upon dozens of measurements in the hope of spotting its effects.
Supersymmetry is the rarest of ideas, one that solves several deep, fundamental problems in a single stroke. It promises to explain how matter gained dominance over antimatter during the big bang, the nature of dark matter, and even suggests that all the forces of nature were once unified in the very earliest moments of our universe. However, perhaps its greatest appeal is that it protects the Higgs field from the violence of the vacuum, naturally explaining why its strength is set at just the right value to allow atoms to exist.
As the name suggests, supersymmetry imposes a new symmetry on nature’s fundamental building blocks, not all that dissimilar to the symmetry relating matter to antimatter. However, instead of relating particles to their antiparticles, supersymmetry relates matter particles like electrons, quarks, and neutrinos to force particles like photons, gluons, and Higgs bosons.
What distinguishes a matter particle from a force particle is its spin. All matter particles are fermions with spin ¹/₂, while the force particles are bosons with spin 1, or 0 in the special case of the Higgs. According to supersymmetry, for every spin ¹/₂ matter particle in the standard model there should be a spin 0 “superpartner”; for every force particle there’s a spin ¹/₂ superversion. These superparticles have identical properties to their standard model partners, only differing in their spins.
These supersymmetric particles all have very silly names; the superversion of the electron is called the “selectron,” while the partners of the quarks are called “squarks.” It’s not any better for the supersymmetric versions of the force particles; the photon’s partner is the photino, and there are gluinos, winos, zinos, and higgsinos. Perhaps my least favorite is the sstrange squark, which when said out loud usually makes you inadvertently spit in your colleague’s eye. Together, these supersymmetric particles are called “sparticles.” Part of me hopes that supersymmetry is never found just so we don’t have to use these silly words ever again.
Clunky nomenclature aside, supersymmetry is regarded by many theorists as one of the most beautiful and powerful ideas to have been discovered in fundamental physics. In particular, it is one of the few ways that theorists have found to save the Higgs field from catastrophe. As we’ve discussed, the Higgs field is uniquely sensitive to fluctuations in the quantum fields that are ever present in the vacuum. Each of the twenty-five or so quantum fields in the standard model contributes its own set of fluctuations, each acting like a hurricane-force wind that should blow the Higgs field down to zero or up to the Planck energy. There is absolutely no reason to expect that all these different quantum winds should balance one another out, which is why the Higgs field hovering stably at 246 GeV is so hard to understand.
Supersymmetry solves this problem. For every quantum field in the standard model there is now a corresponding superfield, and when you study the mathematics you find that the fluctuations in a superfield are almost exactly equal and opposite to the fluctuations in its standard model partner. So, for instance, when the electron field blows the Higgs one way, the selectron (superelectron) field blows it back in the opposite direction, like two countervailing winds that almost completely cancel each other out and turn what was a quantum mechanical hurricane into the equivalent of a clear, calm day.
With supersymmetry, you no longer need to resort to fine-tuning or untestable multiverses. The theory is natural, which means it automatically explains why the world is as it is without the need to fiddle about excessively with the theory. Better still, in many versions of supersymmetry the lightest sparticle is a perfect candidate for dark matter.
However, there is an obvious objection: where are all the sparticles? If the universe is perfectly supersymmetric, then apart from having different spins, the sparticles should have exactly the same properties as their standard model buddies, including the same masses, and if that were true, we would have discovered them already. To get around this, supersymmetry has to be imperfect, like one of those warped fairground mirrors that make you look like you’ve been run over by a steamroller. Breaking supersymmetry allows the sparticles to be heavier than the ordinary standard model particles, heavy enough that previous colliders wouldn’t have had enough energy to make them and so explaining why we haven’t seen them yet—but this comes at a price. The more you break supersymmetry by making the sparticles heavier, the less effective it is at canceling out those nasty quantum fluctuations. The upshot of all this is that if supersymmetry is to save the Higgs, then sparticles can’t be much heavier than the Higgs itself. That would put them squarely in the sights of the LHC.
Given its huge promise, it’s unsurprising that the lure of supersymmetry has been impossible to resist, for theorists and experimenters alike. However, it isn’t the only show in town when it comes to stabilizing the Higgs field. While supersymmetry saves the Higgs by calming the quantum hurricane with a superstorm of equal and opposite strength, another popular set of approaches argues that there was never a hurricane in the first place.
The enormous vacuum fluctuations that are so dangerous to the Higgs are a consequence of the fact that as we zoom in on the vacuum to ever-shorter distances, the fluctuations appear to grow larger and larger. As we’ve seen, this zooming-in process goes on all the way down to the Planck length, the point at which two particles forced together collapse into a black hole.
The Planck length is short ultimately because gravity is an incredibly weak force, a trillion trillion trillion times weaker than electromagnetism. This means that in any particle physics experiment we can currently perform, it is totally overwhelmed by the other three quantum forces. It would only start to match them in strength if you could get two particles incredibly close together, which would in turn mean firing them at each other with an enormous amount of energy. At the LHC we have enough energy to get down to about 10-18 meters, which is darn small but still a hundred thousand trillion times bigger than the Planck length where gravity becomes strong.
But what if gravity is actually stronger than it appears? If that were true, then the point at which you collapse two particles into a black hole would happen earlier, which means that we’d stop zooming in on the vacuum earlier too. And if you stop zooming in earlier, then the size of the quantum fluctuations is also much smaller, effectively reducing what was a hurricane-force wind to a gentle quantum breeze.
The way yo
u do this—and bear with me here—is by introducing extra dimensions of space. We live in a 3D world, where we can move forward and backward, up and down, and left and right, but in these extradimensional theories there are new directions that you can move in. I invite you to imagine what moving in, say, a fourth dimension would be like. No? Me neither. Since our brains evolved to navigate a 3D world, it’s impossible for us to visualize higher dimensions (and if you ever hear a mathematician or physicist telling you they can picture a 4D world I’m pretty sure they’re lying or high). But mathematically at least, these ideas are straightforward to write down. In such theories, the reason that we don’t perceive these extra dimensions is usually because they are incredibly tiny or because the particles we are made from are stuck in our 3D world, like stickmen drawn on a sheet of paper.
Gravity, on the other hand, is able to access these higher dimensions, allowing it to leak away like water from a dodgy pipe. This leaking explains why gravity appears weak in our ordinary 3D world, whereas if we could perceive all the dimensions, we’d realize that gravity is just as strong as the other forces.
This may all sound like sci-fi speculation, but what is neat about these extradimensional theories is that, like supersymmetry, they predict new phenomena that should appear at the LHC. If these extra dimensions exist, then the energies required to make tiny black holes is far lower than the Planck scale, making it possible to create them in the collisions at the LHC after all.
The prospect of making microscopic black holes led to a now-familiar round of apocalyptic headlines, particularly in the British tabloid press. Just before the LHC switched on in 2008 the Daily Mail published a story with the typically levelheaded headline “ARE WE ALL GOING TO DIE NEXT WEDNESDAY?” while in the United States, Time magazine went with the slightly less alarmist but nonetheless startling “COLLIDER TRIGGERS END-OF-WORLD FEARS.” These fears were that once made, a tiny black hole would sink to the center of the Earth and slowly devour the entire planet.