The new phase combines a number of "up" spins of electrons within an atom, which are highly ordered and referred to as cold cycles, with a number of "down" spins, which are highly disordered and referred to as hot cycles — lending the phase its nickname, "half ice, half fire."

"Half ice, half fire" is a significant discovery not only because of its novelty but also because it can produce sharp switching between phases at reasonable temperatures. It's the twin of the "half fire, half ice" state first observed by the same team at Brookhaven National Laboratory — physicists Weiguo Yin and Alexei Tsvelik, alongside their then intern, Christopher Roth — back in 2016.

These discoveries provide insight into some of the central questions in physics and the materials sciences, according to the team, as well as advance the ability to identify new states of matter with exotic properties and manipulate the transition between those states.

"Solving those problems could lead to great advances in technologies like quantum computing and spintronics," Yin said in a statement from Brookhaven National Lab. Tsvelik added that the team's findings "may open a new door to understanding and controlling phases and phase transitions in certain materials."

Related: Exotic new state of matter discovered by squishing subatomic particles into an ultradense crystal

"Missing pieces of the puzzle"

Yin and Tsvelik first discovered "half ice, half fire" when performing research on a type of magnetic material called a ferrimagnet. Ferrimagnets have populations of atoms with opposing magnetic moments, but because the populations are unequal, some magnetization remains.

The specific ferrimagnet in which "half ice, half fire" was observed is Sr3CuIrO6, a compound that consists of strontium, copper, iridium and oxygen. It's the same material in which the team originally discovered "half fire, half ice," which they induced, or caused to occur within the ferrimagnet, by exposing the material to an external magnetic field. In "half fire, half ice," hot spins occurred on the copper sites and had smaller magnetic movements, while the iridium sites yielded cold spins with larger magnetic movements.

Although it was an exciting discovery, Tsvelik admitted that it was only a first step.

"Despite our extensive research, we still didn't know how this state could be utilized," he said. "We were missing pieces of the puzzle."

Now, the recent work, spearheaded by Yin, has revealed that "half fire, half ice" has a hidden and opposite state in which the hot and cold spins swap positions. The team identified an extremely narrow temperature range in which the switch between phases takes place, which has promising implications for a number of fields.

Commercially, this kind of ultrasharp phase switching could lead to advances in refrigeration technology. It may even be possible to utilize the phases themselves as bits in a novel approach to quantum information storage. "The door to new possibilities is now wide open," Yin said.

The team's research into the new phase was published in the journal Physical Review Letters in December 2024.

The discovery — made at the Large Hadron Collider (LHC) at CERN, near Geneva — has revealed that a short-lived cousin of protons and neutrons, the beauty-lambda baryon, decays at a different rate than its antimatter counterpart.

Called charge-parity (CP) violation, this effect refers to particles of opposite charge, like matter and animatter, behaving differently. It's a crucial explanation for why matter was able to dominate over antimatter in the early universe — without it, the universe would be an empty void.

Despite being a key reason why we're here in the first place, the amount of CP violation predicted by the Standard Model of particle physics is far too small to explain the abundance of matter in our universe.

What's more, this violation has previously been only detected in particles made up of quark-antiquark pairs, called mesons. It has not been observed in baryons — three-quark particles, such as protons and neutrons, that make up most of the universe's visible matter.

Related: 'The Majoron' — a bizarre particle that's its own opposite — could explain the biggest mysteries of the universe, scientists claim

This first-of-its-kind detection has changed that, potentially opening up an avenue to search for physics beyond the Standard Model. The researchers presented their findings March 24 at the Rencontres de Moriond conference in La Thuile, Italy, and posted a non-peer-reviewed study on the preprint server arXiv.

"The reason why it took longer to observe CP violation in baryons than in mesons is down to the size of the effect and the available data," Vincenzo Vagnoni, a spokesperson for the Large Hadron Collider beauty (LHCb) experiment that made the detection, said in a statement. "It took over 80,000 baryon decays for us to see matter–antimatter asymmetry with this class of particles for the first time."

The broth of creation

According to the standard model of cosmology, in the aftermath of the Big Bang, the young cosmos was a roiling plasma broth of matter and antimatter particles that popped into existence and annihilated each other upon contact.

Theory predicts that the matter and antimatter inside this plasma soup should have annihilated each other entirely. But scientists believe that some unknown imbalance — likely CP violation in decays involving the weak nuclear force — enabled more matter than antimatter to be produced, sparing it from self-destruction.

To search for CP violation in baryons, the researchers at the LHCb combed through data of the countless particle interactions (where protons collide roughly 25 million times a second) that occurred between 2009 and 2018.

They tallied up the decays of the beauty-lambda baryon by searching for the telltale paths made by its decay products — a proton, a kaon and a pair of oppositely charged pions — alongside the decays of its corresponding antimatter counterpart.

Their analysis revealed that the difference between the decay numbers of beauty-lambda baryons and anti-beauty-lambda baryons was 2.45% from zero with an uncertainty of about 0.47%. This was measured to a statistical significance of 5.2 sigma, passing the the five-Sigma result physicists use as the "gold standard" for heralding a new discovery.

With the finding sealed, the physicists say they will look for even more CP violations when the LHC fires up again in 2030, and collect further data on the key mechanism that likely enabled our universe to exist.

"The more systems in which we observe CP violations and the more precise the measurements are, the more opportunities we have to test the Standard Model and to look for physics beyond it," Vagnoni said. "The first ever observation of CP violation in a baryon decay paves the way for further theoretical and experimental investigations of the nature of CP violation, potentially offering new constraints for physics beyond the Standard Model."

But what determines the way people move in busy spaces?

Karol Bacik, a mathematician at MIT, and colleagues have developed a mathematical theory that accurately predicts pedestrian flow and the point where it changes from organized lanes to an entangled crowd. The work, which they reported in the journal PNAS March 24, could help architects and city planners design safer and more efficient public spaces that promote ordered crowds.

The team started by creating a mathematical simulation of a moving crowd in different spaces, using fluid dynamics equations to analyze the motion of pedestrians across various scenarios.

"If you think about the whole crowd flowing, rather than individuals, you can use fluid-like descriptions," Bacik said in a statement. "If you only care about the global characteristics like, are there lanes or not, then you can make predictions without detailed knowledge of everyone in the crowd."

Crowd math

Both the width of the space and the angles at which people moved across it heavily influenced the overall order of the crowd. Bacik's team identified "angular spread" — the number of people walking in different directions — as the key factor in whether people self-organized into lanes.

Related: 14-year-old known as 'the human calculator' breaks 6 math world records in 1 day

Where the spread of people walking in different directions is relatively small — such as in a narrow corridor or on pavement — pedestrians tend to form lanes and meet oncoming traffic head-on. However, a broader range of individual travel directions — for example, in an open square or airport concourse — dramatically increases the likelihood of disorder as pedestrians dodge and weave around one another to reach their separate destinations.

The tipping point, according to this theoretical analysis, was an angular spread of around 13 degrees, meaning ordered lanes could descend into disordered flow once pedestrians start traveling at more extreme angles.

"This is all very common sense," Bacik said. "[But] now we have a way to quantify when to expect lanes — this spontaneous, organized, safe flow — versus disordered, less efficient, potentially more dangerous flow."

However, the researchers were keen to investigate whether the reality of a human crowd bears out this theory, so they devised an experiment to simulate a busy road crossing. Volunteers, each wearing a paper hat labeled with a unique barcode, were assigned various start and end positions and were asked to walk between opposite sides of a gymnasium without bumping into other participants. An overhead camera recorded each scenario, tracking both the movement of individual pedestrians and the overall motion of the crowd.

Subsequent analysis of the 45 trials confirmed the importance of angular spread, showing a transition from ordered lanes to disordered movement at angles close to the theoretically predicted 13 degrees. Furthermore, as disorder increased, pedestrians were forced to move more slowly to avoid collisions, with a roughly 30% speed reduction for random crowds versus ordered lanes, the team found.

Bacik's team is now looking to test these predictions in real-world scenarios, and they hope the work will ultimately help improve crowded environments.

"We would like to analyze footage and compare that with our theory," he said. "We can imagine that, for anyone designing a public space, if they want to have a safe and efficient pedestrian flow, our work could provide a simpler guideline, or some rules of thumb."

On Monday (March 24), a giant vortex of light was seen floating across the night sky in Europe. But while many speculated that it was the work of aliens, the ethereal light show was actually caused by a dying SpaceX rocket, which was preparing to crash back to Earth after delivering "secret cargo" into orbit around our planet.

Auroras also lit up the skies across several northern U.S. states this week after a large hole in the sun's atmosphere sent streams of charged particles toward Earth, creating a moderate geomagnetic storm.

But the main event this week has been today's (March 29) partial solar eclipse. Between 4:50 a.m. and 8:43 a.m. EDT, the moon will roll in front of the sun, partially obscuring it as if a large bite had been taken out of our nearest star. The exact timings vary by location, and the eclipse will be visible in only 13 U.S. states, mostly in the Northeast.

NASA has released a map showing where and when to view the eclipse, and if you can't see it from your location, you can watch the event online. If the eclipse is visible from where you live, it is important to wear appropriate safety glasses when you observe it, as looking directly at a partial solar eclipse can damage your eyes.

Ancient pyramids yield new surprises

Ancient Egyptian pyramids, thought to contain only the elite, may also hold low-class laborers

Archaeologists long believed that the ancient pyramids of Egypt and Sudan were reserved for the highest echelons of society. But new research from a site called Tombos, which the Egyptians established in what is now Sudan after their conquest of Nubia, has led some archaeologists to question this theory.

Wealthy individuals were buried at Tombos, in tombs with small pyramids built above them. However, an analysis of the bones of 110 skeletons found at these burial sites suggests that many of the people buried in these pyramids performed significant amounts of heavy labor — an unlikely activity for high-status individuals at the time. As a result, the researchers concluded that lower-class laborers may have been buried alongside the elite in these famous ancient structures.

Discover more archaeology news

—Tumaco-Tolita gold figurine: A 2,000-year-old statue with a 'fancy nose ornament' from a vanished South American culture

—Human sacrifices found in a Bronze Age tomb in Turkey were mostly teenage girls

—'Exceptional' hoard of 800 Iron Age artifacts found mysteriously burned and buried in UK field

Life's Little Mysteries

Can animals understand human language?

Many pet owners claim that their furry friends can understand at least some human language. We are increasingly learning about the similarities between the communication styles of animals and humans — but can they really learn to speak our language?

Ancient organism baffles scientists

Giant, fungus-like organism may be a completely unknown branch of life

Scientists have discovered that a bizarre ancient life-form, once thought to be a type of fungus, might belong to a totally unknown branch of the tree of life.

The organism, named Prototaxites, lived around 420 million to 375 million years ago and resembled branchless, cylindrical tree trunks. They are considered by many to be the first giant organisms to grow on land, reaching up to 26 feet (8 meters) in height and 3 feet (1 m) in diameter.

Previous chemical analysis showed that these organisms likely fed off of dead and decaying organisms, just like many fungi do today. However, new research revealed that the organism's internal structure is very different from anything we see in modern fungi today.

What's more, its cells do not appear to contain chitin, a fundamental building block of fungal cell walls and a hallmark of the fungal kingdom. Instead, they contain chemicals similar to the woody lignin found in the bark and stems of plants. Thus, the researchers concluded that these strange organisms may belong to a previously unrecognized branch of the tree of life.

Discover more life on Earth news

—Scientists thought sharks didn't make sounds — until this accidental discovery

—Scientists discover new 15 million-year old fish with last meal fossilized inside its stomach

—'Exquisitely preserved' ginormous claws from Mongolia reveal strange evolution in dinosaurs

Also in science news this week

—Current AI models a 'dead end' for human-level intelligence, scientists agree

—Silent X chromosome genes 'reawaken' in older females, perhaps boosting brain power, study finds

—Why modern humans have smaller faces than Neanderthals and chimpanzees

—Never-before-seen chain of volcanoes discovered hiding near the Cook Islands

Science Spotlight

Record-setting black hole 'echo' accidentally uncovered by high-school student

Between taking classes and considering college admissions, high-school junior Julian Shapiro is an independent astronomer with a keen interest in supernova remnants and planetary nebulas. However, in his quest to find debris from exploding stars, Shapiro came across something even more spectacular: the ghostly echo of a long-lost black hole almost twice the width of the Milky Way.

Long after black holes sputter out of existence, the gas clouds that surround them glow with leftover radiation, like wisps of smoke rising from an extinguished flame. These cosmic ghosts are known as "light echoes," and it is one such echo that Shapiro spotted while sifting through data from the Dark Energy Camera at the Cerro Tololo Inter-American Observatory in Chile.

According to Shapiro's calculations, the light echo measures about 150,000 to 250,000 light-years in diameter — between 1.5 and two times the width of our entire galaxy. If his estimates hold up, the discovery could mark the largest such light echo ever discovered.

"It was a real surprise to stumble upon this," Shapiro told Live Science.

Something for the weekend

If you're looking for something a little longer to read over the weekend, here are some of the best long reads, book excerpts and interviews published this week.

—'We will fight for him': Author John Green meets Henry Reider, a young tuberculosis patient with drug-resistant disease

—Scientists unveil new type of 'time crystal' that defies our traditional understanding of time and motion

—Brain aging accelerates dramatically around age 44 — could ketone supplements help?

Science in pictures

James Webb telescope reveals 'cosmic tornado' in best detail ever — and finds part of it is not what it seems

NASA's James Webb Space Telescope snapped a spectacular image of an outflow of hot gas pouring from a newborn star in what has been dubbed a "cosmic tornado."

The outflow, situated about 625 light-years from Earth in the constellation Chamaeleon, is known as a Herbig-Haro object. These objects occur when jets of ionized gas are ejected from newborn stars and collide with the surrounding interstellar material.

This particular Herbig-Haro object was discovered in 2006 but has never been seen in such great detail.

Follow Live Science on social media

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A standard time crystal is a new phase of matter that features perpetual motion without expending energy. According to Chong Zu, an assistant professor of physics at Washington University in St. Louis and one of the team's lead researchers, a time crystal resembles a traditional crystal.

However, unlike a traditional crystal, which repeats a pattern across the physical dimension of space, a time crystal repeats a pattern of motion, rearranging its atoms in the same way over time, Zu said. This causes the time crystal to vibrate at a set frequency.

A time crystal is theoretically capable of cycling through the same pattern infinitely without requiring any additional power — like a watch that never needs to be wound. The reality, however, is that time crystals are incredibly fragile and thus succumb to environmental pressures fairly easily.

Although time crystals have been around since 2016, a team has achieved something unprecedented: They've created a novel type of time crystal called a time quasicrystal. A quasicrystal is a solid that, like a regular crystal, has atoms arranged in a specific, nonrandom way, but without a repeating pattern.

Related: Scientists create weird 'time crystal' from atoms inflated to be hundreds of times bigger than normal

This means that, unlike a standard time crystal that repeats the same pattern over and over, a time quasicrystal never repeats the way it arranges its atoms. Because there's no repetition, the crystal vibrates at different frequencies. As the researchers state in their findings, published in the journal Physical Review X, time quasicrystals "are ordered but apparently not periodic."

How to build a quasicrystal

To create these new time quasicrystals, the researchers started with a millimeter-sized piece of diamond. Then, they created spaces inside the diamond's structure by bombarding it with powerful beams of nitrogen. The nitrogen displaced carbon atoms within the diamond's interior, leaving behind empty atomic chambers.

Nature abhors a vacuum, so electrons quickly flowed into these empty spaces and immediately began to interact with neighboring particles on a quantum level. Each time quasicrystal represents a network of more than a million of these empty spaces inside the diamond, though each measures just one micrometer (one-millionth of a meter).

"We used microwave pulses to start the rhythms in the time quasicrystals," Bingtian Ye, a researcher at MIT and a co-author of the paper, said in a statement. "The microwaves help create order in time."

Potential applications

One of the most important outcomes of the team's research is that it confirms some basic theories of quantum mechanics, according to Zu. However, time quasicrystals may have practical applications in fields such as precision timekeeping, quantum computing, and quantum sensor technology.

For sensors, the crystal's fragility and sensitivity are actually a boon; because they're so sensitive to environmental factors like magnetism, they can be used to create extremely precise sensors.

For quantum computing, the material's potential perpetual motion quality is the key.

"They could store quantum memory over long periods of time, essentially like a quantum analog of RAM," Zu said. "We're a long way from that sort of technology, but creating a time quasicrystal is a crucial first step."

The analysis, which looked at nearly 15 million galaxies and quasars spanning 11 billion years of cosmic time, found that dark energy — the presumed-to-be constant force driving the accelerating expansion of our universe — could be weakening.

Or at least this is what the data, collected by the Dark Energy Spectroscopic Instrument (DESI), suggest when combined with information taken from star explosions, the cosmic microwave background and weak gravitational lensing.

If the findings hold up, it means that one of the most mysterious forces controlling the fate of our universe is even weirder than first thought — and that something is very wrong with our current model of the cosmos. The researchers' findings were published in multiple papers on the preprint server arXiv and presented March 19 at the American Physical Society's Global Physics Summit in Anaheim, California, so they have not yet been peer-reviewed.

"It's true that the DESI results alone are consistent with the simplest explanation for dark energy, which would be an unchanging cosmological constant," co-author David Schlegel, a DESI project scientist at the Lawrence Berkeley National Laboratory in California, told Live Science. "But we can't ignore other data that extend to both the earlier and later universe. Combining [DESI's results] with those other data is when it gets truly weird, and it appears that this dark energy must be 'dynamic,' meaning that it changes with time."

The evolving cosmos

Dark energy and dark matter are two of the universe's most puzzling components. Together they make up roughly 95% of the cosmos, but because they do not interact with light, they can't be detected directly.

Yet these components are key ingredients in the reigning Lambda cold dark matter (Lambda-CDM) model of cosmology, which maps the growth of the cosmos and predicts its end. In this model, dark matter is responsible for holding galaxies together and accounts for their otherwise inexplicably powerful gravitational pulls, while dark energy explains why the universe's expansion is accelerating.

Related: Could the universe ever stop expanding? New theory proposes a cosmic 'off switch'

But despite countless observations of these hypothetical dark entities shaping our universe, scientists are still unsure where they came from, or what they even are. Currently, the best theoretical explanation for dark energy is made by quantum field theory, which describes the vacuum of space as filled with a sea of quantum fields that fluctuate, creating an intrinsic energy density in empty space.

In the aftermath of the Big Bang, this energy increases as space expands, creating more vacuum and more energy to push the universe apart faster. This suggestion helped scientists to tie dark energy to the cosmological constant — a hypothetical inflationary energy, growing with the fabric of space-time throughout the universe's life. Einstein named it Lambda in his theory of general relativity.

"The problem with that theory is that the numbers don't add up," said Catherine Heymans, a professor of astrophysics at the University of Edinburgh and the Astronomer Royal for Scotland who was not involved in the study. "If you say: 'Well, what sort of energy would I expect from this sort of vacuum?' It's very, very, very, very different from what we measure," she told Live Science.

"It's kind of exciting that the universe has thrown us a curveball here," she added.

Scanning the dark universe

To figure out if dark energy is changing over time, the astronomers turned to three years' worth of data from DESI, which is mounted on the Nicholas U. Mayall 4-meter Telescope in Arizona. DESI pinpoints the monthly positions of millions of galaxies to study how the universe expanded up to the present day.

By compiling DESI's observations, which includes nearly 15 million of the best measured galaxies and quasars (ultra-bright objects powered by supermassive black holes), the researchers came up with a strange result.

Taken on their own, the telescope's observations are in "weak tension" with the Lambda-CDM model, suggesting dark energy may be losing strength as the universe ages, but without enough statistical significance to break with the model.

But when paired with other observations, such as the universe's leftover light from the cosmic microwave background, supernovas, and the gravitational warping of light from distant galaxies, the likelihood that dark energy is evolving grows.

In fact, it pushes the observations' disagreement with the standard model as far as 4.2 Sigma, a statistical measure on the cusp of the five-Sigma result physicists use as the "gold standard" for heralding a new discovery.

Related: After 2 years in space, the James Webb telescope has broken cosmology. Can it be fixed?

Whether this result will hold or fade over time with more data is unclear, but astrophysicists are growing confident that the discrepancy is less likely to disappear.

"These data seem to indicate that either dark energy is becoming less important today, or it was more important early in the universe," Schlegel said.

Astronomers say that further answers will come from a flotilla of new experiments investigating the nature of dark matter and dark energy in our universe. These include the Euclid space telescope, NASA's Nancy Grace Roman Space Telescope, and DESI itself, which is now in its fourth of five years scanning the sky and will measure 50 million galaxies and quasars by the time it's done.

"I think it's fair to say that this result, taken at face-value, appears to be the biggest hint we have about the nature of dark energy in the [rough] 25 years since we discovered it," Adam Riess, a professor of astronomy at Johns Hopkins University who won the 2011 Nobel Prize in physics for his team's 1998 discovery of dark energy, told Live Science. "If confirmed, it literally says dark energy is not what most everyone thought, a static source of energy, but perhaps something even more exotic."

Since those detonations, the development of nuclear weapons has accelerated. Countries around the world have built their own nuclear stockpiles, including over 5,000 nuclear warheads held by the U.S.

Yet, even though the basic components of this technology are no longer secret, nuclear weapon development remains a scientific and engineering challenge. But why are nuclear weapons still so difficult to produce?

A big part of the difficulty comes from deriving the chemical elements used inside these weapons to create an explosion, Hans Kristensen, director of the Nuclear Information Project at the Federation of American Scientists, told Live Science in an email.

"That basic idea of a nuclear explosion is that nuclear [fissile] materials are stimulated to release their enormous energy," he said. "To produce fissile material of sufficient purity and sufficient quantity is a challenge [and] this production requires considerable industrial capacity."

Related: How many nuclear bombs have been used?

The enormous release of energy is called a nuclear fission reaction. When this reaction occurs, a chain reaction starts where the atoms are split apart to release energy. This is the same kind of reaction that makes nuclear energy possible.

Uranium and plutonium enrichment

The fissile material inside a nuclear bomb is primarily isotopes of uranium and plutonium, which are radioactive elements, Matthew Zerphy, a professor of practice in nuclear engineering at Penn State, told Live Science. Natural uranium consists of different isotopes, including a large amount of uranium-238 (U-238) and a smaller amount of uranium-235 (U-235), which is more readily fissionable. To access this more fissionable isotope, uranium ore is mined and then goes through several processes for "enrichment" in which the U-235 concentration is increased so that it can be used for nuclear weapons.

"One way to enrich uranium is to turn it into a gas and spin it very rapidly in centrifuges," Zerphy said. "Because of the difference in mass between U-235 and U-238, the isotopes are split, and you can separate out U-235."

For weapons-grade uranium, this separation continues up to concentrations of over 90% U-235, Zerphy said. The most challenging part of this process, which can take weeks to months, is the chemical transformation of the element itself, which requires intensive energy and specialized equipment. One chemical hazard during this process is the possible release of uranium hexafluoride (UF₆), a highly toxic substance that, if inhaled, can damage the kidneys, liver, lungs, brain, skin and eyes.

The process to produce weapons-grade plutonium is even trickier, he said, because this element does not occur naturally like uranium does. Instead, plutonium is a byproduct of nuclear reactors using uranium fuel, which means to produce plutonium, scientists need to handle radioactive, spent nuclear fuel and process the material through "intense" chemical processing. The processing of this material can also pose a safety risk if a critical mass is collected accidentally, Zerphy said, which is the smallest amount of fissile material needed to sustain a self-sustaining fission reaction.

"You'd be very careful to not have that happen while you're in the process of making these components to make sure that things aren't inadvertently brought together and entering some kind of criticality," he said, which could lead to an accidental explosion.

Related: Why did the atomic bomb dropped on Hiroshima leave shadows of people etched on sidewalks?

Although the scientific principles of bringing these components together is well understood, creating and controlling this reaction in a fraction of a second can still be difficult.

"The weapons are designed such that when they are detonated a 'supercritical' mass of fissile material is created very quickly … in a very small space," Zerphy said. "This causes an exponential increase in the number of fissions spreading throughout the material almost instantaneously."

This quick spread of atomic fission is a big part of what makes a nuclear reaction so destructive, he said.

In the case of thermonuclear weapons, which were developed after World War II and use a combination of both nuclear fission and fusion to create an even stronger explosion, a standard fission reaction then has to spark a secondary and stronger fusion reaction. This fusion reaction is the same kind of power found at the center of the sun.

Nuclear weapons testing

Once these weapons are created, scientists and engineers need to be sure the weapons will work as needed, should they ever be used. When nuclear weapons were first developed, scientists would test the weapons themselves at test sites (which devastated the environment of the "deserted" areas where they were tested, as well as people and animals that lived nearby). In contrast, modern weapon testing relies on computer models. This is part of the work done by the National Nuclear Security Administration (NNSA).

"NNSA … develop[s] tools for qualifying weapon components and certifying weapons, ensuring their survivability and effectiveness in various scenarios," an NNSA spokesperson told Live Science in an email. "This involves advanced simulations using supercomputing systems, materials science, and precision engineering to ensure weapons function as intended."

Ultimately, the complexity and challenges of building these weapons may explain why so few nuclear superpowers exist in the world today.

Editor's note: This article was updated at 12:54 p.m. ET on March 20 to note that nuclear weapons have nuclear reactions, not chemical ones, as was previously stated in the top image caption. It was updated again at 7:05 p.m. ET on March 31 to clarify how natural uranium is enriched to increase U-235 concentrations.

Periodic table of elements quiz: How many elements can you name in 10 minutes?

Pi belongs to a huge mathematical group called irrational numbers, which go on forever and cannot be written as fractions. Scientists have calculated pi to 105 trillion digits, although most of us are more familiar with the approximation 3.14. But how do we know that pi is an irrational number?

Rational numbers, which make up the majority of numbers we use in day-to-day life (although less than half of all possible numbers), can be written in the form of one whole number divided by another. Pi, with its complicated string of decimals, certainly doesn't appear to be part of this group at first glance.

"Rationality is the practical property of having access to the number explicitly, i.e. without any approximation … so being able to write the number in a finite amount of symbols," Wadim Zudilin, a mathematician at Radboud University in the Netherlands, told Live Science.

Related: What is the largest known prime number?

However, actually proving that you can't write pi as a fraction is a surprisingly knotty issue. Mathematicians don't have a universal method to show that a particular number is irrational, so they must develop a different proof for each case, explained Keith Conrad, a mathematician at the University of Connecticut. "How do you know a number is not a fraction?" he said. "You're trying to verify a negative property."

Despite this difficulty, over the past 300 years, mathematicians have established different proofs of pi's irrationality, using techniques from across mathematics. Each of these arguments begins with the assumption that pi is rational, written in the form of an equation. Through a series of manipulations and deductions about the properties of the unknown values in this equation, it subsequently becomes clear that the math contradicts this original assertion, leading to the conclusion that pi must be irrational.

The specific math involved is often incredibly complex, typically requiring a university-level understanding of calculus, trigonometry and infinite series. However, each approach relies on this central idea of proof by contradiction.

"There are proofs using calculus and trigonometric functions," Conrad said. "In some of them, π is singled out as the first positive solution to sin(x) = 0. The first proof by Lambert in the 1760s used a piece of mathematics called infinite continued fractions — it's a kind of infinitely nested fraction."

However, rather than proving pi is irrational directly, it's also possible to confirm irrationality using a different property of the number. Pi belongs to another numerical group called transcendental numbers, which are not algebraic and, importantly, cannot be written as the root of a polynomial equation. Because every transcendental number is irrational, any proof showing that pi is transcendental also proves that pi is irrational.

"Using calculus with complex numbers, you can prove π is transcendental," Conrad said. "The proof uses the very famous equation called Euler's identity: e^iπ +1 = 0."

Although pi's universal importance may arise from this intangible irrationality, seven or eight decimal places is usually more than sufficient for any real-world applications. Even NASA uses only 16 digits of pi for its calculations.

"We approximate the value for practical purposes, 3.1415926 — that's already a lot of information!" Zudilin said. "But of course in mathematics, it's not satisfactory. We care about the nature of the numbers."

Pi Day quiz: How much do you know about this irrational number?

But Einstein had other interests that are less well known — he was a staunch pacifist, invented an early refrigerator and called himself a "deeply religious non-believer." What do you know about the man, the myth, the genius Einstein? Time to take a quantum leap, because this quiz will test what you know about the famous physicist!

Related: 32 fun and random facts about Albert Einstein

Remember to log in to put your name on the leaderboard; hints are available if you click the yellow button. Consider the gravity of the situation and be sure to ace this quiz at the speed of light!

More science quizzes

—Black hole quiz: How supermassive is your knowledge of the universe?

—James Webb Space Telescope quiz: How well do you know the world's most powerful telescope?

—Charles Darwin quiz: Test your knowledge on the 'father of evolution'

For most of us, this fundamental constant is usually approximated to 3.14, but math enthusiasts are constantly trying to push the boundaries and calculate pi to as many digits as possible.

Pi Day is celebrated on March 14th (3/14 — see what they did there?) and is the perfect occasion for mathematicians to celebrate their favourite number. Sharing math puzzles, strange pi facts, and new records is all part of the fun. So to celebrate Pi Day, here's a quick quiz to test your knowledge. If you need a clue, press the yellow button.

More science quizzes

—Periodic table of elements quiz: How many elements can you name in 10 minutes?

—What do you know about psychology's most infamous experiments? Test your knowledge in this science quiz.

—Conspiracy theory quiz: Test your knowledge of unfounded beliefs, from flat Earth to lizard people

Although scientists have made supersolids out of atoms before, this is the first instance of coupling light and matter to create a supersolid and it opens new doors for studying condensed-matter physics, researchers explained in a paper published March 5 in journal Nature.

But what exactly is a supersolid, and why is this new development so exciting? Here's everything you need to know.

Related: 32 physics experiments that changed the world

So you shake the bottle up and down, and a big blob of dressing plops out and hits your plate. Seems like a liquid.

But the dressing doesn't spread all over the plate, like milk or any other liquid would if you spilled it. Rather, it maintains some shape, kind of like the veggies on your plate. Seems like a solid.

But every time you plunge your solid carrot or celery into the blob of dressing, it distorts the shape of the blob a bit. You can even smear and spread the blob around, but the shape and stiffness of the celery isn't affected by this game. Seems like a liquid.

So, is ranch dressing a liquid and a solid? Or is it neither?

I'm a professor of physics and biophysics, and my research focuses on understanding squishy materials that have both liquid and solid properties. Physicists call these materials soft matter. In my lab, we investigate what makes biological materials such as skin and snot squishy — and how we can create bio-inspired materials that have the same fascinating properties. I also host a social media channel, Physics Mama, where my two boys and I ask and answer questions about the physics of everyday life.

The basic states of matter

To figure out what's going on with ranch dressing, you need to understand what the different states of matter are and what makes each one unique. "Matter" is just the scientific word for "stuff," and it is anything that is made up of the microscopic building blocks called atoms and that has mass.

You probably learned in school that there are three states of matter: solid, liquid and gas. Think ice cube, a puddle of water and fog. Maybe you also learned about a fourth state, known as plasma.

These different states are defined by how the extremely tiny molecules making up the matter interact with each other. These molecules are so small that you can't see them with your naked eye. But their invisible interactions determine the properties of the materials that you can see.

Molecules in a solid are physically attached to each other in a way that keeps them from moving around relative to each other. This is what makes solids rigid and able to keep a fixed shape.

The molecules in a liquid, on the other hand, are not connected to each other. They can move around, slide past each other and mix themselves up. This freedom of movement is what allows a liquid to take the shape of whatever container it is in.

The molecules in a gas are completely free to move around without really bumping into the other molecules in the gas too much. Like a liquid, a gas will take the shape of any container it is in and has no fixed shape. But unlike liquids and solids, gases can also change their size or volume.

A plasma is similar to a gas but has much more energy. This energy causes the electrically charged parts of the molecules, called protons and electrons, to break apart. The Sun and stars are examples of plasma, as is the material that makes neon signs glow.

Elasticity and viscosity

While solids hold their shape, they are not completely rigid. The connections between the molecules behave like tiny springs, which makes solids elastic. If you push on a solid, it will deform — but it will bounce back to its original state when you stop pushing, kind of like your mattress when you bounce on your bed. Of course, this happens at the molecular level, so you can't see it happening.

And even though liquids easily change shape, they do resist this change due to the friction between the liquid molecules as they try to move past each other. This friction is called viscosity. Liquids such as honey or syrup are much more viscous than liquids such as milk or water, making them harder to stir. Imagine trying to swim in a swimming pool of honey — delicious but difficult.

A fifth state

Ranch dressing is actually a fifth state of matter known as soft matter. Soft matter can have properties of both liquids and solids, so materials scientists say it is viscoelastic — a combination of viscous and elastic. Other common examples of soft matter include yogurt, cookie dough, shampoo, toothpaste, silly putty, snot, slime and frosting.

These substances aren't quite solid and aren't quite liquid — they're a little of both. You can pour shampoo out of a bottle, but if you put a bit between your fingers and pull them apart, it will stretch between your fingers. Cookie dough can hold its own shape, but if you push on it, it deforms and doesn't bounce back.

Many viscoelastic materials exhibit shear thinning, which means that their viscosity decreases the more you agitate them. This is why shaking your bottle of ranch dressing or ketchup allows you to pour it out — even though before shaking it was too solid-like to leave the bottle. It's also why yogurt that seems quite solid and able to maintain its shape becomes more liquid-like when you stir it quickly.

Squishy materials can also exhibit shear thickening — they become more rigid the harder you try to deform them. This is how Oobleck, a simple mixture of cornstarch and water, works. You can slowly pour it and submerge your hand in it, like any other liquid, but if you squeeze it or shake it up it solidifies.

A different kind of molecule

The reason these squishy materials have both liquid and solid properties is that they're made of polymers: long, chainlike molecules. These long chains get all tangled up, like a bowl of spaghetti, so they are sort of connected, like the molecules in a solid, but also sort of free to move past one other, like molecules in a liquid.

Most store-bought ranch dressing contains xantham gum, which is a natural polymer used to thicken and stabilize many foods.

So the next time you try to pour your ranch dressing out of the bottle, you can imagine the xantham gum polymers all tangled up with one another, making the dressing act like a solid. When you shake the bottle, you're disentangling the polymers so they slide and flow past each other, allowing the dressing to flow easily out of the bottle and onto your plate.

The question "is ranch dressing a liquid or a solid?" was posed by Gabriel, age 8, of DeLand, Florida. Curious Kids is a series for children of all ages. If you have a question you’d like an expert to answer, send it to curiouskidsus@theconversation.com.

This edited article is republished from The Conversation under a Creative Commons license. Read the original article.

Einstein's theory of general relativity describes the relationship between space-time and matter. It successfully explains the structure of neutron stars, the formation of black holes and the evolution of our universe.

But there is one problem — general relativity predicts a singularity, or a point of infinite density at the heart of a black hole where space-time and matter are crushed and stretched into non-existence. A space where nothing exists but that everything falls toward: a paradox.

However, by making a few tweaks to Einstein's famous equations, physicists may have figured out a solution to this paradox while also offering new insights into what happens inside black holes.

Einstein hasn't done too badly from this week's science news, though. Another prediction of general relativity is that the "memory" of ancient cosmological events, like the merging of two black holes, might be etched into the fabric of space-time by gravitational waves.

This prediction of gravitational memory has intrigued physicists for decades, but finding evidence of it has so far remained elusive. Now, researchers have suggested that cosmic background radiation — or microwave radiation left over from the Big Bang — might carry the signatures of these historical events and reveal new insights into these gravitational fingerprints.

And speaking of historical — albeit at a much shorter time-scale — scientists have made a major breakthrough in their quest to "resurrect" the long lost woolly mammoth…

"Woolly mice"

'We didn't know they were going to be this cute': Scientists unveil genetically engineered 'woolly mice'

This week, biotechnology company Colossal Biosciences revealed the latest milestone in their mission to "de-extinct" woolly mammoths — genetically engineered "woolly mice."

To "resurrect" these ancient beasts, the company hopes to genetically engineer the mammoth's closest living relatives — Asian elephants — such that they develop shaggy hair and other woolly mammoth traits to help them to survive in extremely cold environments. However, elephants take a very long time to grow. Therefore, Colossal has tested their tools in an animal that breeds much more quickly and is much easier to keep: mice.

To create the fluffy rodents, the team used CRISPR gene editing technology to tweak six mouse genes involved in fur texture, length and color and one gene involved in fat metabolism and absorption, which is important for staying warm in freezing weather.

Poll: Should we bring back woolly mammoths?

Discover more animal news

—125 million-year-old fossil of giant venomous scorpion that lived alongside dinosaurs discovered in China

—Golden scaleless cave fish discovered in China shows evolution in action

—Animal kingdom's most powerful puncher generates a 'phononic shield' to protect itself

Life's Little Mysteries

When did modern humans reach each of the 7 continents?

Our species has colonized every continent except Antarctica. But when did we arrive in each one?

Most scientists agree that Homo sapiens emerged in Africa at least 300,000 years ago. In that time, we have spread across the globe — and now scientists are finally figuring out when we pulled this off.

Skeleton in chains

1,500-year-old skeleton found in chains in Jerusalem was a female 'extreme ascetic'

While excavating a series of crypts not far from Jerusalem, archaeologists stumbled upon a surprising discovery: a fifth-century burial of a person wrapped in heavy metal chains.

This wasn't entirely unheard of at the time: Toward the end of the fourth century A.D., after Christianity became the main religion of the Roman Empire, monasteries began to pop up everywhere. In their pursuit of physical purity, monks would abstain from worldly pleasures through practices of asceticism. One such practice involved living at the top of a pillar while preaching and praying, often clad in heavy chains.

However, what was surprising about this burial was that the enchained body belonged to a biological female.

Discover more archaeology news

—Scientists realize 'Viking' shipwreck is something else entirely

—2,400-year-old puppets with 'dramatic facial expression' discovered atop pyramid in El Salvador

—Ancient Egyptian city of Alexandria — the birthplace of Cleopatra — is crumbling into the sea at an unprecedented rate

Also in science news this week

—Brain damage reported in 13% of kids who have died of flu this season, CDC finds

—Sunrise on the moon captured by Blue Ghost spacecraft after NASA and Firefly Aerospace announce successful lunar landing

—Italy's Campi Flegrei volcano may unleash devastating eruptions more often than we thought, ancient outburst suggests

—'Primordial' helium from the birth of the solar system may be stuck in Earth's core

Science Spotlight

Is there really a difference between male and female brains? Emerging science is revealing the answer.

If you were to look at a male and female brain in the flesh, would you know which is which?

You wouldn't. However, there are many different disorders of the brain — from psychiatric problems to neurodevelopmental disease — that are expressed in different ways and at different frequencies between the sexes.

Now, thanks in part to AI, scientists are starting to unpick the subtle differences in cellular structures and neural circuitry that reliably distinguish the male and female brain. Whether these differences matter is still unclear, though.

Something for the weekend

If you're looking for something a little longer to read over the weekend, here are some of the best long reads, book excerpts and interviews published this week.

—'This is by far the oldest': Scientists discover 3.47 billion-year-old meteorite impact crater in Australian outback

—'This doesn't appear in computer simulations': Hubble maps chaotic history of Andromeda galaxy, and it's nothing like scientists expected

—If life can exist in your stomach, it can exist on Mars. Here's what it might look like.

And something for the sky watchers

—Where will the 'Blood Moon' total lunar eclipse be visible in March 2025?

Science in pictures

Spectacular photo taken from ISS shows 'gigantic jet' of upward-shooting lightning towering 50 miles over New Orleans

Have you ever wondered what lightning looks like from space? Well, an astronaut on the International Space Station (ISS) has done us all a favor.

In a spectacular photo above the U.S., an unnamed astronaut captured an upward-shooting "gigantic jet" of lightning, extending at least 50 miles (80 kilometers) into the air.

The exact location of the jet is unclear because the Earth's surface is concealed by thunderclouds, but based on the position of the ISS at the time, the jet likely occurred just off the coast of New Orleans.

Follow Live Science on social media

Want more science news? Follow our Live Science WhatsApp Channel for the latest discoveries as they happen. It's the best way to get our expert reporting on the go, but if you don't use WhatsApp we're also on Facebook, X (formerly Twitter), Flipboard, Instagram, TikTok, Bluesky and LinkedIn.

"Singularities are regions of the universe where space, time and matter are crushed and stretched into nonexistence," study co-author Robie Hennigar, a postdoctoral researcher at Durham University in the U.K., told Live Science via email. "This is a very serious problem, as if singularities were to really exist in our universe, it would be catastrophic for science.

"We could no longer use the equations of physics to predict the future from the past and present," he continued. "For these reasons, most practising scientists expect that singularities are not physical, but are telling us that general relativity must be replaced by a more complete theory to describe the universe near singularities."

Related: Scientists may have just discovered 300 of the rarest black holes in the universe

Correcting Einstein

Since its introduction in 1915, general relativity has been remarkably successful in explaining astrophysical and cosmological phenomena, including the formation of black holes, the structure of neutron stars, and the large-scale structure and evolution of the universe.

However, the theory has fundamental limitations. It is incompatible with quantum mechanics, which governs the behavior of particles at the smallest scales, and it predicts singularities — points of infinite density — at the centers of black holes and at the Big Bang.

To address this issue, the researchers used a concept known as quantum gravity, which is commonly applied in attempts to unify Einstein's general relativity with quantum mechanics, which predicts continuous particle creation and annihilation in empty space, along with perpetual fluctuations in all fields, including gravity. Their study, published in February in the journal Physics Letters B, suggests that at extremely high energies or incredibly small distances, general relativity should be modified by an infinite series of additional terms in its equations.

"In quantum gravity, one considers all corrections to the equations relating the energy and momentum of a system with the spacetime curvature that are consistent with known physical principles," Hennigar said. "Different approaches to quantum gravity will place different importance on different terms in the equations, but they all suggest that Einstein's equations need to be refined."

By incorporating these modifications into their calculations, the researchers examined how black holes would behave under this revised framework. Their results showed that when an infinite number of new terms are included, the singularity vanishes. Instead of an infinitely dense point, the black hole's core becomes a highly curved but regular region of space-time.

Testing the theory

Although the new model resolves the singularity problem mathematically, scientific theories must ultimately be tested through observation. The researchers acknowledged that directly confirming their idea presents a significant challenge.

"The absence of singularities itself is hard to test experimentally, because it would occur inside a black hole, or at the very beginning of the universe," Pablo Cano, a postdoctoral researcher at the University of Barcelona and another co-author of the study, told Live Science in an email. "However, we can look for signatures of the theories that lead to singularity resolution.

"The modifications of general relativity that we consider become larger in stronger gravitational fields, but are very small otherwise," Cano added. "This means that, for instance, gravitational waves coming from collisions of black holes — where gravitational fields are much stronger than in the solar system — provide a way of searching for these effects."

Another promising avenue is the study of the early universe. If the effects of this modified gravity theory influenced cosmic inflation — the rapid expansion that followed the Big Bang — evidence of these changes might be imprinted in primordial gravitational waves. Future experiments targeting these signals could help test the validity of the theory.

Next steps

In addition, further theoretical work is needed to determine whether singularity-free black holes can form naturally through gravitational collapse and whether the team's approach can address other types of singularities, such as those associated with the Big Bang.

"We have recently shown that the collapse of a certain type of matter gives rise, within this framework, to the formation of these regular black holes," said Pablo Bueno, a research fellow at the University of Barcelona and a co-author of the study. "We would like to test this under more general assumptions. This may give rise to intriguing features in other areas, such as explicit models of bouncing cosmologies in which the usual Big Bang scenario is replaced by a never ending series of expansive and contracting phases."

Black hole quiz: How supermassive is your knowledge of the universe?

The CEA's (Commissariat à l'énergie atomique et aux énergies alternatives) WEST tokamak nuclear fusion reactor maintained a steady loop of burning plasma for a record 1,337 seconds, according to a Feb. 18 announcement — beating China's previous 1,066-second benchmark, set on Jan. 20, by 25%.

"WEST has achieved a new key technological milestone by maintaining hydrogen plasma for more than twenty minutes through the injection of 2 MW of heating power," Anne-Isabelle Etienvre, CEA director of fundamental research, said in a statement. (2 megawatts being enough to power more than 1,000 homes). "Experiments will continue with increased power.”

Scientists have been trying to harness the power of nuclear fusion — the process that powers the stars — for more than 70 years. By fusing hydrogen atoms together under extremely high pressures and temperatures, stars convert matter into light and heat, generating enormous amounts of energy without producing greenhouse gases or long-lasting radioactive waste.

Related: Nuclear fusion reactor in UK sets new world record for energy output

But replicating the conditions found inside the hearts of stars is no simple task. The most common and advanced design for fusion reactors is called a tokamak. The tokamak works by superheating plasma (one of the four states of matter, consisting of positive ions and negatively charged free electrons) and containing it inside a donut-shaped reactor chamber with powerful magnetic fields.

To reach its new milestone, the WEST reactor did just this, corralling plasma made from heavy hydrogen isotopes that was burning hotter than 50 million degrees Celsius for more than 22 minutes.

Cooking plasma to these temperatures is the relatively easy part, but finding a way to corral it so that it doesn't burn through the reactor without also ruining the fusion process is technically tricky. This is usually done either with lasers or magnetic fields.

The achievement paves the way for the eventual operation of the International Thermonuclear Experimental Reactor (ITER) fusion reactor, a project that brings together China, the European Union, India, Japan, South Korea, Russia and the United States to run the largest fusion reactor ever.

"This excellent result allows both WEST and the French community to lead the way for the future use of ITER," Etienvre said.

Consisting of 19 massive coils looped into multiple toroidal magnets, ITER was originally slated to begin its first full test in 2020, but revisions to its schedule mean it will first fire in 2039 at the earliest. This means the technology is unlikely to progress fast enough to be a practical solution to the climate crisis.

Shulka's feats include setting the fastest known time to mentally add 100 four-digit numbers (30.9 seconds), 200 four-digit numbers (1 minute, 9.68 seconds), and 50 five-digit numbers (18.71 seconds), as well as the fastest time to multiply two five-digit number sets of 10 (51.69 seconds) and two eight-digit number sets of 10 (2 minutes, 35.41 seconds), and the fastest time to divide a set of 10 20-digit numbers by a set of 10-digit numbers (5 minutes, 42 seconds). He crunched these numbers quicker than most people can punch the digits into a calculator.

Shulka set these new records at an event hosted by Guinness in Dubai. Shulka's successful record-setting attempt was captured on video, which is available to watch for free on the Guinness World Records website, and in the player below.

Related: Infamous 'sofa problem' that boggled mathematicians for decades may finally have a solution

A 'one in a billion kind of person'

In addition to these six most recent records, Shulka already holds the record for the quickest time to add 50 five-digit numbers, which he set a year ago. He credits his numerical prowess to his yoga practice, which "helps me keep calm and focused," he told People Magazine in an interview. Shulka also practices math for five or six hours a day, in-between more typical teenage hobbies like reading and playing video games.

In an interview with Guinness, Shulka's father insisted that extraordinary math skills don't run in the family. "We are a normal family," he said. "Aaryan is a one in a billion kind of person, but I don't think that we are a family of mental calculators."

Shulka is not the only teen earning attention for tackling complicated and impressive mathematical problems. In 2022, American high school seniors Ne'Kiya Jackson and Calcea Johnson discovered a new "impossible" proof for the Pythagorean theorem — the 2,000-year-old theorem that describes the relationships between a right triangle's three sides. The teens used trigonometry to prove the theorem, a feat that was previously considered unworkable by mathematicians. Their work was published in the peer-reviewed journal American Mathematical Monthly in 2024, in a paper that included nine more trigonometry-based proofs that no one had ever come up with before.

The truth is that these structures' ability to shield people from the potent heat and blast of a nuclear bomb varies.

"It all depends on where the bunker is and the quality of the bomb," Norman Kleiman, an associate professor of environmental health sciences and director of the Radiation Safety Officer Training course at Columbia University's Mailman School of Public Health, told Live Science.

According to Kleiman, bomb shelters came about during the Cold War as the U.S. and the Soviet Union hinted at mutually assured destruction by nuclear weapons. Both countries' governments designed programs to construct shelters in large public buildings, as well as to encourage individuals to build bunkers inside or outside their homes, Kleinman said.

It's possible that some people marketing these shelters were looking to make a buck amid a crisis. "I'd argue that most of them were being marketed by snake oil salesmen and hucksters," said Peter Caracappa, executive director of the radiation safety program at Columbia University.

Related: Why do nuclear bombs form mushroom clouds?

A bomb shelter doesn't necessarily guarantee safety in the event of a nuclear blast. Its effectiveness comes down to the quality of both the bomb and the shelter.

Modern nuclear weapons are quite different from those of the mid-20th century. Nuclear weapons are much more powerful now, largely because they detonate using a different reaction than they did during World War II and the Cold War. Nuclear bombs in the 1950s had cores made of the radioactive element plutonium or the isotope uranium-235, in which the atoms would split apart in a process called fission, causing a huge explosion. These bombs were a type of nuclear weapon known as atomic bombs, or fission bombs.

"The size of these devices was much smaller, orders of magnitude smaller than current nuclear weapons," Kleiman said. But now we use bombs that rely on hydrogen fusion to create that boom. These bombs utilize the atomic explosion described merely to trigger a larger, thermonuclear explosion. This explosion can have a blast radius of up to 100 miles (160 kilometers). (For comparison, the bombs used on Hiroshima and Nagasaki had blast radii of about 1 mile, or 1.6 km.) Between these two nuclear weapons, hydrogen fusion-powered thermonuclear bombs are far more powerful than fission-powered atomic bombs.

"If you are 600 miles [1,000 km] away from a thermonuclear device, maybe a shelter would help you," Kleiman said. "But if you're anywhere within that blast radius, the blast, the heat, the explosion — those are going to take you out."

And then there's the question of radiation, which is the emission of waves and particles in the wake of the blast. Kleiman said it's possible to build a bunker to protect you from radiation. The walls must be lined with 3 to 5 feet (0.9 to 1.5 meters) of concrete and steel, as well as lead. This lead is embedded in the shelter's walls and doorways, so an intact bunker poses little risk of exposure to its occupants.

Moreover, the entrance "has to be kind of zigzaggy," Kleiman said. Radiation travels in straight lines, so a zigzagging entrance would fend it off.

Capacarra broke down a shelter's protection ability into three components: It must be effective as a structure to withstand an explosion and weather radiation (which, in part, depends on where it is relative to the explosion), how much material is between you and the radiation the explosion emits, and how well it can keep out fallout material, or the material that's generated and released in a nuclear explosion.

Lethal radiation persists for days after the explosion, so if you were to survive the initial blast, you would have to stay in the bunker to avoid radioactive fallout. So your shelter would need to not only be equipped with supplies for the time you'd need to stay put — about a week, according to Kleiman — but also ventilate without letting in any radiation. This estimated timeline depends on how far the shelter is from the blast. However, "that doesn't mean that it's safe, it just means that the radiation levels are low enough that you're not going to die of acute radiation poisoning," Kleiman continued. He added that cancer is one huge long-term risk of radiation exposure, but that and other consequences may not emerge for decades.

So, while a bunker only a few miles from an explosion wouldn't be very helpful, a good shelter dozens of miles from a blast could protect inhabitants from radiation for days. "It's really a question of shielding," Kleiman said — "shielding from heat, shielding from the blast and shielding from radiation."

Modern Hula-Hoops are plastic rings you twirl around your body by moving your hips. This swiveling motion is similar to that seen in the Hawaiian dance known as the hula (hence the name).

There is evidence of humans doing Hula-Hoop-like twirling "as far back as 500 B.C.," said Olivia Pomerenk, a doctoral candidate in math at New York University. It shows up again and again "in a myriad of cultures as a form of recreation, religious ceremony, or exercise."

Considering the activity's long history, you might think it "has been studied to death at this point, but it actually has not," Pomerenk told Live Science. Until recently, research into Hula-Hoop twirling was generally limited to two-dimensional models of a twirling hoop, "rather than the full 3D system," she noted. As such, this prior work could not answer how Hula-Hoops can keep from falling.

In a 2024 study published in the journal PNAS, Pomerenk and colleagues decided to investigate this head-spinning question.

"Our lab tends to gravitate towards these quirky, seemingly simple systems," Pomerenk said. "Many problems we study, when described, elicit the reaction, 'Wait, how has no one solved that already?' This Hula-Hoop problem is no different."

Related: Can we stop time?

To shed light on the question, Pomerenk and her colleagues created miniature robot Hula-Hoopers. They 3D-printed plastic items that were about 6.7 inches (17 centimeters) tall and came in a variety of shapes, such as cylinders, cones and hourglasses. Then, they made the shapes gyrate with a motor to whirl around hoops about 6 inches (15 cm) wide and used computer software to analyze high-speed video recordings of the resulting movements.

The researchers found that stable twirling of the hoop around these robots was possible given a range of gyration motions or bodies. For stable twirling to occur, you must start off by throwing the hoop with a sufficient amount of speed in the same direction as your body's gyration. After that point, centrifugal force and the friction from rolling can keep the hoop twirling stably.

However, keeping the hoop up against gravity for a significant amount of time is more difficult. Ideally, "the body must have 'hips' to provide the proper angle for pushing up the hoop, but also a 'waist' with curves to hold it in place," said study senior author Leif Ristroph, an applied mathematician and experimental physicist at New York University.

These findings suggested that people with hourglass shapes may be natural hoopers. However, "we hope no one takes our results to mean that they cannot Hula-Hoop because of their body shape," Ristroph told Live Science. "We think everyone can, and perhaps different shapes might take a little extra effort or a strategy different from what we investigated in our experiments."

The findings not only help to explain a familiar but poorly understood activity but may also point to a variety of applications involving "transforming one type of motion to another, or suspending and positioning objects without the need to grip or grasp them," Ristroph said.

For instance, with just a slight twitch of their body, a good Hula-Hoop twirler can send a hoop flying around in big orbits, Ristroph noted. This could inspire novel ways of "harvesting or recovering energy from vibrations," he explained.

Another possible application might involve controlling objects without actually holding them, Pomerenk said. For instance, the study presented a relatively simple way to control the vertical position of a twirling hoop along a body without grasping it.

"If you can hoist something up or move something down in a controlled manner without ever actually holding it in a traditional sense, this could be useful in robotic gripping — for example, holding one or several items, or even perhaps in efficiently transporting items vertically in a factory or construction setting," Pomerenk said.

We have an abundance of evidence that something fishy is happening in the universe. Stars orbit within galaxies far too quickly. Galaxies move around inside clusters much too fast. Structures grow and evolve too rapidly. If we count only the matter we can see, there simply isn't enough gravity to explain all of these behaviors.

The vast majority of cosmologists believe all of these phenomena can be explained through the presence of dark matter, a hypothetical form of matter that is massive, electrically neutral and hardly, if ever, interacts with normal matter. This dark matter makes up most of the mass in the universe, far outweighing the amount of luminous matter.

The identity of dark matter remains a mystery, as experiments designed to detect a stray, rare collision have failed to turn up anything. But these experiments have focused on targeting a specific mass range: roughly 10 to 1,000 giga-electron volts (GeV). (A GeV is equivalent to 1 billion electron volts.) That's in the range of the heaviest known particles, like the W boson and the top quark. For decades, theorists favored this mass range because several simple extensions of the Standard Model of particle physics predicted the existence of such particles.

Because we haven't found anything yet, though, we've started to wonder if dark matter might be lighter or heavier than we thought. But heavier dark matter runs into some serious issues, according to a new paper published to the preprint database arXiv.

The problem is that dark matter does sometimes interact with normal matter, if only rarely. But in the early universe, when the cosmos was much hotter and denser, these interactions were much more frequent. Eventually, as the universe expanded and cooled, these interactions slowed and then stopped, leading the dark matter to "freeze out" and remain silent in the background.

Related: Something invisible and 'fuzzy' may lurk at the Milky Way's center, new research suggests

While there are many, many models of potential dark matter candidates, many interact with regular particles through exchanges involving the Higgs boson — a fundamental particle that interacts with almost all other particles and, through those interactions, imbues those particles with mass.

We know the mass of the Higgs boson: around 125 GeV. The researchers found that this mass puts a fundamental upper limit on the possible mass of most dark matter candidates.

The problem is that all interactions in physics are two-way streets. The Higgs talks to both dark matter and regular matter and, in many models, mediates interactions between them. But both kinds of matter also talk back to the Higgs. These interactions appear as slight modifications to the Higgs boson's mass.

For Standard Model particles, we can calculate these corrections and feedback interactions, which is how theorists predicted the mass of the Higgs boson well before it was detected.

The researchers found that if the dark matter particle had a mass greater than a few thousand GeV, its contribution to the Higgs mass would be incredibly important, driving it away from its observed value. And because the Higgs is so central to determining many other fundamental physics, it would essentially shut down particle interactions altogether.

There are possibilities to get around this restriction, however. Dark matter might not interact with regular particles at all, or the interaction might happen through some exotic mechanism that doesn't involve the Higgs. But those models are few and far between and require a lot of fine-tuning and extra steps.

Or it could be that dark matter is lighter than we thought. If we don't think heavy dark matter is a viable candidate, then as we continue to learn about this mysterious component of the universe, we can instead focus our efforts in the other direction. There has already been a surge of interest in axions, ultralight particles that are predicted in some particle physics models and might be a viable dark matter candidate.

On the experimental side, if this result is confirmed and holds to be a widespread restriction on dark matter particle mass, we can refine and redesign our experiments to search for low-mass, instead of high-mass, particles.

Originally posted on Space.com.

"We have previously had two well-established types of magnetism," study author Oliver Amin, a postdoctoral researcher at the University of Nottingham in the U.K., told Live Science. "Ferromagnetism, where the magnetic moments, which you can picture like small compass arrows on the atomic scale, all point in the same direction. And antiferromagnetism, where the neighboring magnetic moments point in opposite directions — you can picture that more like a chessboard of alternating white and black tiles."

Electron spins within an electrical current must point in one of two directions and can align with or against these magnetic moments to store or carry information, forming the basis of magnetic memory devices.

A new form of magnetism

Altermagnetic materials, first theorized in 2022, have a structure that sits somewhere in between. Each individual magnetic moment points in the opposite direction as its neighbor, as in an antiferromagnetic material. But each unit is slightly twisted relative to this adjacent magnetic atom, resulting in some ferromagnetic-like properties.

Altermagnets, therefore, combine the best properties of both ferromagnetic and antiferromagnetic materials. "The benefit of ferromagnets is that we have an easy way of reading and writing memory using these up or down domains," study co-author Alfred Dal Din, a doctoral student also at the University of Nottingham, told Live Science. "But because these materials have a net magnetism, that information is also easy to lose by wiping a magnet over it."

Related: 'A force more powerful than gravity within the Earth': How magnetism locked itself inside our planet

Conversely, antiferromagnetic materials are much more challenging to manipulate for information storage. Because they have a net zero magnetism, however, information in these materials is much more secure and faster to carry. "Altermagnets have the speed and resilience of an antiferromagnet, but they also have this important property of ferromagnets called time reversal symmetry breaking," Dal Din said.

This mind-bending property looks at the symmetry of objects moving forward and backward in time. "For example, gas particles fly around, randomly colliding and filling up the space," Amin said. "If you rewind time, that behavior looks no different."”

This means the symmetry is conserved. However, because electrons possess both a quantum spin and a magnetic moment, reversing time — and, therefore, the direction of travel — flips the spin, meaning the symmetry is broken. "If you look at those two electron systems — one where time is progressing normally and one where you're in rewind — they look different, so the symmetry is broken," Amin explained. "This allows certain electrical phenomena to exist."

Finding ‘the missing link’ of superconductivity

The team — led by Peter Wadley, a professor of physics at the University of Nottingham — used a technique called photoemission electron microscopy to image the structure and magnetic properties of manganese telluride, a material formerly believed to be antiferromagnetic.

"Different aspects of the magnetism become illuminated depending on the polarization of the X-rays we choose," Amin said. Circularly polarized light revealed the different magnetic domains created by the time reversal symmetry breaking, while horizontally or vertically polarized X-rays allowed the team to measure the direction of the magnetic moments throughout the material. By combining the results of both experiments, the researchers created the first-ever map of the different magnetic domains and structures within an altermagnetic material.

With this proof of concept in place, the team fabricated a series of altermagnetic devices by manipulating the internal magnetic structures through a controlled thermal cycling technique.

"We were able to form these exotic vortex textures in both hexagonal and triangular devices," Amin said. "These vortices are gaining more and more attention within spintronics as potential carriers of information, so this was a nice first example of how to create a practical device."

The study authors said the power to both image and control this new form of magnetism could revolutionize the design of next-generation memory devices, with increased operational speeds and enhanced resilience and ease of use.

"Altermagnetism will also help with the development of superconductivity," Dal Din said. "For a long time, there's been a hole in the symmetries between these two areas, and this class of magnetic material that has remained elusive up until now turns out to be this missing link in the puzzle."

Editor's Note: This story was updated on Friday, Jan. 24 at 10:05 a.m. EST to replace a diagram showing altermagnetism with one showing the correct electron spin orientation.

The discovery of dark energy was a real surprise for everyone, including those working on it. When it happened, in 1998, the astronomers who were the first to find themselves in the presence of such surprising data, couldn't believe their eyes. And yet the results left no doubt.

The velocity at which the universe had expanded was not constant; on the contrary, for quite some time now it had been increasing significantly. Everything was moving away from everything at an increasingly frenetic rhythm.

What scientists were seeing contradicted what they were expecting; the idea of the accelerated expansion of the universe was counterintuitive. Everyone expected that the attraction exerted by gravity would slowly reduce the expansion velocity of space-time, whereas the exact opposite was happening.

For many years, different teams of scientists tried to understand whether what the data was pointing to was real or whether, on the other hand, errors had been made in the measurements. In the end, they gave in to the evidence. There was no doubt that a new natural phenomenon was being observed, however completely unexpected it was. In the end even the Royal Swedish Academy of Sciences in Stockholm recognized the importance of the work of Saul Perlmutter, Brian Schmidt and Adam Riess, the three astronomers who had carried out the early research, rewarding their discovery with the 2011 Nobel Prize.

Right from the earliest moments, in an attempt to explain this strange phenomenon, the expression dark energy was coined, indicating the complete ignorance of the mechanism that produced it: an absolutely unknown form of energy seemingly pushing everything away from everything else and growing as the dimensions of the universe grow.

Some imagined a kind of anti-gravity, an extremely strange behaviour of gravity which from being attractive, as we know it, becomes repulsive over great distances. Others imagined a kind of vacuum energy, a positive energy, which creates a kind of negative pressure, thereby pushing everything towards dilation.

The idea that the void contains positive energy which makes it expand goes back many years. And Albert Einstein was the first to come up with it. To make the universe static, that is to counterbalance the effect of gravity, which, acting alone, would sooner or later make everything collapse into one point, Einstein added a positive constant, called the "cosmological constant" into his equations by hand, that is to say arbitrarily. This classification served to build a balance; making the universe expand countered the effects of gravity and made it stable.

Later, when it was discovered that everything had had a turbulent beginning and that galaxies were still moving apart from one another, Einstein regretted this choice, to the extent of referring to it as one of the worst blunders of his life. In fact, with a universe arising from an ultra-dense and super-incandescent singularity, there was no need for this further impetus to expansion to produce a condition of equilibrium. The curious thing is that nobody, least of all Einstein, could predict that by the end of the 20th-century, the discoveries made by Perlmutter, Schmidt and Riess would bring his cosmological constant back into vogue. And so, it seems as if nature will always end up proving Einstein right, even when the great scientist is convinced that he's clearly wrong.

In this case, too, precious information about the presence and distribution of dark energy can be extracted by analyzing the tiniest inhomogeneity in cosmic background radiation and the gravitational lens effects produced by galaxies and clusters. It's curious to discover that it is still light which allows us to take a look at this shady side of the cosmos.

The distribution of dark energy in the cosmos is very homogeneous. It behaves quite differently from matter, whether ordinary matter or dark matter. These latter material substances have reticular distributions with high- density nodes and filaments alternating with broad empty spaces. On the contrary, dark energy is distributed uniformly throughout space and seems to occupy the entire volume of the universe quite happily, exerting a repulsive force on everything.

In an attempt to understand the origin of this mysterious form of energy, scientists have ascertained whether the expansion velocity is the same, over a given period, for all the different regions of the universe. They also realized that this phenomenon has only become dominant in the last billions of years. For a long period, the universe expanded following a very different rhythm from the current one.

Various hypotheses have been tested, including the idea that we are dealing with a new fundamental force or an anomalous behaviour of gravity or even the presence in the fabric of spacetime of very particular structures, similar to defects in its regular pattern. But, as yet, nobody has managed to understand what gives rise to this strange phenomenon, and explaining dark energy remains one of the most formidable challenges of modern science.

While the mystery surrounding its origins remains, the precise measurements taken of the effects of dark energy on the geometry of the universe and on the spatial fluctuations in the density of matter have made it possible to quantify the weight of this component in the material composition of the universe.

The result is sensational; dark energy contributes around 68% of the total mass. Around two-thirds of the universe is made up of this most mysterious of components. Totalling up the contribution of dark energy, we obtain a frankly embarrassing result. Despite the great progress made by contemporary science, we are forced to admit that we don't know anything about 95% of everything that surrounds us.

In a new study, published Dec. 19, 2024 in the journal Monthly Notices of the Royal Astronomical Society, the researchers analyzed data from the Pantheon+ survey — the most comprehensive dataset of type Ia supernovae, whose consistent brightness allows astronomers to measure distances across the universe with incredible precision. Their analysis suggests that what we perceive as acceleration might be an illusion caused by the large-scale structure of the cosmos.

Studying the universe with type Ia supernovae

Type Ia supernovae, the explosive deaths of white dwarf stars, have long served as one of cosmology's most powerful tools. These stellar events occur when a white dwarf accretes enough material from a companion star to trigger a thermonuclear explosion. Because type 1a supernovae produce consistent peak brightness, measuring their brightness when observed from Earth can reveal how far away they are.

"Type Ia supernovae are extremely valuable in astronomy since they act as standardizable candles with which we can measure vast distances in the Universe," study co-author Zachary Lane, a researcher at the University of Canterbury in New Zealand, told Live Science in an email.

By combining this distance information with the redshift of the supernovae — the stretching of light to redder wavelengths due to the universe's expansion — scientists have mapped the universe's growth over time. Decades ago, researchers used this method to show that the universe's expansion was accelerating, a discovery that led to the hypothesis of dark energy — a mysterious, unseen force thought to permeate space and drive this acceleration.

Pantheon+ dataset

The Pantheon+ dataset is the most extensive and precise collection of type Ia supernovae ever assembled. Spanning decades of observations from both ground-based and space telescopes, it contains data on 1,500 supernovae across space-time.

"At the time of this study, the Pantheon+ Type Ia Supernovae spectroscopic dataset was the largest and most pristine collection of purely Type Ia supernovae," Lane said.

The dataset's precision and size make it a goldmine for testing cosmological models. Its detailed records of brightness and redshift offer unparalleled insights into how the universe has evolved, providing a critical testing ground for alternative theories to the standard cosmological model.

Challenging dark energy

While the idea of dark energy explains much of the observed acceleration in the universe, it has always carried an air of mystery. Dark energy has never been directly detected, nor has its origin been explained theoretically, prompting some scientists to explore other explanations.

The new study takes aim at a key assumption of the standard model: that the universe is homogeneous and isotropic on large scales, meaning it looks the same in every direction and from every vantage point.

This assumption underpins the need for dark energy to explain the universe's expansion. However, Lane and his colleagues tested an alternative idea called the timescape model, which suggests that the apparent acceleration could be a byproduct of cosmic structures like voids — vast, near-empty regions of space between galaxy clusters.

"The standard model of cosmology is built on the assumption that the Universe is uniform and featureless on large scales and that cosmic structures do not significantly impact the evolution of the Universe," Lane said. "Timescape abandons these assumptions and finds that the apparent acceleration of the Universe is the result of feedback between cosmic structures."

Because of their sparse matter and gravity, voids expand faster than denser parts of the universe, such as galaxy clusters. According to the timescape model, the dominance of these voids in the cosmic landscape could explain the observed acceleration without the need for dark energy.

Evidence in favor of timescape

The team analyzed the Pantheon+ dataset and found that their results align remarkably well with the timescape model — and in some cases even outperformed the standard cosmological model.

"When considering every supernova, including those very close to us in the Milky Way, which could be influenced by local structures, we find very strong preference in favor of the Timescape model," Lane said. When supernovae in the nearby universe were excluded to account for local differences, the evidence remained supportive, echoing findings from the Dark Energy Survey (DES).

These results pose a direct challenge to the necessity of dark energy. "Consistently finding moderate or stronger evidence for a cosmological model without dark energy using one of the most historically significant observational methods is an exciting prospect to be explored for the future of cosmology," Lane said.

The road ahead

While the findings are compelling, Lane stressed that further research is needed to solidify the case for timescape. "While other factors need to be considered for this to be more established within the cosmology community, it proves a promising initial test," he said.

In the future, the team plans to combine the Pantheon+ dataset with data from the Dark Energy Survey and baryon acoustic oscillations — patterns in the distribution of galaxies that can be used as another cosmic ruler. The astronomers are also conducting simulations of how voids expand under the framework of general relativity and exploring how these effects apply to galaxy formation and evolution.

"Our research group is exploring several extensions to our current work, aiming to challenge foundational aspects of cosmology," Lane said. "A strong competing framework will still enhance the future of cosmology and our current understanding of the challenges facing the field."

Entangled particles are connected to each other, so that a change to one instantaneously causes a change to the other, even if they are separated by vast distances. Albert Einstein famously dismissed the idea as "spooky action at a distance," but later experiments proved that the bizarre, locality-breaking effect is real.

Physicists have observed entanglement between quarks before but had never found evidence that they exist in a quantumly connected state inside protons.

Now, a team of researchers has discovered entanglement between quarks and gluons inside protons over a distance of one quadrillionth of a meter — allowing the particles to share information across the proton. The researchers published their findings Dec. 2, 2024 in the journal Reports on Progress in Physics.

"For decades, we've had a traditional view of the proton as a collection of quarks and gluons, and we've been focused on understanding so-called single-particle properties, including how quarks and gluons are distributed inside the proton," study co-author Zhoudunming Tu, a physicist at Brookhaven National Laboratory in Upton, New York, said in a statement. "Now, with evidence that quarks and gluons are entangled, this picture has changed. We have a much more complicated, dynamic system."

'Spooky action' at the smallest scale

Experimental proof of quantum entanglement first emerged in the 1970s, but many aspects of the phenomenon remain relatively unexplored — including the entangled interactions between quarks. This is mainly because the subatomic particles don't exist on their own and instead fuse into various particle combinations known as hadrons. For example, baryons, such as protons and neutrons, are combinations of three quarks bound tightly together by strong force-carrying gluons.

Related: Heaviest antimatter particle ever discovered could hold secrets to our universe's origins

When individual quarks are ripped from hadrons, the energy used to extract them makes them unstable, transforming them into branching jets of particles in a process called hadronization. This makes the task of sifting through the trillions of particle decay products to reconstruct their original state incredibly difficult.

But that's exactly what the researchers did. To probe the inner workings of protons, the scientists mined data collected by the Large Hadron Collider (LHC) and Hadron-Electron Ring Accelerator (HERA) particle collider experiments.

Then they applied a principle from quantum information science that says a system's entropy (a measure of how many energy states a system can be arranged in, often incorrectly referred to as "disorder") increases with its entanglement — causing the distribution of the particle sprays to appear messier.

By comparing the particle sprays to calculations of their entropy, the physicists discovered that the quarks and gluons inside the colliding protons existed in a maximally entangled state, each sharing the most information possible.

"Entropy is usually associated with uncertainty on some information, while entanglement leads to information 'sharing' between the two entangled parties. So these two can be related to each other in quantum mechanics," Tu told Live Science in an email. "We use the predicted entropy (with entanglement assumed) to check with what the data says, and we found great agreement."

The scientists say their discovery could help to glean more insights into fundamental particles — such as how quarks and gluons remain confined within protons. The research has also prompted further questions about how entanglement changes when protons are locked inside atomic nuclei.

"Because nuclei are made of protons and neutrons, it is natural to ask what would the entanglement do to nuclei structure," Tu said. "We plan to use the electron-ion collider (EIC) to study this. This will come in 10 years. Before that, some collision types, so-called ultra-peripheral collisions in heavy-ion collisions, may work too."

Although astronomers have an abundance of evidence that most of the mass in any given galaxy is invisible, they do not yet know the identity of this "dark matter." In recent decades, the most promising hypothesis has been that dark matter is made of some kind of heavy particle that rarely, if ever, interacts with light or other matter. But this hypothesis struggles to explain the relatively low densities of galaxy cores, because simulations of dark matter's behavior predict that it should easily clump up to extremely high densities, which does not match observations.

One possible answer to this problem is that the dark matter particles are incredibly light — billions of times less massive than the neutrino, the lightest particle currently known. Dubbed "fuzzy" dark matter, these hypothetical particles are so light that their quantum-wave nature manifests on larger, macroscopic — even galactic — scales. This means they can stabilize into giant clumps of invisible matter, forming dark stars.

This is especially interesting because these dark stars can be extended in space for thousands of light-years but still have relatively low masses, since the particles are so light. Thus, they can potentially form the cores of galaxies, providing the bulk of these galaxies' mass without creating superhigh densities at the galactic centers.

But galaxies are made of more than dark matter — fuzzy or otherwise. They also contain normal matter, distributed in the form of diffuse gas clouds and stars, and it's those elements that astronomers can actually observe. So, to test this idea, we need to understand the link between fuzzy dark matter and normal matter within a galaxy.

Related: 800-mile-long 'DUNE' experiment could reveal the hidden dimensions of the universe

The 'fuzz' in our stars

In a paper published Dec. 17, 2024 on the preprint server arXiv, an international team of astrophysicists explored how galaxies might evolve in response to fuzzy dark matter. For this first step, they did not attempt to recreate an entire complex galaxy. Instead they built a simple toy model that contained only two components: a large percentage of fuzzy dark matter and a smaller percentage of a simple, ideal gas.

They then computed how these two components would evolve under their mutual gravitational influence. They found that, despite initially random behavior, the fuzzy dark matter quickly collected into a large clump in the center, with more diffuse clouds of dark matter surrounding it.

The gas followed along, mixing with the fuzzy dark matter in the center, creating what the researchers named a fermion-boson star, in reference to the two kinds of matter that mixed to form the central object. This star was totally unlike our typical conception of one. It would be gigantic — up to 10,000 light-years across — and almost entirely invisible, except for the subtle glow of the gas spread throughout it.

However, the researchers pointed out that this would serve as the ideal representation of a galactic core, which contains higher — but not too high — densities of normal matter, thereby confirming a key prediction of the fuzzy dark matter model.

The next step is to build even more sophisticated models to explore what these "stars" might look like so that astronomers can compare the predictions to real-world observations.

One of the most puzzling questions in modern cosmology is why the universe is filled with matter in the first place. The problem is that almost all fundamental particle reactions produce exact numbers of matter and antimatter particles, which then go on to annihilate each other in flashes of energy. But the universe has an abundance of matter and very little antimatter. So why didn't everything just disappear in the early universe?

The problem is known as baryogenesis, and the leading hypothesis is that some unknown process led to an imbalance of matter over antimatter in the first moments of the Big Bang. But what could that process have been?

New research suggests that the answer may lie in ghostly little particles known as neutrinos. The research was published Dec. 18 on the preprint server arXiv and has not yet been peer-reviewed.

Related: 32 physics experiments that changed the world

There are three varieties of neutrinos, and they all have bizarre properties. For one, they have just a tiny bit of mass, far smaller than even the mass of electrons. They are also all "left-handed," which means their internal spins orient in only one direction as they travel, unlike all other particles that can orient in both directions.

This has led to speculation that there may be more neutrino varieties out there that we haven't detected yet — the right-handed counterparts to the known neutrinos. That's because interactions between the left- and right-handed varieties of neutrinos could cause them to have mass.

A shattered universe

In their recent paper, the researchers proposed a model in which there are two right-handed neutrino species that have very high masses. The model showed that in the earliest moments of the universe, the left- and right-handed neutrinos were in perfect balance. But as the cosmos expanded and cooled, that balance broke, leading to a breaking of symmetries that caused the left-handed neutrinos to acquire their mass and the right-handed neutrinos to disappear from view.

But the researchers' model found that this cataclysmic shift also had other consequences. For one, because neutrinos interact with other particles, their broken symmetry triggered a chain reaction that threw off the delicate balance between matter and antimatter. Second, the right-handed neutrinos mixed together to create an altogether new particle, dubbed the Majoron. The Majoron is a hypothetical particle that is its own anti-particle, and the researchers' calculations showed that this particle would have been made in abundance in the chaos of the early universe.

The Majoron would then survive as a relic of those ancient times, making up the bulk of the mass of every galaxy but remaining invisible and elusive. In other words, it would be a candidate for dark matter, the mysterious hidden substance that fills the cosmos.

It's an audacious proposal, but a comprehensive one. According to the researchers, a single mechanism could explain the strange properties of neutrinos, the baryogenesis that led to the dominance of matter in the universe, and the appearance of mysterious dark matter.

To date, there has been no experimental evidence for the existence of any right-handed neutrinos, let alone something even more exotic like the Majoron. But the researchers predict that if the Majoron exists, it could be within the detectability range of a number of neutrino experiments, like Super-Kamiokande and Borexino — two underground neutrino detectors based in Japan and Italy, respectively. Only time will tell if one of these experiments will find a new signal that lines up with this hypothesis — but if that happens, we may be on the path to solving a number of cosmological mysteries.

Editor's note: This article was updated on Jan. 11 to correct a spelling error. A previous version of the article called the proposed particle the "Majoran"; the correct name is the "Majoron."

Neutrinos are among the universe's most elusive particles, earning them the nickname "ghost particles." There are three known types — or "flavors" — of neutrinos, each with a mass billions of times smaller than an electron's. These particles are remarkable in their ability to transform — or oscillate — into different flavors as they travel through space, even without interacting with other particles.

Studying neutrinos with DUNE

DUNE is a forthcoming neutrino oscillation experiment based in Illinois and South Dakota. "In this experiment, neutrinos are generated by a particle accelerator at Fermilab [in Illinois], travel a distance of 1,300 kilometers [800 miles], and are observed using a massive underground detector in South Dakota," Mehedi Masud, a professor at Chung-Ang University in South Korea and co-author of the study, told Live Science via email.

The experimental setup is ideal for studying neutrino oscillations. Neutrinos created in Fermilab's collisions — primarily muon neutrinos (one of the three flavors) — will traverse Earth to reach the South Dakota detector. Along the way, some of these particles are expected to transform into the other two flavors: electron neutrinos and tau neutrinos.

By observing how the different flavors evolve during their journey, DUNE scientists hope to unravel several fundamental questions in neutrino physics, such as the hierarchy of neutrino masses, the precise parameters governing oscillation, and the role neutrinos may have played in creating the matter-antimatter imbalance in the universe.

Related: Our universe is merging with 'baby universes', causing it to expand, new theoretical study suggests

Probing extra dimensions with neutrino oscillations

The study, published in the Journal of High Energy Physics in November, proposes that the enigmatic behavior of neutrinos could be explained if, in addition to the familiar three dimensions of space, there exist extra spatial dimensions on the scale of micrometers (millionths of a meter). While tiny by everyday standards, such dimensions are remarkably large compared with the femtometer (one-quadrillionth of a meter) scales typical of subatomic particles.

"The theory of large extra dimensions, first proposed by Arkani-Hamed, Dimopoulos, and Dvali in 1998, suggests that our familiar three-dimensional space is embedded within a higher-dimensional framework" of four or more dimensions, Masud explained. "The primary motivation for this theory is to address why gravity is vastly weaker than the other fundamental forces in nature. Furthermore, the theory of large extra dimensions offers a potential explanation for the origin of the tiny neutrino masses, a phenomenon that remains unexplained within the Standard Model of particle physics."

If extra dimensions exist, they could subtly alter neutrino oscillation probabilities in ways detectable by DUNE, according to the study authors. These distortions could appear as a slight suppression of expected oscillation probabilities and as small oscillatory "wiggles" at higher neutrino energies.

Simulating DUNE data to hunt for extra dimensions

In this study, the authors considered the case of a single additional dimension. The effects of an extra dimension are determined primarily by its size. This dependence creates an opportunity for researchers to investigate the presence of such dimensions by analyzing how neutrinos interact with matter within the detector. The extra dimension influences the oscillation probabilities of neutrinos, which, in turn, can reveal valuable clues about its potential existence and properties.

"We simulated several years of neutrino data from the DUNE experiment using computational models," Masud said. "By analyzing both the low-energy and high-energy effects of large extra dimensions on neutrino oscillation probabilities, we statistically assessed DUNE's ability to constrain the potential size of these extra dimensions, assuming they exist in nature."

The team's analysis suggests that the DUNE experiment will be capable of detecting an extra dimension if its size is around half a micron (one-millionth of a meter). DUNE is currently under construction and is expected to begin data collection around 2030. After several years of operation, the accumulated data will likely be sufficient for a comprehensive analysis of the theory of large extra dimensions. The team expects the results of this analysis to be available roughly a decade from now.

Additionally, they think that, in the future, combining data from DUNE with other experimental methods — such as collider experiments or astrophysical and cosmological observations — will enhance the ability to investigate the properties of extra dimensions with greater precision and accuracy.

"In the future, incorporating inputs from other types of data could further tighten these upper bounds, making the discovery of large extra dimensions more plausible, should they exist in nature," Masud said. "Beyond being an exciting avenue for new physics, the potential presence of large extra dimensions could also help DUNE measure standard unknowns in neutrino physics more precisely, free from the influence of unaccounted-for effects."

By combining general relativity, quantum mechanics, and thermodynamics, the study demonstrates that time travel might be feasible without leading to these logical contradictions.

The physics of time loops

Our everyday understanding of time is rooted in Newtonian physics, where events progress linearly from the past to the future. But Einstein's general theory of relativity, completed in 1915, challenges this intuitive assumption. It reveals that the fabric of space-time can behave in ways that defy common sense, as evidenced by phenomena like black holes. One of its most fascinating predictions is the potential existence of closed timelike curves — paths through space-time that loop back on themselves, theoretically allowing a traveler to revisit the past.

"In general relativity, all forms of energy and momentum act as sources of gravity — not just mass," study author Lorenzo Gavassino, a physicist at Vanderbilt University, told LiveScience via email. "This means that if matter is rotating, it can 'drag' spacetime along with it. While this effect is negligible on planets and stars, what if the entire universe was rotating?"

In a universe where all matter rotates, space-time could become so warped that time effectively bends back on itself, forming a loop. A spaceship traveling along such a loop could theoretically return to its starting point, not just in space but also in time. While our universe as a whole doesn't seem to rotate in this way, rotating masses — such as black holes — can produce similar effects, creating potential environments for closed timelike curves.

The paradoxes of time travel

One of the biggest challenges to time travel lies in the paradoxes it creates. The grandfather paradox is just one example. These issues arise because we assume that the laws of thermodynamics, the laws that govern heat and energy, would function normally on a time loop.

"In fact, the law of increasing entropy — a thermodynamic quantity that measures the degree of disorder in a system — is the only law of physics that distinguishes between past and future," Gavassino said. "As far as we know, entropy is the sole reason we remember past events and cannot predict future ones."

Entropy governs many of our daily experiences, from the way our bodies age to how we process memories. Even simple actions, like walking, rely on friction, which itself increases entropy. So how would these processes behave on a time loop?

A quantum solution to paradoxes

Gavassino's research, published Dec. 12, 2024 in the journal Classical and Quantum Gravity, provides an intriguing solution. Drawing inspiration from the work of physicist Carlo Rovelli, he demonstrated that the behavior of thermodynamics fundamentally changes on a closed timelike curve. On such a loop, quantum fluctuations arise that can erase entropy — a process fundamentally different from what we experience in everyday life.

These fluctuations could have dramatic effects on a time traveler. For instance, as entropy decreases, a person's memories might vanish, and aging would reverse. "Entropy increase is the reason why we die. What happens when you invert death?" Gavassino asked. This phenomenon could even render irreversible events, like killing one's grandfather, temporary on a time loop, nullifying the paradox altogether.

"Most physicists and philosophers in the past have argued that if time travel exists, nature will always find a way to prevent contradictory situations," Gavassino said. "A 'self-consistency principle' was introduced, suggesting that everything should align to create a logically coherent story. My work provides the first rigorous derivation of this self-consistency principle directly from established physics. Specifically, I applied the standard framework of quantum mechanics — without additional postulates or controversial assumptions — and demonstrated that the self-consistency of history naturally follows from quantum laws."

Theoretical and practical implications

While Gavassino's findings offer a compelling theoretical framework for time travel, the question remains: Do closed timelike curves actually exist in the real universe? Most physicists are skeptical. In 1992, Stephen Hawking, for example, famously proposed a "chronology protection conjecture," suggesting that the laws of physics might prevent time loops from forming in the first place. This could involve space-time becoming singular — or breaking down — just before a loop could be established.

Still, Gavassino's work is valuable for pushing the boundaries of our understanding.

"What I find interesting about this topic is the way it forces us to think about the role of entropy in generating our experience of the universe, which is probably my favorite topic in all of physics," Gavassino said.

Even if time loops don’t exist, understanding and modeling them could provide insights into real phenomena. For instance, exploring how real entropy evolves and behaves along a closed trajectory at the subatomic scale could yield fascinating insights into the behavior of subatomic systems and their thermodynamics.

Editor's Note: This story was updated on Thursday, Jan. 9 at 10:15 a.m. EST to correct attribution for one quote. Gavassino, not Stephen Hawking, commented on the role of entropy in building our experience of the universe.

This means the Large Hadron Collider (LHC), the most powerful particle accelerator ever built, has given scientists a glimpse into conditions that existed when the universe was less than a second old. The antimatter particle is the partner of a massive matter particle called hyperhelium-4, and its discovery could help scientists tackle the mystery of why regular matter came to dominate the universe, despite the fact that matter and antimatter were created in equal amounts at the dawn of time.

This imbalance is known as "matter-antimatter asymmetry." Matter particles and antimatter particles annihilate on contact, releasing their energy back into the cosmos. That implies that if an imbalance between the two hadn't arisen early in the universe, then the cosmos may have been a much emptier and less interesting place indeed.

The LHC is no stranger to paradigm-shifting discoveries about the early universe. Running in a 17-mile (27-kilometer) long loop beneath the Alps near Geneva, Switzerland, the LHC is most famous for its discovery of the Higgs Boson particle, the "messenger" of the Higgs Field responsible for giving other particles their mass at the dawn of time.

The collisions that occur at the LHC generate a state of matter called "quark-gluon plasma." This dense sea of plasma is the same as the "primordial soup" of matter that filled the universe around one-millionth of a second after the Big Bang.

Exotic "hypernuclei" and their antimatter counterparts emerge from this quark-gluon plasma, allowing scientists a glimpse at the conditions of the early universe.

Related: World's smallest particle accelerator is 54 million times smaller than the Large Hadron Collider, and it works

ALICE through the looking glass

Hypernuclei contain protons and neutrons like ordinary atomic nuclei and also unstable particles called "hyperons." Like protons and neutrons, hyperons are composed of fundamental particles called "quarks." Whereas protons and neutrons contain two types of quarks known as up and down quarks, hyperons contain one or more so-called "strange quarks."

Hypernuclei were first discovered in cosmic rays, showers of charged particles that rain down on Earth from deep space around seven decades ago. However, they are rarely found in nature and are difficult to create and study in the lab. This has made them somewhat mysterious.

The discovery of the first evidence of the hypernuclei that is an antimatter counterpart of hyperhelium-4 was made at the LHC detector ALICE.

While most of the nine experiments at the LHC, each with its own detector, generate their results by slamming together protons at near the speed of light, the ALICE collaboration creates quark-gluon plasma by slamming together much heavier particles, usually lead nuclei, or "ions."

The collision of iron ions (try saying that ten times fast) is ideal for generating significant amounts of hypernuclei. Yet until recently, scientists conducting heavy-ion collisions had only succeeded in observing the lightest hypernucleus, hypertriton, and its antimatter partner, antihypertriton.

That was until earlier in 2024 when scientists used the Relativistic Heavy Ion Collider (RHIC) in New York to detect antihyperhydrogen-4, which is composed of an antiproton, two antineutrons, and a quark-containing particle called an "antilambda."

Now, ALICE has followed this with the detection of a heavier anti-hypernuclei particle, antihyperhelium-4, composed of two antiprotons, an antineutron, and an antilambda.

The lead-lead collision and the ALICE data that yielded the detection of the heaviest antimatter hypernucleus yet at the LHC actually date back to 2018.

The signature of antihyperhelium-4 was revealed by its decay into other particles and the detection of these particles.

ALICE scientists teased the signature of antihyperhelium-4 out of the data using a machine-learning technique that can outperform the collaboration's usual search techniques.

In addition to spotting evidence of antihyperhelium-4 and antihyperhydrogen-4, the ALICE team was also able to determine their masses, which were in good agreement with current particle physics theories.

The scientists were also able to determine the amounts of these particles produced in lead-lead collisions.

They found these numbers consistent with the ALICE data, which indicates that antimatter and matter are produced in equal amounts from quark-gluon plasma produced at the energy levels the LHC is capable of reaching.

The reason for the universe's matter/antimatter imbalance remains unknown, but antihyperhelium-4 and antihyperhydrogen-4 could provide important clues in this mystery.

Before we can answer this question, it's important to define what we mean by "touch," said Christopher Baird, an associate professor of physics at West Texas A&M University.

"On the human scale, what we usually mean when we say that two objects are touching is that the well-defined outer surface of one object resides at the same location as the well-defined outer surface of the other object," Baird told Live Science in an email. "[But] this type of touching does not really make sense at the atomic scale because atoms do not have well-defined outer surfaces."

An atom is neither a solid object nor the smallest unit known to scientists. Instead, an atom is made of many different particles that interact according to specific rules. At its core, an atom is a nucleus surrounded by a cloud of electrons.

But a closer look reveals that this nucleus comprises protons and neutrons, which are made up of particles called quarks and gluons. Atoms of different elements have different numbers of protons, neutrons and electrons. For example, a hydrogen atom has one proton, one electron and zero neutrons, while uranium has 92 protons, 92 electrons and up to 146 neutrons. (The numbers of neutrons in an element can vary depending on which isotope it is.)

Related: Do quantum universes really exist?

An atom's cloud of electrons makes it difficult to determine an exact boundary for "touching," Baird said. Instead, it is more useful to define it as the point that triggers a physical or chemical effect, such as the creation of chemical bonds. This may arise when atoms' electron clouds overlap significantly, he said.

"They touch when the electron orbitals of one atom overlap enough with the electron orbitals of the other atom that physical or chemical effects start happening," Baird explained. "This is probably one of the best definitions for touching on the atomic scale."

This "touching" can be a result of different forces, including electromagnetism, gravity and quantum mechanics. Liquids and solids typically touch through the creation of chemical bonds, Baird said, and gases touch by bouncing off each other.

Another form of touching can take place when particles collide at high speeds, like in a particle accelerator like CERN's Large Hadron Collider in Switzerland, said Zhiquan Sun, a doctoral candidate at MIT's Center for Theoretical Physics.

"When atoms collide with each other with high enough energy so that their electron clouds overlap … the nuclei might undergo elastic or inelastic collisions," Sun told Live Science in an email. "If the collision is elastic, the nucleus simply changes directions and finds its electrons again and becomes the same atom it was. If the nuclei collide inelastically, it breaks apart into protons and neutrons and these may form different nuclei."

At CERN (the European Organization for Nuclear Research), particles collide at very high energies to break particles apart and even form new, subatomic particles, like the Higgs boson. Similar collisions likely took place in the early universe.

At the end of the day, even though atoms don't touch in the same way we do, atomic touching is what makes up life as we know it, Baird said.

"A chair or a rock could not hold itself together in the shape of a chair or a rock if the object's atoms were not touching each other through their chemical bonds," he said. "All material effects arise from some form of atoms touching each other, including chemical reactions, vibrations, sound waves, heat, and so forth."

The infinite monkey theorem was first proposed by mathematician Émile Borel in 1913, and it's been a popular way to understand randomness and probability for decades. But could a monkey really type out Shakespeare?

Although it's an interesting theoretical exercise, this task is probably impossible within the lifetime of our universe, experts told Live Science. That's because the "infinite" component is a key part of the infinite monkey theorem. The chance of a monkey randomly typing anything coherent is very unlikely. However, in the context of infinity, even the most unlikely things could eventually occur.

But our universe isn't infinite, Stephen Woodcock, an associate professor of math and physical sciences at the University of Technology Sydney and co-author of a study about the infinite monkey theorem, told Live Science. "It'll last for a very long time, but it won't last forever," Woodcock said. "There will be a lot of monkeys born, but there will not be an infinite number of monkeys born."

Related: Can you count past infinity?

Not enough monkeys, not enough time

To see whether the infinite monkey theorem was actually applicable in the real world, Woodcock and a colleague did some calculations with theoretical chimpanzees. (Chimpanzees are apes, not monkeys, but the researchers chose them because they, along with bonobos, are our closest relatives.) Assuming that a chimpanzee spent most of its life tapping away on a typewriter, they calculated the probability of the primate typing a word, a sentence, a book and the complete works of William Shakespeare.

They found that the chance a chimp would type the word "banana" in its entire lifetime of about 30 years was only about 5%. A sentence was even less likely. In fact, the likelihood of any of the chimpanzees currently living in the world typing, "I chimp, therefore I am," in their lifetimes was 2 x 10^-20.

"In practical terms, it's basically certain that no chimp alive now would ever type that if you left it for its entire lifetime," Woodcock said. However, the researchers found that in the unlikely event chimps kept breeding and typing for the rest of the universe's lifetime (about 10¹⁰⁰ years), there was a near-certain chance that one chimp would eventually write the sentence.

But when it came to replicating a whole book in the next few trillion years, things started to look very unlikely. Woodcock found there was a "vanishingly small chance" any future chimp would ever mimic "Curious George," let alone Shakespeare, before the heat death of the universe.

The results are a reminder that even in the context of massive numbers, infinity is still incomprehensibly larger. It's also evidence that while thought experiments can help convey interesting concepts, they don't necessarily apply to the real world.

"Just because something is certain in the infinite limit doesn't mean that that has any bearing in our finite universe," Woodcock said.

Real-life infinite monkeys

In their research, Woodcock's team went a little bananas, using calculations that relied on some very generous assumptions. They supposed the chimps typed one character every second of the day for 30 years straight, used a slightly simplified keyboard and pressed each successive key at random.

We know these assumptions probably aren't realistic, because the infinite monkey theorem was once simulated in real life. As part of a 2002 art exhibit, a group at the University of Plymouth in the U.K. gathered six Celebes crested macaques (Macaca nigra) at Paignton Zoo in England and gave them a keyboard for four weeks.

"As the computer was warm, it was quite popular, and there was some writing produced," Geoff Cox, an organizer of the experiment who's now a professor of art and computational culture at London South Bank University, told Live Science in an email.

Unfortunately for Shakespeare enthusiasts, that "writing" was just five pages of gibberish consisting mostly of the letter "S." "It was a hopeless failure in terms of science but that's not really the point," Cox told The Guardian in 2003. "It was more like a little performance."

To him, the "performance" told a story about the nature of animals. "Animals are not machine-like or rule-based systems and instead exhibit unpredictable behaviours," he told Live Science.

Some of those unpredictable behaviors? Bashing the computer with a rock and pooping on the keyboard.

The math problem delineates the largest-size sofa that can fit around a corner of a given width — exactly the problem faced by the characters in an episode of "Friends" that aired in 1999. Ross' pleas of "Pivot!" could have been avoided, it turns out, if he'd only considered a Gerver's sofa with 18 curve sections and a maximum area of 2.2195 units. (Okay, so maybe it wouldn't have been that helpful.)

The solution to the sofa problem is a first for mathematics. The problem was posited by Austrian-Canadian mathematician Leo Moser in 1966. Moser asked for the largest possible area of a single shape in one plane that could move around a right-angled corner of a hallway with a unit width of one. While this might seem simple, the math is quite complicated, as the problem involves both area maximization and movement of the shape.

Now, Jineon Baek, a postdoctoral researcher in mathematics at Yonsei University in South Korea, has arrived at an answer. Baek posted his solution on Dec. 2 on the preprint website ArXiv. In just over 100 pages of mathematical proofs, Baek found that for a hallway with a width of 1 unit, the imaginary sofa's maximum area can be 2.2195 units — narrowing the answer down with precision from the previously known range of between 2.2195 and 2.37 units. The proof has not yet been published in a peer-reviewed journal and will need to be worked through by other mathematicians to determine that it is, indeed, optimal.

Related: High school students who came up with 'impossible' proof of Pythagorean theorem discover 9 more solutions to the problem

The "Gerver" of Gerver's sofa is mathematician Joseph Gerver, an emeritus professor at Rutgers University who posited the lower bound of 2.2195 in 1992. But there had been debate over whether the sofa could be larger, with a team in 2018 using a computer-assisted proof to suggest that 2.37 was actually the upper bound.

Gerver's sofa is a broad U-shaped couch with a curved "seat" that can squeeze around the corner without getting hung up. The question was whether this painstakingly designed sofa — made of 18 separate curves put together — was really the largest, most optimal shape that could make the turn. Baek worked through the geometry of the shape and its movement and found that Gerver's solution was, in fact, correct.

The proof created a ripple of interest on social media.

"This is the optimal sofa," user @morallawwithin wrote on the social platform X on Dec. 6, posting a picture of the rather wide-armed sofa shape. "You may not like it, but this is what peak optimization looks like."

Light's quantum behavior is well established, with over 100 years of experiments showing it can exist in both wave and particle form. But our fundamental understanding of this quantum nature is much further behind, and we only have a limited grasp of how photons are created and emitted, or of how they change through space and time.

"We want to be able to understand these processes to leverage that quantum side," first author Ben Yuen, a research fellow at the University of Birmingham in the U.K., told Live Science. "How do light and matter really interact at this level?"

However, the very nature of light means the answer to this question has almost limitless possibilities. "We can think of a photon being a fundamental excitation of an electromagnetic field," explained Yuen. These fields are a continuum of different frequencies, each of which could potentially become excited. "You can split up a continuum into smaller parts and between any two points, there's still an infinite number of possible points you could pick," Yuen added.

The result is that the properties of a photon are heavily dependent on the properties of its environment, leading to some incredibly complex math. "At first glance, we would have to write down and solve an infinite number of equations to reach an answer," Yuen said.

Related: High school students who came up with 'impossible' proof of Pythagorean theorem discover 9 more solutions to the problem

To tackle this seemingly impossible task, Yuen and co-author Angela Demetriadou, professor of theoretical nanophotonics at the University of Birmingham, employed a clever math trick to dramatically simplify the equations.

Introducing imaginary numbers — multiples of the impossible square root of -1 — is a powerful tool when handling complex equations. Manipulating these imaginary components allows many of the difficult terms in the equation to cancel each other out. Provided all imaginary numbers are converted back to real numbers before reaching the solution, this leaves a much more manageable calculation.

"We transformed that continuum of real frequencies into a discrete set of complex frequencies," explained Yuen. "By doing that, we simplify the equations from a continuum into a discrete set which we can handle. We can put those into a computer and solve them."

The team used these new calculations to model the properties of a photon emitted from the surface of a nanoparticle, describing the interactions with the emitter and how the photon propagated away from the source. From these results, the team generated the first image of a photon, a lemon-shaped particle never seen before in physics.

Yuen stressed, however, that this is only the shape of a photon generated under these conditions. "The shape changes completely with the environment," he said. "This is really the point of nanophotonics, that by shaping the environment, we can really shape the photon itself."

The team's calculations provide a fundamental insight into the properties of this quantum particle — knowledge that Yuen believes will open up new lines of research for physicists, chemists and biologists alike.

"We could think about optoelectronic devices, photochemistry, light harvesting and photovoltaics, understanding photosynthesis, biosensors, and quantum communication," Yuen said. "And there will be a whole host of unknown applications. By doing this kind of really fundamental theory, you unlock new possibilities in other areas."

"Whether light is a particle or a wave is a very old question," Riccardo Sapienza, a physicist at Imperial College London, told Live Science. As a species, we seem driven to understand the fundamental nature of the world around us, and this particular puzzle kept 19th-century scientists busy.

Today, there's no doubt about the answer: Light is both a particle and a wave. But how did scientists reach this mind-bending conclusion?

The starting point was to scientifically distinguish between waves and particles. "You would describe an object as a particle if you can identify it as a point in space," Sapienza said. "A wave is an object that you don't define as a point in space and you need to give a frequency of oscillation and distance between maximum and minimum."

The first conclusive evidence of the wave nature of light came in 1801, when Thomas Young performed his now-famous double-slit experiment. He placed a screen with two holes in front of a light source and observed the behavior of the light after it had passed through the slits. The light hitting the wall showed a complicated pattern of bright and dark bands, known as interference fringes.

As the light waves passed through each hole, they generated partial waves that radiated spherically, intercepting each other and adding or subtracting to the final intensity.

"If the light was a particle, you would have ended up with two bunches on the other side of the screen," Sapienza said. "But we have interference, and we see light everywhere after the screen, not just at the position of the holes. That's proof that light is indeed a wave."

Eighty-six years later, Heinrich Hertz became the first to demonstrate the particle nature of light. He noticed that when ultraviolet light shone on a metal surface, it generated a charge — a phenomenon called the photoelectric effect. However, the significance of his observation wasn't fully understood until many years later.

Related: What is the speed of light?

Atoms contain electrons in fixed energy levels. Shining light on them is therefore expected to give the electrons energy and enable them to escape from the atom, with brighter light liberating electrons faster. But in experiments following Hertz's work, several unusual observations seemed to completely contradict this classical understanding of physics.

It was Einstein who finally solved this puzzle, for which he was awarded a Nobel prize in 1921. Rather than absorbing light continuously from a wave, atoms actually receive energy in packets of light called photons, explaining odd observations such as the existence of a cutoff frequency.

But what determines whether light behaves as a wave or as a particle? According to Sapienza, this isn't the right question to be asking. "Light is not sometimes a particle and sometimes a wave," he said. "It is always both a wave and a particle. It's just that we highlight one of the properties depending on which experiment we do."

In day-to-day life, we mostly experience light as a wave, and it's this form that physicists find most useful to manipulate.

"There's a full field called metamaterials — by shaping a material with the same features as light, we can enhance the interaction of light with the material and control the waves,” Sapienza said. "For example, we can make solar absorbers that can absorb light more efficiently for energy generation or metamaterial MRI probes which are much more effective."

However, light's double nature, known as wave particle duality, is absolutely fundamental to the existence of the world as we know it. This strange twinned behavior also extends to other quantum particles, like electrons.

"You could not have an atom be stable if you didn't have quantum mechanics with the electrons in specific states," Sapienza said. "If you remove the fact that it is a particle, you remove the fact that it has a specific energy and life could not exist."

The agency's Atmospheric Waves Experiment (AWE) captured concentric bands of atmospheric gravity waves stretching across the Southeast as the hurricane progressed miles away.

"Like rings of water spreading from a drop in a pond, circular waves from Helene are seen billowing westward from Florida's northwest coast," AWE principal investigator Ludger Scherliess, a physicist at Utah State University, said in a statement.

Atmospheric gravity waves are vertical ripples that move through quiet areas of the atmosphere, dividing the air into peaks and troughs. According to NASA, these waves can be created by large thunderstorms, wind bursts, hurricanes, tornadoes and even tsunamis. (They are different from gravitational waves, which are ripples in the fabric of space-time that result from violent cosmic events, such as black hole collisions.)

Related: Hurricane season 2024: How long it lasts and what to expect

The AWE instrument is mounted on the International Space Station and detects these waves by measuring airglow — a faint light given off by gasses in the mesosphere, the third layer of Earth's atmosphere. The mesosphere ranges from 31 to 53 miles (50 to 85 kilometers) above Earth's surface. Most weather occurs in the first layer of Earth's atmosphere, the troposphere, though cloud tops can rise into the second layer, the stratosphere, in very strong storms. (These are called "overshooting cloud tops.")

AWE started observing in November 2023, and the Helene gravity-wave images are among the first AWE images that NASA has released publicly. One of the project's goals is to help scientists understand how weather on Earth's surface can affect space weather, the disturbances in the upper atmosphere caused by interactions with charged cosmic particles.

Hurricane Helene was a Category 4 storm with winds up to 140 mph (225 km/h) when it made landfall near Perry, Florida. The storm subsequently moved inland, stalling over eastern Tennessee and western North Carolina, where it caused massive flooding. More than 230 people were killed, according to the Associated Press.

These black hole explosions, powered by Hawking radiation — a quantum process where black holes generate particles from the vacuum due to their intense gravitational fields — could be detected by upcoming telescopes, physicists suggest in a new study. And, once spotted, these exotic explosions could reveal whether our universe contains previously undiscovered particles.

Black holes from the dawn of time

There's already plenty of evidence for the existence of black holes ranging from a few times the mass of the sun to billions of times the sun's mass. These black holes have been directly detected through the gravitational waves they emit during the mergers that help them grow. Some black holes, such as the Milky Way's Sagittarius A*, have even been directly imaged as "shadows" by the Event Horizon Telescope.

PBHs, first proposed by Yakov Zeldovich and Igor Novikov in 1967, are thought to have formed within the first fractions of a second after the Big Bang and may have been as small as subatomic particles, according to NASA. Unlike their larger counterparts, which form from the collapse of massive stars and galaxies, PBHs might have emerged from the collapse of ultradense regions in the extremely hot "primeval soup" of particles in the early universe.

If they exist, these compact objects could provide a natural explanation for dark matter, the invisible entity that makes up about 85% of the matter in the universe. However, PBHs remain elusive. Their theoretical existence is supported by a combination of cosmological models, but they have yet to be directly observed.

The Hawking radiation effect

One of the most interesting aspects of PBHs is their connection to Hawking radiation. According to quantum theory, black holes aren't completely "black"; they can emit radiation and slowly lose mass through a process first theorized by Stephen Hawking. This emission, known as Hawking radiation, occurs when virtual particle pairs pop in and out of the vacuum of space near a black hole's edge — its "event horizon." While these pairs normally annihilate each other, if one falls into the black hole, the other particle can escape as radiation. Over time, this leads to the black hole's gradual evaporation.

"For black holes with masses larger than a few times that of the Sun, Hawking radiation is nearly undetectable," Marco Calzà, a theoretical physicist at the University of Coimbra in Portugal and co-author of the study, told Live Science in an email. "But lighter black holes — such as PBHs — would be much hotter and emit far more radiation, potentially allowing us to detect this process. This radiation can include a variety of particles, from photons to electrons to neutrinos."

Related: Stephen Hawking's black hole radiation paradox could finally be solved — if black holes aren't what they seem

As the PBH evaporates, it loses mass, becoming hotter and emitting more radiation in a feedback loop. Eventually, the black hole should explode in a powerful burst of radiation — a process that existing gamma-ray and neutrino telescopes are actively searching for. Although no definitive PBH explosions have been detected yet, the new study suggests these rare events could be the key to unlocking new physics.

Probing the final moments of a PBH

In their recent study, published in the Journal of High Energy Physics, Calzà and study co-author João G. Rosa, also a theoretical physicist at the University of Coimbra, introduced innovative methods for studying PBHs during their final stages of evaporation. By analyzing the properties of their Hawking radiation, the duo developed tools to estimate a PBH's mass and spin.

"Tracking a PBH's mass and spin as it evaporates could provide valuable clues about its formation and evolution," Rosa told Live Science in an email.

Their work has significant implications for fundamental physics. In a previous study, Rosa, Calzà and collaborator John March-Russell of the University of Oxford explored how string theory — an attempt to unify the fundamental forces of nature within a single quantum theory — could affect an evaporating PBH. String theory predicts the existence of numerous low-mass particles called axions, which have no intrinsic spin. Their research suggested that axion emission could actually spin up a PBH, contrary to Hawking's predictions.

"A spinning PBH would provide compelling evidence for these exotic axions, potentially revolutionizing our understanding of particle physics," Calzà said.

Furthermore, the study suggests that analyzing the evolution of a PBH's mass and spin in its final moments could reveal the existence of other new particles. By tracking the spectrum of Hawking radiation, scientists might be able to distinguish between high-energy particle physics models. Neutrino telescopes, such as IceCube, could even help uncover these new particles as PBHs explode in space.

"If we can catch just one exploding PBH and measure its Hawking radiation, we could learn a tremendous amount about new particles and potentially guide the design of future particle accelerators," Rosa said.

Although no exploding PBH has been detected yet, the tools and methods developed by Calzà and Rosa's team could pave the way for future discoveries. The researchers emphasized that dedicated experiments may not be necessary, as several new gamma-ray and neutrino telescopes with unprecedented sensitivity are already in development.

"Upcoming telescopes could easily spot one if it explodes nearby. If we're lucky enough to detect an exploding PBH, it could change everything we know about the fundamental laws of nature," Rosa said.

While still in high school, Ne'Kiya Jackson and Calcea Johnson from Louisiana used trigonometry to prove the 2,000-year-old Pythagorean theorem, which states that the sum of the squares of a right triangle's two shorter sides are equal to the square of the triangle's longest side (the hypotenuse). Mathematicians had long thought that using trigonometry to prove the theorem was unworkable, given that the fundamental formulas for trigonometry are based on the assumption that the theorem is true.

Jackson and Johnson came up with their "impossible" proof in answer to a bonus question in a school math contest. They presented their work at an American Mathematical Society meeting in 2023, but the proof hadn't been thoroughly scrutinized at that point. Now, a new paper published Monday (Oct. 28) in the journal American Mathematical Monthly shows their solution held up to peer review. Not only that, but the two students also outlined nine more proofs to the Pythagorean theorem using trigonometry.

"To have a paper published at such a young age — it's really mind-blowing," Johnson, who is now studying environmental engineering at Louisiana State University, said in a statement emailed to Live Science. "I am very proud that we are both able to be such a positive influence in showing that young women and women of color can do these things."

Related: Largest known prime number, spanning 41 million digits, discovered by amateur mathematician using free software

By proving Pythagoras' theorem using trigonometry, but without using the theorem itself, the two young women overcame a failure of logic known as circular reasoning. Trigonometry is a branch of mathematics that lays out how the sides, lengths and angles in a triangle are related, and as such, the discipline often includes expressions of the Pythagorean theorem. But Jackson and Johnson managed to prove the theorem using a result of trigonometry called the Law of Sines, dodging circular reasoning.

In the new study, and on top of their initial proof, the young mathematicians described four new ways to prove Pythagoras' theorem using trigonometry, as well as a novel method that revealed five more proofs, totaling 10 proofs.

Jackson and Johnson are only the third and fourth people known to have proven the Pythagorean theorem using trigonometry and without resorting to circular reasoning. The two other people were professional mathematicians, according to the statement.

"I didn't think it would go this far," Jackson, who currently studies pharmacology at the Xavier University of Louisiana, said in the statement. "I was pretty surprised to be published."

In the paper, Jackson and Johnson say there are two ways to present trigonometry and its functions sine and cosine, but these versions are often conflated into one. Sine and cosine are ratios that are defined in the context of a triangle's right angle, and they can be presented according to either the trigonometric method or a method that uses polynomials of complex numbers, according to the paper.

The conflation means that "trying to make sense of trigonometry can be like trying to make sense of a picture where two different images have been printed on top of each other," Jackson and Johnson wrote.

By teasing the two methods apart, researchers can discover "a large collection of new proofs of the Pythagorean theorem," the young mathematicians added.

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The new number is 2^136,279,841 – 1, which beats the previous title holder (2^82,589,933 – 1) by more than 16 million digits.

Prime numbers, described by mathematicians as the "atoms of integers," are numbers that are divisible only by themselves and 1. The smallest prime numbers are 2, 3, 5, 7 and 11. Technically, prime numbers run to infinity, but finding them becomes significantly harder the bigger they get.

To find the new prime, Luke Durant used a free program called the Great Internet Mersenne Prime Search, or GIMPS, to sift through the possibilities with an algorithm. His efforts required the harnessing of thousands of graphics processing units (GPUs) across 24 data centers in 17 countries — a feat that "ends the 28-year reign of ordinary personal computers finding these huge prime numbers," according to a statement released on the GIMPS website.

The newly confirmed prime number contains 41,024,320 decimal digits, according to the statement.

Related: Pi calculated to 105 trillion digits, smashing world record

The new prime number is also the 52nd known Mersenne prime — a series named after Marin Mersenne, a French monk and polymath who devised a formula for finding prime numbers by subtracting 1 from powers of 2. (The smallest Mersenne prime is 3 — or 2 to the power of 2, minus 1.) Though far from being the only way to discover primes, the method is slightly easier than others.

As for the usefulness of the discovery, "At present there are few practical uses for these large Mersenne primes, prompting some to ask, 'Why search for these large primes?'" the GIMPS team wrote in the statement. "Those same doubts existed a few decades ago until important cryptography algorithms were developed based on prime numbers."

The discovery has netted Durant a $3,000 cash prize from GIMPS. Further prizes of $150,000 and $250,000 await those who discover the first hundred-million-digit prime and the first billion-digit prime, respectively.

When solutions to the three-body problem are mapped out based on where the three objects start in relation to one another, islands of stability emerge from the chaos, researchers reported in the September issue of the journal Astronomy & Astrophysics. These islands could help scientists detect colliding black holes, the researchers said.

The gravitational interactions between two bodies can be reliably described and mapped using equations. But when you add in a third object, things get wild — the motions of the bodies are unpredictable and often end with one of the bodies being flung out of the system. Even small changes in their starting masses, velocities or positions often lead to drastically different outcomes.

Broadly speaking, researchers use statistics to predict how often any one of the three bodies will be ejected from the system. But when Alessandro Trani, a theoretical physicist at the Niels Bohr Institute in Denmark, and his colleagues ran computer simulations of the three-body problem, their results didn't match the statistical predictions.

Their experiments began with a binary — two objects orbiting each other — and a single object approaching from elsewhere in space. Across more than a million simulations, the team altered the positions of the two bodies in the binary and the angle at which the single object approached. Then, they let the three bodies interact until one was eventually kicked out of the system.

Related: Mathematicians find 12,000 new solutions to 'unsolvable' 3-body problem

In a purely chaotic system, even a small adjustment to the positions or angles of the three bodies could change which of the three objects got ejected. But Trani and his colleagues found several ranges of positions and angles where the same object got kicked out every time. These "isles of regularity" represent gaps in the chaos of the three-body problem.

These non-chaotic zones could complicate how researchers predict three-body interactions in space. The predictions scientists usually apply to these astrophysical interactions rely on statistics, Trani said. But the purely statistical calculations don't work on problems that include regions of both chaos and regularity.

"We need to have a mix of statistical predictions for the chaotic space and a mix of regular mechanical theory or deterministic theory for the regular one, and we also need to know how to mix the outcomes," Trani told Live Science. "That's the most difficult part: identifying where the three-body problem is chaotic and where it's not, without running simulations."

Finding these regions of stability could also help scientists spot and understand gravitational waves, which are released when black holes interact or merge. Interactions among three black holes, which are relatively common inside star clusters, can send two of them careening toward each other. But predictions of these events capture only those resulting from chaotic interactions. There could be more non-chaotic interactions happening among three black holes and, therefore, more opportunities to study gravitational waves, Trani said.

Dark matter makes up the vast majority of the mass of almost every galaxy in the universe, but its exact nature still eludes scientists. It has gravity, but doesn’t interact with light or produce light of its own, so we only have circumstantial evidence of its existence through its gravitational interactions with everything else.

In these circumstances, researchers are desperate to cook up any scenario that might make dark matter more visible. So why not use black holes? It sounds like a ridiculous question: How could black holes, which devour any light that gets too close to them, make dark matter shine? But researchers have put together a scenario that might make it possible. They reported their findings Sept. 20 in the preprint database arXiv. (The findings haven't been peer-reviewed).

The researchers assume that dark matter can, in principle, interact with regular matter (and produce light in the process), but, for some reason, normally doesn't. Perhaps the interaction requires a certain amount of energy that simply isn’t available or is prohibited without a mediator particle doing the work. Black holes could provide the avenue needed to overcome these barriers and get the dark matter to light up.

But not just any black hole will do the trick, only ultra-tiny primordial black holes. These black holes aren’t the leftovers of giant stars but the remnants of the chaotic eras of the extremely early universe, where matter and energy spontaneously compressed to make them. Primordial black holes were first hypothesized by Stephen Hawking, but observations have so far failed to find any. If they do exist, they are extremely uncommon.

Like all black holes, primordial black holes would evaporate Hawking radiation, a strange quantum effect discovered by Stephen Hawking in which virtual particles pop up near a black hole's edge and some are able to escape. The smaller the black hole, the more radiation it emits.so primordial black holes roughly the mass of an asteroid would be emitting plenty of radiation in the present-day universe.

This radiation emitted by black holes isn’t just packets of light, or photons. It’s almost every kind of particle, including dark matter particles. As the primordial black holes decay, they emit dark matter particles that then energize any ambient dark matter particles in their vicinity, triggering a cascade that can briefly release visible light.

The researchers predict that these signals will typically be in the form of gamma ray flashes. They are far too weak for current experiments to detect, but future observatories, like NASA’s proposed All-sky Medium Energy Gamma-ray Observatory eXplorer (AMEGO-X), might have the sensitivity and resolution needed to find these sorts of signals.

In this scenario, the universe would expand to a finite size, but everything would grow so cold that all activity would essentially cease.

Dark energy is the mysterious force responsible for accelerating the expansion of the universe. It was discovered in the 1990s, but despite over two decades of research, it still remains the central mystery of modern cosmology. Over the years, scientists have presented some fascinating research into what it is and how it works.

One idea is known as holographic dark energy. In this scenario, gravity — and space itself — is an illusion. Our universe is really only two-dimensional, and exotic quantum forces on that surface give rise to the appearance of gravity and the structure of 3D space.

A consequence of this theory is a natural accelerated expansion of the universe, which we identify as dark energy.

Related: Our universe is merging with 'baby universes', causing it to expand, new theoretical study suggests

While many researchers have studied holographic dark energy models and ways to test it, a pair of astrophysicists examined the long-term fate of the universe if it is indeed ruled by holographic dark energy. They published their results Sept. 30 to the preprint database arXiv. (It has not been peer-reviewed.)

Dark energy takes up roughly 70% of the energy density of the entire cosmos. As the universe expands, the density of both regular and dark matter drops, while more and more dark energy manifests. To study the ultimate long-term fate of the universe, the researchers ignored matter and focused solely on the evolution of holographic dark energy.

They found that, as expected, holographic dark energy will continue to expand the universe. But, over time, its influence will slowly peter out and slow acceleration. The universe's expansion rate will steadily decrease until the cosmos reaches a nearly static value, essentially locking it to a final size.

But as the universe's expansion slows down, the density of holographic dark energy dwindles along with it. And since the density of matter also shrinks as the universe expands, the universe grinds to a halt. The researchers dub this scenario "the long freeze," in contrast to other commonly known fates of the universe like the "Big Freeze" (the accelerated expansion continues unabated) and the "Big Crunch" (something causes the universe to contract back toward the Big Bang).

The long freeze isn't a rosy scenario. While the universe's expansion will eventually stop, there won’t be any new sources of energy for all the matter inside of it. This means that eventually all the stars will wink out and decay, and all the subatomic particles will drift away from each other in the cold.

Unfortunately, even in their most exotic theories, cosmologists can't come up with a way to give the universe a happy ending.

It is the most famous graffiti in mathematical history, but it looks rather unassuming:

i ² = j ² = k ² = ijk = –1

Yet Hamilton's revelation changed the way mathematicians represent information. And this, in turn, made myriad technical applications simpler — from calculating forces when designing a bridge, an MRI machine or a wind turbine, to programming search engines and orienting a rover on Mars. So, what does this famous graffiti mean?

Rotating objects

The mathematical problem Hamilton was trying to solve was how to represent the relationship between different directions in three-dimensional space. Direction is important in describing forces and velocities, but Hamilton was also interested in 3D rotations.

Mathematicians already knew how to represent the position of an object with coordinates such as x, y and z, but figuring out what happened to these coordinates when you rotated the object required complicated spherical geometry. Hamilton wanted a simpler method.

He was inspired by a remarkable way of representing two-dimensional rotations. The trick was to use what are called "complex numbers", which have a "real" part and an "imaginary" part. The imaginary part is a multiple of the number i, "the square root of minus one", which is defined by the equation i ² = –1.

Related: Imaginary numbers could be needed to describe reality, new studies find

By the early 1800s several mathematicians, including Jean Argand and John Warren, had discovered that a complex number can be represented by a point on a plane. Warren had also shown it was mathematically quite simple to rotate a line through 90° in this new complex plane, like turning a clock hand back from 12.15pm to 12 noon. For this is what happens when you multiply a number by i.

Hamilton was mightily impressed by this connection between complex numbers and geometry, and set about trying to do it in three dimensions. He imagined a 3D complex plane, with a second imaginary axis in the direction of a second imaginary number j, perpendicular to the other two axes.

It took him many arduous months to realize that if he wanted to extend the 2D rotational wizardry of multiplication by i he needed four-dimensional complex numbers, with a third imaginary number, k.

In this 4D mathematical space, the k-axis would be perpendicular to the other three. Not only would k be defined by k ² = –1, its definition also needed k = ij = –ji. (Combining these two equations for k gives ijk = –1.)

Putting all this together gives i ² = j ² = k ² = ijk = –1, the revelation that hit Hamilton like a bolt of lightning at Broome Bridge.

Quaternions and vectors

Hamilton called his 4D numbers "quaternions", and he used them to calculate geometrical rotations in 3D space. This is the kind of rotation used today to move a robot, say, or orient a satellite.

But most of the practical magic comes into it when you consider just the imaginary part of a quaternion. For this is what Hamilton named a "vector".

A vector encodes two kinds of information at once, most famously the magnitude and direction of a spatial quantity such as force, velocity or relative position. For instance, to represent an object's position (x, y, z) relative to the "origin" (the zero point of the position axes), Hamilton visualised an arrow pointing from the origin to the object's location. The arrow represents the "position vector" x i + y j + z k.

This vector's "components" are the numbers x, y and z — the distance the arrow extends along each of the three axes. (Other vectors would have different components, depending on their magnitudes and units.)

Half a century later, the eccentric English telegrapher Oliver Heaviside helped inaugurate modern vector analysis by replacing Hamilton's imaginary framework i, j, k with real unit vectors, i, j, k. But either way, the vector's components stay the same — and therefore the arrow, and the basic rules for multiplying vectors, remain the same, too.

Hamilton defined two ways to multiply vectors together. One produces a number (this is today called the scalar or dot product), and the other produces a vector (known as the vector or cross product). These multiplications crop up today in a multitude of applications, such as the formula for the electromagnetic force that underpins all our electronic devices.

A single mathematical object

Unbeknown to Hamilton, the French mathematician Olinde Rodrigues had come up with a version of these products just three years earlier, in his own work on rotations. But to call Rodrigues' multiplications the products of vectors is hindsight. It is Hamilton who linked the separate components into a single quantity, the vector.

Everyone else, from Isaac Newton to Rodrigues, had no concept of a single mathematical object unifying the components of a position or a force. (Actually, there was one person who had a similar idea: a self-taught German mathematician named Hermann Grassmann, who independently invented a less transparent vectorial system at the same time as Hamilton.)

Hamilton also developed a compact notation to make his equations concise and elegant. He used a Greek letter to denote a quaternion or vector, but today, following Heaviside, it is common to use a boldface Latin letter.

This compact notation changed the way mathematicians represent physical quantities in 3D space.

Take, for example, one of Maxwell's equations relating the electric and magnetic fields:

∇ × E = –∂B/∂t

With just a handful of symbols (we won't get into the physical meanings of ∂/∂t and ∇ ×), this shows how an electric field vector (E) spreads through space in response to changes in a magnetic field vector (B).

Without vector notation, this would be written as three separate equations (one for each component of B and E) — each one a tangle of coordinates, multiplications and subtractions.

The power of perseverance

I chose one of Maxwell's equations as an example because the quirky Scot James Clerk Maxwell was the first major physicist to recognise the power of compact vector symbolism. Unfortunately, Hamilton didn't live to see Maxwell's endorsement. But he never gave up his belief in his new way of representing physical quantities.

Hamilton's perseverance in the face of mainstream rejection really moved me, when I was researching my book on vectors. He hoped that one day — "never mind when" — he might be thanked for his discovery, but this was not vanity. It was excitement at the possible applications he envisaged.

He would be over the moon that vectors are so widely used today, and that they can represent digital as well as physical information. But he'd be especially pleased that in programming rotations, quaternions are still often the best choice — as NASA and computer graphics programmers know.

In recognition of Hamilton's achievements, maths buffs retrace his famous walk every October 16 to celebrate Hamilton Day. But we all use the technological fruits of that unassuming graffiti every single day.

This edited article is republished from The Conversation under a Creative Commons license. Read the original article.

Conservation of energy

Energy conservation — the idea that energy cannot be created or destroyed, only transformed — is one of the most important laws of physics. James Prescott Joule demonstrated this rule, the first law of thermodynamics, when he filled a large container with water and fixed a paddle wheel inside it. The wheel was held in place by an axle with a string around it and then looped over a pulley and attached to a weight, which, when dropped, caused the wheel to spin. By sloshing the water with the wheel, Joule demonstrated that the heat energy gained by the water from the wheel's movement was equal to the potential energy lost by dropping the weight.

Measurement of the electron's charge

As the fundamental carriers of electric charge, electrons carry the smallest amount of electricity possible. But the particles are truly tiny, with a mass 1,838 times smaller than the already-minuscule proton.

So how could you measure the charge on something so small? Physicist Robert Millikan's answer was to drop electrically charged oil drops through the plates of a capacitor and adjust the voltage of the capacitor until the electric field it emitted produced a force on some of the drops that balanced out gravity — thus suspending them in the air. Repeating the experiment for different voltages revealed that, no matter the size of the drops, the total charge it carried was a multiple of a base number. Millikan had found the fundamental charge of the electron.

 "Gold foil experiment" revealing the structure of the atom

Once thought to be indivisible, the atom was slowly divided and split by a series of experiments during the late 19th and early 20th centuries. These included J.J. Thomson's 1897 discovery of the electron and James Chadwick's 1932 identification of the neutron. But perhaps the most famous of these experiments was Hans Geiger and Ernest Marsden's "gold foil experiment." Under the direction of Ernest Rutherford, the students fired positively charged alpha particles at a thin sheet of gold foil. To their surprise, the particles passed through, revealing that atoms consisted of a positively charged nucleus separated by a significant empty space by their orbiting electrons.

Nuclear chain reaction

By the mid-20th century, scientists were aware of the basic structure of the atom and that, according to Einstein, matter and energy were different forms of the same thing. This set the stage for the wartime work of Enrico Fermi, who in 1942 demonstrated that atoms could be split to release enormous quantities of energy.

While working at the University of Chicago with an experimental setup he called an "atomic pile," Fermi demonstrated the first-ever controlled nuclear fission reaction. Fermi fired neutrons at the unstable isotope uranium-235, causing it to split and release more neutrons in a growing chain reaction. The experiment paved the way for the development of nuclear reactors and was used by J. Robert Oppenheimer and the Manhattan Project to build the first atomic bombs.

Wave-particle duality

One of the most famous experiments in physics is also one that illustrates, with disturbing simplicity, the bizarreness of the quantum world. The experiment consisted of two slits, through which electrons would travel to create an interference pattern on a screen, like waves. Scientists were stunned when they placed a detector near the screen and found that its presence caused the electrons to switch their behavior to act instead as particles.

First performed by Thomas Young to demonstrate the wave nature of light, the experiment was later used by physicists in the 20th century to show that all particles, including photons, were both waves and particles at the same time — and they acted more like particles when they were being measured directly.

Splitting of white light into colors

White light is a mixture of all the colors of the rainbow, but before 1672, the composite nature of light was completely unknown. Isaac Newton determined this by using a prism that bent light of different wavelengths, or colors, by different amounts, decomposing white light into its composite colors. The result was one of the most famous experiments in scientific history and a discovery that, alongside other contributions by Newton, gave birth to the modern field of optics.

Discovery of gravity

In perhaps the most widely repeated story in all of science, Newton is said to have chanced upon the theory of gravity while contemplating under the shade of an apple tree. According to the legend, when an apple fell and struck him on the head, he supposedly yelled "Eureka!" as he realized that the same force that brought the apple tumbling to Earth also kept the moon in orbit around our planet and Earth circling the sun. That force, of course, would become known as gravity.

The story is slightly embellished, however. According to Newton's own account, the apple did not strike him on the head, and there's no record of what he said or if he said anything, at the moment of discovery. Nonetheless, the realization led Newton to develop his theory of gravity in 1687, which was updated by Einstein's theory of general relativity 228 years later.

Blackbody radiation

By the turn of the 20th century, many physicists — having advanced theories that explained gravity, mechanics, thermodynamics and the behavior of electromagnetic fields — were confident that they had conquered the vast majority of their field. But one troubling source of doubt remained: Theories predicted the existence of a "blackbody" — an object capable of absorbing and then remitting all incident radiation. The problem was that physicists couldn't find it.

In fact, data from experiments conducted with close approximations of black bodies — a box with a single hole whose inside walls are black — revealed that significantly less energy was emitted from blackbodies than classical theories led scientists to believe, especially at shorter wavelengths. The contradiction between experiment and theory became known as the "ultraviolet catastrophe."

The discovery prompted Max Planck to propose that the energy emitted by blackbodies wasn't continuous but rather split into discrete integer chunks called quanta. His radical proposal catalyzed the development of quantum mechanics, whose bizarre rules are completely unintuitive to observers living in the macroscopic world.

Einstein and the eclipse

Following its publication in 1915, Einstein's groundbreaking theory of general relativity briefly remained just that — a theory. Then, in 1919, astronomer Sir Arthur Eddington devised and completed stunning proof using that year's total solar eclipse.

Key to Einstein's theory was the notion that space — and, therefore, the path that light would follow through it — was warped by powerful gravitational forces. So, as the moon's shadow passed in front of the sun, Eddington recorded the position of nearby stars from his vantage point on the island of Principe in the Gulf of Guinea. By comparing these positions to those he had recorded at night without the sun in the sky, Eddington observed that they had been shifted slightly by the sun's gravity, completing his stunning proof of Einstein's theory.

Higgs boson

In 1964, Peter Higgs suggested that matter gets its mass from a field that permeates all of space, imparting particles with mass through their interactions with a particle known as the Higgs boson.

To search for the boson, thousands of particle physicists planned, constructed and fired up the Large Hadron Collider. In 2012, after trillions upon trillions of collisions in which two protons are smashed together at near light speed, the physicists finally spotted the telltale signature of the boson.

Weighing the world

Although he's perhaps best known for his discovery of hydrogen, 18th-century physicist Henry Cavendish's most ingenious experiment accurately estimated the weight of our entire planet. Using a special piece of equipment known as a torsion balance (two rods with one smaller and one larger pair of lead balls attached to the end), Cavendish measured the minuscule force of gravitational attraction between the masses. Then, by measuring the weight of one of the small balls, he measured the gravitational force between it and Earth, giving him an easy formula for calculating our planet's density and — therefore, its weight — that remains accurate to this day.

Conservation of mass

Much like energy, matter in our universe is finite and cannot be created or destroyed, only rearranged. In 1789, to arrive at this startling conclusion, French chemist Antoine Lavoisier placed a burning candle inside a sealed glass jar. After the candle had burned and melted into a puddle of wax, Lavoisier weighed the jar and its contents, finding that it had not changed

Leaning Tower of Pisa experiment

Greek philosopher Aristotle believed that objects fall at different rates because the force acting upon them was stronger for heavier objects — a claim that went unchallenged for more than a millennium.

Then came the Italian polymath Galileo Galilei, who corrected Aristotle's false claim by showing that two objects with different masses fall at exactly the same rate. Some claim Galileo's famous experiment was conducted by dropping two spheres from the Leaning Tower of Pisa, but others say this part of the story is apocryphal. Nonetheless, the experiment was perhaps most famously demonstrated by Apollo 15 astronaut David Scott, who, while dropping a feather and a hammer on the moon, showed that without air, the two objects fell at the same speed.

Detection of gravitational waves

If gravity warps space-time as Einstein predicted, then the collision of two extremely dense objects, such as neutron stars or black holes, should also create detectable shock waves in space that could reveal physics unseen by light. The problem is that these gravitational waves are tiny, often the size of a few thousandths of a proton or neutron, so detecting them requires an extremely sensitive experiment.

Enter LIGO, the Laser Interferometer Gravitational-Wave Observatory. The L-shaped detector has two 2.5-mile-long (4 km) arms containing two identical laser beams. When a gravitational wave laps at our cosmic shores, the laser in one arm is compressed and the other expands, alerting scientists to the wave's presence. In 2015, LIGO achieved its task, making the first-ever direct detection of gravitational waves and opening up an entirely new window to the cosmos.

Destruction of heliocentrism

The idea that Earth orbits the sun goes back to the fifth century B.C. to Greek philosophers Hicetas and Philolaus. Nonetheless, Claudius Ptolemy's belief that Earth was the center of the universe later took root and dominated scientific thought for more than a millennium.

Then came Nicolaus Copernicus, who proposed that Earth did, in fact, revolve around the sun and not the other way around. Concrete evidence for this was later offered by Galileo, who in 1610 peered through his telescope to observe the planet Venus moving through distinct phases — proof that it, too, orbited the sun. Galileo's discovery did not win him any friends with the Catholic Church, which tried him for heresy for his unorthodox proposal.

Foucault's pendulum

First used by French physicist Jean Bernard Léon Foucault in 1851, the famous pendulum consisted of a brass bob containing sand and suspended by a cable from the ceiling. As it swung back and forth, the angle of the line traced out by the sand changed subtly over time — clear evidence that some unknown rotation was causing it to shift. This rotation was the spinning of Earth on its axis.

Discovery of the electron

In the 19th century, physicists found that by creating a vacuum inside a glass tube and sending electricity through it, they could make the tube give off a fluorescent glow. But exactly what caused this effect, called a cathode ray, was unclear.

Then, in 1897, physicist J.J. Thomson discovered that by applying a magnetic field to the rays inside the tube, he could control the direction in which they traveled. This revelation showed Thomson that the charge within the tube came from tiny particles 1,000 times smaller than hydrogen atoms. The tiny electron had finally been found.

Deflection of an asteroid

In 2022, NASA scientists hit an astronomical "bull's-eye" by intentionally steering the 1,210-pound (550 kilograms), $314 million Double Asteroid Redirection Test (DART) spacecraft into the asteroid Dimorphos just 56 feet (17 meters) from its center. The test was designed to see if a small spacecraft propelled along a planned trajectory could, if given enough lead time, redirect an asteroid from a potentially catastrophic impact with Earth.

DART was a smashing success. The probe's original goal was to change the orbit of Dimorphos around its larger partner — the 2,560-foot-wide (780 m) asteroid Didymos — by at least 73 seconds, but the spacecraft actually altered Dimorphos' orbit by a stunning 32 minutes. NASA hailed the collision as a watershed moment for planetary defense, marking the first time that humans proved capable of diverting Armageddon, and without any assistance from Bruce Willis.

Faraday induction

In 1831, Michael Faraday, the self-taught son of a blacksmith born in rural south England, proposed the law of electromagnetic induction. The law was the result of three experiments by Faraday, the most notable of which involved the movement of a magnet inside a coil made by wrapping a wire around a paper cylinder. As the magnet moved inside the cylinder, it induced an electric current through the coil — proving that electric and magnetic fields were inextricably linked and paving the way for electric generators and devices.

Measurement of the speed of light

Light is the fastest thing in our universe, which makes measuring its speed a unique challenge. In 1676, Danish astronomer Ole Roemer chanced upon the first estimate for light's propagation while studying Io, Jupiter's innermost moon. By timing the eclipses of Io by Jupiter, Roemer was hoping to find the moon's orbital period.

What he noticed instead was that, as Earth's orbit moved closer to Jupiter, the time intervals between successive eclipses became shorter. Roemer's crucial insight was that this was due to a finite speed of light, which he roughly calculated based on Earth's orbit. Other methods later refined the measurement of light's speed, eventually arriving at its current value of 2.98 × 10^8 meters per second (about 186,282 miles per second).

Disproof of the "luminiferous ether"

Most waves, such as sound waves and water waves, require a medium to travel through. In the 19th century, physicists thought the same rule applied to light, too, with electromagnetic waves traveling through a ubiquitous medium dubbed the "luminiferous ether."

Albert Michelson and Edward W. Morley set out to prove this conjecture with a remarkably ingenious hypothesis: As the sun moves through the ether, it should displace some of the strange substance, meaning light should travel detectably faster when it moves with the ether wind than against it. They set up an interferometer experiment that used mirrors to split light beams along two opposing directions before bouncing them back with distant mirrors. If the light beams returned at different times, then the ether was real.

But the light beams inside their interferometer did not vary. Michelson and Morley concluded that their experiment had failed and moved on to other projects. But the result — which had conclusively disproved the ether theory — was later used by Einstein in his theory of special relativity to correctly state that light's speed through a fixed medium does not change, even if its source is moving.

Discovery of radioactivity

In 1897, while working in a converted shed with her husband Pierre, Marie Curie began to investigate the source of a strange new type of radiation emitted from the elements thorium and uranium. Marie Curie discovered that the radiation these elements emitted did not depend on any other factors, such as their temperature or molecular structure, but changed purely based on their quantities. While grinding up an even more radioactive substance known as pitchblende, she also discovered that it consisted of two elements that she dubbed radium and polonium.

Curie's work revealed the nature of radioactivity, a truly random property of atoms that comes from their internal structure. Curie won the Nobel Prize (twice) for her discoveries — making her the first woman to do so — and later trained doctors to use X-rays to image broken bones and bullet wounds. She died of aplastic pernicious anemia, a disease caused by radiation exposure, in 1934.

Expansion of the universe

While using the 100-inch Hooker telescope in California to study the light glimmering from distant galaxies in 1929, Edwin Hubble made a surprising observation: The light from the distant galaxies appeared to be shifted toward the red end of the spectrum — an indication that they were receding from Earth and each other. The farther away a galaxy was, the faster it was moving away.

Hubble's observation became a crucial piece of evidence for the Big Bang theory of our universe. Yet precise measurements for galaxies' recession, known as the Hubble constant, still confound scientists to this day.

Put simply, the universe is indeed expanding, but depending on where cosmologists look, it's doing so at different rates. In the past, the two best experiments to measure the expansion rate were the European Space Agency's Planck satellite and the Hubble Space Telescope. The two observatories, each of which used a different method to measure the expansion rate, arrived at different results. These conflicting measurements have led to what some call a "cosmology crisis" that could reveal new physics or even replace the standard model of cosmology.

Ignition of nuclear fusion

In 2022, scientists at the National Ignition Facility (NIF) at Lawrence Livermore National Laboratory in California used the world's most powerful laser to achieve something physicists have been dreaming about for nearly a century: the ignition of a pellet of fuel by nuclear fusion.

The demonstration marked the first time that the energy going out of the plasma in the nuclear reactor's fiery core exceeded the energy beamed in by the laser, and has been a rallying call for fusion scientists that the distant goal of near-limitless and clean power is, in fact, achievable.

However, scientists have cautioned that the energy from the plasma exceeds only that from the lasers, and not from the energy from the whole reactor. Additionally, the laser-confinement method used by the NIF reactor, built to test thermonuclear explosions for bomb development, will be difficult to scale up.

Measurement of Earth's circumference

By roughly 500 B.C., most ancient Greeks believed the world was round — citing evidence provided by Aristotle and guided by a suggestion from Pythagoras, who believed a sphere was the most aesthetically pleasing shape for our planet.

Then, around 245 B.C., Eratosthenes of Cyrene thought of a way to make the measurement directly. Eratosthenes hired a team of bematists (professional surveyors who measured distances by walking in equal-length steps called stadia) to walk from Syene to Alexandria. They found that the distance between the two cities was roughly 5,000 stadia.

Eratosthenes then visited a well in Syene that had been reported to have an interesting property: At noon on the summer solstice each year, the sun illuminated the well's bottom without casting any shadows. Eratosthenes went to Alexandria during the solstice, stuck a pole in the ground and measured the shadow from it to be about one-fiftieth of a complete circle. Pairing this with his measurement of the distance between the two cities, he determined that Earth's circumference was about 250,000 stadia, or 24,497 miles (39,424 km). Earth is now known to measure 24,901 miles (40,074 km) around the equator, making the ancient Greeks' measurements remarkably accurate.

Discovery of black holes

The acceptance of Einstein's theory of general relativity led to some startling predictions about our universe and the nature of reality. In 1915, Karl Schwarzschild's solutions to Einstein's field equations predicted that it was possible for mass to be compressed into such a small radius that it would collapse into a gravitational singularity from which not even light could escape — a black hole.

Schwarzschild's solution remained speculation until 1971, when Paul Murdin and Louise Webster used NASA's Uhuru X-ray Explorer Satellite to identify a bright X-ray source in the constellation Cygnus that they correctly contended was a black hole.

More conclusive evidence came in 2015, when the LIGO experiment detected gravitational waves from two of the colliding cosmic monsters. Then, in 2019, the Event Horizon Telescope captured the first image of the accretion disk of superheated matter surrounding the supermassive black hole at the center of the galaxy M87.

Discovery of X-rays

While testing whether the radiation produced by cathode rays could escape through glass in 1895, German physicist Wilhelm Conrad Röntgen saw that the radiation could not only do so, but it could also zip through very thick objects, leaving a shadow on a lead screen placed behind them. He quickly realized the medical potential of these rays — later known as X-rays — for imaging skeletons and organs. His observations gave birth to the field of radiology, enabling doctors to safely and noninvasively scan for tumors, broken bones and organ failure.

The Bell test

In 1964, physicist John Stewart Bell proposed a test to prove that quantum entanglement — the weird instantaneous connection between two far-apart particles that Einstein objected to as "spooky action at a distance" — was required by quantum theory.

The test has taken many experimental forms since Bell first proposed it, but the findings remain the same: Despite what our intuition tells us, what happens in one part of the universe can instantaneously affect what happens in another, provided the objects in each region are entangled.

Detection of the quark

In 1968, experiments at the Stanford Linear Accelerator Center found that electrons and their lepton cousins, muons, were scattering from protons in a distinct way that could only be explained by the protons being composed of smaller components. These findings matched predictions by physicist Murray Gell-Mann, who dubbed them "quarks" after a line in James Joyce's "Finnegans Wake."

Archimedes' naked leap from his bathtub

First recorded in the first century B.C. by Roman architect Vitruvius, Archimedes' discovery of buoyancy is one of the most famous stories in science. The prompting for Archimedes' finding came from King Hieron of Syracuse, who suspected that a pure-gold crown a blacksmith made for him actually contained silver. To get an answer, Hieron enlisted Archimedes' help.

The problem stumped Archimedes, but not long after, as the story goes, he filled up a bathtub with water and noticed that the water spilled out as he got in. This caused him to realize that the water displaced by his body was equal to his weight — and because gold weighed more than silver, he had found a method for judging the authenticity of the crown. "Eureka!" ("I've got it!") Archimedes is said to have cried, leaping from his bathtub to announce his discovery to the king.

Deepest and most detailed photo of the universe

In 2022, the James Webb Space Telescope unveiled the deepest and most detailed picture of the universe ever taken. Called "Webb's First Deep Field," the image captures light as it appeared when our universe was just a few hundred million years old, right when galaxies began to form and light from the first stars started flickering.

The image contains an overwhelmingly dense collection of galaxies, the light from which, on its way to us, was warped by the gravitational pull of a galaxy cluster. This process, known as gravitational lensing, brings the fainter light into focus. Despite the dizzying number of galaxies in view, the image represents just a tiny sliver of sky — the speck of sky blocked out by a grain of sand held on the tip of a finger at arm's length.

OSIRIS-REx asteroid-sampling mission

In 2023, NASA's OSIRIS-REx spacecraft came hurtling back through Earth's atmosphere after a years-long journey to Bennu, a "potentially hazardous asteroid" with a 1-in-2,700 chance of smashing cataclysmically into Earth — the highest odds of any identified space object.

The goal of the mission was to see whether the building blocks for life on Earth came from outer space. OSIRIS-REx circled the asteroid for 22 months to search for a landing spot, touching down to collect a 2-ounce (60 grams) sample from Bennu's surface that could contain the extraterrestrial precursors to life on our planet. Scientists have already found many surprising details that have the potential to rewrite the history of our solar system.

To this day, the seemingly simple equation, developed by an 18th-century Presbyterian minister and amateur mathematician, is used in modeling and forecasting to help us predict everything from future weather events, fluctuations in the stock market to the winners of sporting events.

The book "Everything is Predictable," by award-winning science writer Tom Chivers is a captivating tour of this curious theorem and how it impacts modern life, and has been shortlisted for the prestigious 2024 Royal Society Trivedi Science Book Prize. Below is a short excerpt from the book's introduction, which explores to what extent we can predict the future.

Related: 32 sci-fi technology predictions that came true

Can you predict the future? Yes, of course you can.

You can predict with near-certain accuracy that in the next few seconds, you'll take a breath, and let it out again. Your heart will beat, somewhere between one and three times a second. Tomorrow morning, the sun will come up, at a particular time which depends upon your latitude and the time of year but which nonetheless you can find out with great accuracy. All of these events you can predict with confidence.

You can also predict that the train will arrive at a certain time, or that your friend will arrive on time at the restaurant at which you've arranged to meet her. Though, depending on the rail company, or your friend, you might be less confident in that.

And you can predict that the world's population will continue to grow until around the middle of the century, and then start to fall again. You can predict that global average surface temperatures in the year 2030 will be higher than they were in the year 1930.

The future isn't opaque. You can see into it. Some parts are more predictable than others – the Newtonian dance of the planets we can predict out for thousands of years; the Lorenzian chaos of the weather, really only a few days. But you can peer through the murk, after a fashion.

That's not what people normally mean when they say, "I can predict the future." They are referring to something mystical, some psychic or magical vision. We probably can't do that. (You'll read about a scientist in this book who thinks we can, and you’ll also read about why he's almost certainly wrong.) But we don’t need to. All that we do, all the time, is predict the future. We couldn’t function if we couldn’t. We make very basic predictions, like "the air will continue to be breathable," implicitly, with every breath we take. We make more complex predictions, like "The corner shop will have Alpen [a breakfast cereal] when I get there," each time we make a decision. We're not basing them on mystical visions, but on information we have gathered in the past.

The thing with all these predictions is that they are uncertain. The universe may or may not be deterministic; perhaps if we had perfect, God-like knowledge of the position, movement and qualities of every particle in the universe, we could perfectly predict everything, the fall of every sparrow. But we don't. Instead, we have partial information. We can see bits of the universe, imperfectly, through our imperfect senses. We have best guesses for the way those bits move — we know the human-shaped bits tend to seek food and company; we know the rock-shaped bits tend to sit still. We can make messy, imperfect predictions with that information.

Life isn’t chess, a game of perfect information, one that can in theory be "solved." It's poker, a game where you're trying to make the best decisions using the limited information you have. This book is about the equation that lets you do that.

Excerpted from "Everything is predictable: How Bayesian Statistics Explain our World." Copyright © 2024 by Tim Chivers.

"It took a positive amount of time, but our experiment observing that photons can make atoms seem to spend a *negative* amount of time in the excited state is up!" wrote Aephraim Steinberg, a physicist at the University of Toronto, in a post on X (formerly Twitter) about the new study, which was uploaded to the preprint server arXiv.org on September 5 and has not yet been peer-reviewed.

The idea for this work emerged in 2017. At the time, Steinberg and a lab colleague, then doctoral student Josiah Sinclair, were interested in the interaction of light and matter, specifically a phenomenon called atomic excitation: when photons pass through a medium and get absorbed, electrons swirling around atoms in that medium jump to higher energy levels. When these excited electrons lapse to their original state, they release that absorbed energy as reemitted photons, introducing a time delay in the light's observed transit time through the medium.

Sinclair's team wanted to measure that time delay (which is sometimes technically called a "group delay") and learn whether it depends on the fate of that photon: Was it scattered and absorbed inside the atomic cloud, or was it transmitted with no interaction whatsoever? "At the time, we weren't sure what the answer was, and we felt like such a basic question about something so fundamental should be easy to answer," Sinclair says. "But the more people we talked to, the more we realized that while everyone had their own intuition or guess, there was no expert consensus on what the right answer would be." Because the nature of these delays can be so strange and counterintuitive, some researchers had written the phenomenon off as effectively meaningless for describing any physical property associated with light.

After three years of planning, his team developed an apparatus to test this question in the lab. Their experiments involved shooting photons through a cloud of ultracold rubidium atoms and measuring the resulting degree of atomic excitation. Two surprises emerged from the experiment: Sometimes photons would pass through unscathed, yet the rubidium atoms would still become excited — and for just as long as if they had absorbed those photons. Stranger still, when photons were absorbed, they would seem to be reemitted almost instantly, well before the rubidium atoms returned to their ground state — as if the photons, on average, were leaving the atoms quicker than expected.

The team then collaborated with Howard Wiseman, a theoretical and quantum physicist at Griffith University in Australia, to devise an explanation. The theoretical framework that emerged showed that the time these transmitted photons spent as an atomic excitation matched perfectly with the expected group delay acquired by the light — even for cases where it seemed as though the photons were reemitted before the atomic excitation had ebbed.

Related: Time might be a mirage created by quantum physics, study suggests

To understand the nonsensical finding, you can think of photons as the fuzzy quantum objects they are, in which any given photon's absorption and reemission through an atomic excitation is not guaranteed to occur over a certain fixed amount of time; rather, it takes place across a smeared-out, probabilistic range of temporal values. As demonstrated by the team's experiments, these values can encompass instances when an individual photon's transit time is instantaneous — or, bizarrely, when it concludes before the atomic excitation has ceased, which gives a negative value.

"I can promise you that we were completely surprised by this prediction," Sinclair says, referring to the matchup between the group delay and the time that the transmitted photons spent as atomic excitations. "And as soon as we were confident we hadn't made a mistake, Steinberg and the rest of the team — I had moved on to do a postdoc at [the Massachusetts Institute of Technology] by this point — began planning to do a follow-up experiment to test this crazy prediction of negative dwell time and see if the theory would hold up."

That follow-up experiment, the one led by Angulo that Steinberg touted on X, can be understood by considering the two ways a photon can be transmitted. In one, the photon wears blinders of sorts and ignores the atom entirely, leaving without even a nod. In the other, it interacts with the atom, boosting it to a higher energy level, before getting reemitted.

"When you see a transmitted photon, you can't know which of these occurred," Steinberg says, adding that because photons are quantum particles in the quantum realm, the two outcomes can be in superposition—both things can happen at the same time. "The measuring device ends up in a superposition of measuring zero and measuring some small positive value." But correspondingly, Steinberg notes, that also means that sometimes "the measuring device ends up in a state that looks not like 'zero' plus 'something positive' but like 'zero' minus 'something positive,' resulting in what looks like the wrong sign, a negative value, for this excitation time."

The measurement results in Angulo and her colleagues' experiment suggest that the photons moved through the medium faster when they excited the atoms than when the atoms remained in their ground state. (The photons aren't communicating any information, so the outcome does not contradict the "nothing can travel faster than light" speed limit set by Einstein's special theory of relativity.)

"A negative time delay may seem paradoxical, but what it means is that if you built a 'quantum' clock to measure how much time atoms are spending in the excited state, the clock hand would, under certain circumstances, move backward rather than forward," Sinclair says. In other words, the time in which the photons were absorbed by atoms is negative.

Even though the phenomenon is astonishing, it has no impact on our understanding of time itself — but it does illustrate once again that the quantum world still has surprises in store.

"[Angulo] and the rest of the team have accomplished something really impressive and produced a beautiful set of measurements. Their results raise interesting questions about the history of photons traveling through absorptive media and necessitate a reinterpretation of the physical meaning of the group delay in optics," Sinclair says.

A version of this article originally appeared in Spektrum der Wissenschaft and was reproduced with permission.

This article was first published at Scientific American. © ScientificAmerican.com. All rights reserved. Follow on TikTok and Instagram, X and Facebook.

The observation, made at the Large Hadron Collider (LHC) at CERN, near Geneva, revealed a top quark — the heaviest fundamental particle — quantumly linked to its antimatter counterpart in the highest-energy detection of entanglement ever made. The researchers published their findings Sept. 18 in the journal Nature.

The ATLAS experiment (A Toroidal LHC Apparatus) is the largest detector at the LHC, and picks out the tiny subatomic particles created after beams of particles crash into each other at near light speeds.

"While particle physics is deeply rooted in quantum mechanics, the observation of quantum entanglement in a new particle system and at much higher energy than previously possible is remarkable," Andreas Hoecker, a spokesperson for the ATLAS experiment, said in an email statement. "It paves the way for new investigations into this fascinating phenomenon, opening up a rich menu of exploration as our data samples continue to grow."

Particles that are entangled have their properties connected to each other, so that a change to one instantaneously causes a change to another, even if they are separated by vast distances. Albert Einstein famously dismissed the idea as "spooky action at a distance," but later experiments proved that the bizarre, locality-breaking effect is indeed real. 

Related: Heaviest antimatter particle ever discovered could hold secrets to our universe's origins

But there are many aspects of entanglement that remain unexplored, and the one between quarks is one of them. This is because the subatomic particles cannot exist on their own, instead fusing together into various particle "recipes" called hadrons. Mixtures of three quarks are called baryons — such as the proton and the neutron — and combinations of quarks and their antimatter opposites are called mesons. 

When individual quarks are ripped from hadrons, the energy used to extract them makes them immediately unstable, and they decay into branching jets of smaller particles in a process known as hadronization. 

This means that to observe the entanglement of a top quark and an antiquark, scientists at the LHC's ATLAS and Compact Muon Solenoid (CMS) detectors had to pick out the distinct particles that they decayed into from billions of others. In particular, they looked for particles whose decay products were emitted at a distinct angle that occurs only between entangled particles. 

By measuring these angles and correcting for experimental effects that may have changed them, the team observed entanglement between top particles with a large enough statistical significance to be considered real. Now that the entangled particles have been spotted, the scientists say they want to study them to further probe unknown physics. 

"With measurements of entanglement and other quantum concepts in a new particle system and at an energy range beyond what was previously accessible, we can test the Standard Model of particle physics in new ways and look for signs of new physics that may lie beyond it," Patricia McBride, a spokesperson for the CMS experiment, said in the statement.

While these would share some similarities with black holes, the hypothetical celestial bodies differ in crucial ways that could potentially resolve the infamous Hawking radiation paradox (named for the late physicist Stephen Hawking, who proposed the phenomenon). This paradox arises because the theoretical radiation emitted by a black hole's event horizon seemingly carries no information about the matter that formed the black hole, which contradicts a fundamental principle of quantum mechanics stating that information cannot be destroyed.

Moreover, unlike the conventional black holes, frozen stars are not expected to harbor a singularity — a point of infinite density at their centers — which resolves another contradiction between the classical picture of black holes and the general rule in physics that infinities cannot exist in nature. When infinities do appear in a theory, it usually signals the theory's limitations.

"Frozen stars are a type of black hole mimickers: ultracompact, astrophysical objects that are free of singularities, lack a horizon, but yet can mimic all of the observable properties of black holes," Ramy Brustein, a professor of physics at Ben-Gurion University in Israel, told Live Science in an email. "If they actually exist, they would indicate the need to modify in a significant and fundamental way Einstein's theory of general relativity."

Brustein is a co-author of a study describing the frozen star theory, published in July in the journal Physical Review D.

Resolving the paradox

The classical model of a black hole, first described by Karl Schwarzschild in 1916, portrays black holes as having two key features: a singularity where all the mass is concentrated and an event horizon, a boundary from which nothing, not even light, can escape.

However, this model encounters a serious problem when quantum mechanics is introduced. In the 1970s, Stephen Hawking famously discovered that quantum effects near the event horizon should lead to the creation of particles out of the vacuum of space, a process known as Hawking radiation. This radiation would cause the black hole to gradually lose mass and eventually evaporate completely.

Related: 'Twisty' new theory of gravity says information can escape black holes after all

The paradox arises because this radiation appears to carry no information about the matter that originally formed the black hole. If the black hole evaporates completely, this information seems to be lost forever, violating the principles of quantum mechanics, which dictate that information must be conserved. This contradiction is known as the information loss paradox, and it has been one of the most significant challenges in theoretical physics.

In their new study, Brustein and fellow co-authors A.J.M. Medved of Rhodes University and Tamar Simhon of Ben-Gurion University performed a detailed theoretical analysis of the frozen stars model, and found that it resolves the paradoxes of the traditional model because it lacks both a horizon and a singularity.

The authors found that if black holes are actually very compact objects composed of ultra rigid matter whose properties are inspired by string theory, the leading candidate for the theory of quantum gravity, they don't collapse into infinitely dense points, and have a size slightly larger than the conventional event horizon, preventing the latter from forming.

"We have shown how frozen stars behave as (nearly) perfect absorbers although lacking a horizon and act as a source of gravitational waves," said Brustein, noting that these objects can absorb almost everything that falls onto them, much like black holes. "Moreover, they source the same external geometry as that of a conventional model of black holes and reproduce their conventional thermodynamic properties."

Testing the frozen star hypothesis

While the frozen star model presents a potential solution to the paradoxes associated with traditional black holes, scientists still need to test it experimentally.

But unlike conventional black holes, frozen stars are expected to have an internal structure, albeit one with bizarre properties dictated by quantum gravity. This paves the way to observationally discriminate between the two. The evidence could be present in gravitational waves — ripples in the fabric of space-time — generated during black hole mergers.

"This is when the distinctions would be most pronounced," explained Brustein.

The team still needs to work out exactly what the internal structure of a frozen star would look like, and how it would differ from other extreme cosmic objects like neutron stars, but it's achievable, Brustein said. From there, they could analyze data from existing and future gravitational wave observatories, because the gravitational waves emitted during the mergers are extremely powerful and can carry information about these ultracompact objects' structure.

"A discovery of any of the predictions of the frozen star model will have a revolutionary impact," Brustein said.

Editor's note: This article was updated on Sep. 25 to list Ramy Brustein as a study co-author, rather than the lead author. All researchers contributed to the work equally.

Scientists created the new state of matter, called a photon gas, by firing a laser into a reflective container filled with dye, causing photons in the beam to cool and eventually condense. The researchers published their findings Sept. 6 in the journal Nature Physics. 

"To create these types of gasses, we need to concentrate lots of photons in a confined space and cool them simultaneously," study senior author Frank Vewinger, a physicist at the University of Bonn, said in a statement. 

Photons are bosons, particles that have integer spin, meaning that they can occupy the same state and space at a given time. When a gas of bosons is cooled to near-zero temperatures, all its particles lose their energy, entering into the same energy states. 

As we can only distinguish between the otherwise identical particles in a gas cloud by looking at their energy levels, this equalizing has a profound effect: The once disparate cloud of vibrating, jiggling, colliding particles that make up a warmer gas then become, from a quantum mechanical point of view, perfectly identical, creating an elusive form of matter called a Bose-Einstein condensate.

Related: Inside the 20-year quest to unravel the bizarre realm of 'quantum superchemistry'

Existing in a condensate form causes particles' positions within a gas to become highly uncertain. As a result, the places that each particle could possibly occupy grows to be larger in area than the spaces between the particles themselves. Instead of discrete objects, then, the overlapping photons in a photon gas act as if they are just one giant particle.

Physicists have created photon gasses in two dimensions before. But creating them in just one is way trickier.

"Things are a little different when we create a one-dimensional gas instead of a two-dimensional one," Vewinger said. "So-called thermal fluctuations take place in photon gasses but they are so small in two dimensions that they have no real impact. However, in one dimension these fluctuations can — figuratively speaking — make big waves."

To create a one-dimensional photon gas, the researchers filled a miniscule, reflective container with a dye solution before firing a laser into it. The photons of the laser light bounced back and forth inside the container until they collided with the dye molecules, which robbed them of their energy and caused them to cluster together. 

By applying a transparent polymer to the container’s reflective walls, the researchers were able to tweak the way they reflected the light so that it effectively condensed in one dimension — or a line.

"These polymers act like a type of gutter, but in this case for light," lead author Kirankumar Karkihalli Umesh, a doctoral student at the University of Bonn, said in the statement. "The narrower this gutter is, the more one-dimensionally the gas behaves."

By studying their newly-created 1D photon gas, the researchers confirmed that it behaves quite differently from its 2D form. Unlike in 2D photon gasses, the thermal fluctuations of their 1D cousins prevent them from completely condensing in certain regions. This creates a partial phase transition between laser light and its condensate form that is "smeared out" across the gas, like icy water that has not completely frozen, according to the researchers.

Investigating how the photon gas differs across dimensions could help the researchers to discover as-yet-undiscovered quantum optical effects, the researchers said.

With this in mind, a recent study suggests that dark matter could be composed of black holes formed during a transition from the universe's last contraction to the current expansion phase, which occurred before the Big Bang. If this hypothesis holds, the gravitational waves generated during the black hole formation process might be detectable by future gravitational wave observatories, providing a way to confirm this dark matter generation scenario.

Observations of stellar movements in galaxies and the cosmic microwave background — an afterglow of the Big Bang — indicate that about 80% of all matter in the universe is dark matter, a substance that doesn't reflect, absorb or emit light. Despite its abundance, scientists have not yet identified what dark matter is made of.

In the new study, researchers explored a scenario where dark matter consists of primordial black holes formed from density fluctuations that occurred during the universe's last contraction phase, not long before the period of expansion that we observe now. They published their findings in June in the Journal of Cosmology and Astroparticle Physics.

The bouncing cosmos

The traditional cosmological view of the universe suggests that it started from a singularity, followed by a short period of extremely rapid expansion, called inflation. However, the authors behind the new study analyzed a more exotic theory, known as non-singular matter bouncing cosmology, which posits that the universe first underwent a contraction phase. This phase ended with a rebound due to the increasing density of matter, leading to the Big Bang and the accelerated expansion we observe today.

Related: The universe could stop expanding 'remarkably soon', study suggests

In this bouncing cosmology, the universe contracted to a size about 50 orders of magnitude smaller than it is today. After the rebound, photons and other particles were born, marking the Big Bang. Near the rebound, the matter density was so high that small black holes formed from quantum fluctuations in the matter’s density, making them viable candidates for dark matter.

"Small primordial black holes can be produced during the very early stages of the universe, and if they are not too small, their decay due to Hawking radiation [a hypothetical phenomenon of black holes emitting particles due to quantum effects] will not be efficient enough to get rid of them, so they would still be around now," Patrick Peter, director of research at the French National Centre for Scientific Research (CNRS), who was not involved in the study, told Live Science in an email. "Weighing more or less the mass of an asteroid, they could contribute to dark matter, or even solve this issue altogether."

The scientists' calculations show that this universe mode's properties, such as the curvature of space and the microwave background, match current observations, supporting their hypothesis.

To further test their predictions, the researchers hope to make use of next-generation gravitational wave observatories.The scientists calculated the properties of the gravitational waves produced during black hole formation in their model and found that they could be detected by upcoming gravitational observatories like the Laser Interferometer Space Antenna (LISA) and the Einstein Telescope. These detections could confirm whether primordial black holes are indeed dark matter; however, it could take more than a decade before either facility sees first light.

"This work is important in the sense that it provides a natural way of forming small yet still present black holes forming dark matter in a framework which is not the usual one based on inflation," Peter said. "Other works currently investigate the behavior of such tiny black holes around stars, potentially leading to a way of detecting them in the future."

The new device, a newer version of a transmission electron microscope, captures images of electrons in flight by hitting them with one- quintillionth-of-a-second electron pulses.

This is quite a feat: Electrons travel at roughly 1367 miles per second (2,200 kilometers per second), making them capable of circumnavigating the Earth in only 18.4 seconds.

By using the microscope on the tiny particles, the researchers hope to make some new discoveries on how they take flight. The researchers published their findings Aug. 21 in the journal Science Advances.

"This transmission electron microscope is like a very powerful camera in the latest version of smart phones; it allows us to take pictures of things we were not able to see before – like electrons," lead-author Mohammed Hassan, an associate professor of physics and optical sciences at the University of Arizona, said in a statement. "With this microscope, we hope the scientific community can understand the quantum physics behind how an electron behaves and how an electron moves."

How electrons arrange and rearrange themselves inside atoms and molecules is an essential question in both physics and chemistry, but the zippy nature of the tiny particles makes them incredibly difficult to study.

Related: Razor-thin crystalline film 'built atom-by-atom' gets electrons moving 7 times faster than in semiconductors

To create an exposure time capable of capturing electron movements, physicists developed methods to generate tiny attosecond (or 1X10^-18 seconds) pulses in the early 2000s — an advance which earned the scientists who made it the 2023 Nobel Prize in physics.

By decreasing the exposure time of microscopes to the scale of a few attoseconds (an attosecond being to a second what a second is to the age of the universe), physicists have untangled how electrons carry charge, how they behave inside semiconductors and liquid water, and how chemical bonds between atoms rip apart.

But even the few attosecond scale is too big to capture the individual motions of electrons. To accomplish this, the physicists behind the new study tweaked an electron gun until it produced a pulse of just one attosecond.

These pulses hit the "sample" being studied, and as the electrons pass through it, they slow down and change the shape of the electron beam wavefront. The slowed beam is then magnified by a lens and then hits a fluorescent material that glows when the beam lands on it.

By pairing the electron pulse with two carefully synchronized pulses of light (to excite electrons in the material into motion and assist in the creation of the electron pulse respectively) they were able to probe the ultrafast movements of electrons inside atoms.

"We are able to attain attosecond temporal resolution with our electron transmission microscope – and we coined it 'attomicroscopy,'" Hassan said. "For the first time, we can see pieces of the electron in motion."

The antimatter heavyweight, called antihyperhydrogen-4, is made up of an antiproton, two antineutrons and one antihyperon (a baryon that contains a strange quark). Physicists found traces of this antimatter among particle tracks from 6 billion collisions at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory in New York.

By studying the strange particle, physicists hope to discover some key differences between matter and antimatter, which may help explain why our universe is now filled with matter given that antimatter was created in equal amounts at the beginning of time. The researchers published their findings Aug. 21 in the journal Nature.

"Our physics knowledge about matter and antimatter is that, except for having opposite electric charges, antimatter has the same properties as matter — same mass, same lifetime before decaying, and same interactions," study co-author Junlin Wu, a graduate student at the Joint Department for Nuclear Physics, Lanzhou University and Institute of Modern Physics, China said in a statement. "Why our universe is dominated by matter is still a question, and we don't know the full answer."

According to the standard model of cosmology, after the Big Bang the young cosmos was a roiling plasma broth of matter and antimatter particles that popped into existence and annihilated each other upon contact.

Related: 'Ghostly' neutrinos spotted inside the world's largest particle accelerator for the first time

Theory predicts that the matter and antimatter inside this plasma soup should have annihilated each other entirely. But scientists believe that some unknown imbalance enabled more matter than antimatter to be produced, saving the universe from self-destruction.

To investigate what could have caused this imbalance, the researchers behind the new study produced antimatter particles from a mini-Big Bang simulator. The RHIC collider hurls billions of heavy ions (atomic nuclei stripped of their electrons) at each other, creating a plasma soup from which the primordial elements of our cosmos briefly emerge, combine and then decay.

To fish out new particles from the plasma sea, the physicists searched for the telltale tracks made as the ions decay, or transform into other particles. By retracing the trajectories of these particles from billions of collision events, the researchers found roughly 16 antihyperhydrogen-4 nuclei.

Both hyperhydrogen-4 and its antimatter counterpart antihyperhydrogen-4 seem to wink out of existence very quickly, the researchers found. But the physicists didn't find a significant difference between their lifetimes — indicating that our best models describing the two types of particles are correct.

"If we were to see a violation of [this particular] symmetry, basically we'd have to throw a lot of what we know about physics out the window," study co-author Emilie Duckworth, a doctoral student at Kent State University, said in the statement.

The scientists' next step will be to compare the masses of the antiparticles and their particle opposites, which they hope could reveal some clues as to how our matter-heavy universe came to be.