Gravity is mathematically relatable to dynamics of subatomic particles


Gravity, the force that brings baseballs back to Earth and governs the growth of black holes, is mathematically relatable to the peculiar antics of the subatomic particles that make up all the matter around us.

Albert Einstein’s desk can still be found on the second floor of Princeton’s physics department. Positioned in front of a floor-to-ceiling blackboard covered with equations, the desk seems to embody the spirit of the frizzy-haired genius as he asks the department’s current occupants, “So, have you solved it yet?”

Einstein never achieved his goal of a unified theory to explain the natural world in a single, coherent framework. Over the last century, researchers have pieced together links between three of the four known physical forces in a “,” but the fourth force, gravity, has always stood alone.

No longer. Thanks to insights made by Princeton faculty members and others who trained here, gravity is being brought in from the cold—although in a manner not remotely close to how Einstein had imagined it.

Though not yet a “theory of everything,” this framework, laid down over 20 years ago and still being filled in, reveals surprising ways in which Einstein’s theory of gravity relates to other areas of physics, giving researchers new tools with which to tackle elusive questions.

The key insight is that gravity, the force that brings baseballs back to Earth and governs the growth of , is mathematically relatable to the peculiar antics of the that make up all the matter around us.

This revelation allows scientists to use one branch of physics to understand other seemingly unrelated areas of physics. So far, this concept has been applied to topics ranging from why black holes run a temperature to how a butterfly’s beating wings can cause a storm on the other side of the world.

This relatability between gravity and subatomic provides a sort of Rosetta stone for physics. Ask a question about gravity, and you’ll get an explanation couched in the terms of subatomic particles. And vice versa.

“This has turned out to be an incredibly rich area,” said Igor Klebanov, Princeton’s Eugene Higgins Professor of Physics, who generated some of the initial inklings in this field in the 1990s. “It lies at the intersection of many fields of physics.”

From tiny bits of string

The seeds of this correspondence were sprinkled in the 1970s, when researchers were exploring tiny subatomic particles called quarks. These entities nest like Russian dolls inside protons, which in turn occupy the atoms that make up all matter. At the time, physicists found it odd that no matter how hard you smash two protons together, you cannot release the quarks—they stay confined inside the protons.

One person working on quark confinement was Alexander Polyakov, Princeton’s Joseph Henry Professor of Physics. It turns out that quarks are “glued together” by other particles, called gluons. For a while, researchers thought gluons could assemble into strings that tie quarks to each other. Polyakov glimpsed a link between the theory of particles and the theory of strings, but the work was, in Polyakov’s words, “hand-wavy” and he didn’t have precise examples.

Meanwhile, the idea that fundamental particles are actually tiny bits of vibrating string was taking off, and by the mid-1980s, “string theory” had lassoed the imaginations of many leading physicists. The idea is simple: just as a vibrating violin string gives rise to different notes, each string’s vibration foretells a particle’s mass and behavior. The mathematical beauty was irresistible and led to a swell of enthusiasm for string theory as a way to explain not only particles but the universe itself.

One of Polyakov’s colleagues was Klebanov, who in 1996 was an associate professor at Princeton, having earned his Ph.D. at Princeton a decade earlier. That year, Klebanov, with graduate student Steven Gubser and postdoctoral research associate Amanda Peet, used string theory to make calculations about gluons, and then compared their findings to a string-theory approach to understanding a black hole. They were surprised to find that both approaches yielded a very similar answer. A year later, Klebanov studied absorption rates by black holes and found that this time they agreed exactly.

That work was limited to the example of gluons and black holes. It took an insight by Juan Maldacena in 1997 to pull the pieces into a more general relationship. At that time, Maldacena, who had earned his Ph.D. at Princeton one year earlier, was an assistant professor at Harvard. He detected a correspondence between a special form of gravity and the theory that describes particles. Seeing the importance of Maldacena’s conjecture, a Princeton team consisting of Gubser, Klebanov and Polyakov followed up with a related paper formulating the idea in more precise terms.

Another physicist who was immediately taken with the idea was Edward Witten of the Institute for Advanced Study (IAS), an independent research center located about a mile from the University campus. He wrote a paper that further formulated the idea, and the combination of the three papers in late 1997 and early 1998 opened the floodgates.

“It was a fundamentally new kind of connection,” said Witten, a leader in the field of string theory who had earned his Ph.D. at Princeton in 1976 and is a visiting lecturer with the rank of professor in physics at Princeton. “Twenty years later, we haven’t fully come to grips with it.”

Two sides of the same coin

This relationship means that gravity and subatomic particle interactions are like two sides of the same coin. On one side is an extended version of gravity derived from Einstein’s 1915 theory of general relativity. On the other side is the theory that roughly describes the behavior of subatomic particles and their interactions.

The latter theory includes the catalogue of particles and forces in the “standard model” (see sidebar), a framework to explain matter and its interactions that has survived rigorous testing in numerous experiments, including at the Large Hadron Collider.

In the standard model, quantum behaviors are baked in. Our world, when we get down to the level of particles, is a quantum world.

Notably absent from the standard model is gravity. Yet quantum behavior is at the basis of the other three forces, so why should gravity be immune?

The new framework brings gravity into the discussion. It is not exactly the gravity we know, but a slightly warped version that includes an extra dimension. The universe we know has four dimensions, the three that pinpoint an object in space—the height, width and depth of Einstein’s desk, for example—plus the fourth dimension of time. The gravitational description adds a fifth dimension that causes spacetime to curve into a universe that includes copies of familiar four-dimensional flat space rescaled according to where they are found in the fifth dimension. This strange, curved spacetime is called anti-de Sitter (AdS) space after Einstein’s collaborator, Dutch
astronomer Willem de Sitter.

The breakthrough in the late 1990s was that mathematical calculations of the edge, or boundary, of this anti-de Sitter space can be applied to problems involving quantum behaviors of subatomic particles described by a mathematical relationship called conformal field theory (CFT). This relationship provides the link, which Polyakov had glimpsed earlier, between the theory of particles in four space-time dimensions and string theory in five dimensions. The relationship now goes by several names that relate gravity to particles, but most researchers call it the AdS/CFT (pronounced A-D-S-C-F-T) correspondence.

Tackling the big questionsThis correspondence, it turns out, has many practical uses. Take black holes, for example. The late physicist Stephen Hawking startled the physics community by discovering that black holes have a temperature that arises because each particle that falls into a black hole has an entangled particle that can escape as heat.

Using AdS/CFT, Tadashi Takayanagi and Shinsei Ryu, then at the University of California-Santa Barbara, discovered a new way to study

entanglement in terms of geometry, extending Hawking’s insights in a fashion that experts consider quite remarkable.

In another example, researchers are using AdS/CFT to pin down chaos theory, which says that a random and insignificant event such as the flapping of a butterfly’s wings could result in massive changes to a large-scale system such as a faraway hurricane. It is difficult to calculate chaos, but black holes—which are some of the most chaotic quantum systems possible—could help. Work by Stephen Shenker and Douglas Stanford at Stanford University, along with Maldacena, demonstrates how, through AdS/CFT, black holes can model quantum chaos.

One open question Maldacena hopes the AdS/CFT correspondence will answer is the question of what it is like inside a black hole, where an infinitely dense region called a singularity resides. So far, the relationship gives us a picture of the black hole as seen from the outside, said Maldacena, who is now the Carl P. Feinberg Professor at IAS.

“We hope to understand the singularity inside the black hole,” Maldacena said. “Understanding this would probably lead to interesting lessons for the Big Bang.”

The relationship between gravity and strings has also shed new light on quark confinement, initially through work by Polyakov and Witten, and later by Klebanov and Matt Strassler, who was then at IAS.

Those are just a few examples of how the relationship can be used. “It is a tremendously successful idea,” said Gubser, who today is a professor of physics at Princeton. “It compels one’s attention. It ropes you in, it ropes in other fields, and it gives you a vantage point on theoretical physics that is very compelling.”

The relationship may even unlock the quantum nature of gravity. “It is among our best clues to understand gravity from a quantum perspective,” said Witten. “Since we don’t know what is still missing, I cannot tell you how big a piece of the picture it ultimately will be.”

Still, the AdS/CFT correspondence, while powerful, relies on a simplified version of spacetime that is not exactly like the real universe. Researchers are working to find ways to make the theory more broadly applicable to the everyday world, including Gubser’s research on modeling the collisions of heavy ions, as well as high-temperature superconductors.

Also on the to-do list is developing a proof of this correspondence that draws on underlying physical principles. It is unlikely that Einstein would be satisfied without a proof, said Herman Verlinde, Princeton’s Class of 1909 Professor of Physics, the chair of the Department of Physics and an expert in string , who shares office space with Einstein’s desk.

“Sometimes I imagine he is still sitting there,” Verlinde said, “and I wonder what he would think of our progress.”

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Particle Physicists Turn to AI to Cope with CERN’s Collision Deluge


Can a competition with cash rewards improve techniques for tracking the Large Hadron Collider’s messy particle trajectories?

Particle Physicists Turn to AI to Cope with CERN's Collision Deluge
A visualization of complex sprays of subatomic particles, produced from colliding proton beams in CERN’s CMS detector at the Large Hadron Collider near Geneva, Switzerland in mid-April of 2018. Credit: CERN

Physicists at the world’s leading atom smasher are calling for help. In the next decade, they plan to produce up to 20 times more particle collisions in the Large Hadron Collider (LHC) than they do now, but current detector systems aren’t fit for the coming deluge. So this week, a group of LHC physicists has teamed up with computer scientists to launch a competition to spur the development of artificial-intelligence techniques that can quickly sort through the debris of these collisions. Researchers hope these will help the experiment’s ultimate goal of revealing fundamental insights into the laws of nature.

At the LHC at CERN, Europe’s particle-physics laboratory near Geneva, two bunches of protons collide head-on inside each of the machine’s detectors 40 million times a second. Every proton collision can produce thousands of new particles, which radiate from a collision point at the centre of each cathedral-sized detector. Millions of silicon sensors are arranged in onion-like layers and light up each time a particle crosses them, producing one pixel of information every time. Collisions are recorded only when they produce potentially interesting by-products. When they are, the detector takes a snapshot that might include hundreds of thousands of pixels from the piled-up debris of up to 20 different pairs of protons. (Because particles move at or close to the speed of light, a detector cannot record a full movie of their motion.)

From this mess, the LHC’s computers reconstruct tens of thousands of tracks in real time, before moving on to the next snapshot. “The name of the game is connecting the dots,” says Jean-Roch Vlimant, a physicist at the California Institute of Technology in Pasadena who is a member of the collaboration that operates the CMS detector at the LHC.

After future planned upgrades, each snapshot is expected to include particle debris from 200 proton collisions. Physicists currently use pattern-recognition algorithms to reconstruct the particles’ tracks. Although these techniques would be able to work out the paths even after the upgrades, “the problem is, they are too slow”, says Cécile Germain, a computer scientist at the University of Paris South in Orsay. Without major investment in new detector technologies, LHC physicists estimate that the collision rates will exceed the current capabilities by at least a factor of 10.

Researchers suspect that machine-learning algorithms could reconstruct the tracks much more quickly. To help find the best solution, Vlimant and other LHC physicists teamed up with computer scientists including Germain to launch the TrackML challenge. For the next three months, data scientists will be able to download 400 gigabytes of simulated particle-collision data—the pixels produced by an idealized detector—and train their algorithms to reconstruct the tracks.

Participants will be evaluated on the accuracy with which they do this. The top three performers of this phase hosted by Google-owned company Kaggle, will receive cash prizes of US$12,000, $8,000 and $5,000. A second competition will then evaluate algorithms on the basis of speed as well as accuracy, Vlimant says.

Prize appeal

Such competitions have a long tradition in data science, and many young researchers take part to build up their CVs. “Getting well ranked in challenges is extremely important,” says Germain. Perhaps the most famous of these contests was the 2009 Netflix Prize. The entertainment company offered US$1 million to whoever worked out the best way to predict what films its users would like to watch, going on their previous ratings. TrackML isn’t the first challenge in particle physics, either: in 2014, teams competed to ‘discover’ the Higgs boson in a set of simulated data (the LHC discovered the Higgs, long predicted by theory, in 2012). Other science-themed challenges have involved data on anything from plankton to galaxies.

From the computer-science point of view, the Higgs challenge was an ordinary classification problem, says Tim Salimans, one of the top performers in that race (after the challenge, Salimans went on to get a job at the non-profit effort OpenAI in San Francisco, California). But the fact that it was about LHC physics added to its lustre, he says. That may help to explain the challenge’s popularity: nearly 1,800 teams took part, and many researchers credit the contest for having dramatically increased the interaction between the physics and computer-science communities.

TrackML is “incomparably more difficult”, says Germain. In the Higgs case, the reconstructed tracks were part of the input, and contestants had to do another layer of analysis to ‘find’ the particle. In the new problem, she says, you have to find in the 100,000 points something like 10,000 arcs of ellipse. She thinks the winning technique might end up resembling those used by the program AlphaGo, which made history in 2016 when it beat a human champion at the complex game of Go. In particular, they might use reinforcement learning, in which an algorithm learns by trial and error on the basis of ‘rewards’ that it receives after each attempt.

Vlimant and other physicists are also beginning to consider more untested technologies, such as neuromorphic computing and quantum computing. “It’s not clear where we’re going,” says Vlimant, “but it looks like we have a good path.”

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New analysis shows a way to self-propel subatomic particles


Some physical principles have been considered immutable since the time of Isaac Newton: Light always travels in straight lines. No physical object can change its speed unless some outside force acts on it.

Not so fast, says a new generation of physicists: While the underlying haven’t changed, new ways of “tricking” those laws to permit seemingly impossible actions have begun to appear. For example, work that began in 2007 proved that under special conditions, light could be made to move along a curved trajectory—a finding that is already beginning to find some practical applications.

Now, in a new variation on the methods used to bend light, physicists at MIT and Israel’s Technion have found that subatomic particles can be induced to speed up all by themselves, almost to the speed of light, without the application of any external forces. The same underlying principle could also be used to extend the lifetime of some unstable isotopes, perhaps opening up new avenues of research in basic particle physics.

The findings, based on a theoretical analysis, were published in the journal Nature Physics by MIT postdoc Ido Kaminer and four colleagues at the Technion.

The new findings are based on a novel set of solutions for a set of basic quantum-physics principles called the Dirac equations; these describe the relativistic behavior of , such as electrons, in terms of a wave structure. (In quantum mechanics, waves and particles are considered to be two aspects of the same physical phenomena). By manipulating the wave structure, the team found, it should be possible to cause electrons to behave in unusual and counterintuitive ways.

Unexpected behavior

This manipulation of waves could be accomplished using specially engineered phase masks—similar to those used to create holograms, but at a much smaller scale. Once created, the particles “self-accelerate,” the researchers say, in a way that is indistinguishable from how they would behave if propelled by an electromagnetic field.

“The electron is gaining speed, getting faster and faster,” Kaminer says. “It looks impossible. You don’t expect physics to allow this to happen.”


his image shows the spatial distribution of charge for an accelerating wave packet, representing an electron, as calculated by this team’s approach. Brightest colors represent the highest charge levels. The self-acceleration of a particle predicted by this work is indistinguishable from acceleration that would be produced by a conventional electromagnetic field.

It turns out that this self-acceleration does not actually violate any physical laws—such as the conservation of momentum—because at the same time the particle is accelerating, it is also spreading out spatially in the opposite direction.

“The electron’s is not just accelerating, it’s also expanding,” Kaminer says, “so there is some part of it that compensates. It’s referred to as the tail of the wave packet, and it will go backward, so the total momentum will be conserved. There is another part of the wave packet that is paying the price for the main part’s acceleration.”

It turns out, according to further analysis, that this self-acceleration produces effects that are associated with relativity theory: It is a variation on the dilation of time and contraction of space, effects predicted by Albert Einstein to take place when objects move close to the . An example of this is Einstein’s famous twin paradox, in which a twin who travels at high speed in a rocket ages more slowly than another twin who remains on Earth.

Extending lifetimes

In this case, the time dilation could be applied to that naturally decay and have very short lifetimes—causing these particles to last much longer than they ordinarily would.

This could make it easier to study such particles by causing them to stay around longer, Kaminer suggests. “Maybe you could measure effects in that you couldn’t do otherwise,” he says.

In addition, it might induce differences in the behavior of those particles that might reveal new, unexpected aspects of physics. “You could get different properties—not just for electrons, but for other particles as well,” Kaminer says.

Now that these effects have been predicted based on theoretical calculations, Kaminer says it should be possible to demonstrate the phenomenon in laboratory experiments. He is beginning work with MIT physics professor Marin Soljačić on the design of such experiments.

The experiments would make use of an electron microscope fitted with a specially designed phase mask that would produce 1,000 times higher resolution than those used for holography. “It’s the most exact way known today to affect the field of the electron,” Kaminer says.

While this is such early-stage work that it’s hard to predict what practical applications it might eventually have, Kaminer says this unusual way of accelerating electrons might prove to have practical uses, such as for medical imaging.

“Research on self-accelerating and shape-preserving beams became very active in recent years, with demonstration of different types of optical, plasmonic, and electron beams, and study of their propagation in different media,” says Ady Arie, a professor of electrical engineering at Tel Aviv University who was not involved in this research. “The authors derive shape-preserving solutions for the Dirac equation that describe the wave propagation of , which were not taken into account in most of the previous works.”

Arie adds, “Perhaps the most interesting result is the use of these to demonstrate the analog of the famous twin paradox of special relativity: The authors show that occurs between a self-accelerating particle that propagates along a curved trajectory and its ‘twin’ particle that remains at rest.”

The Large Hadron Collider has observed two brand new particles.


Two never-before-seen “heavy-weight” baryon particles have been detected by the world’s favourite particle accelerator, the Large Hadron Collider. The discovery could help scientists understand more about the interactions of elementary particles.
Physicists from CERN in Geneva have discovered two new types of baryon particlesnamed Xi_b’- and Xi_b*- (before you ask, no, we’re not sure how to pronounce them).

Baryon particles are subatomic particles such as hyperons that are made up of three strongly-bonded tiny elementary particles called quarks – which are generally thought to be some of the smallest units of matter.

Xi_b’- and Xi_b*- were both predicted to already exist by the quantum physics models, but they’d never been seen before this and scientists weren’t sure of their exact mass – something they’ve now managed to calculate. And the heavy-weight subatomic particles impressively big – both are more than six times as massive as protons.

The new baryons were spotted in the Large Hadron Collider (LHC), the particle accelerator most famous for (probably) finding the Higgs boson.

The LHC works by accelerating two opposing beams of particles to speeds approaching the speed of light, and when they collide, they create an extremely hot explosion, which allows never-before-seen particles and types of matter to form very briefly.

In this split-second after-collision is when all the magic happens and physicists can find proof for things they’ve previously only ever hypothesised using formulae.

Just like baryons, protons are almost made of three tightly-bound quarks, but what’s particularly fascinating about Xi_b’- and Xi-b*- is that each of their quarks has a different spin, or direction in which they configure. Both subatomic particles contain one beauty quark (which accounts for most of their weight), one strange quark and one down quark.

As Nicholas St. Fleur explains for The Atlantic:

“The finding helps physicists narrow down the different ways that quarks can be arranged, which provides clues into understanding the forces that keep them and the most basic building blocks of matter held together”.

The results have been submitted to Physical Review Letters, but appear online now on ArXiv.

“There are maybe three-to-five such particles discovered each year,” Patrick Koppenburg, a CERN scientist from the Netherlands’ Nikhef Institute, told The Wall Street Journal. “Here we have two in one go, which is quite extraordinary.”

The researchers have also studied the relative production rates of the baryons, their widths – which can measure how unstable they are – as well as other details of their decay.

All of the results matched up with what they’d predicted of the baryons based on the theory of Quantum Chromodynamics (QCD).

QCD is part of the Standard Model of particle physics, which describes the forces that govern our Universe. Understanding more about the QCD will help refine our knowledge of the Standard Model and possibly even advance it one day.

“If we want to find new physics beyond the Standard Model, we need first to have a sharp picture,” said Patrick Koppenburg, the physics coordinator of the LHCb, the instrument that detected the baryons, in a press release. “Such high precision studies will help us to differentiate between Standard Model effects and anything new or unexpected in the future.”

Of course, particle discoveries are always pretty controversial. St. Fleur reports for The Atlantic:

“In 2011, a collaboration between CERN and the Italian OPERA experiment announced finding faster-than-light neutrinos, a discovery that was later undone after further investigation, as ScienceInsider reported in 2012. Even now, some physicists still debate whether or not physicists actually found the Higgs Boson.”

But although it will take some more peer-reviewed research for the discovery to become widely accepted, it’s still a pretty exciting first step.

“This is a very exciting result. Thanks to LHCb’s excellent hadron identification, which is unique among the LHC experiments, we were able to separate a very clean and strong signal from the background,” said Steven Blusk from Syracuse University in New York, who wasn’t involved in the research, in the CERN press release. “It demonstrates once again the sensitivity and how precise the LHCb detector is.”

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