How theoretical particle physicists theorise
By Dan Garisto
It isn’t hard to imagine how the next great experimental discovery in physics will happen. A powerful machine, tuned to just the right frequency, could observe dark matter. Perhaps a far-seeing telescope will find the secrets of inflation on light signals that predate the oldest stars. Or maybe a lab buried deep underground will find the answer to why there is matter and not antimatter in neutrinos.
But much of the progress in physics also comes through theoretical developments.
In physics, theory and experiment are two sides of the same coin. Theorists suggest solutions to questions that the universe poses; experimentalists verify. Experimentalists find an interesting result; theorists come up with a model that explains it.. This relatively discrete division of labor is at odds with other sciences, such as chemistry and biology, where the line between theory and experiment is often much blurrier.
Over the past century, theorists and experimentalists have specialised further in their respective domains.
Experimental physicists use sophisticated devices such as particle accelerators to gather data. They work in high-tech labs, replete with flashing electronics and arrays of instruments that can weigh thousands of tons. For theoretical physicists, the laboratory can be anywhere that ideas ferment: a conversation or a chalkboard or even a Swiss patent office.
The tools experimentalists use are complex, but they are tangible machines. Charts and displays and videos can illustrate how they function. Unfortunately, there are no simple aides to help us understand how theorists think, or how they might come up with the next great idea.
But there is hope—if you’re a willing listener, theorists are more than happy to try and explain how they theorise.
A Standard Model
Most of what physicists know about the universe can be reduced to two fundamental theories: general relativity and quantum field theory (QFT). Conceived by Albert Einstein, general relativity is a theory governing the very fabric of the universe that lets physicists predict and explain gravity and its effects on space and time. To understand particles and the three other cardinal forces—the strong nuclear force, weak force, and electromagnetic force—physicists turn to QFT.
“It’s the language in which we describe physics that involves very small things like particles,” says Can Kilic, a professor of physics at the University of Texas at Austin.
Quantum field theory uses complicated mathematics to model particles, but Kilic likes to think about QFT as a theatre production.
“You have actors that can come onstage and offstage,” he says. “They have lines, and you can write an essentially infinite number of plays with these rules.”
In Kilic’s analogy, actors are particles and the lines actors recite are exchanges of energy between particles, which dictate how particles move and what they do. Once you have a description of which actors are on stage, who speaks to whom, and what is said, you have a description of a universe. For the past century, theorists and experimentalists have been narrowing their focus and trying to determine just who the actors are and what lines are said.
Their efforts have resulted in the Standard Model, which acts as a dramatis personae of elementary particles. Currently, this cast includes 12 elementary fermions—particles of matter (along with their antimatter counterparts) – 4 gauge bosons – particles that mediate forces, and the Higgs boson. The script is written not in English, but in Math, which is the language of quantum field theory. Set on a grand cosmic stage, the corresponding play tells the story of our universe in a clarity that physicists even a century ago couldn’t have dreamed of.
In spite of this accomplishment, the Standard Model leaves much to be explained.
“Nobody claims that this is the complete picture of nature,” Kilic says. “We know of many of its shortcomings. Quantum field theory does not yet have a good way to describe gravity—which is somewhat ironic given how much we experience it in our everyday lives.”
Unifying QFT with general relativity is an ambitious task that would create a theory many physicists have called a “Theory of Everything,” since it would place all the known forces governing all the particles and their interactions under a single umbrella. Several candidates, such as string theory and loop quantum gravity, have been proposed.
But even if these two theories are supplanted by a single, combined “Theory of Everything,” the Standard Model would likely stick around in some form.
“People today don’t say Einstein destroyed Newtonian mechanics,” Kilic says. “It is a beautiful thing that works to almost perfection, whether you’re talking about the orbit of the Earth or a piano falling from a roof.”
In much the same way, Kilic believes that the Standard Model will have longevity, even as physics evolves.
Over the past two decades in particular, the Standard Model has been refined and further entrenched as the standard in particle physics.
“Twenty years ago, there were theorists that didn’t have a Higgs boson to explain mass,” says Bogdan Dobrescu, a theorist at Fermilab. “There was so much more freedom in coming up with new particles compared to today.”
More data has put better limits on the characteristics of particles, and the discovery of a Higgs boson that fits nicely into the Standard Model has only reinforced it as the accepted theory.
This validation has come at a price: It has yielded a dearth of new, interesting directions for theorists to look.
“In a sense, we are the ‘victims’ of the great success of the Standard Model,” Dobrescu says, smiling.
The observable universe is about one trillion trillion miles wide, but to understand it, physicists often turn to subatomic particles so small we can’t measure their width.
“Particles are the fundamental building blocks of matter,” says Rakhi Mahbubani, a theoretical physicist at CERN. “Everything we see, the world we live in, is made up of particles.”
It’s from these particles that theorists approach questions that the rest of the universe hinges on, such as: “Where does mass come from?”
In the early ‘60s, theorists found a potential answer: mass could be generated by a field that pervades the universe. This is often famously explained by the “cocktail party” analogy: Heavier particles are like celebrities at a cocktail party, given more mass by people clumped eagerly around them. Lighter particles are like anonymous nobodies, unburdened by attention. This mechanism of giving mass would later come to be known as the Higgs field.
Over decades, theorists generated many theories about how the Higgs boson, a particle of the Higgs field, would “look.” Finally, in the summer of 2012, physicists announced that they had found signatures of the Higgs boson hidden in data from CERN’s Large Hadron Collider.
These signatures are the faint trails left by particles in the wake of a collision. Like forensic analysts measuring blood splatter at a crime scene, experimentalists can use computers to render these signatures to see what happened in a particle collision.
Combing through data of high energy particle collisions, they saw a small bump at about 125 GeV, which is roughly the mass of 125 protons. This bump—which turned out to be the Higgs—validated thousands of papers and years and years of work by theorists. Physicists around the world celebrated the monumental accomplishment.
But the story isn’t over for the Higgs.
What experimentalists found is sort of a “vanilla” Higgs. Instead of pointing to new physics, the 125 GeV Higgs fit within the Standard Model. In 2016, the LHC found some data for an additional Higgs at 750 GeV, but more measurements showed it was just a statistical fluctuation.
For decades, many theorists have subscribed to an unproven theory known as super-symmetry, affectionately called “SUSY.” For theorists, SUSY is alluring because it proposes a deep kind of symmetry—both aesthetically and mathematically pleasing—between two types of particles in the Standard Model, fermions and bosons. Finding a 750 GeV Higgs would have been strong evidence for SUSY.
“It’s an elegant idea,” Kilic says. “What if, for every particle that we know about, there was another one with kind of the opposite type of behaviour?”
For example, a fermionic quark would have a bosonic counterpart: a “squark.” Bosonic photons would have a fermionic counterpart: a “photino.” If these “superpartners” existed, they would solve an issue known as the hierarchy problem.
“The mass of a proton or neutron is about 1 GeV. So why is the Higgs mass not too far away from that?” Kilic asks. “It could have been billions and trillions and quadrillions of times heavier and somehow it isn’t.”
As a scalar boson, the Higgs is uniquely sensitive to quantum corrections. Calculating the quantum corrections for the Higgs adds up to infinity. This suggests that the Higgs mass should exist where the laws of physics break down, which is when black holes form, around 1018 GeV—a quintillion times the mass of a proton. But the Higgs is only 125 GeV, so something must be cancelling out the quantum corrections. By proposing superpartners, SUSY answers the question: “Will someone rid me of these meddlesome quantum corrections?”
Under the Standard Model, quantum corrections to the Higgs are caused by fermions and bosons. In SUSY, quantum corrections add up to a nice, round zero because superpartners cancel each others’ effects. For example, a top quark and a top squark have opposing contributions, so the total quantum correction is zero. With superpartners cancelling each other’s effects, the Higgs mass can stay nice and low—around 125 GeV, instead of 1018 GeV. Experimental physicists would also be able to detect these superpartners with powerful particle accelerators. Many experimental searches for particles have been carried out with discovering SUSY in mind.
“The whole design of [the LHC] is focused on signatures inspired by SUSY,” Mahbubani says.
Though there have been tantalising experimental hints, they have all vanished with more and better data. At present, there is no concrete evidence for SUSY.
“We have yet to observe any superpartner, and we’ve looked for them very carefully,” Kilic says. “Now it’s possible they’re just hiding around the next corner, but it’s also possible we’re just wrong in the way we think about this.”
Going above and beyond
So, with no real experimental leads, how do theorists come up with new theories?
“It’s not a complete shot in the dark. You know the framework, you know the rules of the game,” Kilic says. “You might say in the script so far, for my theatre play, a murder has taken place and I have to figure out ‘Who is the murderer?’ Is it a character that has not yet appeared? Maybe it’s one of the characters I’ve already seen, maybe it’s the butler.”
Mahbubani, in particular, is interested in where experimentalists are not looking. One major assumption most experiments make is that particles will decay almost immediately—likely the case if SUSY is true. But in a non-SUSY theory, some particles might be “long-lived” and decay outside of where experimentalists are looking. If particles traveled even a few meters before decaying, the instruments in the LHC could be completely blind to them.
“My argument is that maybe we should start moving away from these theory biases when designing experimental searches because our theory biases haven’t yielded any fruit,” Mahbubani says. “There’s a whole world out there that’s not SUSY and that doesn’t have the same sort of signatures.”
That doesn’t mean theorists can just come up with anything that would be difficult to find and call it a day.
“You want to write a theory that tells you how to compute things,” Dobrescu says. “Then you can ask questions like ‘How would the particle show up differently in different experiments?’”
Sometimes it’s not clear where a theory will lead. In 2017, a paper published in Physical Review Letters proposed a connection between two hypothetical particles: the dark photon and the axion. The authors demonstrated how this hypothetical connection, known as a portal, would affect dark matter production.
“When we got this study started, we did not intend to find a new dark matter production mechanism,” lead author Kunio Kaneta contended.
Kaneta’s paper is just one possibility of where new physics could go; there’s no telling right now whether it will turn out to be true. It’s just a hypothetical connection between two hypothetical particles. The vast majority of theories will turn out to be false or flawed in major ways. But because science—especially theoretical particle physics—is a collaborative effort, the worth of a paper is often measured not by whether it is accurate, but if it motivates other physicists along new lines of thought.
“A lot of the time it’s like: ‘Oh, that’s a really interesting paper—let me try and reproduce the results or play around with the scenario that they’re talking about,’” Mahbubani says.
It may seem tempting to scoff at notions of “dark photons” and “portals” because of how fantastical and outlandish the ideas seem, but many physicists urge skeptics to be cautious with their skepticism.
“If you test the laws of physics in a regime where nobody looked before, it’s perfectly fine to expect weird, strange things that theorists have conjured up,” Dobrescu says.
Time and again, what originally sounded wild and unusual has become the new reality for physicists. As they say, rules exist to be broken.
The most steadfast rules of physics are enshrined as symmetries.
We see symmetries in everyday life: The shape of a circle, no matter how it is rotated, always appears the same. This invariance is reflected in the cosmos as well. For instance: Physical laws do not change from day to day, or from place to place. Gravity—as far as we know—works the same at 6 p.m. as it does at 7 p.m., and the same in New York as in Beijing.
Thanks to work done by mathematician Emmy Noether in the early 20th century, we know that symmetry is deeply intertwined with principles of conservation. Her work helped prove that conservation of energy results from symmetry in time. In other words: Energy can neither be created nor destroyed when the laws of physics do not change over time.
These symmetries and their corresponding conservation laws are abiding truths that have persisted over decades and even centuries.
“Conservation of energy has been probed, attacked, scrutinised. It’s withstood all of these tests,” Kilic says.
There are no unimpeachable laws in physics, but conservation of energy comes close.
When theorists propose new ideas or models to explain the universe, they do so within a hierarchical set of constraints. At the bottom level are fundamental rules like conservation of energy and symmetries of time and space. Above them are well established theories like special relativity, which rest on conservation principles. Theories like the Standard Model are much more recent, and rest upon special relativity and conservation principles. At the precarious top are widely subscribed to, but unproven theories, such as SUSY or string theory.
The further up this hierarchy one goes, the more acceptable and easier it is to overturn conventions. Finding a flaw in the Standard Model—which many physicists hoped the discovery of the Higgs would do—would be a grand accomplishment, but it would not obviate deeper truths in physics.
“If you ever found a problem with conservation of energy, you might want to rethink your whole picture of the universe,” Kilic says, with a caveat. “Nothing could galvanise and excite our community more than a very unexpected result like that.”
Barring an earth-shattering experimental result that places doubt on conservation of energy, theorists will continue to treat it as axiomatic law.
This is not to say that theorists haven’t seen their fundamental picture of the universe overturned. When Einstein introduced his theory of special relativity, he challenged a fundamental presumption about how we understood the universe. Before special relativity, space and time were thought of as two discrete phenomena. After Einstein, space and time became irrevocably intertwined in the minds of physicists.
Thomas Kuhn, the philosopher and historian of science, famously dubbed these rare, world-changing moments as “paradigm shifts.” They were not only shifts in what knowledge scientists had, but from what perspective they saw the world. According to Kuhn, these shifts occurred during a time of “crisis”—when contemporary, competing theories were burdened by anomalies and insufficient explanations. Kuhn posited that these crises would free scientists to breach conventions and come up with a new theory, which would become the new paradigm.
Today, many theorists believe that physics is in a similar type of “crisis,” with the conflicting theories of general relativity and QFT, and many more unanswered questions in the cosmic unknowns of dark matter and dark energy.
Biased toward beauty
“We are trying to find out what the deepest laws of nature are,” Dobrescu says.
To pursue these questions, physicists may be forced to reexamine their most fundamental precepts.
One difficulty is that the search is operating in a realm where intuition and common sense—skills that all good detectives use—can lead theorists astray.
To probe the most fundamental parts of the universe, physicists have to operate in a regime of energies and distances that is utterly foreign. The world of electrons and quarks obeys quantum laws that differ from reality we experience. There, even things as simple as position and velocity are uncertain. At high enough energies, particles do strange and unseemly things and blip in and out of existence.
“It’s kind of this extreme limit of nature that we don’t normally have any intuition for,” Kilic says.
Still, theorists try to develop a type of intuition for this realm. Visual aids, such as Feynman diagrams, can help theorists better understand and “picture” how particles interact with one another.
For the past half-century, theorists have made predictions based on QFT that were, again and again, reinforced by experiment. Theorists’ confidence in their ability to divine the secrets of the universe grew. They extended their insight, intuition, and mathematical prowess to craft grander theories such as SUSY.
But now, with no clear evidence for these “Beyond the Standard Model” theories, some physicists are reconsidering their biases.
“Maybe our biases are less well founded in reality than we might wish,” says Mahbubani.
Many of these biases, toward particular models or ways of thinking about the universe, are like an acquired taste or aesthetic, according to Mahbubani. Physicists develop them after working within the field for years, and they exist as guidelines for which ideas are acceptable and which are not.
Simplicity and beauty have been hallmarks of theorists’ preferred aesthetics. In a 2016 BBC competition for “the most beautiful equation,” the Dirac equation took first place.
Jon Butterworth, a physicist at University College London, commented: “I love the Dirac equation because it combines elegant mathematics with huge physical consequences.” This ideal of aesthetic simplicity and elegance can be found throughout theoretical physics, and yet it remains elusive.
A New Yorker article posed the question of “elegance” to a number of physicists, including Edward Witten, a leading scholar of string theory at Princeton’s Institute for Advanced Study. Witten put it simply: “After you define music for me, I will try to define elegance.”
There are many good reasons to subscribe to the biases theorists hold. Reductionism has served physicists well ever since Democritus proposed the atom. Universalising principles gave Newton unparalleled insight into gravity. Beauty, in part, led Dirac to an equation that predicted antimatter well before it was discovered by experiment.
But perhaps it was luck that aligned our biases with theory. Or perhaps those biases align only with select theories, and not others.
“I don’t know how much faith to put in … our conventionally held views of aesthetics,” Mahbubani says. “Are they going to serve us in good stead when it comes to finding a theory that describes nature? I have no clue. It would be great if they did, but I’m worried that they don’t.”
It is not an easy job.
“You never know when inspiration will strike or if it’s going to strike at all,” Mahbubani says. Sometimes, she admits, it’s like pulling teeth.
In theory, it would be easy to lose hope, to give up and tackle a less insurmountable problem than how the universe works.
Yet, that is not what theorists do. Instead, they whittle away at barriers to knowledge. They come up with ideas they know may ultimately be unfounded because they know that’s part and parcel of scientific progress.
In the decades prior to the discovery of the Higgs, physicists came up with dozens of alternative mass-giving mechanisms, like “technicolor,” “top quark condensate,” and even “unparticle physics.” These were stabs in the dark, but they were part of a necessary process. As Richard Feynman put it: “In order to make progress, one must leave the door to the unknown ajar.”
Why theorists subject themselves to this arduous process of potential dead ends that take years to reach can be mystifying—until they start talking. Their excitement and passion for the subject tells it all.
“Once you’ve got an idea—the seed of an idea that you really want to know the answer to—from there it’s really easy,” Mahbubani says. “It’s almost not work anymore. It’s pure play, and you just don’t want to stop doing it.”
Details about the next great theoretical revolution in physics are vague. We don’t know when it will happen, who will conceive it first, or what this great idea will be. But if history teaches us anything, it’s not to count out people who have dedicated their lives to understanding the universe.