For three decades, researchers have been futilely searching for new elementary particles to explain why nature is the way it is. As physicists face this failure, they are revisiting a long-standing hypothesis: that any object is made up of something smaller.
By Natalie Wolchover
Translator: Li Yuting
In The Structure of the Scientific Revolution, the philosopher of science Thomas Kuhn observes that scientists spend a long time moving forward slowly. They propose and solve difficult problems while interpreting all the data uniformly within a fixed worldview or theoretical framework, which Kuhn calls a paradigm. Sooner or later, though, there will be facts that come into conflict with existing paradigms. A crisis ensued. Scientists racked their brains, revisited their hypotheses, and eventually made a revolutionary shift to a new paradigm with a completely different and more real understanding of the natural world. Then gradual progress resumed.
For several years, particle physicists who study the fundamental building blocks of nature have been in the midst of a textbook Kuhn crisis.
The crisis became undeniable in 2016, when, despite a major upgrade, the Large Hadron Collider in Geneva still did not produce any of the new elementary particles that theorists had been expecting for decades. These extra particles will solve a major puzzle about one known particle, the famous Higgs boson. The hierarchy problem, as the puzzle goes, asks why the Higgs boson is so lightweight—a hundred million times smaller than the mass of the highest energy scale that exists in nature. Relative to these higher energies, the Higgs mass seems to be unnaturally lowered, as if the enormous numbers in the underlying equation that determine its value are miraculously all offset.
The extra particles should have explained tiny Higgs masses, restoring what physicists call the "naturalness" of their equations. But after the Haktron Colliders— the third and largest collider — have also been futile in their search for them, it seems that the logic of what is natural in nature may be wrong. Gian Giudice, head of the theory department at CERN (the laboratory where the Large Hadron Collider is located), wrote in 2017: "We are faced with the need to rethink the guiding principles that have been used for decades to solve the most fundamental problems about the physical world. ”
At first, the scientific community despaired.
"You can feel that pessimism," says Isabel Garcia Garcia, a particle theorist at the Caffrey Institute for Theoretical Physics at the University of California, Santa Barbara, who was a graduate student at the time. Not only has the $10 billion proton shredder failed to answer a 40-year-old question, but the beliefs and strategies that have long guided particle physics are no longer trustworthy. More than ever, people are wondering whether the universe is just unnatural, the product of fine-tuned mathematical cancellation. Maybe there's a multiverse made up of multiple universes, and all the Higgs masses and other parameters are random, and we find ourselves here only because the special properties of our universe promote the formation of atoms, stars, and planets that form life. This "anthropic principle", while it may be correct, is frustratingly unproven.
Many particle physicists have moved on to other areas of research, "where the puzzle hasn't gotten as hard as the hierarchy problem," says Nathaniel Craig, a theoretical physicist at UCLA.
Figure | Nathaniel Craig and Isabel Garcia explore how gravity helps reconcile nature's vastly different energy scales. (Source: Jeff Liang)
Some of those who stayed behind began to pore over the assumptions of decades ago. They began to rethink the salient features of nature that seemed to be unnatural fine-tuning—the small mass of the Higgs boson, and a seemingly unrelated question about the unnatural low energy of space itself. "The real fundamental problem is a matter of naturalness," Garcia Garcia said.
Their introspection is bearing fruit. Researchers are increasingly looking to what they see as a weakness in traditional reasoning about naturalness. It is based on a plausible hypothesis that has been incorporated into science since ancient Greece. The big stuff is made up of smaller, more basic things—a phrase called reductionism. "The reductionist paradigm ... It's inherent in naturalness issues," said Nima Arkani-Hamed, a theorist at the Institute for Advanced Study in Princeton, New Jersey.
Now, a growing number of particle physicists believe that the problem of naturalness and the ineffective outcome of the Large Hadron Collider may be related to the collapse of reductionism. "Is this going to be a game changer?" Arkani-Hamed said.
In a recent series of papers, researchers have thrown reductionism out of the clouds. They are exploring new ways in which size distance scales may be coordinated, producing parameter values that are unnaturally fine-tuned from a reductionist perspective.
"Some people call it a crisis. There's an atmosphere of pessimism here, but I don't feel that way," Garcia Garcia said. This is a time when I feel like we're doing something meaningful. "
What is naturalness
The Large Hadron Collider did make a key discovery: In 2012, it eventually discovered the Higgs boson, the cornerstone of a 50-year-old theory known as the Standard Model of Particle Physics, which describes 17 known elementary particles.
Higgs's discovery confirms a fascinating story written in Standard Model theory.
Instantly after the Big Bang, an entity known as the Higgs field that penetrated into space was suddenly injected with energy. This Higgs field cracks to produce the Higgs boson, which have mass because of the field's energy. As electrons, quarks, and other particles move through space, they interact with the Higgs boson, and in this way, they also acquire mass.
After the Standard Model was completed in 1975, its designers noticed a problem almost immediately.
When Higgs gives other particles mass, they also immediately reciprocate; the particles' masses shake together. Physicists can write an equation for the mass of the Higgs boson, which includes the relationship of each particle that interacts with it.
All massive Standard Model particles contribute to this equation, but these are not the only contributions. The Higgs boson should also be mathematically mixed with heavier particles, including the Planck-scale phenomenon, an energy level associated with the quantum nature of gravity, black holes, and the Big Bang. The contribution of the Planck-scale phenomenon to the Higgs mass should be enormous—almost a hundred million times greater than the actual Higgs mass.
Naturally, you'd expect the Higgs boson to be as heavy as they are, so that other elementary particles are strengthened as well. Particles will be too heavy to form atoms, and the universe will be empty.
For the Higgs boson, although it relies on enormous amounts of energy, it ends up being so light that you have to assume that Planck's contribution to its mass is positive or negative, and that they all have just the right amount to completely offset it.
This offset is ridiculous unless there is some reason for it — just as impossible as the airflow and the vibration of the table cancel each other out to keep the pencil tip balanced. The offsetting of this fine-tuning is considered "unnatural" by physicists.
Within a few years, physicists have found a satisfactory solution: supersymmetry theory, which assumes that elementary particles in nature have duality. Supersymmetry theory holds that every boson (one of the two types of particles) has a partner fermion (the other type) and vice versa. Bosons and fermions contribute plus or minus terms to higgs mass, respectively.
Therefore, if these items always appear in pairs, they will always be offset.
Exploration of supersymmetric partner particles began with the large positron-electron collider in the 1990s. The researchers hypothesized that the particles were slightly heavier than their Standard Model partners and required more primordial energy to achieve, so they accelerated the particles to near the speed of light, smashed them together, and looked for the appearance of heavy objects in the debris.
At the same time, another question of naturalness surfaced.
The structure of space, even in the absence of matter, seems to possess energy—the net activity of all the quantum fields that flow through it.
When particle physicists added up all the presumptive contributions to the energy of space, they found that, like the Higgs mass, the injection of energy from the Planck-scale phenomenon should blow it up.
Einstein believed that the energy of space—which he called the cosmological constant—had a gravitational repulsion effect that made space expand faster and faster. If space were injected with the energy of Planck density, the universe would tear itself apart in the instant after the Big Bang. But that didn't happen.
Instead, cosmologists observe that the expansion of space is only slowly accelerating, suggesting that the cosmological constant is small.
The 1998 measurements set it at a value of one hundred billion times lower than Planck's energy. Similarly, in the equation of the cosmological constant, it seems that all these huge energy injections and extractions are perfectly counteracted, making space unusually calm.
"Gravity... Mixed physics at all length scales — short distances, long distances. Because it does that, it gives you this way out. ”—— Nathaniel Craig
These two big naturalness problems were already evident in the late 1970s, but for decades physicists have treated them as insignificant questions.
"This is at a stage where people feel divided about it." Arkani-Hamed said. The cosmological constant problem seems to be related to the mysterious, quantum aspect of gravity, since the energy of space is detected only through its gravitational effects. The hierarchy problem looks more like a "nasty little detail problem," Arkani-Hamed explains — a problem that, like two or three other problems in the past, will eventually reveal some missing pieces of the puzzle. The "weakness of higgs," as Giudice puts it, its unnatural lightness, is not something that several supersymmetric particles of the Large Hadron Collider cannot cure.
In hindsight, these two naturalness problems seem more like the surface symptoms of a deeper problem.
"It's useful to think about how these problems came about," Garcia Garcia said in a Zoom call from Santa Barbara this winter. "The hierarchical problem and the cosmological constant problem arise in part because of the tools we use to try to answer the question—the way we try to understand certain features of our universe."
Just the right reductionism
Physicists honestly count the contributions of the Higgs mass and cosmological constants in their own interesting way.
This method of calculation reflects the strange nested structures of nature.
Zoom in on something and you'll see that it's actually a lot of smaller stuff.
From a distance, something like a galaxy is actually a collection of stars; each star is many atoms; an atom dissolves further into the hierarchy of subatomic parts.
In addition, when you zoom in to shorter distance scales, you see heavier, more energetic elementary particles and phenomena — a deep link between high energy and short distances that explains why the high-energy particle collider is like a microscope of the universe.
There are many examples of the connection between high energies and short distances throughout physics. For example, quantum mechanics holds that each particle is also a wave, and the larger the mass of the particle, the shorter its associated wavelength. The other is that the energies must be squeezed together more densely to form smaller objects. Physicists call low-energy, long-distance physics "infrared" and high-energy, short-range physics "ultraviolet," which is an analogy between the wavelengths of infrared and ultraviolet light.
In the 1960s and 1970s, particle physics giants Kenneth Wilson and Steven Weinberg pointed out the extraordinary nature hierarchy: it allowed us to describe some of the interesting properties of the large, infrared scale without knowing what was "really" happening on the more microscopic, ultraviolet scale. For example, you can use a hydrodynamic equation to simulate water as a smooth fluid that masks the complex dynamics of its H2O molecules. The fluid mechanics equation includes a term that represents the viscosity of water—a single number that can be measured at the infrared scale—and it summarizes the interaction of all these molecules that occur at the ultraviolet scale. Physicists say that infrared and ultraviolet scales "decouple" allow them to effectively describe aspects of the world without having to know what's going on deep inside the Planck scale— the ultimate ultraviolet scale, equivalent to one billionth of a trillionth of a centimeter, or 10 billion billion electron volts (GeV) of energy, where the structure of space-time might dissolve into something else.
Kenneth Wilson, an American particle and condensed matter physicist active from the 1960s to the early 2000s, developed a formal mathematical method to describe how the properties of a system vary depending on the scale of its measurements. (Source: Cornell University Faculty Biography Archives, #47-10-3394. ）
Riccardo Rattazzi, a theoretical physicist at the Swiss Federal Institute of Technology in Lausanne, said: "We can study physics because we can be ignorant of what happens over short distances. ”
Wilson and Weinberg have each developed fragments that particle physicists use to simulate our nested world's different-level framework: effective field theory. It is in the context of effective field theory that the question of naturalness arises.
Efficient field theory models a system—say, a bundle of protons and neutrons—at a scale within a certain range. Enlarge protons and neutrons over time, and they will always look like protons and neutrons, and you can use "chiral effective field theory" to describe their dynamics in this range. But then the effective field theory will reach its "UV cutoff point," a short-range, high-energy scale at which the effective field theory is no longer a valid description of the system. For example, at the cutoff point of 1 GeV, chiral effective field theory stops working because protons and neutrons no longer behave like individual particles, but rather like trio of quarks. A different theory began to work.
The point is that there is a reason for the effective field theory to collapse at its UV cutoff. The cutoff point is where new, energetic particles or phenomena that are not included in the theory must be found.
Within its valid range, efficient field theory accounts for UV physics below the cutoff point by adding "corrections" representing these unknown effects. It's like a fluid equation with a viscosity term to capture the net effect of short-range molecular collisions. Physicists don't need to know what actual physical phenomena are at the cutoff to write these corrections, they just use the scale of the cutoff as a rough estimate of the range of validity.
Typically, when you calculate something on the infrared scale of interest, the UV correction is small, proportional to the (relatively small) length scale associated with the cutoff point. But that's a different situation when you use efficient field theory to calculate parameters like Higgs mass or cosmological constants, because those parameters have units of mass or energy. The UV correction of the parameter is large because (in order to have the correct units) the correction is coordinated with the energy, not with the length associated with the cutoff point. When the length is small, the energy is high. Such parameters are called "UV sensitive".
The concept of naturalness emerged in the 1970s with efficient field theory itself as a strategy for identifying where effective field theory must stop.
Therefore, new physics must exist. The logic goes like this. If a mass or energy parameter has a high cutoff, its value should naturally be large, pushed higher by all UV corrections. Therefore, if this parameter is small, then the cut-off energy must be very low.
Some critics argue that naturalness is merely an aesthetic preference. But others point out that this strategy reveals precise, hidden truths about nature. "This logic works," said Craig, who is a leader in recently recommitting to it. The question of naturalness "has always been a sign of changes in circumstances and of the emergence of new things".
What nature can do
In 1974, a few years before the term "naturalness" appeared, Mary K. Gaillard and Ben Lee surprisingly used this strategy to predict the mass of an imaginary particle then known as a cannabis quark. Craig said: "Her predictions of success and their relevance to the hierarchy problem are grossly underestimated in our field. ”
In the summer of 1974, Gaillard and Lee were confused by the difference in the masses of two tallen particles, a composite of quarks. The difference in measurements is small.
But when they tried to calculate this mass difference using the efficient field theory equation, they saw that its value was in danger of exploding. Because the alton mass difference has mass units, it is sensitive to ultraviolet, receiving high-energy corrections from unknown physics at the cutoff point. The cut-off point of the theory was not well known, but physicists at the time deduced that it could not be very high, otherwise the resulting difference in high-techn mass would be smaller than the corrected value— which was unnatural, as physicists now say.
Gaillard and Lee deduced the low cutoff scale of their effective field theory, where new physics should emerge. They argue that a type of quark proposed at the time, known as a cannabis quark, must be discovered with a mass of no more than 1.5 GeV.
Three months later, the quark appeared, weighing 1.2 GeV. The discovery ushered in a revival of awareness known as the November Revolution and quickly led to the completion of the Standard Model. In a recent video call, Gallard, 82, recalled that she was visiting CERN in Europe at the time of the news. Lee sent her a telegram: Charm had been discovered.
In 1974, Mary K. Gaillard (pictured in the 1990s) and Ben Lee used the naturalness argument to predict the mass of a hypothetical elementary particle called a cannabis quark. After a few months, the charm has already appeared. (Source: AIP Emilio Segrè Visual Archive)
Such triumphs have convinced many physicists that the hierarchy problem should also indicate that new particles will not be much heavier than those in the Standard Model.
If the Standard Model's dividing line is near the Planck scale (the researchers are sure the Standard Model failed here because it didn't take quantum gravity into account), then the ultraviolet correction to the Higgs mass would be huge and would make it mildly unnatural. Setting a cutoff point not far above the mass of the Higgs boson itself will make the Higgs mass as heavy as the correction from the cutoff point, and everything will look natural.
"For the past 40 years, this approach has been the starting point for efforts to try to solve hierarchical problems," says Garcia Garcia. "Great ideas have been put forward, such as supersymmetry, synthesis of [Higgs], and we haven't seen them happen in nature yet."
In 2016, Garcia Garcia studied for her PhD in particle physics at Oxford University. For several years, she became acutely aware of the need for liquidation. "That's when I started to get more interested in the missing part, which we usually don't think about when we discuss the problem, which is gravity. This problem can be seen more in quantum gravity than in efficient field theory. ”
Gravity mixes everything together
Theorists learned in the 1980s that gravity does not follow the usual reductive rules.
If you smash two particles together, their energy becomes concentrated at the point of collision, forming a black hole—a region of extreme gravity from which nothing can escape. By slamming the particles together harder, they form a larger black hole. The more energy no longer allows you to see shorter distances, on the contrary, the harder you crash, the larger the invisible area is generated. The black hole and the theory of quantum gravity that describes its interior completely reverse the common relationship between high energy and short distances. Sergei Dubovsky, a physicist at New York University, said: "Gravity is anti-reductionist. ”
Quantum gravity seems to be playing with the architecture of nature, making a mockery of the neat system of nested scales of effective field theory, to which physicists have become accustomed. Craig, like Garcia Garcia, began thinking about the meaning of gravity shortly after the LHC's search for nothing. Trying to think of new solutions to the hierarchy problem, Craig reread an article on naturalness written in 2008 by CERN theorist Giudice.
He began to ponder what Giudice meant: Giudice wrote that the solution to the cosmological constant problem might involve "some complex interaction between the infrared and ultraviolet effects." If there is a complex interaction between infrared and ultraviolet, it would violate the usual decoupling, which allows the efficient field theory to work. "I just Googled for something like 'UV-IR hybrid,'" Craig said, which led him to some interesting 1999 papers, "and then I started." ”
"It's a time when I feel like we're doing something meaningful." ——IsabelGarcia Garcia
UV-IR hybrids have the potential to solve the problem of naturalness by breaking the reductionist scheme of effective field theory. In effective field theory, the problem of naturalness arises when the Higgs mass and cosmological constants are equally sensitive to ultraviolet, but somehow there is no explosion, as if there is a conspiracy between all UV physics to invalidate their effects on the infrared. "In the logic of efficient field theory, we discard this possibility," Craig explains.
Reductionism tells us that infrared physics comes from ultraviolet physics—the viscosity of water comes from its molecular dynamics, and protons derive their properties from their internal quarks, explaining as they zoom in to appear—not the other way around. Ultraviolet is not influenced or explained by infrared, "so [the UV effect] could not have had a conspiracy to make the Higgs thing work out on a very different scale." ”
The question Craig now asks is, "Will this logic of efficient field theory be broken?" "Maybe the explanation can really flow in both directions between ultraviolet and infrared."
It's not entirely whimsical because we know that gravity is like that," he said. "Gravity violates normal effective field theory reasoning because it mixes physics on all length scales, including short and long distances. Because it does, it gives you this way out. ”
How UV-IR blending can save nature
Several new studies on UV-IR hybrids and how it might solve the problem of naturalness mention two papers that emerged in 1999. Patrick Draper, a professor at the University of Illinois at Urbana-Champaign, said: "There is growing interest in these more exotic, non-effective field-theoretic approaches to problem solving, and his most recent work was in a 1999 paper.
Draper and his colleagues studied the CKN constraint, named after the 1999 paper authors Andrew Cohen, David B. Kaplan, and Ann Nelson. They argue that if you put particles in a box and heat them up, you can only add so much energy to the particles before the box collapses into a black hole.
They calculated that before the box collapsed, the number of high-energy particle states you could hold was raised to the third of the box's surface area to three-quarters of the power, rather than the volume of the box you might think it would be.
They realized that this represented a strange ultraviolet-infrared relationship. The size of the box, which sets the infrared scale, severely limits the number of high-energy particle states in the box - the ultraviolet scale.
Then they realized that if its same constraints applied to the entire universe, then it solved the cosmological constant problem. In this case, the observable universe is like a very large box. The number of high-energy particle states it can contain is proportional to the three-quarters of the surface area of the observable universe, not the (much larger) volume of the universe.
This means that the efficient field theory calculations of the usual cosmological constants are too simple.
This calculation tells people that when you zoom in on the structure of space, high-energy phenomena should appear, and there should be energy to blow up space. But CKN constraints mean that there may be much less high-energy activity than is assumed by efficient field theory calculations, which means that there are very few high-energy states available for particles to occupy. Cohen, Kaplan, and Nelson did a simple calculation, and for a box the size of our universe, their constraints more or less accurately predicted tiny values of observed cosmological constants.
Their calculations suggest that scales of magnitude may be interrelated in a way that becomes apparent when you look at infrared properties across the universe, such as cosmological constants.
Draper and NikitaBlinov confirmed in another rough calculation last year that the CKN constraint predicts observed cosmological constants. They also confirmed that this does not undermine many of the successes of efficient field theory in small-scale experiments.
The CKN constraint doesn't tell you why UV and IR are related, i.e. why the size of the box (IR) severely limits the number of high-energy states within the box (UV). For this, you may need to understand quantum gravity.
Other researchers have looked for answers in a specific theory of quantum gravity: string theory. Last summer, string theorists Steven Abel and Keith Dienes demonstrated how ultraviolet-infrared hybrids in string theory solve the hierarchy and cosmological constant problems.
As a candidate for the basic theory of gravity and everything else, string theory holds that all particles, up close, are small vibratory strings. Standard Model particles like photons and electrons are the low-energy vibration modes of the fundamental strings. But strings can also swing more energetically, resulting in an infinite spectrum of string states with increasingly high energies. In this case, the hierarchy question asks why these chordal corrections would not inflate the Higgs if there was no such thing as supersymmetry to protect the Higgs.
Dienes and Abel calculated that due to a different symmetry of string theory, the module invariance, the chordal correction of all the energies in the infinite spectrum from infrared to ultraviolet would cancel each other out in just the right way, making the Higgs mass and cosmological constant small. The researchers note that this conspiracy between low-energy and high-energy chords does not explain why there was such a large gap between higgs mass and Planck energy in the first place, but only that the gap was stable. Still, in Craig's opinion, "it's a really good idea." ”
The new model represents a growing number of hybrid UV-IR ideas. Craig's research can be traced back to another 1999 paper written by renowned theorist Nathan Seiberg and two co-authors at the Institute for Advanced Study. They studied the situation where there is a background magnetic field filling the space. To understand how the ultraviolet-infrared hybrid here is produced, imagine a pair of spring-connected charged particles flying in space, perpendicular to the magnetic field. As you increase the energy of the magnetic field, the charged particles accelerate apart, stretching the spring. In this scenario, higher energies correspond to longer distances.
"Gravity is anti-reductionist." ——Sergei Dubovsky
Seiberg, they found that UV correction in this case has a special feature that reductivism can be reversed, that is, infrared affects what happens in UV. This model is not realistic, because the real universe does not have a magnetic field that imposes background directionality. Still, Craig has been exploring whether something similar could serve as a solution to the hierarchical problem.
Craig, Garcia Garcia, and Seth Koren also worked together on an argument about quantum gravity known as the weak gravitational conjecture. If true, it may impose consistency conditions that naturally require a huge separation between the Higgs mass and the Planck scale.
New York University's Dubovsky has been pondering these questions since at least 2013, when it became clear that supersymmetric particles were very sluggish on the Large Hadron Collider. That year, he and two collaborators discovered a new model of quantum gravity that solved the hierarchy problem: in that model, the arrow of reductionism pointed at both ultraviolet and infrared at one intermediate scale. As appealing as it sounds, the model only works in two-dimensional space, and Dubovsky has no clue how to unfold it. He turned to other issues. Last year, he again encountered the ultraviolet-infrared hybrid. He found that the naturalness problems that arise when studying colliding black holes are solved by a "hidden" symmetry that links low- and high-frequency deformations of the shape of the black hole.
Like other researchers, Dubovsky doesn't seem to think that any of the specific models discovered so far have clear signs of the Kuhn Revolution. Some argue that the entire UV-IR hybrid concept lacks promise. "There is no sign of an effective field theory collapsing at the moment," said David E. Kaplan, a theoretical physicist at Johns Hopkins University who has no relationship with the authors of the CKN paper. "I don't think there's anything there."
To convince everyone, the idea requires experimental evidence, but so far, existing hybrid ultraviolet-infrared models have been woefully inadequate in terms of testable predictions. They're often designed to explain why we're not seeing new particles beyond the Standard Model, rather than predicting what we should see. But in cosmology, even if not from the collider, there is always hope for future predictions and discoveries.
Taken together, the new hybrid ultraviolet-infrared model illustrates the weakness of the old paradigm — a paradigm based entirely on reductionism and efficient field theory — and this may be just the beginning.
"When you get to the Planck scale, you lose reductionism, so gravity is anti-reductionist," Dubovsky says, "and I think, in a sense, it would be unfortunate if that fact had no profound effect on what we observe." ”
https://www.quantamagazine.org/crisis-in-particle-physics-forces-a-rethink-of-what-is-natural-20220301/
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