All of today’s quantum computers are prone to errors. These errors may be due to imperfect hardware and control systems, or they may arise from the inherent fragility of the quantum bits, or qubits, used to perform quantum operations. But whatever their source, they are a real problem for anyone seeking to develop commercial applications for quantum computing. Although noisy, intermediate-scale quantum (NISQ) machines are valuable for scientific discovery, no-one has yet identified a commercial NISQ application that brings value beyond what is possible with classical hardware. Worse, there is no immediate theoretical argument that any such applications exist.

It might sound like a downbeat way of opening a scientific talk, but when Christopher Eichler made these comments at last week’s Quantum 2.0 conference in Rotterdam, the Netherlands, he was merely reflecting what has become accepted wisdom within the quantum computing community. According to this view, the only way forward is to develop fault-tolerant computers with built-in quantum error correction, using many flawed physical qubits to encode each perfect (or perfect-enough) logical qubit.

That isn’t going to be easy, acknowledged Eichler, a physicist at FAU Erlingen, Germany. “We do have to face a number of engineering challenges,” he told the audience. In his view, the requirements of a practical, error-corrected quantum computer include:

• High-fidelity gates that are fast enough to perform logical operations in a manageable amount of time
• More and better physical qubits with which to build the error-corrected logical qubits
• Fast mid-circuit measurements for “syndromes”, which are the set of eigenvalues that make it possible to infer (using classical decoding algorithms) which errors have happened in the middle of a computation, rather than waiting until the end.

The good news, Eichler continued, is that several of today’s qubit platforms are already well on their way to meeting these requirements. Trapped ions offer high-fidelity, fault-tolerant qubit operations. Devices that use arrays of neutral atoms as qubits are easy to scale up. And qubits based on superconducting circuits are good at fast, repeatable error correction.

The bad news is that none of these qubit platforms ticks all of those boxes at once. This means that no out-and-out leader has emerged, though Eichler, whose own research focuses on superconducting qubits, naturally thinks they have the most promise.

In the final section of his talk, Eichler suggested a few ways of improving superconducting qubits. One possibility would be to discard the current most common type of superconducting qubit, which is known as a transmon, in favour of other options. Fluxonium qubits, for example, offer better gate fidelities, with 2-qubit gate fidelities of up to 99.9% recently demonstrated. Another alternative superconducting qubit, known as a cat qubit, exhibits lifetimes of up to 10 seconds before it loses its quantum nature. However, in Eichler’s view, it’s not clear how either of these qubits might be scaled up to multi-qubit processors.

Another promising strategy (not unique to superconducting qubits) Eichler mentioned is to convert dominant types of errors into events that involve a qubit being erased instead of changing state. This type of error should be easier (though still not trivial) to detect. And many researchers are working to develop new error correction codes that operate in a more hardware-efficient way.

Ultimately, though, the jury is still out on how to overcome the problem of error-prone qubits. “Moving forward, one should very broadly study all these platforms,” Eichler concluded. “One can only learn from one another.”

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Quantum technologies have enormous potential, but achieving that potential is not going to be cheap. The US, China and the EU have already invested more than $50 billion between them in quantum computing, quantum communications, quantum sensing and other areas that make up the so-called “second quantum revolution”. Other high-income countries, notably Australia, Canada and the UK, have also made significant investments. But what about the rest of the world? How can people in other countries participate in (and benefit from) this quantum revolution?

In a panel discussion at Optica’s Quantum 2.0 conference, which took place this week in Rotterdam in the Netherlands, five scientists from low- and middle-income countries took turns addressing this question. The first, Tatevik Chalyan, drew sympathetic nods from her fellow panellists and moderator Imrana Ashraf when she described herself as “part of the generation forced to leave Armenia to get an education”. Since then, she said, the Armenian government has become more supportive, building on a strong tradition of research in quantum theory. Chalyan, however, is an experimentalist, and she and many of her former classmates are still living abroad – in her case, as a postdoctoral researcher in silicon photonics at the Vrije Universiteit Brussel, Belgium.

Another panellist, Vatshal Srivastav, followed a similar path, studying at the Indian Institute of Technology (IIT) in Kanpur before moving to the UK’s Heriot-Watt University to do his PhD and postdoc on higher-dimensional quantum circuits. He, too, thinks things are improving back home, with the quality of research in the IIT network becoming high enough that many of his friends chose to remain there. Countries that want to improve their research base, he said, should find ways to “keep good people within your system”.

For panellist Taofiq Paraiso, who says he was “brought up in several African countries” before moving to EPFL in Switzerland for his master’s and PhD, the starting point is simple. “It’s about transferring skills and knowledge,” said Paraiso, who now leads a team developing chip-based hardware for quantum cryptography at Toshiba Europe’s Cambridge Research Laboratory in the UK. People who return to their home countries after being educated abroad have an important role to play in that, he added.

Returning is not always easy, though. The remaining two panellists, Roger Alfredo Kögler and Rodrigo Benevides, are both from Brazil, and Kögler, who did his PhD in Brazil’s Instituto Nacional de Ciência e Tecnologia de Informação Quântica, said that Brazilians who want to become professors in their home country are strongly urged to go abroad for their postdoctoral research. But now that he has seen the resources available to him as a postdoc in nanooptics at the Humboldt University of Berlin, Germany, Kögler admitted that he is “rethinking whether I want to go back” even though he worries that staying in Europe would make him “part of the problem”.

It’s much easier to freely have ideas if you have a lot of money

Rodrigo Benevides

Benevides, whose PhD was split between Brazil’s University of Campinas and the Netherlands’ TU Delft, elaborated on the reasons for this dilemma. In Brazil, he and his colleagues “used to see all these papers in Nature or Science” while they were “in the lab just trying to make our laser work”. That kind of atmosphere, he said, “leads to a lack of self-confidence” because people begin to suspect that they, and not the system, are the problem. Now, as a postdoc working on hybrid quantum systems at ETH Zurich in Switzerland, Benevides wryly observed that “it’s much easier to freely have ideas if you have a lot of money”.

As for how to remedy these challenges, Benevides argued that the solutions will be diverse and tailored to local circumstances. As an example, Paraiso highlighted the work of an outreach organization, Photonics Ghana, that motivates students to engage with quantum science. He also suggested that cloud-based quantum computing and freely-available software packages such as IBM’s Qiskit will help organizations that lack the resources to build a quantum computer of their own. Chalyan, for her part, pointed out that a lack of resources sometimes has a silver lining. Coming up with creative work-arounds, she said, “is what we are famous for [as] people from developing countries”.

Finally, several panellists emphasized the need to focus on quantum technologies that will make a difference locally. Though Kögler warned that it is hard to predict what will turn out to be “useful”, a few answers are already emerging. “Maybe we don’t need quantum error correction, but we do need a quantum sensor that brings better agriculture,” Benevides suggested. Paraiso noted that information security is important in African countries as well as European ones, and added that quantum key distribution is one of the more mature quantum technologies. Whatever the specifics, though, Srinivastav recommended identifying the problems your society is facing and figuring out how they overlap with your current research. “As scientists, it is our job to make things better,” he concluded.

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The uranium craze that hit America in the 1950s was surely one of history’s strangest fads. Jars of make-up lined with uranium ore were sold as “Revigorette” and advertised as infusing “beautifying radioactivity [into] every face cream”. A cosmetics firm applied radioactive soil to volunteers’ skin and used Geiger counters to check whether its soap could wash it away. Most astonishing of all, a uranium mine in the US state of Montana developed a sideline as a health spa, inviting visitors to inhale “a constant supply of radon gas” for the then-substantial sum of $10.

The story of this craze, and much else besides, is entertainingly told in Lucy Jane Santos’ new book Chain Reactions: A Hopeful History of Uranium. Santos is an expert in the history of 20th-century leisure, health and beauty rather than physics, but she is nevertheless well-acquainted with radioactive materials. Her previous book, Half Lives, focused on radium, which had an equally jaw-dropping consumer heyday earlier in the 20th century.

The shift to uranium gives Santos the license to explore several new topics. For physicists, the most interesting of these is nuclear power. Before we get there, though, we must first pass through uranium’s story from prehistoric times up to the end of the Second World War. From the uranium-bearing silver mines of medieval Jachymóv, Czechia, to the uranium enrichment facilities founded in Oak Ridge, Tennessee as part of the Manhattan Project, Santos tells this story in a breezy, anecdote-driven style. The fact that many of her chosen anecdotes also appear in other books on the histories of quantum mechanics, nuclear power or atomic weapons is hardly her fault. This is well-trodden territory for historians and publishers alike, and there are only so many quirky stories to go around.

The most novel factor that Santos brings to this crowded party is her regular references to people whose role in uranium’s history is often neglected. This includes not only female scientists like Lise Meitner (co-discoverer of nuclear fission) and Leona Woods (maker of the boron trifluoride counter used in the first nuclear-reactor experiment), but also the “Calutron Girls”, who put in 10-hour shifts six days a week at the Oak Ridge plant and were not allowed to know that they were enriching uranium for the first atomic bomb. Other “hidden figures” include the Allied prisoners who worked the Jachymóv mines for the Nazis; the political “undesirables” who replaced them after the Soviets took over; and the African labourers who, though legally free, experienced harsh conditions while mining uranium ore at Shinkolobwe (now in the Democratic Republic of the Congo) for the Belgians and, later, the Americans.

Most welcome of all, though, are the book’s references to the roles of Indigenous peoples. When Robert Oppenheimer’s Manhattan Project needed a facility for transmuting uranium into plutonium, Santos notes that members of the Wanapum Nation in eastern Washington state were given “a mere 90 days to pack up and abandon their homes…mostly with little compensation”. The 167 residents of Bikini island in the Pacific were even less fortunate, being “temporarily” relocated before the US Army tested an atomic bomb on their piece of paradise. Santos quotes the American comedian Bob Hope – nobody’s idea of a woke radical – in summing up the result of this callous act: “As soon as the war ended, we located the one spot on Earth that hadn’t been touched by war and blew it to hell.”

The most novel factor that Santos brings to this crowded party is her regular references to people whose role in uranium’s history is often neglected.

These injustices, together with the radiation-linked illnesses experienced by the (chiefly Native American) residents of the Trinity and Nevada test sites, are not the focus of Chain Reactions. It could hardly be “a hopeful history” if they were. But while mentioning them is a low bar, it’s a low bar that the three-hour-long Oscar-winning biopic Oppenheimer didn’t manage to clear. If Santos can do it in a book not even 300 pages long, no-one else has any excuse.

Chain Reactions is not a science-focused book, and in places it feels a little thin. For example, while Santos correctly notes that the “gun” design of the first uranium bomb wouldn’t work for a plutonium weapon, she doesn’t say why. Later, she states that “making a nuclear reactor safe enough and small enough for use in a car proved impossible”, but she leaves out the scientific and engineering reasons for this. The book’s most eyebrow-raising scientific statement, though, is that “nuclear is one of the safest forms of electricity produced – only beaten by solar”. This claim is neither explained nor footnoted, and it left me wondering, first, what “safest” means in this context, and second what makes wind, geothermal and tidal electricity less “safe” than nuclear or solar?

Despite this, there is much to enjoy in Santos’ breezy and – yes – hopeful history. Although she is blunt when discussing the risks of nuclear energy, she also points out that when countries stop using it, they mostly replace nuclear power plants with fossil-fuel ones. This, she argues, is little short of disastrous. Quite apart from the climate impact, ash from coal-fired power plants carries radiation from uranium and thorium into the environment “at a much larger rate than any from a nuclear power plant”. Thus, while the 2011 meltdown of Japan’s Fukushima reactors killed no-one directly, Japan and Germany’s subsequent phase-out of nuclear power contributed to an estimated 28,000 deaths from air pollution. Might a revival of nuclear power be better? Santos certainly thinks so, and she concludes her book with a slogan that will have many physicists nodding along: “Nuclear power? Yes please.”

• 2024 Icon Books 288pp £20hb

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A painstaking study of sensor-laden European starlings has confirmed what scientists have long suspected: birds use significantly less energy when they fly behind a leader. The study, which was carried out by an interdisciplinary team of researchers in the US, is the first to measure birds’ in-flight energy expenditure directly, and team co-leader Ty Hedrick thinks the findings could have implications for other bird species, too.

“There’s nothing particularly ‘special’ about a trio or pair of starlings that would lead us to believe that we’d find the effect in them but not in (for example) small shorebirds,” says Hedrick, a biologist at the University of North Carolina, Chapel Hill who conducted the work alongside postdoctoral researcher Sonja Friman and colleagues in physics and engineering departments at the University of Massachusetts Amherst, Brown University, Howard University, the Rochester Institute of Technology and the University of Southern California, Los Angeles. According to Hedrick, the energy savings he and his colleagues identified may even apply to birds that fly in dynamic flocks, not just those that adopt the familiar, fixed V-formation used by geese and other large migratory species.

First, catch some starlings

To measure how a starling’s position in a flock affects its energy use, Hedrick, Friman and colleagues needed three things. The first was a controlled flying environment big enough to accommodate up to three starlings without compromising their safety or impeding their natural flight. The team found this at Brown, which operates a purpose-built, mesh-enclosed animal flight wind tunnel with an active volume 1.2 m wide, 1.2 m tall and 2.8 m long.

The second thing the researchers needed was a way to monitor the starlings’ movements in flight. They achieved this by fitting the birds with miniature backpacks containing inertial measurement units (IMUs) and different-coloured LEDs. The IMUs recorded three-dimensional data on the birds’ linear accelerations and angular velocities, while the LEDs helped the team distinguish the positions of individual birds on video recordings of test flights.

The final ingredient was a means of measuring the starlings’ energy use. For this, the researchers injected the birds with a dose of sodium bicarbonate that contained carbon-13. This non-radioactive isotope of carbon is often used as a label in metabolic testing because biological processes preferentially take up carbon-12 atoms, which are lighter. By placing the starlings in a metabolic chamber and using a spectrometer to monitor the ¹³C/¹²C ratio in their exhaled breath before and after flights, the team could therefore calculate how much energy the birds used.

Together, these three elements enabled the team to go beyond previous bird-flight studies that measured biomechanical and physiological correlates of energy use, but not energy itself, Hedrick says. “The effect of formation flight on flight costs has been investigated for so long and in so many ways, but we realized that the existence of a large animal flight wind tunnel and the new ‘turn-key’ equipment for doing the metabolic measurements would let us go after the question experimentally in a way that had not been done before,” he tells Physics World.

“A lot of effort”

Even with the latest equipment, things did not always go to plan. “The most challenging part was getting everything to work together at once,” Hedrick says. “We needed two (or three) birds to fly well in the wind tunnel, all of the inertial measurement unit backpacks to function at least well enough to provide the bird ID light colours, and the ¹³C sodium bicarbonate metabolic measurement to work as well.”

As for what happened when things went wrong, the materials and methods section of the team’s paper makes illuminating reading. Data from several test flights had to be discarded after birds “repeatedly veered toward the floor, attempted to land on the floor or cameras, or clung to the front or rear mesh” of the wind tunnel. Noise from whirring feathers masked the indicator tones meant to help synchronize IMU data with video images. And of course, the researchers needed to catch the birds cleanly and transfer them to the metabolic chamber quickly to avoid messing up the post-flight ¹³C/¹²C readings. “All of these things are pretty likely to [work] on their own, but getting them to all work at once took a lot of effort from a skilled and dedicated research team,” Hedrick says.

The reward for this effort was twofold. First, the researchers found that when a starling spent most of a test flight in a “follower” position, it expended up to 25% less energy than it did when flying solo. Second, they noticed that the most energy-efficient solo flyers were far more likely to adopt the “leader” role when flying with other birds. The researchers say that this difference is likely related to the birds’ wing-flapping frequency, which was generally lower for “leader” birds. A more complete explanation, however, will require additional experiments.

“The next thing we’d really like to do is directly visualize the wake interaction between a lead bird and a follower using digital particle image velocimetry to get a better understanding of the fluid dynamic mechanism that produces the energy savings,” Hedrick says.

The research is published in PNAS.

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Climbers on Mars’ equatorial volcanoes would wake up to frost-covered peaks, but aspiring Martian scuba divers would find no liquid water beneath the planet’s polar ice caps – contradicting previous reports. These findings, from two independent teams, tell us more about where water does and doesn’t exist on the red planet, with important implications for its climate.

While the temperature and pressure on Mars are too low for liquid water to exist on its surface, scientists have long suspected that the planet could harbour an ocean beneath its ice caps. In 2018 researchers in Italy found strong evidence for such an ocean in data from ESA’s Mars Express spacecraft. The smoking gun (or should that be “flowing gun”?) in this case was a strong radar echo picked up by the Mars Advanced Radar for Subsurface and Ionosphere Sounding instrument (MARSIS) instrument during a survey of the planet’s south pole. The presence of this echo indicates an abrupt change in the dielectric permittivity of material beneath the planet’s surface – and on Earth, this kind of change typically occurs at the interface between solid and liquid water.

Mars is not Earth, however, and other scientists have since proposed alternative explanations. The latest of these alternatives is described in Science Advances and comes from Daniel Lalich and colleagues at Cornell University in the US. Using radar reflectivity simulations, the Cornell scientists showed that the MARSIS echo could be due to constructive interference generated as a radar pulse passes through tightly-packed layers of dusty ice. While they cannot definitively rule out the presence of liquid water, Lalich says, “we’re showing that there are much simpler ways to get the same observation without having to stretch that far, using mechanisms and materials that we already know exist” on Mars.

An ice surprise

As for frost on Martian mountains, the evidence for this comes from a study that compared high-resolution colour images taken by another ESA spacecraft, the Trace Gas Orbiter, at different times of day and in different seasons. During colder seasons, images taken in the morning show bluish deposits atop the four volcanoes in the Tharsis group near the planet’s equator: Olympus Mons, Arsia Mons, Ascraeus Mons and Ceraunius Tholus. Images taken in the afternoon, however, show no such deposits, leading an international team of planetary scientists to conclude that the deposits must be frost.

For Earthbound observers, the idea that frost might appear on high ground overnight, only to melt by the afternoon, might not sound so remarkable. But again, Mars is not Earth, and in a Nature Geoscience paper on the study, the team notes that “the presence of frost at the tropics…was not expected because of higher average surface temperatures and lower humidity”. The scientists speculate that hollow depressions known as calderas at the volcanoes’ summits create unique microclimates, allowing thin patches of frost to form overnight even at low latitudes. They also conclude that the source of the frost is more likely to be atmospheric than volcanic due to its strongly seasonal pattern.

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Whales gotta swim, and birds gotta fly – and when they do, they flap their wings and fins at a rate determined by the same simple mathematical expression and coefficient of proportionality. The expression, which relates wingbeat frequency to body mass and wing area, is valid regardless of the animal’s size or flying style, and the physicists who derived it say it matches biological data on insects, bats and flapping robots as well as birds and whales.

“We were surprised to see how well the data follows the prediction and kept expanding the data set to include other flying animals to see how far this universality goes,” says study leader Tina Hecksher of Roskilde University, Denmark. “When we saw that even swimming/diving animals follow the same line, we thought that this may interest a broader audience.”

Scientists have long searched for universal patterns in animal flight. In 1990, for example, the British biologist Colin James Pennycuick related wingbeat frequency f to a bird’s body mass and wing area via the expression f = 1.08(m^1/3g^1/2b^-1A^-1/4ρ^-1/3), where m is the mass, g is the acceleration due to gravity, b is the wing span, A is the wing area and ρ is the density of air. His work followed that of the Australian mathematician and educator Michael Deakin, who in 1970 derived a simpler relationship for insects. Both analyses, however, were partly based on empirical observations, and neither sought to generalize them to other flying animals.

Dimensional arguments

The latest work was inspired by an exam question that asked students to explain how quickly a bird should flap its wings if it wants to remain hovering. The course was designed to teach students to “think like physicists,” Hecksher tells Physics World, and after the exam she and her Roskilde colleagues Jens Højgaard Jensen and Jeppe Dyre began to wonder whether the formula they derived using dimensional analysis would apply to real-world flight.

On the face of it, it might seem unlikely that any simple expression could capture much about an animal flapping its wings. Writing in PLOS One, the Roskilde team acknowledge that there is “obviously a significant difference” between the flight of a dragonfly and that of a bat, so past researchers had “good reasons” for focusing on similar species. Previous studies also showed that the shapes and angles a wing assumes during flight – which can be highly complex and vary widely across species – play a role in determining flapping rate.

Shapes and angles, however, are dimensionless quantities. The Roskilde physicists therefore folded these and other unknown dimensionless functions of dimensionless quantities into a single constant of proportionality. By hypothesizing that this constant must be the same for all flying animals, and ignoring minor variations in air density and gravitational field strength, they arrived at their expression: f ~ m^1/2/A.

Empirical tests

To test the validity of this expression, the Roskilde team collected 414 data points from published studies that reported wing area, mass and wingbeat frequencies of birds ranging from swans to hummingbirds; flying insects such as bees, moths, dragonflies, beetles and mosquitoes; and a flapping robot called an ornithopter. The team also included data from whales and penguins. Unlike fish, which use air-filled bladders to regulate their position in the water, these animals have a positive buoyancy, and must swim to stay submerged. The physics governing their fin- and fluke-flapping frequencies should therefore be similar to the physics of wingbeat frequencies, barring a correction factor for the different densities of air and water.

When the Roskilde physicists plotted f against m^1/2/A for all the animals (plus one robot) in their dataset, the result was a straight line with only a small amount of scatter in the data points. According to the team, this means that, despite huge physical differences, flying animals must have evolved in a way that keeps the relationship between their mass, wing area and wingbeat frequency relatively constant. “We were initially surprised that the data fall on the same line,” Hecksher says. “The basic relationship follows from physics. But the constant of proportionality could in principle be different for different flying styles.”

Matt Wilkinson, who did his PhD on pterodactyl flight and is now a director of studies in natural sciences at Cambridge University, UK, was also surprised, at first, that an analysis based on hovering, rather than forward flight, is so widely applicable. “There is a highly constrained relationship between wingbeat frequency and wingspan due to the enormous drop-off in efficiency when operating the wings away from their resonant frequency, but for larger flying animals, that frequency isn’t enough to support the animal’s weight on its own – some minimum forward velocity becomes essential,” he explains.

After some reflection, however, Wilkinson, who was not involved in the Roskilde study, suspects that this size-dependent factor “must be another phenomenon buried in the proportionality coefficient”. Identifying this coefficient is, he says, the study’s most important contribution. “Unpicking that, despite the enormous differences in wing shape and flight kinematics, is where the real insights will be found,” he concludes.

As for why no-one had uncovered this simple relationship before, Hecksher cites the study’s interdisciplinary nature. “Our formula is theoretically derived based on physics principles [and it] also devises how to compare swimming/diving animals in the same plot as the flying animals,” she notes. “This approach is less common among biologists…it takes the combination of physics and a large amount of empirical data to arrive at this result.”

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Now here’s a discovery that’s pretty sweet: the most distant Solar System object ever visited by a spacecraft appears to be dusted with sugar. Known as Arrokoth, this small, irregularly shaped world is reddish in colour, and scientists in the US and France say that its unusual hue may be due to the presence of glucose and other forms of sugar on its surface. The discovery has implications for the origins of life, as comets could have delivered organic molecules from “sugar worlds” like Arrokoth to the early Earth.

Arrokoth orbits the Sun as part of the Kuiper belt of objects beyond the planet Neptune. Because it formed when two objects collided and fused together, it looks a little like a flattened snowman, with a “head” and “body” 15 and 21 km in diameter. Nicknamed “Ultima Thule” by scientists working on the New Horizons mission, it gets its formal name from a word meaning “sky” or “cloud” in the Powhatan language spoken by Native Americans who lived on what is now the US East Coast before European settlers arrived there.

Apart from its knobbly shape, Arrokoth’s most distinctive feature is its colour. Unlike pink-tinged Pluto – the largest Kuiper belt object (KBO), and the subject of New Horizons’ first flyby in 2015 – Arrokoth is darker and reddish. The cause of this unusual colouring, which also occurs in a few other KBOs, is not fully understood. However, New Horizons detected abundant frozen methanol (CH₃OH) on Arrokoth’s surface when it flew past in 2019, and scientists had previously found that irradiating methanol with ions significantly reddens its spectrum.

Enter the energetic electrons

In the new study, a team led by chemists Ralf I Kaiser of the University of Hawai’i at Mānoa and Cornelia Meinert of the Université Côte d’Azur, France, together with planetary scientist Leslie A Young of the Southwest Research Institute in Boulder, Colorado, US, explored this possibility further by bombarding samples of methanol ice at 10 K and 40 K with energetic electrons. After exposing the samples to the equivalent of 1.8 billion years of galactic cosmic rays, they used a variety of spectroscopic methods to characterize the composition and colour of the organic molecules that formed.

The results showed that radiation bombardment can indeed replicate the colouration found on Arrokoth, with a dose of 57 eV per atomic mass unit creating an especially good colour match. Using gas chromatography and time-of-flight mass spectrometry, the team also identified sugar-related compounds such as glucose (C₆H₁₂O₆) and ribose (C₅H₁₀O₅) in residues of the radiation-exposed methanol ices. Some of these compounds, the researchers note, are incorporated into the molecules that make up RNA and lipids, providing what they call “a plausible source of this key class of prebiotic molecules for the evolution of life on early Earth”.

As for how these chemicals got from Arrokoth or other Kuiper belt objects to Earth, in a PNAS paper describing the study, the researchers point out that the Kuiper belt is thought to be a major source of short-period comets. “These sugars and their derivatives could have been delivered by KBOs like Arrokoth in the form of short-period comets impacting the early Earth, thus providing a source of a variety of sugars and the feedstock for important biomolecules,” they write. Future experiments on more complex ice mixtures containing ammonia, water and carbon dioxide as well as methane could, they suggest, yield further insights on the optical spectra and composition of KBOs not visited by spacecraft.

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If you’ve ever tried to remain friends with both halves of a couple going through a nasty divorce, or hung out with a crowd of mutuals that also includes someone you can’t stand, you’ll know what an unbalanced social network feels like.

You’ll probably also sympathize with the 20^th-century social psychologist Fritz Heider, who theorized that humans strive to avoid such awkward, unbalanced situations, and instead favour “balanced” networks that obey rules like “the friend of my friend is also my friend” and “the enemy of my enemy is my friend”.

But striving and favouring aren’t the same thing as achieving, and the question of whether real-world social networks exhibit balance has proved surprisingly hard to answer. Some studies suggest that they do. Others say they don’t. And annoyingly, some “null models” – that is, models used to assess the statistical significance of patterns observed in real networks – fail to identify balance even in artificial networks expressly designed to have it.

Two physicists at Northwestern University in the US now report that they’ve cracked this problem – and it turns out that Heider was right. Using data collected from two Bitcoin trading platforms, the tech news site Slashdot, a product review site called Epinions, and interactions between members of the US House of Representatives, István Kovács and Bingjie Hao showed that most social networks do indeed demonstrate strong balance. Their result, they say, could be a first step towards “understanding and potentially reducing polarization in social media” and might also have applications in brain connectivity and protein-protein interactions.

Positive and negative signs

Mathematically speaking, social networks look like groups of nodes (representing people) connected by lines or edges (representing the relationships between them). If two people have an unfriendly or distrustful relationship, the edge connecting their nodes carries a negative sign. Friendly or trustful relationships get a positive sign.

Under this system, the micro-network described by the statement “the enemy of my enemy is my friend” looks like a triangle made up of one negative edge connecting you to your enemy, another negative edge connecting your enemy to their enemy, and one positive edge connecting you to your enemy’s enemy. The total number of negative edges is even, so the network is balanced.

Complicating factors

While the same mathematical framework can be applied to networks of any size and complexity, real-world social networks contain a few wrinkles that are hard to capture in null models. One such wrinkle is that not everyone knows each other. If the enemy of your enemy lives overseas, for example, you might not even know they exist, never mind whether to count them as a friend. Another complicating factor is that some people are friendlier than others, so they will have more positive connections.

In their study, which they describe in Science Advances, Kovács and Hao created a new null model that preserves both the topology (that is, the structure of the connections) and the “signed node degree” (that is, the “friendliness” or otherwise of individual nodes) that characterize real-world networks. By comparing this model to three- and four-node mini-networks in their chosen datasets, they showed that real-world networks are indeed more balanced than would be expected based on the more accurate null model.

So the next time you have to choose between two squabbling friends, or decide whether to trust someone who dislikes the same people as you, take heart: you’re performing a simple mathematical operation, and the most likely outcome will be a social network with more balance. Problem solved!

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