Scientists melted diamonds with a powerful laser to take some of the most precise measurements of the mineral's elusive melting point — and found that previous experiments were off by more than 1,300 degrees Fahrenheit (700 degrees Celsius).

It's odd to think of diamond, the hardest natural material on Earth, melting — but melt it does when blasted with extremely powerful lasers under the right conditions. Understanding how diamond responds to shock waves from lasers is an important part of developing nuclear fusion, the process that powers stars. Nuclear fusion is also a potential energy source for the future, so researchers have put a lot of effort into developing models that describe and predict how diamond behaves.

However, diamond is weird. Although the experimental data and theoretical models match up pretty well most of the time, there have been some strange discrepancies scientists haven't been able to explain. The biggest one is the 2,240 F (1,244 C) ‪—‬ roughly 20% ‪—‬ difference between previous experimental data and model-predicted melting temperatures of diamond. There's also been some debate about whether diamond reorganizes its atoms into a different kind of solid carbon before turning into a liquid at the end of the melting process.

Researchers have struggled to explain these discrepancies because the conditions diamond melts at are so extreme that it's extraordinarily difficult to measure it in labs on Earth. However, new experiments may finally offer the solution that scientists have pursued for two decades.

In a study published Aug. 13 in the journal Nature Physics, scientists zapped tiny plates of synthetic diamond with an ultraviolet laser, creating shock waves that were so powerful that as they passed through the samples, the diamond changed from transparent to mirror-like. The strong increase in reflectivity is one indication the diamond melted. By combining this change with measurements of how brightly the diamonds glowed while being zapped, the researchers mapped the melting temperature with great precision.

"We were able to take tiny diamond samples and shock compress them to temperatures hotter than the surface of the sun and to pressures higher than the center of Neptune and Uranus — and still measure atomic structure, temperature, density and optical reflectivity," study co-author Marius Millot, a research scientist at Lawrence Livermore National Laboratory in California, said in a statement.

The team found that the diamond sample's melting temperature was more than 1,300 F lower than previously thought — putting the melting point in line with theoretical predictions and finally explaining the long-held discrepancy.

The team also measured the samples' atomic structure with X-ray diffraction and saw that the diamond didn't transition to a different kind of solid carbon before melting, possibly because the energy required to rearrange the atoms was too large, the researchers wrote.

However, they also hypothesized that multiple shocks could be powerful enough for this transition to occur and that the way the shocks are applied to the diamond might affect how it changes phase. Understanding this is important for nuclear fusion research, as certain types of experiments involve lasers melting and crushing a diamond capsule to put the capsule’s contents, solid deuterium and tritium, under more than 30 petapascals of pressure and temperatures higher than 180 million F (100 million C), the requisite conditions for a fusion chain reaction to occur.

The researchers found that between about 660 and 1,060 gigapascals of pressure and at around 12,140 F (6,727 C), diamond exists as solid chunks floating in liquid carbon. As the pressure increases, more diamond transitions into liquid carbon, which is thought to be a very strange material. Unlike most forms carbon takes on Earth ‪—‬ like coal, graphite and diamond ‪—‬ liquid carbon is metallic, so it conducts electricity. It's also denser than diamond. So hypothetically, if you somehow were to put liquid carbon in a cup without instantly vaporizing it, a chunk of solid diamond could happily bob around in it like an ice cube in a glass of water.

Knowing how diamond behaves under such extreme conditions is also important for understanding the ice giant planets Uranus and Neptune. Based on measurements from the Voyager 2 spacecraft in the late 1980s and lab experiments on Earth, scientists think it literally rains huge chunks of diamond inside these planets and that their mantles may have liquid carbon oceans with diamonds floating around like icebergs. The new research means scientists can make better predictions about the planets’ interiors and their carbon cycles.

See how much you know about gemstones with our gold and gems quiz!

Tristan Buckmaster, a mathematician at New York University, had just spent months working on what he believed could be a life-defining mathematical proof. Then, during a Sept. 6 meeting with OpenAI employees, he claims that he was issued a stark warning: "Why would you ruin your career?"

That exchange, which Buckmaster described in a detailed public statement this week, sits at the heart of a ballooning controversy around a famous set of mathematical equations called Navier-Stokes.

OpenAI says its artificial intelligence (AI) model has solved an outstanding problem tied to this 200-year-old set of fluid dynamics equations. The set of equations appears on the list of one of the seven Millennium Prize Problems posed by the Clay Mathematics Institute, and its solution comes with a $1 million reward. Buckmaster had been working on the same problem. And he has questions about how the company got there so fast.

The OpenAI breakthrough

The Navier-Stokes equations were formulated in the early 1800s by Claude-Louis Navier and George Gabriel Stokes. They're basically Newton's second law of motion for fluids, describing how any fluid moves: Push air with a fan blade, and the equations predict how that air will flow; or heat the atmosphere with sunlight, and they help forecast tomorrow's weather. They describe how planes fly and how blood moves through your arteries.

The problem is that nobody has proved whether the equations always produce finite answers. Could there be rare conditions that make the equations go haywire? This is called a "blowup," or singularity, which happens when a quantity that should represent something physical (like fluid speed or pressure) spirals toward impossible infinities at certain points in space and time.

Imagine the swirl of water circling a bathtub drain. The Navier-Stokes equations describe how it spins faster as it tightens toward the center. A blowup would mean the math predicts that spin is accelerating forever ‪—‬ an infinite speed at a single point. The bathtub can't do that, but if the equations can, that means the model we trusted for years is wrong and we wouldn't even know where it breaks.

Whether the Navier-Stokes equations can blow up is one of the most famous unsolved questions.

To find the answer, OpenAI used a technique called "forcing" ‪—‬ giving the simulated fluid a smooth, controlled nudge from the outside. Imagine flicking a spinning top with your finger to see if it would fall over ‪—‬ or, in the case of the Navier-Stokes equations, blow up.

OpenAI set roughly 10,000 AI agents to simultaneously work on the problem. The agents worked for about 88 hours straight, with 100 of them starting with the related Euler equations. This is a simpler cousin of Navier-Stokes that discards viscosity to describe fluid motion without internal friction.

After roughly 50 hours, OpenAI's agents found blowups in the Euler equations, OpenAI representatives wrote in a statement. This discovery convinced them that Navier-Stokes was within reach, and they turned their attention to the bigger problem.

OpenAI described the singularity as a vortex spiraling tighter and tighter, stretching and thinning like pulled taffy. The result was a fluid that, mathematically, spins itself into infinity.

OpenAI ran the proof through a program called Lean, software that checks every step of a mathematical argument. The agents "sent 2.7 million messages and used approximately 130 billion output tokens," OpenAI representatives wrote in the statement. At a Sept. 8 news conference, company representatives said a similar effort performed by a customer would have cost $15 million.

The controversy

The result has created a blowup of its own within mathematics, centered around claims that OpenAI's models may have been given a head start by using the work of Tristan Buckmaster and Levent Alpöge, a mathematician at rival AI company Anthropic.

The two mathematicians had been working on the same strategy (smooth forcing) applied to those same Euler equations. The approach itself was developed by Diego Córdoba, a mathematician at the Institute of Mathematical Sciences in Madrid, and Luis Martínez-Zoroa, another mathematician at CUNEF University in Madrid. Almost no one else in the field was using it.

Buckmaster said that on Aug. 15 that he and Alpöge achieved blowup results for the Euler equations with smooth forcing. On Sept. 3, Buckmaster wrote that he received word through Alpöge that OpenAI had caught wind of their progress and adopted the same method.

"When I heard 'forced,'" Buckmaster wrote in his public statement, "it was a bright red flag."

His concern was that the smooth-forcing approach wasn't obvious or widespread. "The ideas making this line of attack possible are due to Córdoba and Martínez-Zoroa," Buckmaster wrote, crediting the two mathematicians who developed the technique. "Almost nobody else I know of was working on it."

And yet, according to OpenAI, the company launched its Navier-Stokes effort on Sept. 1 ‪—‬ the same day it heard "rumors of other Millennium Prize resolutions." Buckmaster claimed, in his public statement, that those rumors were about his and Alpöge's work specifically.

Sam Altman, OpenAI's CEO, acknowledged that the company had learned of Buckmaster and Alpöge's work before making its announcement. "We were curious if ours could do it too," he wrote on X. He added that "the approaches appear to be different" — a claim Buckmaster disputes.

OpenAI's statement names both Buckmaster and Alpöge, credits their independent resolution of the forced Euler problem, and says the company offered to co-publish.

"I did not get an answer"

Buckmaster also revealed that he had been using OpenAI's Codex coding assistant throughout his research, putting drafts of the work into the tool. OpenAI trains its models on user interactions, and Buckmaster said he asked the company directly whether his Codex sessions had been accessed.

"I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts," he wrote. "I asked again, about training, and I did not get an answer."

OpenAI's enterprise agreements govern how customer data can be used. But it's unclear whether Buckmaster was using Codex under an enterprise agreement or as an individual consumer — a distinction that may determine whether his drafts were available for training.

In a statement on X, OpenAI representatives denied that company employees or agents saw the pair's work "by any means" until it was publicly released. However, "we cannot rule out that de-identified data derived from their usage of our products helped improve our models," they added.

Then, there is the question of authorship. Buckmaster alleges that Sébastien Bubeck, who leads OpenAI's math research, twice pushed for Alpöge to be cut from the paper that the two mathematicians were preparing. Buckmaster emphasized that Alpöge works at Anthropic, a rival AI company.

It was at that same Sept. 6 meeting that Buckmaster claimed that OpenAI presented him with two options, both of which required cutting Alpöge from authorship. He declined and said he told Bubeck that if OpenAI released its result as proposed, he would go public. Bubeck allegedly replied, "If you don't want me to be nice, then I don't have to be nice."

Bubeck has flatly denied the allegations, calling them "false and inflammatory" in a statement on X. "We did not use their prompt or proofs to prompt our models," Bubeck told Wired. Mark Chen, OpenAI's chief research officer, said at last night's news conference that he was "a little disappointed with the allegations."

"I have not seen OpenAI's proof," Buckmaster wrote. "I do not know what their model did, or how. I do not know whether our data was used. I am not accusing anyone of anything." He has called for an independent investigation into how OpenAI's work began.

In a closing line, he wrote, "I would much rather be talking about mathematics, Luis and Diego's ideas, and what this all means for the rest of us."

The community response

Córdoba, one of the original developers of the forcing technique, said he was stunned by how quickly the result had materialized. "We're a little bit in shock," he told Scientific American.

Other mathematicians have also responded to the news, with some expressing open dismay at how the results were released.

"We have now seen that even the rumor of someone working on a massive problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential," Terence Tao, a professor of mathematics at UCLA, wrote on Mastodon. "The incentives may now be pointing in the direction of no longer sharing any promising research directions with the broader community, which would reverse centuries of traditions of open science and do serious long-term damage to the future of the field."

OpenAI's proof still awaits formal peer review, and the Clay Mathematics Institute has not yet issued an official verdict confirming or denying OpenAI's proof. But the episode has already surfaced troubling questions for the mathematics community. For example, when a company trains its models on the interactions of millions of users, who really owns the answers that emerge? And what does AI's involvement mean for the future of the field?

Those questions, unlike the Navier-Stokes problem, may not have a clean proof.

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Over dinner at a gaming convention around 2010, board game designer James Ernest turned to his friend Eric Harshbarger and asked a question: Could you design a set of dice so that each player in a group — whether two people or any number — could grab one, roll and have a perfectly equal shot at going first? The rule is simple: Roll your dice, and whoever lands the highest number goes first. The hard part is making that outcome truly fair for every player, no matter how many are at the table.

There could be no ties and no rerolls.

Harshbarger, a mathematician at Auburn University in Alabama, didn't have an answer that night. But the question stuck. Over the next 15 years, he and a loose network of collaborators casually worked to crack what became known as the "go first dice" problem.

Now, they finally have the answer: a set of five 60-sided dice, collectively engraved with every number between 1 and 300, with no repeats. To mark the achievement, Harshbarger built five giant, wooden replicas of these hexecontahedrons (60-sided 3D shapes), each carved from a different type of wood. They are now on permanent display in Auburn's new mathematics building.

The problem with dice

To understand why it was so hard to crack the problem, it helps to understand the simple part.

"The easy thing is to avoid ties; you just put different numbers on all the dice," Harshbarger told Live Science. "The problem comes in how you distribute those different numbers across the dice so that the probability is equal not only for the whole set but for any subset."

That second condition is what makes the problem devilish. Ernest's request wasn't just that eight players could roll fairly; it was that any subset of players could grab any dice from the bag roll and still have equal odds. If five people are playing, each takes a die. Three people? Same thing. The numbers on each die had to be arranged so that the fairness held no matter how many people showed up to play.

Harshbarger looped in his childhood friend Robert Ford, a mathematician at Dalton State College. Within weeks, they had a three-player solution: numbers 1 through 18, spread across three standard six-sided dice in exactly the right arrangement. Four 12-sided dice, Ford later worked out entirely by hand, could accommodate four players fairly.

By 2012, Harshbarger was giving talks about the four-player set at math conferences, and The Guardian covered the story. His inbox erupted. He started selling handmade sets from home — buying blank, 12-sided dice; etching numbers onto each face with a laser cutter in his workshop; and then inking every number by hand. At his peak, he was dropping off 30 envelopes at the post office at a time, several times a week, shipping sets to customers around the world.

But as the team dug deeper into the math, they discovered that the dice were doing something even more remarkable than they'd realized: The configurations determined not only who went first but also the entire turn order, with every possible sequence of players equally likely to come up.

"If four people rolled, the chance that players finished in the order A, B, C, D was just as likely as C, B, D, A, or any of those combinations," Harshbarger said. "'Go first dice' is actually a bit of a misnomer, because they do much more than just determine who goes first; they actually determine the ordering of all the players."

This property, which the team calls permutation fairness, became the standard they chased for every set of dice from that point on.

More combinations than atoms in the universe

Four players was one thing. Five was another entirely.

Mathematically, the team knew a five-player same-shape set was feasible. But finding it meant searching an incomprehensibly large space of possible number arrangements.

"We're talking literally more than the number of atoms in the universe ‪—‬ like 10 to the 128th power combinations," Harshbarger said. "There's just no way, even if we had a billion billion years and all the computers, all the AI. We still couldn't do it today."

They couldn't brute-force their way to an answer. They needed mathematical shortcuts: symmetries and patterns to shrink the search space. But even then, years passed without a practical solution. Every path they found hit the same wall: dice too large to hold, too many sides to manufacture.

"My goal was a set for five players that can actually be manufactured, that you can hold in your hand, that board gamers could buy and roll," Harshbarger said. "Even for a problem that is silly and pointless as far as gameplay — just mathematically, can you buy these things and roll them, and they work? You can't do that with 180-sided dice."

Then, in mid-2023, Canadian software engineer Paul Meyer emailed Harshbarger out of the blue. He had been studying patterns in Harshbarger's four-player data and had written a program to exploit them. He hadn't expected it to work right away.

It did. Meyer found a configuration of five 60-sided dice that satisfied every condition.

"I double-checked his work and went, 'Oh my goodness; we've been searching for so long for this. This is amazing,'" Harshbarger said.

From workshop to gallery wall

The four-player set had long since been picked up by retailers — Maths Gear in the U.K. and Math Art Fun in the U.S. — so Harshbarger had stopped hand-making those years earlier. Now, the five-player version was real and small enough to manufacture.

But the story had one more turn. Auburn University was building a new home for its mathematics department and was looking for sculptural ideas to fill it. Harshbarger proposed building giant versions of the five new dice out of wood. The department agreed.

He spent months in his wood shop, constructing five oversize dice. Each is from a different type of wood: pine, poplar, oak, walnut or mahogany. The five sculptures now stand in Auburn's new math building, which opened this fall.

For Harshbarger, the whole point is making math impossible to walk past.

"When people see giant dice or little dice, they're fascinated just by the geometry," he said. "The hope is, they see these things and go, 'Oh, this is math too, and this is interesting.' Some of the most fun math problems are ones that are easily understood and not easily answered."

For the first time, physicists have measured the tiny quantum shift an object acquires by falling through Earth's gravity — an effect of Einstein's relativity that was predicted almost a century ago but never observed.

Researchers placed ultracold rubidium atoms into a superposition, a quantum state in which a single particle takes two paths at once. In this experiment, one path put the atom in free fall while the other kept it motionless. Recombining the atoms revealed an almost imperceptible difference between the two paths.

The measurement, published Sept. 2 in the journal Science Advances, shows that Einstein's equivalence principle — the idea at the heart of general relativity — still holds when it is pushed into the quantum world, creating a small but tantalizing link between relativity and quantum mechanics.

"The principle says that acceleration and gravity cannot be distinguished locally," Vlatko Vedral, a physicist at the University of Oxford and a co-author of the new study, told Live Science via email.

Einstein's happiest thought

The classic illustration of the equivalence principle is a thought experiment known as Einstein's elevator. A person sealed in a windowless elevator cannot tell whether the floor is pressing against their feet because the elevator is parked motionless on Earth or because it is being accelerated through empty space. Einstein called that realization the "happiest thought" of his life and built general relativity around it.

For heavy, everyday objects, the equivalence principle has been tested to extraordinary precision. Quantum objects are a different matter. They behave like waves, and each wave carries a quantity called phase — essentially, where its crests and troughs sit. Phase cannot be seen directly, but when two versions of the same particle are recombined, any mismatch between their phases shows up as an interference pattern. The two waves reinforce each other in some places and cancel each other out in others, thereby changing the odds of where the particle turns up.

Theory says that a wave in free fall should build up phase relative to an identical wave held still and that this phase should grow with the cube of the falling time. Therefore, doubling the fall time multiplies the effect eightfold. Charles Galton Darwin, a grandson of the famous naturalist, and Earle Kennard both documented this prediction in 1927 ‪—‬ but no one had measured it until now.

An atom that falls and stays still at once

Catching the effect required an instrument with one arm genuinely at rest with respect to Earth and the other in genuine free fall ‪—‬ something no previous experiment could supply. Matter-wave experiments going back to the neutron interferometry of the 1970s had measured gravity in other ways, but never with that pair of trajectories.

The team behind the new study, led by physicist Ron Folman at Ben-Gurion University of the Negev in Israel, chilled roughly 20,000 rubidium atoms into an exotic state of matter called a Bose-Einstein condensate, released them from their magnetic trap and ran the interferometer about 113 micrometers beneath an "atom chip" patterned with gold wires only 2 micrometers thick.

Radio and microwave pulses put each atom into a superposition of two magnetic states. A magnetic kick launched one of them upward, and a fraction of a millisecond later, a second pulse made that half insensitive to magnetic fields so that it rose and fell under gravity alone. The other half remained magnetically sensitive and felt a force tuned to cancel gravity exactly, leaving it suspended in place.

At the top of the arc, the two halves of a single atom stood about 7.5 micrometers apart ‪—‬ about seven times the width of the atomic wave itself — before the sequence was reversed to bring them back together. The team named the device the quantum Galileo interferometer, after the scientist who first argued that all objects fall at the same rate.

"Two different accelerations can be superposed, zero [acceleration] and the Earth's gravitational acceleration, and the resulting quantum interference measured," Vedral said.

A phase predicted almost 100 years ago

The researchers tracked the interference signal as they stretched the free-fall time to about 2.4 milliseconds. Across 633 runs over 5.3 hours, they recorded 13 complete oscillations, each one a full cycle of phase built up between the two halves of the atom. The growth followed the cube of the falling time, matching the theoretical model to within about 2.5%.

"The phase between the two elements of the superposition, which grows as the cube of the duration of the experiment and which was predicted a long time ago, in 1927, has now finally been observed for the first time," Vedral said.

The result matters because the same phase can be derived in two completely different ways: One treats gravity as a force acting on a quantum wave; the other moves into the falling frame, where gravity vanishes, and invokes the equivalence principle. Both give the same answer, and that agreement is what allows quantum mechanics and general relativity to coexist.

"They tell us that, at this level of accuracy, there is no conflict between quantum physics and gravity," Vedral said. "In other words, the equivalence principle is perfectly compliant with quantum mechanics."

The difficulty of bringing the two halves back together

The hardest part of the experiment was the recombination. Because the two halves of the atom end up moving at very different speeds, returning them to overlap in both position and motion is extremely demanding. Physicists Marlan Scully, Berthold-Georg Englert and Julian Schwinger named the problem the "Humpty-Dumpty effect." The magnetic fields also curve across the atom cloud, distorting the two halves in different ways.

The contrast of the interference fringes started at 80% for short runs and faded to 20% for the longest run, setting a practical ceiling on how long the experiment can run. The authors also cautioned that their measurement does not rule out every theory in which the equivalence principle breaks down, because some of those theories predict the same phase.

What comes next

The team now wants to test the equivalence principle under more general conditions, such as the "same experiment in a rotating frame," Vedral said. "Even more interestingly, performing an experiment in which two such systems are superposed and can gravitationally affect one another" would further test the results, he added.

That last idea points toward one of the field's central open questions. Scaling up the technique from atoms to far heavier objects, such as nanodiamonds, would let physicists ask whether gravity itself follows quantum rules and would open a route to testing the conjecture — championed by study co-author and Nobel laureate Roger Penrose — that gravity is what destroys quantum superpositions in the first place.

See how much you know about Albert Einstein with our Albert Einstein quiz!

Every second of every day, Earth is bombarded by particles from outer space. Some of these particles are obstructed by our planet's atmosphere but can spray down other particles, while others can zoom through the atmosphere and easily pass through anything, including us.

You won't feel these particles darting through you, but it raises a question: How many cosmic particles are actually passing through your body at any moment?

The most common particles that stream through us from outer space are ghostly specks known as neutrinos. "An estimated 100 trillion neutrinos pass through each of us every second," Michael Pravica, a professor of physics at the University of Nevada, Las Vegas, told Live Science.

Neutrinos barely interact with regular matter. Nearly all of them pass through us and the rest of the planet without leaving a trace. "The fact that most of these particles never interact with us demonstrates that there is an underlying reality to our existence, much of which we are not even aware of," Pravica said.

Neutrinos originate from nuclear activity. Nearly all of the neutrinos zipping through us come from the nuclear fusion reactions that power the sun, although some neutrinos originate much farther away, even other galaxies, Lu Lu, an assistant professor of physics at the University of Wisconsin-Madison, told Live Science.

Other extraterrestrial particles that continually strike Earth are cosmic rays — electrically charged, highly energetic particles that travel at nearly the speed of light from all directions, according to the University of Chicago. Although the sun's nuclear reactions produce very-low-energy cosmic rays, the vast majority of cosmic rays come from beyond the solar system. These may be created when faraway stars explode as supernovas, matter falls into supermassive black holes, or galaxies collide, per the University of Chicago.

Cosmic rays are mostly either protons, which are the nuclei of hydrogen atoms, or the atomic nuclei of heavier elements (which contain both protons and neutrons), such as helium or iron. Electrons and positrons (the antimatter counterparts of electrons) also make up a tiny fraction of cosmic rays.

When cosmic rays hit Earth, they are generally blocked by molecules of air high in our planet's atmosphere, Lu said. However, these collisions can generate showers of secondary particles that make it to the ground. These include muons, which are negatively charged subatomic particles that are much like electrons except more than 200 times more massive.

At sea level on Earth, about one muon passes through per 0.15 square inch (1 square centimeter) per minute, Lu said. "For a person, the number ranges from tens to hundreds per second," she noted. "Roughly one or two pass through a hand each second."

Because muons are electrically charged, they can interact with matter they encounter. "Their paths can be made visible in a cloud chamber," a box of vapor in which a trail of mist can be seen when a charged particle streaks through the vapor, Lu said.

In contrast, neutrinos are not electrically charged. They also have almost no mass. These two qualities make it very difficult to detect neutrinos, which is why they're often dubbed "ghost particles."

Detecting cosmic particles

Scientists estimate the number of neutrinos that pass through our bodies by recording "the tiny fraction that happen to collide with matter inside or close to a detector," Lu said. "Everything else follows by working backward from those few."

For instance, the IceCube Neutrino Observatory in Antarctica surrounds 0.24 cubic mile (1 cubic kilometer) of ice with thousands of light sensors. "When a neutrino interacts with an atomic nucleus in the ice, it produces fast-moving charged particles, and those particles emit a faint flash of blue Cherenkov light, which the sensors record," Lu said. "From the pattern and brightness of that light, we can reconstruct the neutrino's energy and direction."

To estimate how many neutrinos pass through Earth based on these recorded interactions, "we account for the size of the detector, how long it operated, its detection efficiency, and the probability that a neutrino of a given energy interacts at all," Lu said. "It is a bit like estimating the number of fish in a river from the few caught in a very coarse net. If you know the size of the net, how long it was in the water, and how easily fish slip through it, you can work backward to the whole river."

When it comes to the neutrinos that IceCube studies, although trillions pass through each of our bodies every second, nearly none of them interact with our atoms. "You would expect no more than roughly one interaction in your body, perhaps a few, over an entire lifetime," Lu said.

These rare interactions would have virtually no effect on us. Given how little energy such an interaction would deposit, such neutrinos "pose no health risk at all," Lu said.

In contrast, the showers of particles resulting from cosmic ray impacts can potentially affect human biology. "At ground level, muons dominate the penetrating charged particles reaching us from cosmic-ray showers," Lu said. "At higher altitudes, and especially during air travel, other secondary particles, particularly neutrons, contribute a significant share of the biologically relevant dose."

Still, any effects from these cosmic-ray showers are generally small. "For an average person, cosmic radiation contributes roughly 0.4 millisieverts per year, about the same as a few chest X-rays spread across the year, out of a total natural background of about 2.4 millisieverts from all sources," Lu said. "The dose varies with altitude, latitude and shielding. At typical ground level, muons and other cosmic-ray particles are not considered a significant health hazard. Life on Earth has been bathed in them from the beginning."

So, every second, there are about 100 trillion neutrinos and tens to hundreds of muons passing through your body per second, and maybe a tiny scattering of neutrons and other cosmic particles or debris from cosmic particles impacting the atmosphere.

These cosmic particles may lead to a variety of discoveries. For instance, scientists have used muon detectors to identify hidden passageways in pyramids. And "high-energy neutrinos allow us to study some of the most violent and otherwise hidden environments in the universe, such as the regions surrounding black holes, exploding stars and other powerful cosmic accelerators," Lu said.

"Because neutrinos interact so weakly, they can escape from dense regions that light may not be able to penetrate," she explained. "They therefore carry information directly from the places where some of nature's most energetic particles are produced."

All in all, "the particles streaming through us are a constant reminder that we are not separate from the universe," Lu said. "We are part of a cosmic story stretching back 13.8 billion years."

See how much you know about black holes with our black hole quiz!

There's a commonly cited idea that water in a drain swirls in opposite directions in the Northern and Southern hemispheres. But is there any truth to it? When you pull the plug from a bathtub, does the water circle one way in New York and the other way in Sydney?

Although the idea is based on a real scientific principle, you probably won't see it play out in a small drain in your house, experts told Live Science.

The Coriolis effect

The idea that water spins in opposite directions in the Northern and Southern hemispheres stems from a phenomenon known as the Coriolis effect. When something, including air or water, moves across Earth as it rotates on its axis, that substance appears to curve because the ground beneath it is rotating at different speeds in different places. Points close to the equator move faster than points near the poles because they have a bigger circle to travel in the same 24 hours.

Over the immense distances covered by weather systems and ocean currents, that small deflection can accumulate and become important. The key words here are "immense distances." The Coriolis effect is weak, so it needs enough time and space to produce a noticeable change. Storms and weather patterns can persist for days and stretch across hundreds of miles. But water in a sink, bathtub or toilet has only seconds to move before disappearing down the drain.

"You always need to think about the right timescales and length scales," Susanne Horn, a professor of numerical and mathematical fluid dynamics at Coventry University in the U.K., told Live Science.

At your bathroom's scale, seemingly trivial details take control. The water may already be rotating slightly because of how it entered the basin, how somebody moved in the bath or how the plug was removed. The sink and drain are unlikely to be perfectly symmetrical, which can also play a part, and the design of a toilet deliberately guides its water. All of these factors are more influential on your basin than the Coriolis effect is. (In other words, that episode of "The Simpsons", which features Bart investigating drainage direction in Australia versus the U.S., got it wrong.)

Consequently, the same sink can drain clockwise on one occasion and counterclockwise on another, depending on the variation of these variables on any given day; the direction depends principally on how the water was introduced and the geometry of the container and drain, according to the Library of Congress.

So, although the Coriolis effect behind the claim is real, the water in a bathroom drain is normally overwhelmed by much stronger influences.

How to see the Coriolis effect in action

To make Earth's rotation ‪—‬ and, thus, the Coriolis effect ‪—‬ matter in a drainage experiment, Horn said, "there are essentially two tricks: let it drain very slowly, or make it much bigger."

Fluid dynamicists describe this using the Rossby number, which compares a flow's inertia with the influence of the planet's rotation. A small Rossby number indicates the Coriolis effect is important; a large one means the flow is moving too quickly or across too short of a distance, for Earth's rotation to have much influence. A typical household drain falls firmly into the latter category. In Horn's words, it "doesn't feel rotation."

Still, there are ways to see the Coriolis effect in action. In a meticulously designed experiment researchers suppressed those larger disturbances to give the Coriolis effect enough time to emerge.

In the 1962 experiment, described in the journal Nature, an MIT researcher used a large, carefully prepared tank that removed residual movements in the water before it drained. The water eventually developed the counterclockwise rotation predicted for the Northern Hemisphere.

Three years later, in another study published in Nature, researchers at the University of Sydney published a Southern Hemisphere counterpart. After taking similarly stringent precautions against outside disturbances, they observed the predicted clockwise rotation. The two experiments demonstrated that Earth's rotation could select the direction of a draining vortex — but only under extremely well-controlled conditions. In other words, the Coriolis effect appears only once you've removed practically every other variable.

That is very different from saying every sink or toilet flows in the same direction according to which hemisphere they're in. In normal plumbing, the drain's shape, the water's starting motion and the way it is released are all far more influential.

"Just ask yourself whether what you're looking at happens slower than Earth's rotation and for long enough, only then does the Coriolis force really start to matter," Horn said.

In the early hours of July 16, 1945, in a remote part of the New Mexico desert, a group of scientists, engineers and military personnel attended an event that would define the course of history and change a war that had ravaged much of the world for years. Moments after a giant fireball rose high into the sky, a huge shock wave thundered toward the onlooking crowd. The Trinity nuclear test had been a success.

The story of the Manhattan Project is well known. But one area that may be overlooked is the human effort involved in bringing the mission to life. In her new book "Trinity: An Illustrated History of the World’s First Atomic Test" (The University of Chicago Press, 2026), author Emily Seyl, a science writer and editor at the Los Alamos National Laboratory's National Security Research Center, uses never-before-seen photography from the laboratory’s legacy collections to highlight the physical and mental effort that went into the project.

In this excerpt, Seyl examines one of the key elements of any scientific experiment — how to successfully measure the results. She looks at how experiments were decided upon and the ways in which success would be measured, beyond the visual spectacle of a successful detonation of "the Gadget."

T‌he most rudimentary measure of success would, of course, be the eye test: Did the Gadget produce a nuclear explosion? Beyond the answer to this simple question, however, the detonation was also a monumental and complicated science experiment — one that naturally gave rise to as many smaller experiments as could be squeezed, sometimes impractically, into the test plans.

Alongside a crowd of Trinity contributors, a robust collection of electronic and mechanical observers was stationed carefully throughout the desert to bear witness to the shot. Although deceptively rugged and nondescript, these devices were highly sophisticated, often employing first-of-their-kind technologies — invented and built by some of the world's preeminent researchers to study a first-of-its-kind event.

After two years of leapfrogging basic nuclear studies in their rush to produce a workable device, the pioneering scientists now "yielded to temptation and conceived experiment after experiment" in anticipation of the Trinity test — much to Kenneth Bainbridge's [director of the Manhattan Project's Trinity nuclear test] alarm. In December of 1944, with base camp still under construction at the test site, a selection committee, headed by Bainbridge, had been established to evaluate what was quickly becoming a deluge of ideas.

The committee implemented a detailed submission process, requiring scientists to scrupulously outline the personnel and material needs associated with carrying out each idea. Proposed subtests were triaged into three categories: essential experiments, which were fully greenlit no matter the required effort or resources; desirable experiments, which were approved only if they did not interfere with work on the Gadget itself; and unnecessary (i.e., nonessential) experiments, of which only the simplest were allowed.

Completing the Gadget remained the top priority. But while most of the lab continued to work feverishly on readying the test device, a significant battery of physicists, photographers, chemists, engineers, and other specialists began coming and going between Los Alamos and the Trinity site in March, as Jumbo [a containment vessel for use in case the nuclear explosion failed] faded into the background. With confidence increasing and a clear emphasis on learning everything possible about the performance of the test device, they were consumed from dawn to dusk with readying cameras and other diagnostic instrumentation to track the effects of the blast from detonation to dissipation.

The greatest unknown was how much energy would be released by the weapon. This value — also known as the yield — would depend on how much of the plutonium fuel underwent fission. The aim was to get as much energy from the explosion as possible.To quantify whatever success or failure awaited, scientists made plans to observe three manifestations of that energy: the amount of radiation emitted from the core (including neutrons, gamma rays, and fission fragments); the pressures and speeds of the air and ground shock waves; and the size and temperature of the fireball, which would indicate the amount of energy released as heat.

With the right combination of approaches and protections, they hoped to record in several ways all effects of the explosion. If the experiments were to have any chance of capturing the various expected phenomena, however, they had to be set up close enough to absorb and record the effects while simultaneously far enough away to withstand them. Difficult decisions about siting and fortification were made harder by the fact that only rough and frequently changing estimates of the Gadget's capacity for destruction were available to serve as guideposts.

Nevertheless, scientists brought the rigor of the laboratory to the desert in dozens of clever ways. Some of the myriad devices relied on communication lines to quickly carry data back to recording instruments in bunkers. Others were programmed to send up visual signals that would be filmed by timestamped cameras placed at safer distances.

Still others were purely mechanical, installed dangerously close to the blast but made of resilient materials or buried underground, the plan being to recover them in the aftermath to harvest data. Not knowing which approaches to the balancing act would turn out to be successful, they relied on overlap and redundancy to account for failure.

Although the cameras and instruments ultimately, and not unexpectedly, varied in their performance, the experimental program altogether would succeed in committing to history a comprehensive visual record and a trove of data, built upon the talents and toils of many.

We all know that a dropped or shaken soda can comes with the risk of a fizzy eruption. People use different techniques to prevent these bubbly blasts, including tapping the top of the can. This advice has been passed around for years, but does it actually work?

The answer lies in the physics of what's happening inside the can.

Building the bubbles

To make a carbonated drink, carbon dioxide is injected into the liquid — such as soda, beer or Champagne — at a high pressure and cold temperature.

"[Bubbles] are formed as a result of what is called supersaturation of carbon dioxide," Roberto Zenit, a professor of engineering at Brown University who studies fluid mechanics, told Live Science.

Supersaturation is an unstable state where a liquid or gas can hold more dissolved materials than normal conditions allow. Thanks to its instability, there are some actions, like shaking a can, that can encourage more bubble production.

"The mechanical action (tapping or shaking) generates violent pressure waves inside the liquid; these waves rebound at the walls, creating low-pressure zones where tiny bubbles form," Javier Rodríguez Rodríguez, an associate professor of fluid mechanics at Carlos III University of Madrid, told Live Science in an email. "If given enough time (minutes to tens of minutes, depending on the drink and container), these bubbles dissolve again and the can 'forgets' that it has been perturbed."

However, if the soda can is open while the bubbles are suspended in the liquid, the sudden pressure drop from opening the can encourages more bubble production, resulting in more spillover, Rodríguez Rodríguez said.

In some rare cases, like spraying Champagne after a NASCAR victory, creating a geyser of foam is exactly the goal, which the drivers accomplish by vigorously shaking the bottles beforehand.

Does tapping actually work?

Unlike NASCAR drivers, most people are looking to save their drink‬, so they may try tapping the top of the can.

The idea behind this strategy has some merit. According to Zenit, carbon dioxide bubbles can expand out of tiny imperfections called nucleation sites, which can include dust particles or rough spots on the can.

"The reason why you tap is basically to remove possible bubbles or dust particles within the soda can," Zenit said. If you remove those, you can reduce the rate of bubble formation, he added.

In theory, a few gentle taps could knock loose some bubbles clinging to the walls of the can, allowing them to float into the pocket of air above the soft drink before it's opened. With fewer nucleation sites left in the liquid, there would be fewer places for bubbles to rapidly grow once the can was opened and the pressure dropped.

But that explanation comes with an important caveat: While gentle tapping might dislodge a handful of bubbles, tapping too hard, or tapping repeatedly, could create more bubbles, Rodríguez Rodríguez said. The same principle applies to carbonated drinks in glass or plastic bottles, as tapping down on a beer bottle can encourage foam to fizz over.

Those competing effects make it difficult to determine whether tapping actually helps, and some experiments suggest that overall, it probably doesn't.

In one preprint study from 2019, researchers tested 1,031 cans of beer by dividing them into four groups: shaken and tapped, shaken and untapped, unshaken and tapped, and unshaken and untapped. The tapped cans were flicked three times on the side with a finger before being opened. The researchers found no statistically significant difference in the amount of beer lost between the tapped and untapped cans, regardless of whether they had been shaken. They concluded that tapping "does not prevent beer loss" and that the practice isn't supported by their observations.

That doesn't necessarily settle the question for soda, but it hints that tapping is not an effective method.

"Beer and soda differ in composition and foaming behavior, but the study provides relevant experimental evidence that tapping is not a demonstrated solution," Kit Yam, a food scientist at Rutgers University, told Live Science in an email.

How do you prevent a soda can from fizzing?

If tapping isn't the answer, time probably is. Letting a shaken can sit upright for several minutes gives the bubbles time to dissolve or rise into the air pocket at the top of the can. Keeping the drink cold can also help, because carbon dioxide stays dissolved more easily at lower temperatures.

"Put the can you accidentally dropped or hit in the fridge for half an hour and open another one in the meantime!" Rodríguez Rodríguez said.

If you don't have another can or you don't want to wait, Rodríguez Rodríguez suggested another option: opening the can slowly.

"In this way, the gas can escape, but I only leave a tiny slit for foam to fizz out," he explained. "Then, when you hear the gas is no longer escaping, you can safely open the can completely."

You can use the same process to reduce the amount of foam that spills over when you pour a carbonated drink into a glass.

"If you pour it slowly," Zenit said, "then you reduce this agitation."

Astronomers have discovered the closest, fastest star ever seen orbiting Sagittarius A* (Sgr A*), the 4.3 million-solar-mass black hole at the heart of our galaxy. The faint star, named S301, completes a lap every 8.7 years and skims past the black hole at roughly 55 million mph (90 million km/h) — about 8% the speed of light. Its orbit is so tight that, within about a decade, researchers should be able to measure its spin rate. The discovery was reported Aug. 19 in the journal Nature.

Stars as lanterns in warped space

The center of the Milky Way, some 27,000 light-years away, is one of the best natural laboratories physicists have. A few dozen stars swarm the galaxy's central black hole on tight orbits, and because gravity there is far stronger than anywhere else we can watch closely, those stars behave in ways Isaac Newton never anticipated.

"Stars orbiting Sgr A* are very interesting objects, as they serve as luminous probes of the curved spacetime around the black hole," study co-author Felix Mang, a doctoral student at the Max Planck Institute for Extraterrestrial Physics in Germany, told Live Science via email.

Until now, the star doing most of that work was S2, a bright star on a 16-year orbit. Astronomers have followed S2 since 1992, through more than two full laps, and that tracking revealed two hallmark predictions of Einstein's theory of general relativity: light from the star losing energy as it climbs out of the black hole's gravity well, and the slow rotation of its elliptical orbit, known as Schwarzschild precession.

Those effects depend only on the black hole's mass. But black holes have a second property: rotation. A spinning black hole drags the fabric of space around with it, like a spoon stirring honey. That effect fades extremely quickly with distance, so measuring rotation requires a star that dives much closer to the black hole than S2 ever does.

Measurements of black holes' rotations also matter beyond black hole physics. One leading alternative to general relativity "postulates the existence of a fundamental fifth force that arises, for example, from unifying gravity and quantum physics," Mang said.

Any deviation from Einstein's predictions should show up in these stellar orbits. So far, he said, "only an upper limit could be derived, which gets progressively lower" — in other words, there are no cracks in Einstein's theory yet, but the tests keep tightening.

A record-breaking orbit

That is where S301 comes in. In images captured by the GRAVITY instrument on the European Southern Observatory's Very Large Telescope in Chile, the astronomers "discovered a new, very faint star in the Galactic Center that is orbiting the central massive black hole Sgr A* so closely that its orbit is sensitive to the spin of the black hole," Mang said.

The star first showed up in spring 2023 as a faint smudge northwest of the black hole. Once the team had a rough orbit, they went back through archival observations and found it again in data from 2021 and 2017. In total, 19 measured positions spanning eight years trace out a complete, closed ellipse in the sky.

The orbit is extreme by every measure. S301 takes 8.7 years to orbit the black hole, beating the previous record holder — a star on a 12-year orbit — and S301's path is stretched into a needle-thin ellipse. At its closest approach, it passes within about 12 astronomical units from the black hole ‪—‬ 12 times the distance between Earth and the sun ‪—‬ and around 10 times closer than S2 ever gets.

Even at that distance, S301 is safe. It appears to be an ordinary main-sequence star of about 1.5 solar masses — compact enough that the black hole's tides cannot tear it apart. Its wildly elongated orbit suggests a violent origin; the team proposed that S301 was probably once half of a tight double star that strayed too close, was ripped in two, and had its partner flung out of the galaxy as a hypervelocity star.

The tight orbit is already showing relativity at work. "We found that the orbit of S301 succumbs to strong general relativistic effects, as the so-called Schwarzschild precession — the turning of the orbital ellipse within its own plane — is very apparent," Mang said. The ellipse swings around by about 2 degrees every lap. "Within the next ten years," he added, "a measurement of the spin of Sgr A* with S301 is within reach."

The hard part, and what comes next

Finding S301 was itself a feat. From Earth, the star appears about 2 billion times fainter than Betelgeuse ‪—‬ one of the brightest stars in our sky — and it sits in a crowded field beside far brighter neighbors, making it the observational equivalent of picking out a single fly buzzing over a full orchestra. It took a new image-reconstruction method, plus GRAVITY's recent upgrade to GRAVITY+, which boosted its sensitivity by a factor of 10 to 100, to pull the signal out.

One piece is still missing: The team can see how S301 moves across the sky, but not toward or away from us, which leaves two mirror-image orbits equally consistent with the data.

Now, they plan to fill in that gap. "We will keep following S301 closely along its orbit," Mang said, both with GRAVITY and an upcoming instrument that measures how light from the star shifts toward the red or blue end of the spectrum as it moves away from or closer to Earth.

Simulations by the team suggest that a decade of such combined observations could pin down the black hole's spin well enough to distinguish a rapidly rotating black hole from a stationary one with high confidence. Statistically, S301 should not be alone; roughly 100 similar stars may lurk on comparable orbits, but most of them are too faint to be seen today.

See how much you know about black holes with our black hole quiz!

Physicists have built a crystal out of an "einstein" tile — an elusive shape mathematicians spent years searching for — and found that it bends light in a way no ordinary crystal can.

In the new study, published July 29 in the journal Nature Communications, researchers arranged this never-repeating tile shape into a pattern of nanoscale holes. This structure, known as a photonic crystal, is designed to control the way light moves through it. When the team shined a laser at it, the crystal produced a swirling, pinwheel-shaped scattering pattern that responded differently depending on which direction the incoming light was spinning.

The tile solves what mathematicians call the "einstein problem," a decades-old puzzle asking whether a single shape could cover a flat surface endlessly without ever repeating its pattern. (The name is a pun on "ein stein," German for "one stone," not a reference to Albert Einstein).

In the 1970s, mathematician Roger Penrose showed that two different shapes, used together like floor tiles, could cover a surface without the pattern ever repeating. Then, in 2023, geometry enthusiast David Smith and collaborators finally found one: a 13-sided shape that they nicknamed the "Smith hat"

Yuto Moritake, an experimental physicist at the University of Tokyo, first came across the hat tile in a popular science book in 2024. Moritake specializes in photonic crystals — materials patterned with repeating structures (often much thinner than a human hair) that bend and steer light for uses like lasers and optical sensors. Almost all photonic crystals rely on patterns that repeat in a regular grid. Moritake wondered what would happen if he swapped that repetition for the hat tile's never-repeating arrangement.

"I decided to include it in our photonic crystal structure," Moritake told Live Science, describing it as the starting point for the project.

To build the structure, Moritake and his colleagues used two precision manufacturing techniques, called electron beam lithography and etching, to punch hundreds of thousands of tiny holes — each just 100 nanometers in radius, or roughly 500 times thinner than a human hair — into a thin film of silicon nitride. This ceramic material is commonly used in computer chips. The holes were arranged according to the hat tile's pattern, covering a chip roughly half a millimeter across ‪—‬ about the width of a pencil tip.

When the team shined a laser at the finished chip, the light scattered, or diffracted, into a pinwheel-shaped pattern that appeared on a screen. Moritake first photographed the colorful pattern using his iPhone's long-exposure mode. The setting captured faint light over several seconds. Then, he switched to specialized cameras for more precise measurements.

The pattern was made up of well-defined bright spots, called Bragg peaks, that stayed in the same positions no matter where on the chip the laser hit. That consistency confirmed that the structure had the kind of long-range, predictable order found in a quasicrystal — a class of material whose atoms (or, in this case, holes) follow an orderly pattern that never repeats, unlike the repeating grids found in ordinary crystals such as table salt or diamonds.

Because the hat tile itself has no mirror symmetry — meaning it doesn't look the same as its own reflection, similar to how a left hand differs from a right hand — the scattering pattern it produced was also asymmetrical in this way. Scientists call this property chirality.

That chirality led to the study's biggest surprise. Light can be circularly polarized, meaning it spins either clockwise or counterclockwise as it travels, like a corkscrew. When Moritake tested the structure with both types of spinning light, he found a subtle difference in how each direction scattered off the crystal. Ordinary quasicrystals, which do have mirror symmetry, cannot produce this kind of effect.

"This structure can have some kind of circular polarization dependence," Moritake said, adding that the effect — made only possible by the tile’s asymmetry — was not something he initially expected to find .

Now, Moritake wants to apply this never-repeating pattern to control light traveling inside a photonic chip, rather than light that simply bounces off its surface. This could lead to future uses in optical communications and optical computing ‪—‬ technologies that use light instead of electricity to transmit or process information, Moritake said.

See how much you know about Albert Einstein with our Albert Einstein quiz!

Researchers have designed a material that can "program" the way it releases heat, paving the way for more efficient energy systems and, potentially, devices that store information using heat instead of electricity.

The design, described in a June 25 study in the journal Laser & Photonics Reviews, sidesteps a nearly 160-year-old rule of physics linking how materials absorb and emit heat. Under ordinary conditions, a material that's good at absorbing heat from one direction is equally good at emitting heat in that direction. This rule of reciprocity, first described by physicist Gustav Kirchhoff in the 19th century, has limited engineers' ability to control incoming heat independently from and outgoing heat.

In the new study, the researchers designed a theoretical device that could direct heat radiation in different directions and remember that setting even after the power was switched off.

The new device pairs two materials that don't normally work together. Using a magnetic field, the team broke the natural symmetry in a layer of indium arsenide ‪—‬ a material that absorbs and emits infrared light ‪—‬ so that radiation traveling in one direction behaves differently than radiation traveling the other way.

On top of that layer sits a grating made of germanium-antimony-tellurium (GST) — a phase-changing substance that can switch between two distinct physical structures and stay in whichever structure it's set to until it's deliberately switched again. Once the GST is set into position, it locks the directional difference of radiation in place and holds it there without needing continuous power, which is what lets the device's heat-directing behavior be "programmed."

"I was impressed by the elegant combination of magneto-optical nonreciprocity with a nonvolatile phase-change material," Juejun Hu, a professor of materials science and engineering at MIT who wasn't involved in the study, told Live Science in an email.

That's significant because earlier attempts at this kind of directional control typically worked only at steep angles, which made them impractical. It's "particularly noteworthy" that this device functions when radiation arrives just 3 degrees off an otherwise-straight line, making it far easier to fit into real-world optical systems, Hu said.

The researchers compared their design to computer memory, since it holds onto its programmed state after the power is cut. However, the device stores a material state rather than heat itself, Hu told Live Science. GST simply keeps its amorphous or crystalline structure without power, which preserves the programmed response.

For now, the device exists only on paper; it hasn't been built or tested. Still, Hu thinks it's realistic, since it relies on well-established materials and manufacturing methods. However, the GST layer is thick enough that switching it back and forth repeatedly would be difficult, though other materials could fix this problem. Once that hurdle is surpassed, Hu expects the first real-world use to be infrared sensing, where compact, direction-selective heat absorption is most directly useful.

Richard Feynman was a serious physicist who loved to answer unserious questions. Can math tell you how to order the optimal lunch? Can a human track scents like a bloodhound can by smelling his own footprints? Now, researchers have picked up one of Feynman's most curious unanswered questions by looking at the physics of "silly" sprinklers.

A typical lawn sprinkler with an S-shaped nozzle spins in a given direction as it spews water from its two openings. But if you throw that sprinkler into a swimming pool and hook it up to a vacuum so it sucks water in instead of spraying it out, which way will it spin — the same direction as before, or the opposite?

Feynman posed that question as a Princeton graduate student in the 1940s. According to Feynman's telling, he rigged a glass sprinkler in his university's lab. It gave a brief "tremor," then barely moved even as he raised the pressure. He repeated the process until the glass shattered, leaving the answer ambiguous. Since then, decades of follow-up experiments have turned up every possible answer — the sprinkler spinning one way, spinning the other way, jittering back and forth, or not moving at all — depending on how carefully the tests were built.

In 2024, a team at New York University led by applied mathematician and experimental physicist Leif Ristroph took a first crack at the question, finding that the reverse sprinkler rotates opposite to a forward sprinkler. But that explanation was tested only on ordinary S-shaped sprinklers, and it hadn't yet been pitted directly against two other leading theories.

One, which traces back to Austrian physicist Ernst Mach, holds that the total angular momentum of the swirling water inside the sprinkler's arms must be balanced by an opposite spin of the sprinkler itself. The other, associated with Feynman himself, focuses on pressure and suction effects right at the outer nozzles.

So Ristroph's team asked, what if the sprinkler weren't shaped like a sprinkler at all? What if its arms spiraled, bent the wrong way or curled back on themselves?

In a new study published July 13 in the journal PNASs, the researchers built seven deliberately "silly" sprinklers with unusual arm geometries to pit the leading theories against each other. That includes one sprinkler with arms that spiraled several times to maximize the water's angular momentum, and another with a counter-bend at the nozzle.

In the process, they tore down both ideas. If Mach were right, the spiral design should have spun dramatically differently. If Feynman were right, reversing the nozzle bend should have flipped the sprinkler's direction. Neither happened.

"We were forced to say, 'Feynman and followers, you guys are off,'" Ristroph told Live Science.

The spiral-armed sprinkler, meant to test Mach's theory, was just as unyielding. Even though the fluid inside carried substantially more angular momentum, "the solid barely cared," Ristroph said.

All three measurements across the seven designs pointed instead to the sprinkler's central hub, where the arms meet. There, incoming water collides and swirls, generating a flux of angular momentum inside the device that the solid structure pushes back against. The finding suggests that the reverse sprinkler is not much more than an inside-out version of a forward sprinkler governed by the same physics playing out at the opposite ends of the arms.

Ristroph emphasized that this result was made possible because of Jesse Smith, who just completed his physics doctorate at NYU while working on the project, along with a small team of Ristroph’s own students, and Ristroph's longtime collaborator Brennan Sprinkle, a computational fluid dynamics expert at the Colorado School of Mines whose surname is a coincidence.

Now, the team is building computer simulations to test whether the momentum-flux model holds up beyond the flow conditions already studied, and they hope to eventually derive it from fundamental fluid dynamics equations.

Ristroph said this "silly" problem does have real-world applications: Understanding how curved channels convert fluid flow into rotational force could inform the design of turbines and other devices that harvest energy from wind and water currents.

"If we can do something that would help with engineers designing devices to better make use of all the huge amounts of wind and water energy we have all around us," he said, "that would be, of course, a fantastic thing."

Beyond familiar particles such as electrons and protons, scientists have discovered a zoo of "quasiparticles" with exotic names, such as magnons, angulons, dropletons and polaritons. But what are quasiparticles, exactly? And given the "quasi" in their name, are they considered real particles?

One way to understand quasiparticles is to explore what a particle is. The standard mental picture of a particle "is of a discrete object, like a ball," Douglas Natelson, a condensed matter physicist at Rice University in Houston, told Live Science. However, this classic image of particles changed with the advent of quantum physics, which revealed that the universe becomes fuzzy at its smallest levels. For example, in 1924, French physicist Louis de Broglie showed that particles such as electrons could also behave as waves ‪—‬ a discovery that earned him a Nobel Prize.

Modern physics suggests that particles are excitations in fields that permeate the entire universe, a bit like a ripple in a pond, Ross McKenzie, a theoretical condensed matter physicist and professor emeritus at the University of Queensland in Australia, told Live Science. Each type of particle has its own corresponding field. For instance, photons of light are ripples of the electromagnetic field, McKenzie noted.

The quantum nature of particles means they can not only fly through an empty vacuum but also ripple through matter. For instance, photons can zip through transparent and translucent materials, and electrons can flow inside wires.

If you can picture a standard particle, such as an electron, as a ripple traveling within a material, you can also envision other kinds of excitations within matter. These other types of ripples are quasiparticles.

For example, think of "the wave" done at a sporting event. "You can watch it propagate around a football stadium; it has a location and a speed," Natelson said. "It only exists within the stadium, though, and it's made up of the collective response of all the interacting fans."

In much the same way, "quasiparticles can only exist within some medium or material, because they are built up from the response of that material's constituents or building blocks," Natelson said; in contrast, particles such as electrons and protons "can exist in free space."

In other words, quasiparticles can't exist in a vacuum and they can't exist on their own. They're reliant on particles acting together and being in a material where they can emerge, just as a wave carried out in a stadium can only exist when there is a group of people there who can perform it.

A philosophical question concerning quasiparticles is whether they are real, McKenzie noted. After all, "quasi" in Latin means "almost."

"Fundamental particles can exist in isolation in a vacuum, and quasiparticles need many interacting particles to exist," McKenzie said. "Still, I would say quasiparticles are, for all intents and purposes, just as real as particles, in how you can detect them and manipulate them."

A zoo of quasiparticles

The concept of quasiparticles originated with theoretical physicist Lev Landau in the 1950s, McKenzie said, and the idea ultimately helped Landau win the Nobel Prize in physics in 1962. Scientists have now proposed the existence of dozens of quasiparticle types, including the following:

• The phonon, which is a quasiparticle of sound — it is the smallest packet of vibrational energy that makes up sound in matter, McKenzie said.
• The electron hole, often simply called a hole, is the positively charged vacancy left behind once an electron has left its original place, McKenzie noted.
• The electron quasiparticle, which essentially consists of an electron and its interactions with its surrounding environment. This combined package means the electron quasiparticle requires more force to move, so it effectively has more mass than a regular electron, McKenzie explained.
• The exciton, a quasiparticle made of an electron and a hole orbiting each other.
• The anyon, a kind of quasiparticle so far only seen in two-dimensional systems, which may carry only a fraction of an electric charge.

"How many kinds of quasiparticles are there?" McKenzie said. "Just like there are an infinite number of possible states of matter, I would say that, in principle, there are an infinite number of types of quasiparticles."

Scientists describe activity in material as quasiparticles "because it simplifies everything dramatically," McKenzie said. In the same vein, Natelson said that "very often the math behind physical phenomena in solids is described well by quasiparticles."

Quasiparticles are not simply useful for bookkeeping. For instance, researchers typically describe the behavior of electricity in electronic devices in forms of quasiparticles such as holes and excitons, Natelson said.

All in all, the answer to the question of whether quasiparticles are real is a matter of interpretation. If the question is whether or not a quasiparticle is an elementary particle such as an electron, the answer is no — they cannot exist on their own, and they depend on the materials in which they manifest.

However, if the question is whether or not quasiparticles are real phenomena, the answer is yes — they are things that scientists can measure that can behave like particles and effectively have many of the same properties that other particles do.

The 2026 Fields Medal, one of the world’s most prestigious mathematics prizes, has just been awarded to four pioneering young researchers — including mathematician Hong Wang, the third woman ever to win the prize in the 90 years since the award was established.

The Fields Medal is an award presented every four years to mathematicians under the age of 40 for their outstanding discoveries. The International Mathematical Union announced Thursday (July 23) that Wang, a professor at New York University, is among the four recipients of the 2026 medal for her work on a decades-old conjecture about how needles move in 3D spaces. .

The 2026 Fields Medal winners also include Yu Deng of the University of Chicago, who was recognized for connecting microscopic and macroscopic descriptions of gases; John Pardon of Stony Brook University, whose work solved major problems in topology and geometry; and Jacob Tsimerman of the University of Toronto, who developed powerful new techniques in algebraic geometry that have advanced progress on longstanding mathematical puzzles.

Wang joins an exceptionally small group of women to receive the Fields Medal. Iranian mathematician Maryam Mirzakhani was the first, in 2014, followed by Ukrainian mathematician Maryna Viazovska in 2022. No woman received the award at all in the nearly 80 years before Mirzakhani's win.

Wang was recognized for her work on the Kakeya conjecture, a problem that asks how little space is needed to rotate a needle so that it points in every possible direction in three dimensions. Mathematicians had chased a solution for roughly 50 years.

Working with collaborator Joshua Zahl, Wang showed that if you track every direction the needle could point as a bundle of thin tubes, there's a precise trade-off between how thin those tubes are and how much total space they must occupy. Solving the puzzle required tools from harmonic analysis, a field that studies how complex shapes and signals can be broken down into simpler pieces.

The proof wasn't a triumphant moment for Wang, at least not right away. She and Zahl spent months checking their 127-page proof before making it public — and even then, Wang worried that their argument might be unclear. The paper nonetheless earned comparisons to a "once-in-a-century" result and set off a string of honors culminating in the Fields Medal, according to Quanta Magazine.

The 2026 Fields Medals were presented during the International Congress of Mathematicians in Philadelphia. The first Fields Medal was awarded in 1936. So far, 65 men have received the award.

Science word of the day: Cryptology

Pronunciation: Krip-TAH'-leh-jee

What it means: Cryptology is the study of secret codes ‪—‬ both making them (cryptography) and breaking them (cryptanalysis). Once associated with spy networks' secret codes and ciphers, cryptology now often refers to the computer algorithms used to encrypt data to protect passwords and personal information from prying eyes.

How to use it in a sentence: Native American soldiers known as "code talkers" harnessed cryptology in World War II by developing codes and ciphers based on their Indigenous languages.

Can you crack our science word of the day puzzle, Chain Word?

Two physicists have used generative artificial intelligence (AI) to solve a stubborn mathematical problem in physics that had vexed researchers for more than a decade.

Their solution, described July 1 in the Journal of Statistical Mechanics: Theory and Experiment, came about when the physicists chose to revisit a problem they thought they had attempted to solve exhaustively within a topic they knew intimately. This concept, known as jamming, refers to the sudden transition from a fluid system to a rigid-but-disordered one.

The simplest way to understand this idea is to imagine a pool table covered with billiard balls. If you keep adding balls, eventually the table becomes so congested that there is no space for any more and each ball on the table is securely held in place by its neighbors. This is a disordered, completely frozen situation known as a jammed state.

The study authors —‬ ‪Giorgio Parisi, winner of the 2021 Nobel Prize in physics, and Francesco Zamponi, ‪both physicists at the Sapienza University of Rome ‪—‬ and collaborators had mathematically described jamming and offered numerical solutions in a 2014 paper. In the process, they noticed that two parameters — $a$ and $b$ — would mysteriously always add up to 1.

"The parameters $a$ and $b$ dictate exactly how the distribution of contact forces and small gaps [between balls] scales as the physical system hits that critical jamming point," Zamponi told Live Science in an email. "We were quite bothered by the fact that we had never been able to mathematically prove the relation $a+b=1$."

Moreover, separate work by Matthieu Wyart, a physicist at the Swiss Federal Technology Institute (EPFL), took a completely different approach but yielded the same relation. For Zamponi and colleagues, this suggested "entirely new physical concepts" were needed to link their and Wyart's work and simultaneously explain why $a+b=1$.

Fast-forward a decade, and no progress had been made in finding these new concepts nor a reason for why $a+b=1$. Stuck in a rut, Parisi had a thought: perhaps generative AI could offer a fresh perspective. For this, he turned to Anthropic's Claude. After Claude successfully reproduced the 2014 numerical result, Parisi prompted the AI to prove why $a+b=1$.

"Giorgio initially sent me Claude's output while I was traveling, so I ended up reviewing it on an airplane," Zamponi recalled. "As I read through the LaTeX file Claude generated, it became immediately clear that the core idea was correct … That moment significantly shifted my perspective on what these models can achieve in theoretical physics."

Though the initial output contained some errors that required revision, the fundamental idea was correct. And in a total of just 40 prompts, the researchers had a verified publishable analytical solution. To their surprise, this solution was hidden directly within the equations themselves; they didn't need any external physical assumptions or deep connections between functions.

"It is entirely possible that a pure mathematician who works full time on such kind[s] of equations might have spotted the solution," Zamponi told Live Science. "But this is a particularly interesting point for us, as it highlights how Claude gave us instant access to a vast repository of mathematical training and formal skills that lay just outside our usual domain."

Whether Claude simply trawled the vast mathematical literature and used pattern matching to find a way to solve their problem or if it applied something akin to creativity is, for Zamponi, moot because they "could not see the path forward, and Claude did," he said. And although he admitted that interacting with AI forces him to reconsider his definitions of reasoning, intuition, and creativity, Zamponi will continue to collaborate with the technology to speed up mundane tasks and provide fresh perspectives on challenging problems.

Now, Zamponi is applying this collaborative approach to a problem involving the “random sequential addition of hard hyperspheres," he said. “It is another excellent case study because, while the AI drastically accelerates writing and optimizing code, I have had to provide the vast majority of the conceptual ideas, which suggests that human guidance remains indispensable, at least in this case."

Physicists have coaxed a black hole's most famous glow out of a strand of optical fiber and, for the first time, watched that light react back on the simulated black hole that produced it.

The result gives researchers a rare, hands-on look at Hawking radiation ‪—‬ the faint thermal emission that Stephen Hawking predicted should leak out of black holes ‪—‬ and offers a first clue about the tiny push that could, in principle, make a real black hole slowly evaporate, the research team said in a new study.

Working with a tabletop experiment in optical fibers, the international team detected both the radiation and its long-sought "back reaction" — the way the radiation feeds energy back and reshapes the object that created it.

According to the new study, published July 1 in the journal Nature, the light behaved exactly as Hawking predicted it should: like the glow of a warm object, with a definite temperature and a spectrum that fades away steadily toward higher frequencies. It did so even in a regime where the usual textbook description of a black hole should break down.

Where three great theories collide

Hawking radiation is famous because it sits at the crossroads of physics' biggest ideas.

"Jacob Bekenstein predicted that black holes have an entropy and a temperature, and Hawking calculated the thermal radiation of the black hole," study co-author Ulf Leonhardt, a physicist at the Weizmann Institute of Science in Israel, told Live Science via email. "In Hawking-Bekenstein radiation, quantum physics, general relativity and thermodynamics come together — subjects that are normally in conflict with each other."

The conflict runs deep: General relativity pictures space and time as smooth and continuous, while quantum mechanics describes a world of discrete, unpredictable jumps ‪—‬ and no one has managed to fully reconcile the two.

That combination is exactly what makes Hawking radiation so hard to study. Astronomers have never seen Hawking radiation from a real black hole and probably never will; the glow is far too faint to pick out across the cosmos. So physicists have turned to laboratory stand-ins that obey the same equations, building black hole analogues out of flowing water, ultracold atoms and, as in this study, light.

Building a black hole from light

The trick behind every black hole analogue is a moving medium. "Imagine a swimmer in the sea with a current faster than he can swim," Leonhardt explained. "He is swept away. This is what happens beyond the [event] horizon, and this is why normally nothing can escape the black hole."

A black hole's event horizon is the boundary where that current — space itself, in real life — starts moving faster than anything can travel. To recreate it, the team needed a material that appears to rush along at the speed of light. Their solution was elegant: use light to make the "material."

"In optics we need a material that appears to move at the speed of light," Leonhardt said. "For this we use light itself — in nonlinear optics, light acts like a material."

In practice, the researchers fired an intense, ultrashort "pump" pulse into a thin photonic-crystal fiber — a strand of glass threaded with a pattern of tiny air channels running along its length, which lets researchers fine-tune how light moves through it. As it traveled, the pulse slightly changed how the glass bent light, creating a moving speed bump that raced along with it. A second, much weaker "probe" pulse then ran into this moving front. Where the probe could no longer keep up, an artificial horizon formed — and the black hole analogue was born.

Catching the glow and its pushback

The payoff came in the ultraviolet. According to theory, Hawking radiation is created in pairs: One partner escapes, while the other, carrying "negative" energy, is the mirror image that would fall into a real black hole. In the fiber, that partner showed up as ultraviolet light.

"We counted photons in the ultraviolet that correspond to the Hawking partners beyond the horizon," Leonhardt explained. "They have a wavelength around 233 nanometers. This was our signal."

Just as important as seeing the glow was understanding how it was made. For years, researchers assumed the fiber built up its Hawking radiation through a cascade — a chain of separate steps in which the light is converted first into one intermediate form, and then another, each feeding the next before the radiation finally emerges. The team found that, instead, a single, direct interaction does the job, with the pump and probe light producing the Hawking pair in one clean step. It is a much simpler picture that the researchers said may carry over to other analogues and perhaps even to real black holes.

Because energy has to come from somewhere, making Hawking radiation should nudge the source that created it. For a real black hole, that nudge is how it loses mass and, over unimaginable timescales, evaporates entirely — the process Hawking described in his landmark 1974 paper. No experiment had ever captured that recoil.

Here, the team saw it. Producing the radiation shifted a small fraction of the pump pulse's own light to a slightly different color, leaving a telltale lopsided pattern in the spectrum. That asymmetry, absent in earlier experiments, is the fingerprint of the back reaction, or recoil — the black hole analogue quietly paying the energetic price for its own glow.

The road to a quantum experiment

The result also speaks to one of the thorniest puzzles in black hole physics: the trans-Planckian problem. Trace Hawking's radiation back to where it was born and the calculation runs into territory no physicist can vouch for — the Planck scale, the vanishingly small size at which space and time are thought to lose their familiar meaning and all known physics gives out. Hawking's prediction, in other words, appears to rest on a foundation that may not exist.

"Any light getting away from the horizon is stretched out enormously," Leonhardt said. "So it must come from waves smaller than the tiniest scale in nature, where the physics is unknown. Would that still give Hawking radiation? That was the question, and we have answered it in our experiment." Remarkably, the glow stayed perfectly thermal even in this extreme regime.

The team's next step is concrete. So far, they have used ordinary laser light, which reproduces the spectrum of Hawking radiation but not its deepest quantum weirdness. Next, the team plans to "go quantum," Leonhardt said. "We will explore how to get into the quantum regime and observe quantum features such as entanglement" — the ghostly link that should tie each escaping Hawking particle to its lost partner.

See how much you know about black holes with our black hole quiz!

Albert Einstein gave us the theory of relativity, explained the photoelectric effect and predicted the existence of gravitational waves. He revolutionized our understanding of space, time and gravity.

In fact, he is so famous for his brilliance that "Einstein" is synonymous with "genius." But being a genius doesn't mean you're infallible. So was Einstein wrong about anything?

"For sure, he was wrong about tons of things," Nicolás Yunes, a theoretical physicist at the University of Illinois Urbana-Champaign, told Live Science. "We remember him for the things he was right about, for the most part, because the things he was right about shocked the scientific world and eventually those ripples affected everyone on Earth."

For example, one of his most famous predictions was marred by a mathematical mistake. In 1916, Einstein correctly realized that the acceleration of matter could produce ripples in space-time that we now call gravitational waves. But when he and the physicist Nathan Rosen described these waves using mathematics, they ran into a problem: Any solution to the equations of general relativity that would allow for gravitational waves "blew up," Yunes said. "They had these singularities … these divergences. And solutions that diverge and explode like that, they can't be physical representations of reality."

As a result, Einstein changed his mind and decided that gravitational waves couldn't exist. He wrote up his results and submitted them to the journal Physical Review, which had recently begun sending papers to outside experts for peer review. An anonymous reviewer caught an error in Einstein's math, and when Einstein learned about it, he was so furious that he withdrew the paper and submitted it to a different journal.

But the reviewer had spotted a real error: Einstein's mathematical infinities were a coordinate artifact. Much like Earth's lines of longitude seem to converge to a "singularity" at the North Pole even though nothing unusual is happening there on the ground, Einstein's math could have been fixed by using a different set of coordinates.

Without Einstein's knowledge, the reviewer befriended and demonstrated the error to Einstein's assistant, who explained it to Einstein. Einstein corrected the error and republished the paper with the opposite conclusion, showing that gravitational waves do, in fact, exist.

Calculating "impossible infinities"

Remarkably, Einstein stumbled on the same error twice — at least, it seemed that way. When examining the mathematics around black holes, he once again calculated impossible infinities ‪—‬ this time, at the edge of a black hole. And once again, he concluded that this must mean the object couldn't exist.

"Einstein remained skeptical of the existence of black holes," John D. Norton, a professor in the Department of History and Philosophy of Science at the University of Pittsburgh, told Live Science in an email. "He was resolute in his judgment that there would be a singularity in space-time already at the event horizon of a black hole, which is now merely regarded as marking the point of no return for those falling into a black hole."

But this time, Einstein was not convinced that he made a mistake. Norton argues this wasn't just stubbornness; it reflected a philosophical belief in how Einstein thought mathematics and physics should relate to each other.

"He was unmoved by alternative analyses that found his mathematical infinities to be merely artifacts of the particular mathematical methods he preferred," Norton said.

Einstein and quantum mechanics

Einstein's resistance to quantum mechanics is probably his most famous wrong turn. His central objection was to a phenomenon called quantum entanglement: the idea that two particles can be linked in such a way that measuring one instantly affects the other, no matter the distance between them. In a 1947 letter to his colleague Max Born, he wrote, "I cannot seriously believe in it because the theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance."

Einstein thought this instantaneous phenomenon seemed to violate special relativity, which says that nothing can travel faster than light. As a result, he believed quantum mechanics must be incomplete and that there was some deeper, unknown description of reality that would restore order.

"He died not liking quantum mechanics," Yunes said. It wasn't until 1964, almost a decade after Einstein's death, that John Bell proved entanglement was real.

"Today, a lot of the technology that we have relies on quantum mechanics, and so we know it's correct," Yunes said. "But it's still incompatible with general relativity, with [Einstein's] classical theory."

"It's possible that general relativity is wrong," Yunes said. "It's also possible that quantum mechanics is not the right description when you're talking about systems that are very strongly gravitating and you're looking at Planck-scale-type dynamics," which are incredibly small scales at which quantum effects dominate. For instance, the center of a black hole, which is both compressed to the quantum scale but also sits inside the most intense gravitational field in the universe, is a place where general relativity predicts a singularity that quantum mechanics has no way to describe.

But many of Einstein's mistakes still moved science forward. "General relativity is a good example," Norton said. "Einstein based it on the idea that he was generalizing the principle of relativity to acceleration and on what he soon called Mach's principle. Neither proved compatible with his final general theory of relativity."

Einstein's mistakes might come as a surprise to others, but they didn't to him. Once, when writing a book with his collaborator Leopold Infeld, Infeld told him he was taking special care with it because Einstein's name would appear on it. Einstein laughed and said, "There are incorrect papers under my name, too."

See how much you know about Albert Einstein with our Einstein quiz!

This week's science news was filled with big discoveries from the world of the small, led by a physicist's creation of a mini-universe, which was designed so we can watch time emerge from within an isolated quantum system.

The experiment was performed using a Bose-Einstein condensate — a strange state of matter that consists of thousands of atoms blended into a single quantum object at near absolute zero (minus 273.15 degrees Celsius, or minus 459.67 degrees Fahrenheit). The system showed time speeding up, slowing down and even stopping, depending on what the system was doing.

Those weren't the only highbrow high jinks using a Bose-Einstein condensate we reported on this week. We also covered NASA's upgrade to its mini-fridge-sized laboratory on the International Space Station that will use the bizarre state of matter to probe the quantum world. Back on Earth, physicists also found that complex numbers aren't necessary for quantum mechanics to work and used quantum computers to create a rare material critical to nuclear fusion. And to stick with news from the small (and weird) things of the world, we also reported that scientists have created little diving suits to transform cockroaches into search-and-rescue cyborgs.

Arctic ice thickening shows promise

First experiment to thicken Arctic ice with seawater shows promise — but there's a big catch

The Arctic is the world's fastest-warming region, where sea ice is rapidly disappearing at a rate of 12.2% per decade.

The ice is crucial for maintaining stable sea levels and marine nutrient flows, and for reflecting solar radiation away from our planet, so its precipitous decline is deeply concerning. That's why one team of researchers turned to a surprisingly simple method to stem the ice loss: flooding ice sheets with seawater to thicken them.

The results, despite some major caveats, showed a lot of promise.

Discover more planet Earth news

—Extreme heat waves are making our cities buckle. Investing in urban nature is no longer optional.

—Colorful 'painting-like' ripples cover an ancient seafloor structure in the Bahamas — Earth from space

—'Uncharted territory': Record-high ocean temperatures confirmed for June as El Niño strengthens its grip

Life's Little Mysteries

Does fast charging damage your battery more than regular charging?

If you're as shamefully attached to your devices as I am, you may have wondered about the wildly differing times it can take for them to charge. So what's the science behind fast charging, and does it damage a device's battery more than regular charging does?

—If you enjoyed this, sign up for our Life's Little Mysteries newsletter

One of the oldest gravestones of a free Black person in the U.S. found

'One of the oldest gravestones of a free Black person in America' discovered in Boston

It was found amid photos of headstones during a restoration project at Boston's Granary Burying Ground — a gravestone with only one name, "Boston."

That's how a team of conservationists chanced upon the tombstone of Sebastian, a formerly enslaved man who died free in 1729 and chose the city's name as his own.

A search through the historical archives has produced a wealth of information about Boston's past, including his reputation as a hardworking handyman throughout the city, and his emancipation following the death of the man who held him in slavery.

"It's been there all along. We just had to go look and share the story," Michelle Wu, the mayor of Boston, said in a July 4 speech.

Discover more archaeology news

—100,000 years ago, one of the earliest Homo sapiens outside Africa was stabbed in the face, analysis finds

—6,000-year-old broken ribs discovered in Syria may be one of the oldest known cases of child abuse in the world

—Neanderthals and modern humans may have shared culture 59,000 years ago in Turkey, study finds

Also in science news this week

—New sodium metal battery design charges in just 4 minutes and retains its capacity for years

—Dirty 'button' unearthed by metal detectorist turns out to be a rare 900-year-old coin from Norway's last Viking king, Magnus Barefoot

—'Astronomers have to revise estimates': The Milky Way may be larger, heavier and more lopsided than we realized

—2,500-year-old tomb of a 'warrior prince' with chariot and helmet discovered on Italy's Adriatic coast

—Malaria had nearly been eliminated around a giant dam in the Amazon — but then it came roaring back. Experts just discovered why.

Science interview

'800 seconds for a sick visit': Some factors driving antibiotic resistance have nothing to do with biology, says medical sociologist Julia Szymczak

Antibiotic resistance continues to pose a growing danger across the U.S., with more than 2.8 million antimicrobial-resistant infections occurring in the country each year. Last week, we brought you a report from Live Science health editor Nicoletta Lanese, who visited Japan to investigate how that country is curbing its overuse of antibiotics.

Now, in the second part of a feature series into the fight against this "silent pandemic," Nicoletta interviewed medical sociologist Julia Szymczak to dig into the social and emotional drivers of antibiotic overprescription.

Something for the weekend

If you're looking for things to keep you busy over the weekend, here's a selection from our best opinion pieces, interviews, diagnostic dilemmas and crosswords that we published this week.

—Superintelligent AI in space could explain the Fermi paradox [Opinion]

—'It's more than a hope; it's a guarantee': The Vera C. Rubin Observatory's 10-year movie of the universe is about to 'blow our minds,' chief scientist Tony Tyson says [Interview]

—Diagnostic dilemma: A woman heard voices for years — but not because of psychosis [Diagnostic Dilemma]

—Live Science crossword puzzle #51: Largest rodent on Earth — 4 down [Crossword]

Science photo of the week

Secretive Chinese probe snaps first photo of Earth's mysterious 'quasi-moon' — and it may pose a big problem

It doesn't look like much, but this blurry, gray image is the first-ever close-up photo of one of Earth's temporary "quasi-moons" — a fast-spinning asteroid temporarily orbiting the sun in sync with our planet.

Of equal intrigue is the spacecraft that took the image: a secretive Chinese probe that is likely gearing up to land on the space rock and snag a sample ‪—‬ although an unexpected hiccup will make that more difficult.

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.

A new upgrade to the International Space Station's (ISS) quantum laboratory is enabling NASA to probe the behavior of atoms further than ever before, the space agency has announced.

Combining the ISS's newly upgraded "Cold Atom Laboratory" with the near zero-gravity of low Earth orbit, scientists are attempting to understand the properties of so-called "ultracold" atoms in an environment impossible to replicate on Earth. The aim of the mission is to study how clouds of atoms behave at temperatures close to absolute zero (minus 459.67 degrees Fahrenheit or minus 273.15 degrees Celsius) — the coldest possible temperature in the universe, where atoms lose all their energy of motion.

"At the coldest temperatures, matter behaves drastically different from anything we have experienced," Jason Williams, project scientist for the Cold Atom Lab at NASA’s Jet Propulsion Laboratory in Southern California, which built the facility, said in a statement. "The wavelike nature of matter dominates, and ultracold matter can behave in ways that are not only unexpected, but that also enable extremely precise measurements of time, gravity, and motion. The lab has lots of tools — especially with this latest upgrade — to let us probe the nature of the universe."

Rule-breaking particles

Atoms and their subatomic particles are quantum mechanical objects whose behavior is fundamentally different from that of the large-scale world. For example, the laws of quantum mechanics predict that particles can be in more than one place at the same time (quantum superposition); can be mysteriously linked with each other over great distances (quantum entanglement); and move through spacetime as waves as well as moving like fixed, solid objects.

But observing these behaviors is notoriously difficult. Firstly, atoms are so tiny that if an atom were the size of a golf ball, then a human teeing one off would stand roughly as tall as the distance from Earth to the moon. Secondly, it’s impossible to isolate measurements of these behaviors for atoms in "normal" environments (like on Earth), as the desired quantum behavior is disturbed by energy from heat and gravity.

To overcome these challenges, the ISS's Cold Atom Laboratory — which is the size of a mini-fridge — uses lasers to cool gases of rubidium and potassium to just above absolute zero. At these temperatures, atoms form a state of matter known as a Bose-Einstein condensate, in which many atoms behave like a single wave of quantum matter.

Not only does this setup allow scientists to observe quantum behaviors on a much larger scale than that of single atoms, but the reduced gravity enables the condensate matter waves to expand and evolve undisturbed for much longer periods than would be possible on Earth.

This is the fourth major upgrade to NASA’s Cold Atom Laboratory since it arrived aboard the ISS in 2018. According to NASA, the significant improvements in this most recent upgrade include a redesigned magnetic trap to contain the cloud of atoms, improved atom sources, and better measurement capabilities.

Scientists launched these upgrades to the ISS in April 2026, and they have since been installed, switched on, and started making state-of-the-art measurements. As well as enabling novel tests of fundamental physics, measurements of these effects are critical in demonstrating future, space-based, highly precise quantum technologies related to positioning, navigation, timing, and gravity sensing. These technologies could one day enable astronauts to navigate on the moon without GPS and produce high-precision maps of Earth’s gravity.

"In the previous century, there was a quantum revolution that led to lasers, cellphones, and MRIs for medical imaging," Ethan Elliott, deputy project scientist at NASA’s Jet Propulsion Laboratory in California said in the statement. "We’re performing Quantum 2.0 – direct manipulation of large quantum states – and we hope for similar gains in quantum technology by advancing this science in orbit."

For the first time, physicists have built a working version of quantum mechanics without complex numbers — numbers that have been considered essential to the theory for nearly a century.

Complex numbers combine a regular "real" number with an "imaginary" one — a multiple of the square root of -1, represented by the symbol i — into a single value, like 3 + 4i. The square root of -1 doesn't correspond to any quantity you could count or measure directly (you can't have negative one apple, for instance), which is why mathematicians call it imaginary.

Still, complex numbers have many useful applications. Engineers use them to describe alternating electrical current. Physicists use them to describe waves. And ever since quantum mechanics was first documented in the 1920s, complex numbers have been built directly into its equations. Quantum mechanics describes particles using something called a wave function, and that description relies on complex numbers.

In 2021, a team of physicists predicted that a version of quantum mechanics built with only real numbers would make incorrect predictions in certain experiments involving multiple particles. The following year, other researchers ran those experiments, and the results matched standard quantum mechanics, not the real-number version. Complex numbers seemed unavoidable.

But that 2021 result rested on one specific assumption: a particular mathematical rule for combining particles. That led physicists to ask a question: Are complex numbers actually necessary to describe reality at the quantum level, or are they just a convenience?

Now, in a new study published June 18 in the journal Physical Review Letters, researchers have found a way around the 2021 result.

"Complex numbers are not needed for quantum mechanics," study first author Pedro Barrios Hita, a theoretical physicist and doctoral student at the German Aerospace Center and Heinrich Heine University Düsseldorf, told Live Science.

A different rule

The 2021 result relied on a specific mathematical rule called the tensor product, which combines two separate quantum systems into one. If you have two particles and you want to combine them into a single mathematical description, you can use the tensor product. It's a rule taught in every quantum mechanics textbook.

It works well for ordinary complex-number quantum mechanics, but past attempts to build a real-number version around that same rule ran into trouble. They couldn't reproduce the correlations seen in experiments involving three or more entangled particles.

In their new study, Barrios Hita and his colleagues found that the tensor product isn't the only option. They built quantum mechanics around a different rule based on an idea: An action taken on one part of a system shouldn't have any effect on a separate part of it.

In ordinary quantum mechanics, multiplying a particle's state by i is undetectable on its own. But when two particles combine, that i can shuffle over and effectively attach itself to the other particle instead. Physicists call this phase kickback, and it's built automatically into the tensor product.

Barrios Hita's team had to recreate that shuffling using only real numbers. They attached a small "flag" to each particle to keep track of what the imaginary part used to store. Then, they treated certain flag combinations as physically identical, even though they looked different on paper. That grouping step allowed their real-number version to match every prediction of standard quantum mechanics, including the multiparticle cases that had tripped up earlier attempts.

At its core, the trick is simple. A complex number, like 3 + 4i, is really just a pair of ordinary real numbers (3 and 4) — the i is only a label marking which one is the imaginary part. "A complex number is nothing but two real numbers," Barrios Hita said. His team essentially built a bookkeeping system that tracks those two real numbers separately, instead of combining them into one complex number. It took a long time to figure out how to make that work consistently across multiple combined particles. But once they did, Barrios Hita said, the underlying structure turned out to be elegant.

The result puts quantum mechanics in the same boat as other physics theories that are often written using complex numbers purely for convenience, Barrios Hita said.

"There are many other theories, like, for example, electromagnetism," Barrios Hita added, "which has complex numbers at its core. So, these theories are formulated using complex numbers, but [they] are not fundamental. They're just helpful tools to help express equations."

The work doesn't change any experimental predictions or point to new quantum technology. It's also currently limited to systems with a finite number of quantum states. Extending it to infinite-dimensional systems, which show up in many real physics problems, is a natural next step, and other researchers are already looking into it. Barrios Hita is moving on to different research, on how quantum properties like entanglement can be used as a resource.

Still, the study settles a decades-long debate. Complex numbers make quantum mechanics easier to write down, but they aren't required to make it work.

For the first time, a physicist has experimentally watched time emerge from within an isolated quantum system — by creating a “mini-universe.” This bizarre experiment raises an intriguing question: If the universe has nothing outside it, where does time come from?

In a new study published June 11 in the journal Physical Review Research, Giovanni Barontini, an experimental physicist at the University of Birmingham in the U.K., used a cloud of ultracold atoms to build his mini-universe. The system was so well isolated from its surroundings that, like the universe itself, it had nothing external to use as a clock. He split that system in two and ignored one half — what he called the "dark sector" — to show that time could arise entirely from within the system.

The result offers the first experimental look on why the universe has time at all. "When you put everything together, things really start to make sense," Barontini told Live Science. "How time inside the system was speeding up or slowing down, or even stopping — this was quite surprising, how well everything came together. Very neatly, in a way. Which is something that doesn't happen that often in experiments."

The work is an experimental verification of ideas that have been floating around in quantum cosmology and thermodynamics for decades. This is not a bombshell claim that time is an illusion, but it is the first time anyone has put those ideas to a direct, quantitative test in the lab.

A universe with nothing outside

Barontini set out to look at a problem that physicists have puzzled over for nearly 60 years. The Wheeler-DeWitt equation — a central equation in quantum gravity, the field that seeks to unify Einstein’s theory of gravity with quantum mechanics — describes the universe as a whole system with no external time parameter. There is no cosmic clock ticking away outside the universe. So where does our experience of time come from?

One influential idea, called relational time, says that time doesn't exist as a fundamental ingredient of reality. Instead, it emerges from relationships inside the universe, with one part of the system acting as a clock for another. But this idea had never been tested directly in the lab.

Barontini's inspiration came from watching his son play with building toys. "I thought that it's something very similar to what we do in our labs," he told Live Science. "We play with very expensive toys. We create our own small samples of reality."

In his lab, that sample is a Bose-Einstein condensate — a state of matter that forms only at near absolute zero. In a Bose-Einstein condensate, thousands of atoms slow to a near standstill and blur together into a single quantum object, behaving as one.

The dark side of time

To mimic a universe with nothing outside it, Barontini placed the condensate in a trap and divided it down the middle with a thin sheet of laser light. He watched one half, the "bright sector," closely and deliberately ignored the other half, which he called the "dark sector."

The atoms in the bright sector sloshed back and forth in the trap, periodically spilling over the barrier and back again. Barontini called the moments when atoms flooded into the bright sector the "Big Bang" and the times when they drained out the "Big Crunch" (the nickname for one theory of how the universe will end, with the universe collapsing in on itself). Then, he tracked how entropy — a measure of disorder, or how spread out energy is within a system — was exchanged between the two halves as atoms crossed the barrier.

Instead of using laboratory time to order events, he built an "entropic time" — a clock defined entirely by how much entropy was flowing between the two halves of the system. If entropy was flowing, time was ticking. If no entropy was exchanged, time stopped. "The entropy exchange between the two systems could be transformed into an internal time variable," Barontini said.

Time speeds up, slows down and stops

What surprised Barontini most was how cleanly everything fit together. The internal, entropic time reliably ordered events in the bright sector. It matched the sequence seen in laboratory time, but it flowed at a different rate.

When entropy was flooding between the sectors, entropic time ran fast. When the exchange slowed, so did the clock. And when the two halves reached equilibrium (no more entropy flowing), the internal clock stopped altogether.

"Time was speeding up or slowing down, or even stopping, depending on what the system was doing," Barontini said.

He then went a step further: Using this internal time, he derived a version of the Schrödinger equation and showed it accurately reproduced what he saw in the experiment. "This was quite surprising, how well everything came together," he said — "very neatly, in a way, which is something that doesn't happen that often in experiments."

Both time itself and the arrow of time — why time flows in one direction rather than the other — may arise from the same source: an observer giving up information. When Barontini chose not to look at the dark sector, he gave up knowledge of that half of the system. That act of ignorance, encoded in entropy, is what gave rise to time in the other half.

"Both time and the arrow of time — maybe they just are born from ignorance," Barontini said. "To have time and to observe, you have to give up some degrees of freedom."

Barontini sees this as just the beginning. The same cold-atom tool kit that generated a miniature Big Bang and Big Crunch in his trap could, in principle, be engineered to simulate far more exotic phenomena, such as black hole analogues, the conditions of the early universe, and what will happen at the moment of the Big Crunch itself.

"These are things we can do very simply, using the tools we already have to engineer our systems," he said.

The study is a proof of concept ‪—‬ a first demonstration that controlled quantum systems can serve as a test bed for some unanswered questions in physics. For now, those questions remain open.

The Large Hadron Collider (LHC), the world's largest and most powerful atom smasher, has entered a planned four-year shutdown that will upgrade it to its most capable form yet.

The particle accelerator was switched off Monday (June 29) and is scheduled to come back online in 2030 as the High-Luminosity Large Hadron Collider (HiLumi LHC), with improvements that will allow it to smash together roughly 10 times more particles than its original design. That data could help spark new discoveries in fundamental physics and shed light on the nature of dark matter, antimatter and the early universe.

"This is a very important moment," HiLumi LHC project chief Markus Zerlauth told Agence France-Presse. "From Monday, we will be entering a new phase."

Since its first successful proton collision in 2009, the LHC has allowed physicists to test theories about particle physics and the Standard Model of the subatomic world. It was essential to the discovery of the Higgs boson in 2012, which helped explain how tiny fundamental particles acquire mass. The collider covers a 17-mile (27 kilometers) loop at the border between France and Switzerland near Geneva.

The current shutdown is the third long-term, planned pause in the collider's operations. The first, a two-year shutdown beginning in 2013, consolidated connections between superconducting magnets and boosted the energy of the colliding proton beams. A second pause, from 2018 to 2022, involved a series of upgrades, replacements and preventive maintenance.

In the current period of dormancy, dubbed Long Shutdown 3 (LS3), specialists will install upgrades to boost the collider's luminosity by a factor of 10. That will increase the number of particle collisions, roughly tripling the number of times particles will smack into each other compared with the existing setup. Once the final version of the particle accelerator is online, it will run until the end of its operational lifespan in the 2040s and will be earmarked for replacement by a new, higher-energy particle accelerator in the years that follow.

"It really is an opportunity to explore the universe in a way we haven't done before," Mark Thomson, director general of CERN (the European Organization for Nuclear Research), where the LHC is housed, told New Scientist.

That jump means that experiments will produce much more data, which will allow scientists to study known phenomena, such as the Higgs boson, in more detail and increase the odds of observing rare events. For example, the HiLumi LHC is expected to produce about 380 million Higgs bosons over its lifetime of a decade or so, compared with the 55 million it's made to date. The data could help scientists solve problems with the Standard Model, which currently doesn't incorporate dark matter or dark energy, the primary forms of mass and energy in the universe.

"The LS3 represents a huge and complex logistical and engineering undertaking," Jean-Philippe Tock, head of the LS3 coordination team, said in a statement. "In the LHC alone, 1.2 km [0.75 miles] of magnets and components will be removed and replaced with new equipment, and across the whole complex, dozens of projects are planned, involving thousands of engineers, physicists, technicians and support personnel."

While the LHC won't be smashing any particles together during the shutdown period, researchers will continue to analyze data already collected during experiments during the prior operational window.

Though the LHC's primary purpose is fundamental physics research, technologies used to upgrade the collider could find their way into everyday life. For example, some instruments and techniques originally developed at CERN are now being used in medical imaging, sensors and art restoration.

For years, scientists have suspected that, at the molecular level, water is two different liquids ‪—‬ a denser one and a less-dense one ‪—‬ that are constantly switching places. Catching real molecular evidence of this microscopic transformation has been hard. But now, with help from artificial intelligence, researchers say they've finally found it.

"It's hard to imagine — here is just one water, right?" said Xiao Cheng Zeng, a physical chemist at the City University of Hong Kong and co-author of the new study, told Live Science while holding a water bottle in the air. That puzzle sent him digging through scientific literature, where he found the possible explanation: the two-state hypothesis. "That got my attention. We have literature to talk about it but no evidence."

The findings, published June 4 in the journal Nature Physics, could not only prove this long-sought molecular change is real, but also help to explain dozens of water's weird behaviors.

Most liquids become denser as they cool, but water behaves differently; it becomes denser until about 4 degrees Celsius, then starts to expand, which is why ice floats. Water also resists temperature changes better than similar liquids and has a viscosity that decreases under certain pressures. Scientists have documented various anomalies related to water and suspect they may be interconnected.

The two-state model is an attempt to be that unifying explanation.

A 30-year hunch

Zeng has been studying water since his postdoc days in the late 1990s, when he worked on liquid freezing. The two-state hypothesis itself came onto his radar later — around 2006, when he first encountered it at scientific conferences. But for years, he set it aside as too difficult to tackle directly. That changed roughly around 2016, as researchers began reporting experimental evidence that supercooled water could split into distinct high-density and low-density forms.

Around two and a half years ago, Zeng handed the problem to Liwen Li, a postdoctoral researcher in his lab. Rather than repeating the conventional approaches other groups had already struggled with, Li suggested the use of "unsupervised deep learning" — AI trained to spot patterns in data without being told what to look for.

"So AI [is] forced to learn — to use [its] knowledge to create, to explore," Zeng told Live Science.

The team ran massive molecular dynamics simulations, using the GROMACS simulation package. They tracked how hundreds of thousands of water molecules moved and interacted and generated tens of millions of data points.

"Traditionally, you may need a lot of students to figure that out. ... With computers and AI, it took [Li] maybe a year and a half," Zeng said. Without AI, he estimated, the same analysis might have taken closer to a decade.

The AI came back with "reaction coordinates" — a small number of variables, distilled out of all that molecular motion, that describe exactly how a water molecule's local arrangement shifts from the denser structure to the looser one and back. They plotted the system's behavior along those coordinates to see the shape of the conversion. That included the number and location of energy barriers, or saddle points, that molecules have to cross to make the switch.

Two paths up the mountain

The team found that the path the two structures take to convert into each other changes depending on certain conditions. Most of the time, the switch happens along what the researchers call a "semi-loop" pathway, with a single energy barrier to cross.

But near the boundary between high-density and low-density water — the same kind of threshold where ice and liquid water coexist at 32 degrees Fahrenheit (zero degrees Celsius) — the molecules can take a more roundabout "full-loop" path, with three separate barriers instead of one.

Zeng compared it to hiking a mountain that's been sliced in half, with a gentle slope on one side and a sheer cliff on the other. Most hikers stick to the slope; that's the semi-loop. But near the boundary where the two halves meet, it's as if the mountain were becoming whole again, letting hikers circle the entire peak. That's the full loop.

Zeng and his team are now building a more rigorous machine-learning model to confirm the result. They hope to eventually connect it to properties like density, viscosity and temperature.

Confirming the structure in real water won't be simple. Zeng said it will likely require new and sensitive experimental techniques — the kind developed by labs like Pacific Northwest National Laboratory, which previously found indirect spectroscopic evidence for water's two-state behavior.

"Once we have this ... confirmed by experiment," he said, "this model can be used to [understand] how water interacts with nature."

Since most biological and pharmaceutical processes happen in water, a better understanding of water's molecular structure could shed light on how dissolved salts, proteins, and drug molecules interact in solution. "These interactions are vital for injectable drugs and cell function," he noted, but applying this knowledge to practical uses is still a long way off.

Physicists recently wondered what would happen if you tried to split a photon ‪—‬ and they found some unexpected behavior that may transform the way we think about particles.

The experiment, in which researchers simulated a photon being sliced by a shutter under various conditions, showed that a severed photon can lead to a complex mixture of zero to infinitely-many photons — raising some big questions about the nature of particle interactions.

Photons are elementary packets of light, which means they are not made up of anything else. So what does it even mean to try splitting a photon? It may be possible thanks to wave-particle duality — a core principle of quantum mechanics, the bizarre physics of the very small.

According to wave-particle duality, a photon is not only a particle but also a wave. Using theoretical calculations, the researchers investigated what would happen if you sent this photon through a shutter and closed it while the photon was passing through, effectively cutting off the tail end of the photon wave.

"I think that most physicists would expect there to be a certain probability that you have zero photons and a certain probability that you have a single photon left after you have done this," Johannes Skaar, co-author of the new study and a professor of theoretical physics at the University of Oslo, told Live Science. "And that is approximately true, but it is not exactly true."

What are the chances?

This brings up another strange aspect of quantum mechanics: its probabilistic nature. Particles exist as a cloud of probabilities stretching to infinity. Until a particle is observed, its properties, such as its position or energy, are in a superposition of possible values; all we can know are the chances of finding it in a certain state.

Through their calculations, Skaar and his colleagues determined how cutting a photon affects these probabilities. In their study, recently accepted in the journal Physical Review Letters, they found that it would create a complex mixture of photon states, including one with an infinite number of photons.

Each of these states has a probability that depends on how quickly the shutter cuts the photon. The expected number of photons becomes infinite only if the shutter is closed infinitely quickly. For realistic shutter speeds, even a thousand photons would be extremely unlikely.

This may sound very strange, but the quantum physicists were unfazed. In fact, what surprised Skaar and his colleagues was what happens if you make measurements of the cut photon from different perspectives.

"When you measure from one side of the shutter, then it will look like a single photon state," Skaar said. "Then, on the other side, it will look like a vacuum state — that means no photons. And that is very strange because the actual state globally is this mixture from zero to infinity."

Changing how we think about particles

The fact that these complex mixtures can be treated locally as very simple states raises fundamental questions about the nature of particles. Skaar said they are still reckoning with the full extent of these implications and they are now considering how this process could play out for other quantum particles, such as electrons.

They hope that by following this theoretical thread through, they may be able to develop a neater way of describing particle interactions. Currently, particles' infinite stretching means they have been interacting for an infinite amount of time. This then poses a problem for causality ‪—‬ the order of cause and effect ‪—‬ in particle interactions, the team said.

These new theoretical photons with a cutoff tail would not have this problem, meaning the causal link in an interaction would be clear, Skaar said. He admitted that there is much more work to be done to develop the theoretical description of this interaction. However, the new result is an important step toward describing particle interactions with a clear causal relationship, which Skaar described as the team's "ultimate goal."

For decades, physicists have pursued a goal that sounds nearly impossible: to build a clock that keeps time using an atom's nucleus rather than the electrons orbiting it.

Now, researchers have demonstrated the first functioning nuclear clock ‪—‬ an advancement that could eventually lead to more robust timekeeping devices and new ways to search for dark matter and physics beyond the Standard Model.

"Having worked in this field for more than 15 years, it is just beautiful, how a very 'wild' idea such as manipulating an atomic nucleus with a laser has turned into reality," Thorsten Schumm, a professor of quantum metrology at the Vienna University of Technology and a member of the research team, told Live Science via email.

How is a nuclear clock different from an atomic clock?

Today's most accurate clocks are optical atomic clocks, which measure the frequency of electrons jumping between different energy levels inside atoms. These clocks are so precise that they would lose less than a second over a 100 million years.

A nuclear clock works similarly, but it uses a transition within the nucleus itself, where the nucleus jumps between energy levels. Because the nucleus sits deep inside the atom, it's far less affected by external disturbances from things like electric or magnetic fields. According to Schumm, the nuclear transition can be 1,000 to 10,000 times less sensitive to environmental noise than atomic transitions are.

"This means that it would be easier to stabilize a nuclear clock over long periods of time," Jacob Higgins, a postdoctoral researcher at Northwestern University who previously worked on thorium clock experiments at JILA in Colorado but was not affiliated with the study, told Live Science in an email. "The transition used for the nuclear clock experiment has a higher quality factor than optical atomic clock transitions, which means that in principle, it can be measured more precisely given the same amount of measurement time."

Together, those advantages could allow nuclear clocks to outperform even today's best atomic clocks according to Higgins.

Why thorium-229 is special

The nuclear clock relies on a rare isotope called thorium-229, whose nucleus contains an unusually low-energy excited state that can be manipulated with ultraviolet laser light.

For decades, scientists had suspected thorium had a low transition, but identifying and controlling it proved extremely challenging. Researchers spent years testing different thorium-containing materials, laser systems and detection methods before finally pinning down the transition.

"It was a long road," Higgins said.

One key advancement was the development of continuous-wave lasers that operate at the precise wavelength needed to excite the thorium nucleus. Before those lasers existed, researchers had to excite the nucleus and then wait several minutes for it to decay and emit a detectable signal. That process was too slow to build a practical clock.

"With the continuous lasers, we can measure the nucleus in absorption and get an immediate response, whether the laser is still at the right frequency (and if not, correct it back)," Schumm said. "Once we had that, it was 'just' implementing some electronics and atomization to have the clock stabilize itself to the nucleus."

Thanks to this set-up, the researchers kept the nuclear clock running continuously for 24 hours.

Unlike many optical atomic clocks, which require ultracold atoms to be suspended in a vacuum chamber, the thorium nuclei are embedded inside a crystal at room temperature.

Because the thorium transition remains stable inside a solid material, researchers may eventually be able to build compact clocks that are useful for navigation systems, telecommunication networks and data synchronization.

A tool for studying the universe

Some physicists are more excited about what nuclear clocks could reveal about fundamental physics, rather than the clocks' timekeeping abilities.

Atomic clocks primarily probe electromagnetic interactions involving electrons. Nuclear clocks, by contrast, are sensitive to the strong nuclear force, weak nuclear force and electromagnetism — three of the four fundamental forces of the universe, along with gravity. This can make them useful detectors of new physics, in a way.

"The nuclear clock is foremost a different clock, ticking on different fundamental physics mechanisms," Schumm said. "Essentially all modern theories beyond the standard model predict additional particles or 5th forces … which can be probed with the nuclear clock in some parameter regime."

Thorium-229 is particularly intriguing because the energy difference between its two nuclear states results from a delicate balance between electromagnetic and nuclear forces. Because those large contributions nearly cancel each other out, even tiny changes in the underlying forces could shift the clock's frequency.

"So small shifts in these forces — like if the nucleus were to couple to certain forms of dark matter or if there were an oscillation of a fundamental constant — will be amplified in our measurement," Higgins said.

Researchers, including Higgins, have already used early versions of the clock to place constraints on some dark matter models, and they expect its sensitivity to improve as the technology itself gets better.

Although the first functioning nuclear clock is a major achievement, these timekeepers remain in their infancy. Scientists still need to gain a better understanding of how the thorium transition responds to factors like temperature and magnetic fields while developing more powerful and stable laser systems.

"I think it will be many years before the thorium clock can compete with today's best optical atomic clocks," Higgins said, "but we will learn a lot of new science on the pathway to getting there."

It started with a plate of ginger chicken. In the late 1970s, physicist Richard Feynman — best known for his earlier work on the Manhattan Project — sat down for lunch with his friend Ralph Leighton at a restaurant in Glendale, California. Leighton was agonizing over ordering his usual favorite, or risking something new.

Feynman turned the choice into a math problem, and solved it on a piece of notebook paper. His equation showed exactly when Leighton — or any indecisive diner, for that matter — should stop taking risks and stick with what one knows is good.

For decades, Feynman’s notes on the "restaurant problem” were unreadable. But now, researchers reconstructed a decision-making problem from Richard Feynman's previously undeciphered notes and proved him to be right. The findings were published on June 1 in the journal Proceedings of the National Academy of Sciences.

The problem with picking lunch

Imagine you're visiting a new city for a week. Each night, you can either try an unknown restaurant or return to the best one you've already found. You want to maximize your total dining experience over the whole trip.

That kind of problem has a name in mathematics: an "optimal stopping problem." The same logic shows up in apartment hunting and job searching. But Feynman argued you can always go back to a previous restaurant. The goal is to maximize your cumulative enjoyment, not just find the single best spot.

Feynman's notes showed that the optimal strategy involves a quality threshold — a minimum score you require before committing — that starts high and drops as your trip runs out.

Brian Christian, a computer scientist and cognitive scientist at University of Oxford, began working on the problem about 13 years ago alongside his collaborator Tom Griffiths. They tracked down Feynman's original notes through the Feynman Lectures website.

The team proved that Feynman's solution was indeed optimal, then extended it to other versions of the problem: do people actually solve the problem this way?

They recruited 2,520 participants online and presented them with a digital version of the scenario: a grid of restaurants in a virtual city, each with a hidden quality score revealed only on the first visit. Participants aimed to maximize their total score over a fixed number of nights. Each person played just once.

"We wanted to really capture people's gut intuitions," Christian told Live Science. "When you just get thrown into this situation, what do you do?"

The answer: People don't follow Feynman's optimal curve in reality. Instead of the precise mathematical threshold, participants used a much simpler rule. Their quality bar started high and dropped by the same fixed amount each night regardless of how long the trip was or what the restaurant landscape looked like.

The simple strategy captured about 90% of the value that the optimal approach would yield.

"People are not doing the optimal thing. They're doing something radically simpler," Christian said. "And still the simple strategy is being tailored in a way that feels very situationally appropriate."

The slope of people's declining threshold was identical across every condition — a week-long trip or a month-long one, restaurants distributed evenly in quality or skewed toward extremes. What did shift was where people set their starting bar, adjusting it appropriately based on the landscape they'd seen.

In other words, people used a universal rule for how fast to lower their standards, but calibrated how high to set them in the first place.

An order of redemption

The results fit into an emerging framework in cognitive science called "resource rationality." The idea that humans aren't perfectly rational, but make good use of the limited time and brainpower they have.

"People don't do the perfect thing, but they make nearly perfect use of their constrained resources," Christian said. "I think this is a little bit more of a redemptive story about the human mind than we are used to from the 20th century."

That's a shift from the long tradition in behavioral economics emphasizing human irrationality and cognitive bias.

Christian says the findings also have implications for AI. Most AI systems assume people behave as perfectly rational agents. This study suggests that AI designed around how humans actually think — imperfectly — might work better.

Feynman died in 1988, never having published his restaurant analysis. But more than four decades after he scrawled those notes over lunch, the puzzle he left behind has finally been solved — and it turns out to say as much about the human mind as it does about what to eat.

Of the four fundamental forces of nature, gravity is the one we experience most directly ‪—‬ it's what keeps our feet on the ground and the sun in the sky. Yet we still can't pin down its exact strength. Since the 1980s, scientists have made more than a dozen measurements to calculate the precise value of gravity, and many of those numbers contradict one another.

So why is it so hard to figure out how strong gravity is?

One problem is that gravity is weak. Gravity feels strong because we constantly feel the pull of Earth. But the force of gravity between any two objects in everyday life — or any two objects that can fit in an experimental lab — is extraordinarily weak.

"It's weak, and you have to measure this against the background of the Earth's gravitational field," Stephan Schlamminger, a physicist at the National Institute of Standards and Technology, told Live Science. "If we measure gravity, we have to use everyday objects, because these are the only ones where we know the mass. What you have to do in the lab is basically use two very controlled masses, bring them close together, and measure the force between them."

In an April 2026 study, Schlamminger and colleagues replicated a precision experiment to determine the strength of gravity and calculated a value different from the previous result. They used 13 tons (12 metric tons) of mercury to run their experiment, but even then, "the change in the gravitational field was only a millionth of the change that we have here from local gravity," he said.

The team’s measured value was 6.67387x10^-11 m³kg^-1s^-2, which was 0.0235% lower than the previous result — a small difference in everyday terms, but significant in the field of metrology.

Christian Rothleitner, a physicist at the German National Metrology Institute, co-authored a comprehensive review of all gravity measurements with Schlamminger in 2017 but was not involved in the new study.

"This small force has to be determined to six or more decimal places," Rothleitner told Live Science in an email. "This is equivalent to trying to measure the weight of 7 human cells."

Physics, engineering and psychology

One explanation for the discrepancy in values could be that all of the measurements are so imprecise that the true value lies somewhere within them. But each experiment reports a small margin of error, and those ranges don't overlap.

Schlamminger thinks there are three possible reasons for this.

"I have it as a handy-dandy acronym: It's PEP: P stands for physics, E stands for engineering, and the second P stands for psychology," Schlamminger said. "It's sorted by excitement."

The least probable explanation, he said, is the physics one: Maybe there's some element of physics that scientists don't yet understand. Just as general relativity extended scientists' understanding of gravity, there may be another realm of physics yet to be discovered.

"I think it's a remote possibility, but we should not exclude it," Schlamminger said.

Then, there's the engineering explanation: Every experiment uses a slightly different setup, resulting in different values. Some use a torsion balance, a device that senses tiny forces by measuring the twisting of a small fiber. Others use pendulums or free-falling objects. Each approach has its own potential sources of error, and those mistakes are difficult to untangle from the gravitational signal.

"I personally do not believe that the reason lies in the physics, but in the measurement technology," Rothleitner said.

Human error is another part of the engineering explanation. "Such an experiment requires expert knowledge in many areas of physics and measurement technology," Rothleitner said. "You cannot be an expert in all those fields. This kind of measurement is on the cutting edge of measurement science."

The most likely possibility, Schlamminger said, relates to psychology.

"There is a driver for these people who measure these numbers to give really, really small uncertainties" — that is, margins of error — "because it makes them famous," Schlamminger said. "Because the pressure is there, the uncertainties may be a little bit too small, and that's why they don't agree with each other."

In the end, though, a precise measurement of gravity may not matter. We know the product of G times Earth's mass, and that's enough for practical applications like launching rockets into space. That may be all we need for now.

"The value of Newton's gravitational constant is rather of academic interest," Rothleitner said. "If it were different, nations would have spent much more effort in determining it better."

Schlamminger still finds it exciting, though. "We live in a society where we think everything is discovered," he said. "But if you look, there's still terra incognita. There are still problems, and the problems may be small, but they're still problems we can solve and contribute to and find mesmerizing and intriguing. And this is one of those problems."

Researchers at ETH Zurich have demonstrated a means of generating "perfect randomness" by using entangled superconducting qubits.

Creating true randomness is extremely difficult. Even the most sophisticated conventional random number generator can carry tiny biases. While in most everyday uses those biases are harmless, in cryptography — where the security of encrypted systems depends on unpredictability — even the most subtle pattern can become an exploitable weakness.

The team at ETH Zurich, led by physics professors Renato Renner and Andreas Wallraff, say they have shown how to overcome this flaw and create perfectly random numbers using quantum physics, a milestone they describe as the first certified realization of perfect randomness.

Random acts of qubits

Traditional random-number generators often rely on physical processes such as photon behavior, but those systems can still be slightly skewed and exhibit a bias that causes certain numbers to appear more frequently than others. The ETH team's approach uses quantum entanglement to push randomness beyond that limit.

The experiment revolves around two superconducting chips cooled to temperatures near absolute zero. Each chip acts as a qubit, the quantum equivalent of a binary bit. The chips are connected by a 98-foot (30-meter) tube that is also supercooled, allowing microwave photons to shuttle between them and create entanglement — a "spooky" quantum state where two particles can become linked such that measuring one instantly affects the other.

By keeping the qubits nearly 100 feet apart, the researchers ensured that, during measurement, even light-speed signals could not travel between the qubits quickly enough to influence the outcome. In the language of quantum physics, that helps preserve the integrity of the entanglement and prevents unwanted communication from spoiling the randomness.

The team then started with an imperfect random-number generator to choose the measurement basis for the qubits. After the quantum measurement, they used a special algorithm to amplify the randomness in the results. The key idea is that the quantum system can cleanse the input of bias and produce an output sequence of zeros and ones that is certifiably random, meaning its randomness is not merely assumed or inferred from standard statistical tests.

Practical randomness

The method also significantly reduces computational cost, Renner told Live Science by email.

"Our method does not really require a computation," Renner said, "as all the randomness is generated by measuring quantum bits. In this sense, the computational cost of our approach is negligible compared to that of pseudo-random number generators."

The researchers argue that the output remains perfect for all practical and analytical purposes, no matter how future methods might try to assess it.

The practical implications are significant. The ETH team compares the advance to an atomic clock for timekeeping: a physically reliable reference that other systems can rely on. Future potential applications include message encryption, digital identities, lottery systems and blockchain operations.

Renner stated that their work would be most useful in network architectures. "Our experiment would be most useful in networks where every node has access to a 'server' that implements it to produce randomness."

When a beam of light passes through a cloud of atoms, photons (particles of light) sometimes appear to spend a negative amount of time there, with light seeming to exit the cloud before it even enters. Now, physicists have confirmed this quantum quirk by asking the atoms themselves.

"This doesn't mean that we're on the verge of building a time machine or anything like that," study co-author Howard Wiseman, a theoretical quantum physicist at Griffith University in Australia, told Live Science. "It can all be understood with standard physics, but it's yet one more weird property of quantum physics that people hadn't suspected."

Photons that pass through an atomic cloud can be temporarily absorbed. They vanish as particles of light and reappear as atomic excitations — a kind of stored energy — before being reemitted. Some photons, called transmitted photons, make it through in roughly the same direction they entered Others scatter off in random directions.

Experiments dating back to 1993 had already hinted that transmitted photons tend to arrive at a detector before the center of their own pulse even enters the cloud. That implies a negative transit time.

But there was a problem with this setup: Photons at the front of a pulse may be more likely to make it through than photons at the back. If you look only at the ones that are transmitted, of course, they look early. But this left a door open for a simpler explanation.

"People were convincing themselves that this is not actually as crazy as it sounds," Wiseman told Live Science.

Confirming the crazy

In a new paper published April 13 in the journal Physical Review Letters, physicists tried a different approach. Rather than watching when a photon arrived at a detector, they monitored whether the atoms were in an excited state while the photon was passing through.

When a photon is absorbed by an atom, it is stored as energy, causing the atom to enter what physicists call an excited state. The atom remains in this excited state until it reemits the photon. Therefore, measuring the duration of the atom's excited state reveals how long the photon was absorbed by the atom.

The team measured this using a second beam of light, which picked up a tiny phase shift depending on the atoms' excitation levels. The light beam acted as a live readout of what the atoms were experiencing from moment to moment.

This atomic readout confirmed the quantum craziness of the earlier experiments.

"You get the same answer if you ask the atoms, 'How long was the photon staying with you?'” Wiseman said. "They will also tell you an answer, which is a negative time."

A million-test milestone

Getting that answer wasn't easy, because measuring quantum systems disturbs them. In this case, it potentially prevents the photon from being absorbed at all. So the team used "weak measurements," which are gentle but extremely noisy. Any single run of the experiment was swamped by noise — random fluctuations that made it impossible to tell signal from static in any individual measurement. Only after averaging roughly 1 million runs did a clear signal emerge. Across roughly seven sets of experimental parameters, the total data collection ran to approximately 70 hours.

"Even in this really simple thing — a photon interacting with atoms — people were already doing calculations on that almost 100 years ago," Wiseman said. "Just the fact that it can still show surprises after all this time is interesting."

The team's next target is the photons that don't make it through the cloud. Theory predicts that those scattered photons carry extra positive excitation time. That is enough to balance the negative time of the transmitted ones, keeping the overall average for the beam of light at zero or above. That prediction has never been tested.

Recently, a cheerful 100-year-old message in a bottle was found on the south-west coast of Australia. In it, a world war one soldier proclaimed to be "as happy as Larry."

If you're a betting person, you probably wouldn't expect great odds of this happening. A bottle cast into the ocean could end up absolutely anywhere.

If it floats to a remote location, there is little chance of somebody stumbling upon it. And if it lands somewhere more favorable where people could potentially find it, there are other issues. The message itself will deteriorate over time as light degrades it. If the bottle fills with water, it will sink and almost certainly never be found.

So, what are the chances of a message in a bottle being found and it being over 100? And what are your chances of finding this bottle?

Despite these many possibilities during a bottle's lifetime, the probability we are after is a straightforward calculation. Just count up the number of bottles with messages that have been found and are over 100 years old, and divide by the number of messages that have been sent this way (assuming we know how many are sent):

Our diagram below shows a hypothetical situation where 20 bottles are sent in total, of which six are found (indicated in gold) and one of these is over 100 years old (indicated by the "100" stamp). So, one in 20 bottles are found and over 100 years old. (Note: This is only a hypothetical calculation, not the real data.)

Instead of calculating the probability directly, another way to do it is by breaking the problem into two parts: (A) a bottle with a message is found, and (B) the found bottle is over 100. These two probabilities can be calculated separately and multiplied together to get what we want:

This is known as the "multiplication rule" of probability, and we confirm from our hypothetical numbers that (6/20)×(1/6) = 1/20, as before.

Both approaches to calculating this probability are simple. However, the direct calculation requires knowing the total number of bottles sent out, which is very difficult to know in the real world.

The multiplication rule has the advantage that it breaks the calculation into two parts. We can tackle each separately, then bring the two results together to get the probability we want. This is useful in the real-world situation where we can draw information from different sources.

First, we'll deal with the probability that a bottle with a message is found, irrespective of its age.

Experts from the Federal Maritime and Hydrographic Agency of Germany suggest a 1 in 10 chance that a message in a bottle will be found. This aligns broadly with various historical "drift bottle" experiments, where oceanographers released large numbers of bottles to understand ocean currents.

For example, studies from the 1960s and '70s in the North Atlantic Ocean led to recovery rates of 14% from the Gulf of Mexico, 8% from the Caribbean Sea and 7% from the northern Brazilian coast. A more recent and more northerly study (between Canada and Greenland) from the 2000s led to a 5% recovery rate.

We would expect the results to vary naturally from different experiments in different parts of the world. But to keep things simple, we will stick with 1/10 as the probability that a bottle with a message is found.

Now for the second piece of the calculation: of the bottles that are found, what proportion are over 100 years old?

The table below summarises data from news articles collected on Wikipedia about very old bottles with messages that have been found. However, only data on bottles over 25 years old has been collected, presumably because older bottles are more newsworthy.

So, we needed to estimate the number of 0- to 25-year-old bottles with messages ourselves — here’s how we did this.

The table shows that fewer bottles with messages are found as they get older. Messages in bottles degrade over time, which means the bottles have an increased chance of breaking and sinking, or just getting covered in layers of sediment. Plotting this data in the graph below helped us see the trend in the ages of found bottles more clearly.

We drew a line to match this observed trend in the ages of found bottles. This red line in the graph corresponds to the equation:

This equation provides an estimate of how many bottles have been found for any specific age range (where 25 = 0-to-25, 50 = 25-to-50 and so on). We are interested in the the 0- to 25-year-old bottles, so the equation suggests 46 bottles have been found in this range.

Adding up this and all of the numbers in the table gives a total of 106 bottles found, of which 12 are over 100 years old, and 12/106 is about one in ten.

Recapping the above, we have that: (A) one in ten bottles with messages are found, of which (B) one in ten are over 100 years old. Bringing these results together using the multiplication rule, we estimate the chance of a message in a bottle being found and it being over 100 years old to be (1/10)×(1/10) = 1/100.

So, if there are 100,000 bottles with messages floating around the oceans waiting to be found, we’d expect 1,000 of these to be found and be 100 or more years old. Assuming anybody in the world is equally likely to find one of these, with 8 billion people currently, that’s about a 1 in 8 million chance of you finding one – pretty unlikely.

However, some people are more persistent at message-in-a-bottle hunting than others. Following the paths of ocean currents (known as gyres) could provide clues on where to look.

Specifically, peninsulas or islands intersecting with these gyres could be good spots. For this reason, it has been suggested the Caribbean islands are ideally placed for finding bottles as they lie on the path of the North Atlantic Gyre. Which seems like a great reason to travel to the Carribean!

But let's also spare a thought for the poor soul stranded on their desert island, who surely won't appreciate the low odds of their SOS being found.

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

For the first time, researchers have detected empty voids moving faster than the speed of light — and they blazed past that cosmic speed limit without breaking the laws of relativity.

A recent study shows the voids' acceleration. Researchers used recent advances in ultrafast electron microscopy to measure voids in phonon-polariton waves zooming around inside a thin flake of boron nitride. Phonon-polaritons are quasiparticles formed from photons (quantized light) coupled with tiny vibrations, and they act like light and sound waves combined.

Waves are often visualized as a single squiggle, but in many applications, imagining them as a lake could give a better idea of what's going on. Lakes are full of waves and ripples that interfere with each other. If the waves interact when they're at their maximum height, they combine to create an even higher wave. But if they make contact when they're at their lowest points, they create deeper troughs than they would on their own.

Sometimes, waves cancel each other out, creating points where the waves' magnitude drops to zero. In a lake, this would make a temporary whirlpool (a vortex) that moves around that empty point, also called a singularity. These singularities are found throughout nature and mathematics and, since the 1970s, have been theorized to move faster than light speed in some instances, according to a recent statement from the Technion-Israel Institute of Technology.

Blazing past the limit

Einstein's theory of special relativity states that the speed of light in a vacuum ‪—‬ 299,792,458 meters per second, or about 186,000 miles per second ‪—‬ is the fastest speed information, matter and energy can travel through space. So how do singularities move faster than light speed? Because singularities are empty points of nothingness, they contain no information, no matter and no energy. They are tiny voids, so they don't have to obey the cosmic speed limit.

These voids don't just exceed the speed of light ‪—‬ they blaze past it. When two singularities encounter each other, they can sometimes exponentially speed up toward each other until their velocities approach infinity just before they cancel each other out. However, the faster they go, the harder it is to observe them. The recent study, published March 25 in the journal Nature, shows researchers doing just that.

"Our discovery reveals universal laws of nature shared by all types of waves, from sound waves and fluid flows to complex systems such as superconductors," Ido Kaminer, an electrical and computer engineering professor at the Technion-Israel Institute of Technology and a member of the research team, said in the statement.

The study's results apply to more than just tiny whirlpools; the null points act enough like particles that scientists can study them to better understand particle interactions. To do this, researchers need to know where the comparison breaks down. The new study shows the voids' need for speed is a point where the singularities stop acting like particles, since particles obey the cosmic speed limit that voids ignore.

In addition, the team's new techniques for observing very small, very fast things could light up some previously unexplored pockets across multiple scientific disciplines.

"We believe these innovative microscopy techniques will enable the study of hidden processes in physics, chemistry, and biology, revealing for the first time how nature behaves in its fastest and most elusive moments," Kaminer added.

For the first time, scientists have observed quantum entanglement in the way atoms physically move — bringing a phenomenon once described by Albert Einstein as "spooky action at a distance" into even sharper reality.

In the new study, published in the journal Nature Communications, researchers demonstrated that pairs of ultracold helium atoms can be quantum mechanically linked through their momentum — a measure of how fast and in which direction a particle moves, factoring in its mass.

Quantum entanglement is one of the strangest features of quantum mechanics. When two particles are entangled, a measurement of one instantly affects the other. Scientists had demonstrated this before in photons (packets of light) and in the internal spin states of atoms but never in the motion of particles with mass. This is important because atoms have mass, and mass responds to gravity; photons don't. Momentum-entangled atoms could one day power quantum sensors precise enough to detect space-time ripples called gravitational waves or to map Earth's interior.

Catching entanglement in the act

First, the team chose helium as their atom, because it can be held in a long-lived excited state with a lifetime of around two hours — which is “essentially infinite” in experiments that only last 20 to 30 seconds, Sean Hodgman, an experimental physicist at the Australian National University and senior author of the study, told Live Science. That internal energy means each atom hits a detector with enough force to register individually. It allows the team to reconstruct the full three-dimensional momentum of the cloud with single-atom resolution.

To create momentum-entangled atom pairs, the team started with a cloud of helium cooled to near absolute zero. Normally, atoms zip around independently. But if you cool them enough, they slow to a near standstill. Their quantum identities blur together into a single collective object called a Bose-Einstein condensate.

Then, they used tuned laser pulses to split that condensate into three groups: one kicked upward, one kicked downward, and one left stationary. As the moving clouds passed through the stationary one, pairs of atoms collided and scattered in opposite directions, forming spherical shells of correlated pairs. Physicists call it "scattering halos." At low enough density, only a single pair scatters per experimental shot. "You either have a pair at one position, or a pair at another," Hodgman said. "Your entangled state is a superposition of both."

To prove the entanglement was real, the team used a device called a Rarity-Tapster interferometer. This method, first demonstrated with photons in 1990, now extended to matter waves for the first time.

"The atoms scatter apart; then you reflect them back onto themselves and interfere with them together," Hodgman explained. "Interference only occurs if the atom is truly in a superposition of both states." The correlations the team measured cannot be explained by any classical theory.

To get their final result, the team collected data continuously for nearly a month and spent a month to a year just setting up the experiment.

"This has kind of been a long-term goal for our lab for probably 20 years or so," Hodgman said. "To be able to finally demonstrate it is really exciting."

A surreal win for quantum mechanics

The result, while exciting, mainly served to validate “textbook” physics theories, Hodgman added. Quantum mechanics predicts this exact kind of behavior, but that doesn't make it any less disorienting.

"Our brains aren't really equipped to process it," Hodgman added. "Atoms appear as smeared out at small scales, not concrete blobs or little balls. And that just seems really, really weird."

The team is already working on a stronger version of the test. But the experiment Hodgman describes as the most consequential next step involves colliding two isotopes of helium ‪—‬ helium-3 and helium-4, which are fundamentally different kinds of particles — to create pairs entangled in both momentum and mass simultaneously.

"From a quantum gravity point of view, how do you even write down the gravitational description of that kind of state?" Hodgman said. "You can't really describe it in a general relativity framework at all. These sorts of states would provide a real challenge for quantum gravity theories to explain."

Athreya, Y. S., Kannan, S., Yan, X. T., Lewis-Swan, R. J., Kheruntsyan, K. V., Truscott, A. G., & Hodgman, S. S. (2026). Bell correlations between momentum-entangled pairs of 4He* atoms. Nature Communications, 17(1). https://doi.org/10.1038/s41467-026-69070-3

How much do you know about Albert Einstein and quantum physics? Try your luck with our Einstein quiz!

Physicists have successfully transported antimatter by truck for the first time — a milestone that allows them to study the elusive material with unprecedented precision and could eventually help to explain how matter came to dominate the universe.

The short, tightly controlled journey around the campus of the European Organization for Nuclear Research (CERN) in Geneva demonstrated that antimatter, one of the most fragile substances known to science, can be moved without being destroyed. That capability allows scientists to transport antimatter to quieter labs across Europe, where ultrasensitive experiments are less affected by interference than they are at CERN.

"This opens, in principle, an entire new universe for precision measurements outside of CERN," Stefan Ulmer, a spokesperson for the BASE (Baryon Antibaryon Symmetry Experiment) collaboration that carried out the experiment, said in a recent video.

What’s the matter with antimatter?

According to current theories, the Big Bang should have produced equal amounts of matter and antimatter. If that were the case, the two would have annihilated each other completely, leaving behind a dark, empty universe. Instead, the observable universe is puzzlingly, overwhelmingly made of matter, and physicists believe that any measurable difference between matter and antimatter could offer a crucial clue to resolving that mystery.

CERN has been producing antimatter for decades through high-energy particle collisions at its "antimatter factory." But the same powerful equipment used to create the particles also generates tiny magnetic fluctuations that can disrupt the extremely precise measurements scientists are trying to make. Relocating antimatter to more stable environments could help, but transporting it is notoriously difficult.

When antimatter comes into contact with ordinary matter, both are instantly destroyed in a burst of energy. To prevent that, scientists confine antimatter particles using carefully tuned electric and magnetic fields in a near-perfect vacuum — conditions that are challenging to maintain even in a stationary laboratory, let alone in a moving vehicle.

To test whether transport was feasible, Ulmer and his team loaded 92 antiprotons, the antimatter counterparts of protons, into a portable trap and drove them about 5 miles (8 kilometers) around CERN's campus.

Inside the device, the particles were suspended in a near-perfect vacuum and held in place by electric and magnetic fields, preventing them from touching the container walls. The team monitored the particles throughout the trip and reported that they remained stable despite road vibrations and motion, according to a CERN statement.

Even in a worst-case scenario, the experiment posed little risk. The amount of antimatter involved was extremely small, and its annihilation would have released only a negligible amount of energy. According to CERN, even all the antimatter ever produced at the facility would generate only enough energy to power a single light bulb for just a few minutes.

Beyond the Standard Model

The successful test does not immediately change how antimatter is studied, but it demonstrates that transporting it is technically feasible. That, in turn, opens the possibility of moving antiprotons to quieter laboratories across Europe, such as the Heinrich Heine University Düsseldorf in Germany, located about eight hours by road from CERN, where quieter conditions could enable more precise measurements.

Such measurements could help scientists detect even the faintest differences between matter and antimatter. If those differences exist, they could point to why matter came to dominate the universe, offer clues to physics beyond the Standard Model, and ultimately explain why anything — from stars, to planets, to people — exists at all.

"We are at the beginning of an exciting scientific journey that will allow us to further deepen our understanding of antimatter," Gautier Hamel de Monchenault, CERN's director for research and computing, said in the statement.

The Big Bang is often described as the moment everything began — a point of infinite density where the laws of physics broke down. But what if that picture is incomplete?

A new study proposes a different account of the universe's birth: Instead of an abrupt beginning from a singularity, as predicted by Einstein's theory of general relativity, the early cosmos may have passed through a more controlled high-energy phase governed by a modified theory of gravity known as QQG.

"QQG stands for quadratic quantum gravity," study co-author Niayesh Afshordi, a professor of physics at the University of Waterloo and the Perimeter Institute for Theoretical Physics, told Live Science via email. "In simple terms, it is an extension of Einstein's theory of gravity that includes additional terms which become important at extremely high energies, such as those that would have existed near the beginning of the universe."

The study was published March 18 in the journal Physical Review Letters.

Why Einstein's theory may not be enough

Einstein's theory of general relativity has been extraordinarily successful in describing gravity on large scales. It explains the motion of planets, the behavior of black holes, and the expansion of the universe. However, it struggles to explain the ultra-small world of quantum mechanics and is widely believed to contain some fundamental inconsistencies.

"The main problem is that Einstein's general relativity predicts its own failure under extreme conditions, most famously at the Big Bang singularity," Afshordi said.

At that point, densities and space-time curvature become infinite — a clear indication that the theory is incomplete. Physicists have long sought a deeper framework that can describe gravity under such conditions.

"What makes [quadratic quantum gravity] interesting is that it may provide a mathematically consistent way to describe gravity at very short distances and very high energies, where ordinary general relativity is expected to break down," Afshordi said. "In that sense, it offers a possible conservative route toward a quantum theory of gravity, while still remaining close to Einstein's theory at ordinary scales."

A universe without a singularity

In the new study, the researchers explored how QQG would reshape the earliest moments of the cosmos if it is indeed a correct completion of Einstein’s theory. Their results suggest that the universe may not have started from a singular point at all.

"Our main result is that, within quadratic gravity, the very early universe can avoid the usual Big Bang singularity and instead pass through a better-controlled high-energy phase," Afshordi said.

Rather than emerging from an infinitely dense state, the universe would have begun in a smoother, more stable configuration with finite density and finite temperature, with its precise properties depending on the particles and fields present at extremely high energies and temperatures. This avoids one of the most troubling predictions of standard cosmology.

The theory also offers a fresh perspective on cosmic inflation, the brief period of extremely rapid expansion thought to have occurred just after the Big Bang.

"In our analysis, this framework can also generate an inflation-like period without having to introduce an extra hypothetical field by hand," Afshordi said.

In standard models, inflation is typically driven by a mysterious field known as the inflaton. That field has never been directly observed. In contrast, QQG produces inflation naturally as a consequence of gravity itself.

"In other words, some of the key ingredients we normally add separately to cosmology may arise directly from the gravitational theory itself," Afshordi added.

From exotic physics to the familiar universe

One striking feature of QQG is that it behaves very differently depending on the energy scale. At extremely high energies, it follows new quantum rules. But as the universe expands and cools, it transitions back to the familiar physics described by Einstein.

The theory suggests that gravity becomes simpler at very high energies — a property known as asymptotic freedom — before evolving into the form we observe today. Eventually, the universe enters the hot, radiation-filled phase described by standard cosmology.

This framework provides a continuous bridge between an exotic early universe and the well-tested physics of later times. The key question, however, is whether this idea can be tested.

"Yes, at least in principle," Afshordi said. "The most promising tests come from cosmology, especially from the imprint of the early universe on primordial gravitational waves and the cosmic microwave background."

These ancient signals carry information about the universe's earliest moments. According to the new theory, these signals should contain subtle differences compared with predictions from standard inflation models.

"One particularly interesting aspect of our scenario is that it can lead to distinctive predictions for the gravitational-wave signal produced in the early universe," Afshordi noted. "As observational sensitivity improves over the coming years and decades, future measurements of primordial gravitational waves could begin to distinguish this kind of model from more conventional inflationary scenarios."

Although the idea is still being explored, it offers a compelling possibility: that the Big Bang may not have been a singular beginning but rather part of a deeper, quantum description of gravity. If confirmed, this framework could reshape how scientists understand the origin of the universe — replacing a breakdown of physics with a new, more complete picture of cosmic beginnings.

Think you know about Einstein's theories? Test your knowledge with our Albert Einstein quiz!

Molecular vibrations can "catapult" electrons across solar materials in quadrillionths of a second‬ ‪— much faster than previously thought, a new study shows.

The findings could help scientists find more efficient ways to convert solar energy into electricity, according to the study, which was published March 5 in the journal Nature Communications.

"We're effectively watching electrons migrate on the same clock as the atoms themselves," study co-author Pratyush Ghosh, a researcher who studies ultrafast spectroscopy at the University of Cambridge, said in a statement.

Organic molecules go solar

Organic solar cells use carbon-based molecules, rather than silicon, to convert sunlight into electricity. In theory, organic solar cells could provide that electricity at lower cost than conventional solar cells, but they are much less efficient.

In a typical organic solar cell, an electron donor and an electron acceptor are sandwiched between two conductive electrodes. When light hits the cell, it generates an "exciton," an electron-hole pair. Excitons split at the interface between the donor and the acceptor, generating electricity.

To achieve fast charge transfer at the interface and limit energy loss, the donor and acceptor molecules usually have strong electronic coupling, or overlap between their electronic states, which allows charges to move easily between molecules. They also often have a large energy difference between them, but that limits the voltage available from the device.

In the new study, researchers observed ultrafast charge transfer at a junction between the electron donor and electron acceptor in an organic solar cell, without needing to conform to either of these constraints. The team used a short laser pulse to excite the electron donor, a polymer called TS-P3, and then used a different laser to measure how the system changed during charge transfer.

That charge transfer happened in 18 femtoseconds ‪—‬ about as fast as an individual molecule vibrates. A few other systems without strong driving forces exhibit charge transfer over 100 to 200 femtoseconds, but most take ten to a thousand times that long.

"Seeing it happen on this timescale within a single molecular vibration is extraordinary," Ghosh said in the statement.

A 'molecular catapult'

That similar timescale wasn't a coincidence. In a second set of laser experiments, the team found that vibrations in the polymer donor molecule launched an electron across the junction to an acceptor molecule. When the electron arrived, it triggered overlapping vibrations in the acceptor molecule. This overlap allowed charge transfer to happen much more quickly than expected, and without the need for strong coupling or a large energy difference.

"Instead of drifting randomly, the electron is launched in one coherent burst," Ghosh said in the statement. "The vibration acts like a molecular catapult. The vibrations don't just accompany the process, they actively drive it."

The findings help to explain the processes that control the speed of charge transfer and establish new strategies for designing more efficient organic solar cells and materials, the researchers wrote in the study.

"Instead of trying to suppress molecular motion, we can now design materials that use it ‪—‬ turning vibrations from a limitation into a tool," study co-author Akshay Rao, a physicist at Cambridge, said in the statement.

Today's top story

Hex appeal

Researchers in China claim to have synthesized the very first samples of "hexagonal diamond" — a mysterious and coveted material believed to be harder, stiffer and chemically tougher than natural diamond.

Scientists have been arguing about hexagonal diamonds (whose carbon atoms arrange themselves in hexagons instead of the cubic lattices seen in natural diamonds) for decades. First theorized in 1962, the diamonds were later discovered in meteorites that arrived to Earth from the mantles of shattered dwarf planets, although the evidence for this is disputed.

Now, three separate research groups appear to have made pure to nearly pure hexagonal diamond samples. If their findings are replicated consistently and can be scaled up, they could open up all kinds of new applications.

The trend

Scaling down

Climate change is making fish smaller, according to an alarming new study published in the journal Science. It warns that the shift may worsen fishery losses by 50%.

As ocean temperatures soar, fish are evolving to grow faster and mature earlier, reducing their maximum size. This in turn leads to smaller catches for fisheries, putting a vital protein source relied upon by billions of people on a very thin line.

The scientists behind the study say this is yet another reason to reduce carbon emissions, preserving millions of tons of food production that would otherwise be lost.

Three to read

1. Measles' resurgence in the US is a grim sign of what's coming [Live Science]
2. China creates a clock so accurate it could redefine the second [ScienceAlert]
3. GPS is being weaponized in electronic warfare ‪—‬ and it's putting ships at risk [Live Science]

Say it, said it

Word of the day: Zugzwang — Starting as a chess term, this German word is used in psychology and game theory to describe a situation where any move you make will worsen your position.

Quote of the day: "We are now faced with a 30-million-tonne question: we need to determine if this is just a small, natural leakage of ancient carbon, or the onset of broadscale destabilization."

Travis Drake, a carbon biogeochemist at the Swiss Federal Institute of Technology Zurich (ETH Zurich), on the detection of ancient carbon seeping into the atmosphere from the Congo Basin.

Fun and games

Today's game is Chain Word, which is a bit like another popular word game, but with science.

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Researchers in China have made what they claim to be the first samples of pure hexagonal diamond, a theorized rare variant of superstrong diamond found in meteorites from shattered dwarf planets.

Natural diamond, also called cubic diamond, has been considered the hardest natural material on Earth for so long that the Mohs hardness scale, which rates minerals' resistance to scratching, uses diamond as the scale's upper limit. It's called cubic diamond for its neat arrangements of carbon atoms in a cubic structure. In contrast, hexagonal diamond organizes carbon atoms in a lattice made of hexagons, like a honeycomb.

An elusive mineral

In 1962, researchers at the Pittsburg Coal Research Center theorized that layers of carbon atoms making up diamond could be organized in a hexagonal lattice instead of a cubic one, thanks to how carbon forms bonds with other carbon atoms. In 1967, researchers discovered hexagonal diamond — or lonsdaleite — in the lab, suspecting it could be harder than cubic diamond.

They started looking for it in a special type of diamond-rich meteorite called ureilite, which forms from the mantle of smashed dwarf planets. The first detections of hexagonal diamond in the wild were documented in a 1967 paper; three Canyon Diablo meteorites (fragments of an asteroid that created a large crater in Arizona) with about 30% hexagonal and 70% cubic diamond phases, and Goalpara meteorites (found in Assam, India) that had a small amount of hexagonal diamond.

Not everyone agrees that the Canyon Diablo lonsdaleite exists. Some scientists thought the evidence could be explained by flawed cubic diamond that was stacked chaotically, and they weren't convinced that lonsdaleite had been detected in previous studies. However, multiple recent studies have identified lonsdaleite in meteorites and in lab samples, including a 2025 study that made small amounts of it in the lab.

The biggest challenge in identifying lonsdaleite is the lack of pure samples; in many cases, it is mixed with cubic diamond, graphite and other minerals. This makes it difficult ‪—‬ or even impossible ‪—‬ to test and measure its unique properties.

The new study, published March 4 in the journal Nature, addressed this problem by creating several pure hexagonal diamond samples about 0.06 inches (1.5 millimeters) in diameter ‪—‬ big enough to measure the samples' material properties. The team found that hexagonal diamond is both stiffer and harder than cubic diamond, and that it resists oxidation much more than cubic diamond does. This means hexagonal diamond can tolerate much higher temperatures without its surface getting all gunked up by reacting with oxygen, which is important for applications like drilling.

First evidence of hexagonal diamond?

The study also provides major evidence that hexagonal diamond is a real material. According to the study, "structural and spectroscopic analyses, supported by large-scale molecular dynamical simulations, unambiguously confirm the identity of HD (hexagonal diamond)."

To make the samples, the researchers compressed very organized graphite (graphite with carbon atoms neatly arranged) for 10 hours at 20 gigapascals, or about 200,000 times Earth's atmospheric pressure at sea level, and subjected them to temperatures ranging from 2,300 to 3,450 degrees Fahrenheit (1,300 to 1,900 degrees Celsius). At higher temperatures and pressures, the lonsdaleite started morphing into cubic diamond.

Hexagonal diamond could improve processes and tools that currently rely on cubic diamond, like drilling and cutting tools, polishing abrasive coatings, and dissipating heat from electronics. Its presence in meteorites can also tell us a lot about how the meteorite formed and where it came from, giving more clues about our solar system.

The elusive material "has potential applications in many fields, for example in cutting tools, in thermal management materials and in quantum sensing", Chong-Xin Shan, co-lead of the new Nature study and a physicist at Zhengzhou University, told Nature in an article.

The new study also provides "a practical strategy for producing HD (hexagonal diamond) in bulk form," opening the way for bigger samples, more scientific exploration, and industrial applications no longer limited by cubic diamond's hardness, according to the authors.

As an irrational number, pi has no end — but that has not stopped computer engineers from chasing its eternal string of decimal places deeper into the unknown. Recently, technology media company StorageReview achieved a staggering new record, calculating 314 trillion digits of pi on a single Dell PowerEdge R7725 server that ran constantly for nearly four months.

The result shows that in modern pi calculations, the real battle is no longer just about processor speed but also storage space and efficiency. StorageReview's Dell PowerEdge R7725 server had 1.5 terabytes of memory to get the job done.

"The storage layer, specifically, is where this record was actually won," StorageReview representatives wrote in a December 2025 statement.

An irrational arms race

Previous pi records have jumped fast in the past few years, from Google Cloud's 100 trillion-digit run in 2022 to StorageReview's own 105 trillion-digit and 202 trillion-digit marks in 2024. In April 2025, Linus Media Group and Kioxia stole the crown by calculating pi to 300 trillion digits — but StorageReview reclaimed the record in November 2025.

The results were announced in time for Pi Day, March 14 (or 3/14) — a nod to the number's famous first three digits (3.14). The day has become a lighthearted tribute to math, marked by pie jokes, slices of pie, classroom contests and a public fascination with a number that never ends.

Why pi is important

Pi is a key constant in mathematics, linking every circle's circumference to its diameter. It appears in geometry, physics, engineering and statistics, showing up in everything from waves and orbits to bridges, buildings and computer models. Most people encounter pi in school as a simplified number used to find the area or circumference of a circle. But for engineers and scientists, it's a building block that helps describe how the physical world works.

Pi is considered an irrational number because it cannot be written as a simple fraction of two whole numbers. Its decimal form never ends and never settles into a repeating pattern. Mathematician Johann Lambert was the first to prove pi was irrational in 1761, showing that no fraction can exactly equal the ratio of a circle's circumference to its diameter. So, even though pi is a precise number, its decimal expansion is endless.

All those digits aren't strictly necessary for accurate calculations; NASA typically stops at 16 digits in its most precise calculations about the universe. Still, researchers challenge themselves to calculate pi to ever-more decimal places for multiple reasons. It's a way to test the limits of computers, storage and software, as a huge pi run can expose weaknesses in hardware better than many standard benchmarks. Calculating pi also helps researchers refine algorithms for handling other large calculations.

Then, of course, there's the fame of being the one to calculate pi out to the most decimal places yet. To achieve the mind-boggling result of 314 trillion digits of pi, StorageReview delivered around 280 GB/s bandwidth on its Dell server to handle the huge stream of intermediate calculations required for such a large run.

"If someone wants to take the record, we would like to see them take the whole thing: more digits, less power, shorter wall time, and the same zero-downtime reliability," the company said in the statement. "Until then, this is the benchmark for efficiency."

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

Researchers have developed a technology to invisibly transmit information disguised as background thermal radiation. Using a phenomenon called "negative light," they transferred 100 kilobits of data per second in a way that was completely undetectable to outside observers.

Most methods for concealing data during transfer involve hiding it among other data or encrypting it in a way that makes it impossible to read without a cipher or other means of decryption. The new technique, by contrast, makes the data almost impossible to intercept because there's no indication it's being sent at all. It can also be encrypted through traditional means to further harden security, the team wrote in a paper published March 5 in the journal Light: Science & Applications.

This hidden transfer is possible due to a phenomenon called "negative light." It relies on infrared radiation, which is the band just beyond the red end of the visible light spectrum. Infrared radiation is invisible to the naked eye, but it can be detected with thermal cameras. We experience it as heat from warm objects, and all objects emit a faint glow in the infrared.

The negative luminescence the team used could make that glow dimmer, rather than brighter. In a statement, Michael Nielsen, a professor of engineering at the University of New South Wales Sydney and lead author of the study, compared it to a flashlight that could "project darkness" as compared to background light, rather than simply turning off.

Using devices called thermoradiative diodes, the team created patterns of brighter- or darker-than-usual states that blended into typical infrared background "noise" but that can be read as data by specialized receivers.

The thermoradiative diodes were born as part of another project, in which the team proved that it was possible to generate solar power even after the sun had set. This "night-time solar" tech captured infrared radiation that Earth had absorbed during the day and was releasing at night as it cooled. The team then used thermoradiative diodes to generate a small amount of power.

While the initial transfer rate of 100 kbps is quite modest, Nielsen said higher speeds are achievable. The main hurdle was the availability of some of the sophisticated electronics the team required. In principle, there's nothing stopping this method from transferring tens of megabits per second with existing devices, with better devices and detector design pushing the speed to gigabits per second, the team said.

In fact, a commercial product delivering megabit-per-second data rates may be possible in just a few years, Ned Ekins-Daukes, a professor of photovoltaic and renewable energy engineering at UNSW and co-leader of the research, said in the statement.

By using graphene ‪—‬ a single-atom-thick sheet of carbon atoms arranged in a honeycomb pattern ‪—‬ instead of the current semiconductor material in the diodes, "we can potentially achieve data transfer rates in the gigabits-per-second range, if not hundreds of gigabits," Ekins-Daukes said.

Improved data security would have major applications in a variety of industries, including health care, defense, finance and manufacturing. Nielsen believes that virtually any communication that could benefit from security beyond standard encryption could take advantage of his team's breakthrough.

"The real advantage of this technique is that the very signal or act of communication is hidden if an outside observer doesn't have the same technology required to intercept the communication," Nielsen told Live Science in an email.

Earlier this month an artificial intelligence (AI) startup announced that their AI agent had confirmed a proof of two cases of the devilishly challenging "higher dimensional sphere-packing problem." In 2022, the proofs earned Ukrainian mathematician Maryna Viazovska a Fields Medal, one of the most prestigious prizes in math.

This was a giant step forward, and speaks to the emergence of a quiet revolution in the field.

On the surface, it may not seem so extraordinary. After all, mathematicians have long used tools to extend their abilities — abacuses, slide rules, calculators and, eventually, computers. Yet none of these tools ever replaced mathematicians; they just allowed us to refocus our attention on more interesting problems. The arrival of AI in mathematics might feel like another step in that same process. But there's a crucial difference: This time, the tools aren't just helping us calculate; they're helping us reason, or at least perform many of the routines that sit underneath human reasoning.

This represents a seismic shift in what it means to do mathematics. Instead of working unassisted, struggling at the boundaries of our own cognitive limits, we are starting to build and tune the instruments that will allow us to extend these limits, pairing human intuition with machine-level discipline. This might mean that our most sophisticated proofs won't be works a single mind can grasp; rather, they will be fully understood only in a collective mind that relies heavily on AI tools. It also means the scope of the math we can tackle will increase dramatically.

The change has been coming for a while. For years, our biggest proofs have not been the endeavours of single mathematicians. Many modern research articles in pure mathematics now rely on huge conceptual frameworks, long dependency chains, and catalogs of results that no single person can fully internalize. Computers have played a role in large proofs before, like the four-color theorem and the Kepler conjecture. But what's changing now is the level of autonomy and reliability we can expect from AI systems working alongside formal proof assistants — programs designed to check mathematical arguments.

These formal verification languages express mathematical arguments in a way a computer can check step by step, guaranteeing that every part of the proof is logically sound. Take the language Lean, for example. Unlike ordinary mathematical writing, Lean requires every definition and inference to be made explicit, and it checks each step mechanically and methodically. It's unforgiving, but in a productive way: If the argument is passed by Lean, that, in theory, means the proof doesn't have hidden assumptions or leaps of faith. Over the past few years, Lean has become a proving ground for research‑level mathematics, and mathematicians have been building "libraries" to support increasingly complex problems.

These libraries are huge collections of definitions and already‑verified theorems that have been painstakingly programmed, allowing researchers to prove new results in the language. But until recently, turning cutting‑edge proofs into machine‑checkable form required specialists to devote months or years to the work.

That's the context in which the recent formal verification of Viazovska's higher-dimensional sphere‑packing results should be understood. The sphere‑packing problem asks how tightly identical spheres can be packed together in spaces of any dimension, not just the 3D world we live in. Before Viazovska's breakthrough, the sphere‑packing problem had only been fully solved in dimensions one, two and three, with all higher‑dimensional cases remaining open. Viazovska's proofs of the eight- and 24‑dimensional sphere-packing problem, are profound pieces of mathematical insight that solve problems previously thought out of reach.

Fields Medal-level advancements

The recent important step forward is that a human-AI collaboration has now translated those arguments into fully verified Lean code, which then checked every step. The sheer scale of that achievement is astonishing; these are recent Fields Medal‑level results, and they have now been certified at a level of detail and certainty that would be impossible for individual referees, or even large human specialist teams, to reproduce unaided.

A key ingredient was Math, Inc.'s AI reasoning agent Gauss which had played a vital role in helping to turn human mathematical arguments into Lean proofs. The AI system wasn't working entirely unaided; mathematicians still had to set out the blueprint, shape the overall structure, and ensure the right concepts were in place. But once that scaffolding existed, the system could fill in the missing pieces at extraordinary speed. In the eight‑dimensional case, it completed work that the human contributors had estimated would take them months, and it did so in days. The 24‑dimensional case, which is even more intricate, followed soon after.

This is more than a technical accomplishment. It points toward a shift in the way mathematicians might organize their work. When I talked to UCLA mathematician and Fields Medalist Terence Tao, he suggested that the immediate value of AI might come not from cracking our hardest problems outright but from relieving us of the drudgery — the thousand small cases that are conceptually straightforward but too time‑consuming for any one person to tackle by hand.

Some AI systems, he argued, are already surprisingly good at handling these tasks, letting mathematicians devote their attention to strategy rather than bookkeeping. Tools like Lean matter because they give us a way to separate the creativity of generating ideas from the rigor of checking them.

AI proof expert Kevin Buzzard, of Imperial College London, expressed a complementary view. He worries, rightly, about the dangers of relying on large language models that sound authoritative without guaranteeing correctness. But he also argues that formalization offers a way through this. In Lean, if the program accepts all the steps, then it's a valid proof. This doesn't mean the computer has necessarily done something "intelligent" but rather that the formal verification language leaves no room for hidden steps or suggestive-but-incomplete arguments. The challenge, as he sees it, is that most of modern mathematics still hasn't been translated into formal libraries, so the systems don't yet have the concepts they need.

This latest step forward suggests the gap is beginning to close. The sphere‑packing project is probably the clearest demonstration yet of what is becoming possible.

None of this means mathematicians are on the brink of extinction. In fact, I suspect the opposite is true. As the space of verifiable mathematics expands, so too does the need for people who can pose good questions, create new definitions, and recognize when an argument is genuinely insightful. But we are going to have to adapt. We may find ourselves acting more like scientific-instrument builders and less like lone theorists, weaving together human intuition and AI tenacity to produce machine‑verified certainty.

Mathematics has always moved forward by partnering with assistive tools. AI doesn't change that practice; it just takes it to the next level. Mathematical concepts won't get easier to prove, but our capacity to test, verify and build upon them will surely increase.

Opinion on Live Science gives you insight on the most important issues in science that affect you and the world around you today, written by experts and leading scientists in their field.

Researchers have developed a method for steering microscopic swimming robots using light patterns and the principles of Einstein's theory of relativity. The technology is a potential first step toward deploying tiny robots in applications ranging from medicine to manufacturing.

One of the major challenges of developing microrobots for practical applications is creating ones capable of navigation without the inclusion of bulky sensors and other electronics, which would make the machines too large to operate at the desired scale (like inside a human body). In an attempt to overcome this issue, physicists at the University of Pennsylvania created "artificial space-time" to direct machines to travel in the same way that spacecraft or light does while crossing the universe.

In the study, researchers submerged 100-micron (roughly the width of a human hair) electrokinetic (EK) swimming robots in an ionized solution and tasked them with navigating a simple maze. The bots were covered with tiny solar cells with electrodes on both ends; when the solar cells were exposed to light, they powered the electrodes, which created an electric field that propelled the robots through the solution.

The challenge was to guide the microscopic machines with enough precision for them to reach a specific point in space, without being stymied by the maze's walls. That's where relativity came in. According to Einstein's theory of general relativity, gravity bends space-time around objects with mass. Light and objects follow "straight" geodesics ‪—‬ the shortest paths ‪—‬ that look bent around masses. A great example of this is gravitational lensing: Although light travels in a straight line across the cosmos, it can appear bent and magnified when passing through the gravitational well of a massive object, such as a large galaxy cluster.

"We showed that the way EK robots behave in patterned light fields is identical to the paths light follows in general relativity," lead study author Marc Miskin, an assistant professor of electrical and systems engineering at the University of Pennsylvania, told Live Science in an email. "Amazingly, you can use the robots as a gravity analog since the correspondence is exact. Alternatively, you can turn general relativity ideas around to use them to guide robots: in the same way gravity pulls objects together, you can guide robots to a specific spot."

Artificial space-time

To mimic the effect, the team modeled the maze as curved virtual space using relativity equations. Paths to the target inside the maze became simple straight lines in the model. Then, they converted the model back to a 2D light map. Dark spots naturally attracted the bots, while brighter spots repelled them. The end point of the maze was the darkest spot (a kind of faux black hole), with obstacles being more brightly lit.

Regardless of where they were initially placed, the EK bots naturally followed these geodesics, dodging walls automatically, as if sliding downhill in warped space. The team published their findings in November 2025 in the journal npj Robotics.

For Miskin, the study is a bridge between the worlds of physics and technology, "rather than a competition between them," he said. "On the one hand, relativity and light are very well understood; connecting reactive control to them invites new ways of thinking and established tools for robotics. On the other hand, general relativity and optics are also very abstract (think bending spacetime), while robotics is mechanistic and concrete (it's very easy to understand why the robot does what it does). In addition to showing how new types of robots behave according to known theories of optics, the experiments give researchers "a bit more" insight into general relativity, particularly in exploring the impact of "flat space-times" in 2D spaces, Miskin added.

While the maze study is a very early step, Miskin said practical applications may emerge over the next 10 years.

"Some use cases we're interested in exploring include checking up on teeth following a root canal, a kind of dental biopsy to make sure everything was cleared, eliminating tumors after making local measurements to confirm cells are cancerous, or even, outside of bio, assembly of microchips with tiny robotic helpers," Miskin said. "The microworld is a fascinating place; I wouldn't be surprised if these ideas are just the tip of the iceberg."

We all know we live in three-dimensional space. But what does it mean when people talk about four dimensions?

Is it just a bigger kind of space? Is it "space-time," the popular idea which emerged from Einstein's theory of relativity?

If you have wondered what four dimensions really look like, you may have come across drawings of a "four-dimensional cube". But our brains are wired to interpret drawings on flat paper as two- or at most three-dimensional, not four-dimensional.

The almost insurmountable difficulty of visualising the fourth dimension has inspired mathematicians, physicists, writers and even some artists for centuries. But even if we can't quite imagine it, we can understand it.

What is dimension?

The dimension of a space captures the number of independent directions in it.

A line is one-dimensional. We can move along it forwards and backwards, but these are opposite, not independent, directions. You can also think of a string or piece of rope as practically one-dimensional, as the thickness is negligible compared with the length.

A surface, such as a soccer field or the skin of a balloon, is two-dimensional. There are independent directions forwards and sideways.

You can move diagonally on a surface, but this is not an independent direction because you can get to the same place by moving forwards, then sideways. The space we live in is three-dimensional: in addition to moving forwards and sideways, we can also jump up and down.

Four-dimensional space has yet another independent direction. This is why space-time is considered four-dimensional: you have the three dimensions of space, but moving forward or backward in time counts as a new direction.

One way to imagine four-dimensional space is as an immersive three-dimensional movie, where each "frame" is three-dimensional and you can also fast-forward and rewind in time.

Consider the cube

A powerful tool for understanding higher dimensions is through analogies in lower dimensions. An example of this technique is drawing cubes in more dimensions.

A "two-dimensional cube" is just a square. To draw a three-dimensional cube, we draw two squares, then connect them corner to corner to make a cube.

So, to draw a four-dimensional cube, start by drawing two three-dimensional cubes, then connect them corner to corner. You can even continue doing this to draw cubes in five or more dimensions. (You will need a large piece of paper and need to keep your lines neat!)

This experiment can help accurately determine how many corners and edges a higher-dimensional cube has. But for most of us, it will not help us "see" one. Our brains will only interpret the images as complex webs of lines in two or at most three dimensions.

Knots

We can tie knots in three dimensions because one-dimensional ropes "catch on each other". This is why a long rope wound around itself, if done right, won't come apart. We trust knots with our lives when we're sailing or climbing.

But in four dimensions, knots would instantly come apart. We can understand why by using an example in fewer dimensions, like we did with cubes.

Imagine a colony of two-dimensional ants living on a flat surface divided by a line. The ants can't cross the line: it's an impassable barrier for them, and they don't even know the other side of the line exists.

But if one day an ant, and its world, becomes three-dimensional, that ant will step over the line with ease. To step over, it needs to move just a tiny bit in the new, vertical direction.

Now, instead of an ant and a line on a flat surface, imagine a horizontal and a vertical piece of rope in three dimensions. These will catch on each other if pulled in opposite directions.

But if the space became four-dimensional, it would be enough for the horizontal piece of rope to move just a little bit in the new, fourth direction, to avoid the other entirely.

Thinking of four dimensions as a movie, the pieces of rope live in a single, three-dimensional frame. If the horizontal piece of rope shifts just slightly into a future frame, in that frame there is no vertical piece, so it can easily move to the other side of the vertical piece before shifting back.

From our three-dimensional perspective, the ropes would appear to slide through each other like ghosts.

Knots in more dimensions

Is it impossible, then, to knot a rope in higher dimensions? Yes: any knot tied on a rope will come apart.

But not all is lost: in four-dimensional space you can knot two-dimensional surfaces, such as balloons, large picnic blankets or long tubes.

There is a mathematical formula that determines when knots can stay knotted: take the dimension of the object you want to knot, double it, and add one. According to the formula, this is the maximum dimension of a space where knotting is possible.

The formula implies, for example, that a rope (one-dimensional) can be knotted in at most three dimensions. A (two-dimensional) balloon surface can be knotted in at most five dimensions.

Studying knotted surfaces in four-dimensional space is a vibrant topic of research, which provides mathematical insight into the the still poorly understood mysteries into the intricacies of four-dimensional space.

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

Physicists may have a brand-new way to measure the expansion rate of the universe — one of the biggest outstanding mysteries in cosmology — using space-time ripples predicted by Einstein.

A new study suggests that the faint gravitational wave background produced by numerous merging black holes across the universe can be used to independently measure how fast space is expanding. Even without detecting this background "hum" directly, the researchers show that it already places limits on the Hubble constant — a key quantity at the heart of one of modern cosmology's biggest puzzles.

If confirmed, the technique could settle the debate about whether we need to come up with new physics to explain the nature of the universe.

An independent test of the Hubble constant

The expansion rate of the universe, encoded in the Hubble constant, has become the focus of intense debate in recent years. Measurements based on the early universe, such as those inferred from the leftover radiation from the Big Bang (known as the cosmic microwave background), disagree with measurements derived from more nearby objects, like flickering supernovas and galaxies. This discrepancy, known as the Hubble tension, has now reached high statistical significance.

"The Hubble tension is one of the most important open problems in cosmology," Chiara Mingarelli, an assistant professor of physics at Yale University who was not involved in the new study, told Live Science via email. "Early-Universe and late-Universe measurements of the expansion rate disagree at over 5 sigma [the "gold standard" of statistical significance in physics], and we don't know why. Either there's an unidentified systematic error or new physics. Any genuinely independent measurement of the expansion rate is extremely valuable."

The new research, accepted for publication in the journal Physical Review Letters and available as a preprint, proposes such an independent method based almost entirely on gravitational waves — subtle ripples in the fabric of space-time predicted by Einstein's theory of general relativity.

"This result is very significant," study co-author Nicolás Yunes, a professor of astrophysics at the University of Illinois Urbana-Champaign, said in a statement. "Our method is an innovative way to enhance the accuracy of Hubble constant inferences using gravitational waves."

Listening to the background hum of black holes

Since 2015, detectors such as the Laser Interferometer Gravitational-Wave Observatory (LIGO), the Virgo interferometer, and the Kamioka Gravitational Wave Detector (KAGRA) have observed dozens of individual black hole mergers through gravitational waves. Each merger provides information about the masses of the black holes involved and their distances from Earth.

"Because we are observing individual black hole collisions, we can determine the rates of those collisions happening across the universe," lead study author Bryce Cousins, a graduate student at the University of Illinois Urbana-Champaign, said in the statement. "Based on those rates, we expect there to be a lot more events that we can't observe, which is called the gravitational-wave background." This gravitational wave background, sometimes described as a stochastic (or random) signal, is the faint, collective effect of numerous distant mergers. Its overall strength depends on how quickly the universe is expanding. A slower expansion implies larger cosmic volumes and, therefore, more mergers contributing to the background.

"It's a clever idea," Mingarelli said. "The gravitational-wave background — the collective hum of distant black hole mergers too faint to detect individually — depends on the expansion rate. A slower expansion means larger volumes, more mergers, and a louder background. So even the non-detection of this background disfavors low values of the Hubble constant."

Using current data from gravitational wave detectors, the team showed that the absence of a detected background already rules out some lower values of the Hubble constant. While the present constraints are broad, the method establishes a new framework for cosmological inference.

A new tool for cosmology

The approach builds on the concept of "standard sirens," in which individual gravitational wave events act as distance markers. But instead of relying on single bright events, the new method exploits the entire unresolved population of colliding black holes.

"It's not every day that you come up with an entirely new tool for cosmology," study co-author Daniel Holz, a professor of physics and astronomy at the University of Chicago, said in the statement. "We show that by using the background gravitational-wave hum from merging black holes in distant galaxies, we can learn about the age and composition of the universe.

"This is an exciting and completely new direction, and we look forward to applying our methods to future datasets to help constrain the Hubble constant, as well as other key cosmological quantities," Holz added.

While the new method shows promise, Mingarelli also emphasized the current limitations. "The main strength is that this is an almost entirely gravitational-wave-based measurement — independent of the electromagnetic distance ladder and the cosmic microwave background," Mingarelli said. "The limitation is that uncertainties are still large, and the result depends on the assumed black hole population model. But the authors are upfront about this and show their choices are conservative."

Looking ahead, detector upgrades are expected to significantly improve sensitivity to the gravitational wave background.

"With planned detector upgrades, the background should be detected within a few years, turning this from a lower bound into a real measurement," Mingarelli said.

If successful, this stochastic siren method could become a powerful new tool for probing the expansion history of the universe and for investigating whether the Hubble tension signals new physics or hidden systematic errors in existing measurements.

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

Elevators have a strange way of messing with your sense of gravity. The moment an elevator lurches upward, you feel it in your feet. For a second, the floor presses harder than usual. When the elevator slows, that pressure eases, leaving you briefly lighter.

If you stand on a scale inside an elevator going up, the number jumps. When it slows to a stop, the number dips. On the way down, the opposite happens.

So what's really going on? Do you weigh more when the elevator goes up or when it goes down?

The short answer is that you can feel heaviest at two points: when the elevator starts moving up (accelerating upward) and when it's slowing down at the very end of a downward trip (decelerating downward). But the explanation depends on what "weight" actually means and what your body can feel.

"The word 'weight' in physics has different meanings," Miguel Morales, a physics professor at the University of Washington in Seattle, told Live Science. In physics, weight can refer to at least three related ideas: your mass (how much matter you're made of), the gravitational force pulling on you, or how hard the scale beneath you is pushing up, Morales explained.

"When you're just standing still, those can all be the same thing," Morales said. "But as soon as the elevator starts to speed up or slow down, you get three different answers. It's just physics."

Your mass never changes, no matter what the elevator does. Gravity near Earth's surface also stays essentially the same between the bottom and top of a building. What does change is the third definition: how hard the scale pushes upward. That upward push is what a scale actually measures.

Looking at gravity

This distinction reveals something counterintuitive: "You can't feel gravity. You never could," Jason Barnes, a physics professor at the University of Idaho, told Live Science.

Barnes pointed to astronauts aboard the International Space Station. "The actual gravity of the Earth up there is almost the exact same as here," he said. "But they don't feel it."

That's not because gravity disappears in orbit. At the station's altitude (about 250 miles, or 400 kilometers, above our planet), Earth's gravitational pull is still about 90% as strong as it is at the surface. The difference is that astronauts and the space station are in continuous free fall toward Earth.

The station is moving sideways at more than 17,000 mph (27,300 km/h). As it falls, Earth curves away beneath it. Instead of hitting the ground, it keeps missing it. The result is a constant fall around the planet.

Because the astronauts and the space station are falling together at the same rate, the floor never needs to push up on them. And that upward push is what we actually feel as weight (also called the normal force).

On Earth, the ground constantly prevents you from falling by pushing upward against you. In orbit, there's no such push. The astronauts are still under the influence of gravity, but nothing is stopping them from falling. Without the floor pressing upward, they feel weightless.

Why do elevators make you feel heavier or lighter?

An elevator briefly changes how hard the floor pushes back on you. When the elevator starts rising, it must accelerate you upward, too. "To start going up, that's when you feel heavier," Barnes said. "The elevator pushes back harder than normal in order to accelerate you upward."

In a typical building elevator, that extra acceleration might be about 1 meter per second squared. That is roughly one-tenth of Earth's gravity. For someone who normally weighs 150 pounds (68 kilograms), that would briefly add about 10% to the scale reading. Instead of 150 pounds, the scale might show around 165 pounds (75 kg).

Morales described the same effect from the scale's perspective. "The force of gravity hasn't changed at all," he said. "But now, in order for you to be speeding up, something's got to be pushing you harder than gravity. And so your weight on the scale will go up."

Once the elevator reaches a steady speed, the acceleration stops. Gravity and the upward push balance again, and the scale returns to its normal reading, even though you're still moving.

At the top, when the elevator slows to a stop, the opposite happens. Even though you're still moving upward, the elevator must accelerate downward slightly to slow you down.

The force of gravity hasn't changed. But because the elevator is now accelerating downward, the floor doesn't need to push up as hard to control your motion. With less upward push (normal force), the scale reading drops.

"You kind of feel yourself get a little light," Morales said.

The same pattern repeats on the way down. When the elevator accelerates downward, you feel lighter because the floor pushes up less than usual. But as it approaches the bottom and slows to a stop, the acceleration flips upward again, making you feel heavy again.

This everyday experience turns out to be connected to one of the most important ideas in modern physics.

"It is an effect that Einstein first noted when he was developing general relativity," Barnes said. That insight, known as the equivalence principle, helped Einstein understand gravity not as a force but as a consequence of acceleration and the curvature of space-time itself.

The ubiquitous squeak of sneakers on a basketball court may be caused by more than just friction, a new study suggests.

Researchers have found that the sharp chirp of rubber on a hard floor happens when tiny areas of slipping between the shoe's sole and the floor move at supersonic speeds — and, in some experiments, the process involved miniature, lightning-like sparks. What's more, the findings could lead to an improved understanding of earthquakes and aid in the design of grippy surfaces.

The new study, published Feb. 25 in the journal Nature, shows that soft rubber does not slide the way many people imagine. Instead of the whole sole sticking and then slipping at once, motion bunches into fast, wrinkle-like fronts called "opening slip pulses" that detach and reattach the rubber across the contact zone. Those repeating pulses generate the vibrations that our ears hear as squeaks.

Scientists have long explained squeaks from shoes, bicycle brakes and tires using stick-slip friction, a stop-and-go cycle in which surfaces repeatedly catch and then break free. That model works well for many hard-on-hard systems, like door hinges.

But soft materials like rubber behave differently when they slide across rigid surfaces.

To understand the physics of this process, researchers at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) teamed up with experts from the University of Nottingham in the U.K. and the French National Center for Scientific Research. They used high-speed optical imaging and synchronized audio to watch soft rubber move quickly along smooth glass.

But what they saw was not smooth sliding. Instead, motion bunched up into opening slip pulses, sweeping across the rubber in starts and stops.

"Fundamentally, these findings challenge the long-held assumption that soft-material friction can be fully captured by simplified, one-dimensional ‘stick-slip’ models," first study author Adel Djellouli, a postdoctoral fellow at Harvard, told Live Science in an email.

Tiny lightning everywhere

The findings reveal more about the physics of friction. In classic stick-slip friction, the whole contact surface alternates between sticking and slipping. In this study, however, the motion was more localized, as only small regions opened and slipped, and then moved on, while other regions stayed in full contact.

For some experiments, the team also saw tiny flashes caused by the friction, which they described as miniature "lightning" sparks. In some tests, those sparks, or electrical discharges, appeared to trigger the slip pulses. The sparks were not the main source of the squeaking noise, but they showed how electrical energy could build up in the system when the rubber moved.

The researchers also found that the rubber's shape, more than its movement, was the main determinant of the squeak's pitch.

When flat rubber blocks slid across the glass, the slip pulses were irregular, producing a broad "whoosh" rather than a clean squeak. But when the researchers added thin ridges to the rubber, the ridges confined the pulses and made them repeat at regular intervals.

In effect, the ridges acted like guides, channeling the pulses into a repeating cycle. This locked the sound into a specific frequency, or tone. The team found that this squeak frequency depended mainly on the height of the rubber ridges.

In fact, the pattern was so reliable that the team designed blocks of different heights and used them to play the Imperial March theme from "Star Wars" by hand.

"When it came time to actually play the Star Wars theme song, we had to rehearse for three solid days to get the video right," said Djellouli. "None of us are exactly trained in making music with squeaky rubber blocks, so getting the timing and technique down took a lot of practice. I think the funniest part was the relief in the lab when we finally finished the recording after three days of constant, high-pitched squeaking. Our colleagues were very happy to finally have some quiet again!"

What sneakers may have in common with earthquakes

The findings have implications beyond shoe design. The slip pulses in the experiments share key features with rupture fronts in earthquakes, where sections of a fault suddenly break and slide at very high speeds.

"Soft friction is usually considered slow, yet we show that the squeak of a sneaker can propagate as fast as, or even faster than, the rupture of a geological fault, and that their physics is strikingly similar," study co-author Shmuel Rubinstein, a professor of physics at the Hebrew University of Jerusalem and a visiting professor at SEAS, said in a statement.

Beyond shedding light on the physics of earthquakes, the work could help engineers design surfaces that switch between slippery and grippy states on demand.

"Tuning frictional behavior on the fly has been a long-standing engineering dream," Katia Bertoldi, a professor of applied mechanics at Harvard, said in the statement. "This new insight into how surface geometry governs slip pulses paves the way for tunable frictional metamaterials that can transition from low-friction to high-grip states on demand."

At a secret meeting in 2025, some of the world's leading mathematicians gathered to test OpenAI's newest large language model, o4-mini.

Experts at the meeting were amazed by how much the model's responses sounded like a real mathematician when delivering a complex proof.

"I've never seen that kind of reasoning before in models," Ken Ono, a professor of number theory at the University of Virginia said at the time. "That's what a scientist does."

But was the artificial intelligence (AI) model being given more credit than it deserved? And do we run the risk of accepting AI-derived proofs without fully understanding them?

Ono acknowledged that the model might be giving convincing — but potentially incorrect — answers.

"If you say something with enough authority, people just get scared," Ono said. "I think o4-mini has mastered proof by intimidation; it says everything with so much confidence."

In the past, confidence and the appearance of a good argument were good signs because only the best mathematicians could make convincing arguments, and their reasoning was usually sound. That has changed.

"If you were a terrible mathematician, you would also be a terrible mathematical writer, and you would emphasize the wrong things," Terry Tao, a mathematician at UCLA and the 2006 winner of the prestigious Fields Medal, told Live Science. "But AI has broken that signal."

Naturally, mathematicians are beginning to worry that AI will spam them with convincing-looking proofs that actually contain flaws that are difficult for humans to detect.

Tao warned that AI-generated arguments might be incorrectly accepted because they look rigorous.

"Unfortunately, the AI is much better at sounding like they have the right answer than actually getting it … right or wrong; they will always look convincing," Tao said.

He urged caution on the acceptance of AI '"proofs." "One thing we've learned from using AIs is that if you give them a goal, they will cheat like crazy to achieve the goal," Tao said.

While it may seem largely abstract to ask whether we can truly "prove" highly technical mathematical conjectures if we can't understand the proofs, the answers can have significant implications. After all, if we can't trust a proof, we can't develop further mathematical tools or techniques from that foundation.

For instance, one of the major outstanding problems in computational math, dubbed P vs. NP, asks, in essence, whether problems whose solutions are easy to check are also easy to find in the first place. If we can prove that, we could transform scheduling and routing, streamline supply chains, accelerate chip design, and even speed up drug discovery. The flip side is that a verifiable proof might also compromise the security of most current cryptographic systems. Far from being arcane, there is real jeopardy in the answers to these questions.

Proof is a social construct

It might shock non-mathematicians to learn that, to some extent, human-derived mathematical proofs have always been social constructs — about convincing other people in the field that the arguments are right. After all, a mathematical proof is often accepted as true when other mathematicians analyze it and deem it correct. That means a widely accepted proof doesn't guarantee a statement is irrefutably true. Andrew Granville, a mathematician at the University of Montreal, suspects there are issues even with some of the better-known and more scrutinized human-made mathematical proofs.

There's some evidence for that claim. "There have been some famous papers that are wrong because of little linguistic issues," Granville told Live Science.

Perhaps the best-known example is Andrew Wiles' proof of Fermat's last theorem. The theorem states that although there are whole numbers where one square plus another square equals a third square (like 3²+4²=5²), there are no whole numbers that make the same true for cubes, fourth powers, or any other higher powers.

Wiles famously spent seven years working in almost complete isolation and, in 1993, presented his proof as a lecture series in Cambridge, to great fanfare. When Wiles finished his last lecture with the immortal line "I think I'll stop there," the audience broke into thunderous applause and Champagne was uncorked to celebrate the achievement. Newspapers around the world proclaimed the mathematician's victory over the 350-year-old problem.

During the peer-review process, however, a reviewer spotted a significant flaw in Wiles' proof. He spent another year working on the problem and eventually fixed the issue.

But for a short time, the world believed the proof was solved, when, in fact, it hadn't been.

Mathematical verification systems

To prevent this sort of problem—where a proof is accepted without actually being correct—there's a move to shore up proofs with what mathematicians call formal verification languages.

These computer programs, the best known example of which is called Lean, require mathematicians to translate their proofs into a very precise format. The computer then goes through every step, applying rigorous mathematical logic to confirm the argument is 100% correct. If the computer comes across a step in the proof it doesn't like, it flags it and doesn't let go. This encoded formalization leaves no room for the linguistic misunderstandings that Granville worries have plagued previous proofs.

Kevin Buzzard, a mathematician at Imperial College London, is one of the leading proponents of the formal verification. "I started in this business because I was worried that human proofs were incomplete and incorrect and that we humans were doing a poor job documenting our arguments," Buzzard told Live Science.

In addition to verifying existing human proofs, AI, working in conjunction with programs like Lean, could be game-changing, mathematicians said.

"If we force AI output to produce things in a formally verified language, then this, in principle, solves most of the problem," of AI coming up with convincing-looking, but ultimately incorrect proofs, Tao said.

Buzzard agreed. "You would like to think that maybe we can get the system to not just write the model output, but translate it into Lean, run it through Lean," he said. He imagined a back-and-forth interaction between Lean and the AI in which Lean would point out errors and the AI would attempt to correct them.

If AI models can be made to work with formal verification languages, AI could then tackle some of the most difficult problems in mathematics by finding connections beyond the scope of human creativity, experts told Live Science.

"AI is very good at finding links between areas of mathematics that we wouldn't necessarily think to connect," Marc Lackenby, a mathematician at the University of Oxford, told Live Science.

A proof that no one understands?

Taking the idea of formally verified AI proofs to its logical extreme, there is a realistic future in which AI will develop "objectively correct" proofs that are so complicated that no human can understand them.

This is troubling for mathematicians in an altogether different way. It poses fundamental questions about the purpose of undertaking mathematics as a discipline. What is ultimately the point of proving something that no one understands? And if we do, can we be said to have added to the state of human knowledge?

Of course, the notion of a proof so long and complicated that no one on Earth understands it is not new to mathematics, Buzzard said.

"There are papers in mathematics where nobody understands the whole paper. You know, there's a paper with 20 authors and each author understands their bit," Buzzard told Live Science. "Nobody understands the whole thing. And that's fine. That's just how it works."

Buzzard also pointed out that proofs that rely on computers to fill in gaps are nothing new. "We've had computer-assisted proofs for decades," Buzzard said. For instance, the four-color theorem states that if you have a map divided into countries or regions, you'll never need more than four distinct colors to shade the map such that neighboring regions are never the same colors.

Almost 50 years ago, in 1976, mathematicians broke the problem into thousands of small, checkable cases and wrote computer programs to verify each one. As long as the mathematicians were convinced there weren't any problems with the code they'd written, they were reassured the proof was correct. The first computer-assisted proof of the four-color theorem was published in 1977. Confidence in the proof built gradually over the years and was reinforced to the point of almost universal acceptance when a simpler, but still compute-aided, proof was produced in 1997 and a formally verified machine-checked proof was published in 2005.

"The four-color theorem was proved with a computer," Buzzard noted. "People were very upset about that. But now it's just accepted. It's in textbooks."

Uncharted territory

But these examples of computer-assisted proofs and mathematical teamwork feel fundamentally different from AI proposing, adapting and verifying a proof all on its own — a proof, perhaps, that no human or team of humans could ever hope to understand.

Regardless of whether mathematicians welcome it, AI is already reshaping the very nature of proofs. For centuries, the act of proof generation and verification have been human endeavors — arguments crafted to persuade other human mathematicians. We're approaching a situation in which machines may produce airtight logic, verified by formal systems, that even the best mathematicians will fail to follow.

In that future scenario — if it comes to pass — the AI will do every step, from proposing, to testing, to verifying proofs, "and then you've won," Lackenby said. "You've proved something."

However, this approach raises a profound philosophical question: If a proof becomes something only a computer can comprehend, does mathematics remain a human endeavor, or does it evolve into something else entirely? And that makes one wonder what the point is, Lackenby noted.

Heavy collisions at the Large Hadron Collider (LHC) have revealed the faintest trace of a wake left by a quark slicing through trillion-degree nuclear matter — hinting that the primordial soup of the universe may have literally been more soup-like than we thought.

The new findings from the LHC's Compact Muon Solenoid (CMS) collaboration show the first clear evidence of a subtle "dip" in particle production behind a high-energy quark as it traverses quark-gluon plasma — a droplet of primordial matter thought to have filled the universe microseconds after the Big Bang.

A study describing the results, published Dec. 25, 2025, in the journal Physics Letters B, provides a tantalizing look at the universe in its first moments.

Re-creating early-universe conditions in the lab

When heavy atomic nuclei collide at near-light speed inside the LHC, they briefly melt into an exotic state known as quark-gluon plasma.

In this extreme environment, "the density and temperature is so high that the regular atom structure is no longer maintained," Yi Chen, an assistant professor of physics at Vanderbilt University and a member of the CMS team, told Live Science via email. Instead, "all the nuclei are overlapping together and forming the so-called quark-gluon plasma, where quarks and gluons can move beyond the confines of the nuclei. They behave more like a liquid."

This plasma droplet is extraordinarily small — about 10^-14 meters across, or 10,000 times smaller than an atom — and vanishes almost instantly. Yet within that fleeting droplet, quarks and gluons — the fundamental carriers of the strong nuclear force that holds atomic nuclei together — flow collectively in ways that resemble an ultrahot liquid more than a simple gas of particles.

Physicists want to understand how energetic particles interact with this strange medium. "In our studies, we want to study how different things interact with the small droplet of liquid that is created in the collisions," Chen said. "For example, how would a high energy quark traverse through this hot liquid?"

Theory predicts that the quark would leave a detectable wake in the plasma behind it, much as a boat slicing though water would. "We will have water pushed forward with the boat in the same direction, but we also expect a small dip in water level behind the boat, because water is pushed away," Chen said.

In practice, however, disentangling the "boat" from the "water" is far from straightforward. The plasma droplet is tiny, and the experimental resolution is limited. At the front of the quark's path, the quark and plasma interact intensely, making it difficult to tell which signals come from which. But behind the quark, the wake — if present — must be a property of the plasma itself.

"So we want to find this small dip in the back side," Chen said.

A clean probe with Z bosons

To isolate that wake, the team turned to a special partner particle: the Z boson, one of the carriers of the weak nuclear force — one of the four fundamental interactions, along with the electromagnetic, strong, and gravitational forces — responsible for certain atomic and subatomic decay processes. In certain collisions, a Z boson and a high-energy quark are produced together, recoiling in opposite directions.

Here's where the Z boson becomes crucial. "The Z bosons are responsible for the weak force, and as far as the plasma is concerned, Z just escapes and is gone from the picture," Chen said. Unlike quarks and gluons, Z bosons barely interact with the plasma. They leave the collision zone unscathed, providing a clean indicator of the quark's original direction and energy.

This setup allows physicists to focus on the quark as it plows through the plasma, without worrying that its partner particle has been distorted by the medium. In essence, the Z boson serves as a calibrated marker, making it easier to search for subtle changes in particle production behind the quark.

The CMS team measured correlations between Z bosons and hadrons — composite particles made of quarks — emerging from the collision. By analyzing how many hadrons appear in the "backward" direction relative to the quark's motion, they could search for the predicted wake.

A tiny-but-important signal

The result is subtle. "On average, in the back direction, we see there is a change of less than 1% in the amount of plasma," Chen said. "It is a very small effect (and partly why it took so long for people to demonstrate it experimentally)."

Still, that less-than-1% suppression is precisely the kind of signature expected from a quark transferring energy and momentum to the plasma, leaving a depleted region in its wake. The team reports that this is the first time such a dip has been clearly detected in Z-tagged events.

The shape and depth of the dip encode information about the plasma's properties. Returning to her analogy, Chen noted that if water flows easily, a dip behind a boat fills in quickly. If it behaves more like honey, the depression lingers. "So studying how this dip looks … gives us information on the plasma itself, without the complication of the boat," she said.

Looking back to the early universe

The findings also have cosmological implications. The early universe, shortly after the Big Bang, is believed to have been filled with quark-gluon plasma before cooling into protons, neutrons and, eventually, atoms.

"This era is not directly observable through telescopes,” Chen says. "The universe was opaque back then.” Heavy-ion collisions provide "a tiny glimpse on how the universe behaved during this era," she added.

For now, the observed dip is "just the start," Chen concluded. "The exciting implication of this work is that it opens up a new venue to gain more insight on the property of the plasma. With more data accumulated, we will be able to study this effect more precisely and learn more about the plasma in the near future."

Scientists have used the loudest gravitational-wave signal ever recorded to put Albert Einstein's more than 100-year-old theory of gravity to its toughest test yet — and once again, it passed.

The signal, called GW250114, came from the merger of two black holes — each about 30 times the mass of the sun — about 1.3 billion light-years from Earth. The event caused ripples through space-time, called gravitational waves, which washed over Earth on Jan. 14, 2025, and were detected by the U.S.-based Laser Interferometer Gravitational-Wave Observatory (LIGO).

Scientists say the event closely resembles the one that resulted in the first direct detection of gravitational waves in 2015. That suggests the black holes in both mergers were similar in size and distance from Earth.

However, this new signal was recorded with roughly three times the clarity of that groundbreaking 2015 discovery, allowing scientists to test Einstein's theory of general relativity more rigorously than ever before.

"It was very clearly the loudest event," Keefe Mitman, a postdoctoral researcher at the Cornell Center for Astrophysics and Planetary Science and co-author of the new paper, told Live Science. "This one event provided more information than everything we've seen before regarding certain tests of general relativity."

The signal's exceptional clarity stems from a decade of steady upgrades to the detectors, Mitman said. Those improvements reduced noise from sources that once interfered with cosmic signals, including seismic vibrations and even passing trucks. As a result, the detectors were sensitive enough to the minuscule distortions in space-time — changes 700 trillion times smaller than the width of a human hair — caused by the recently detected black hole merger.

The findings are detailed in a study published Jan. 29 in the journal Physical Review Letters.

A black hole's "ring"

Because the recently detected signal was so clear, Mitman and his colleagues could zoom in on a fleeting stage after the merger known as the "ringdown." During this phase, the newly formed black hole briefly vibrates — much like a struck bell — emitting gravitational waves in distinct patterns, or "tones," that encode key properties of the black hole, including its mass and spin.

In GW250114, researchers detected the two primary tones predicted for such a merger. Each tone yielded an independent measurement of the black hole's mass and spin — and both matched, effectively verifying general relativity, the team reported in the study.

For the first time, scientists also confidently identified a more subtle, short-lived "overtone" that appears right at the start of the ringing — another feature long predicted by general relativity.

"This event made it very, very obvious that, indeed, this prediction of general relativity was present in the signal, which was really exciting," Mitman told Live Science.

Had the measurements disagreed, he added in a statement, "we would have had a lot of work to do as physicists to try to explain what's going on and what the true theory of gravity would be in our universe."

Earlier analyses of the same event, published in September 2025, confirmed another major prediction rooted in general relativity that Stephen Hawking proposed more than 50 years ago. Hawking predicted that a black hole's surface area — the size of its event horizon — can never shrink, even though enormous amounts of energy escape during a merger as gravitational waves.

In GW250114, scientists estimated that the two original black holes had a combined surface area of about 93,000 square miles (240,000 square kilometers) — roughly the size of Oregon. After the merger, the resulting black hole had a surface area of about 155,000 square miles (400,000 square km) — closer to the size of California — which is consistent with Hawking's prediction.

The golden age

Despite general relativity's repeated success at describing large-scale cosmic phenomena, physicists suspect the theory cannot be the complete description of gravity in our universe. For example, it cannot explain dark matter or dark energy, which are needed to hold galaxies and their clusters together and to explain the universe's accelerating expansion, respectively. Nor does it reconcile cleanly with quantum mechanics, the framework that governs nature at the smallest scales.

Scientists hope gravitational waves from energetic black hole mergers might someday show subtle deviations from Einstein's predictions, which could potentially reveal new physics.

The ringdown phase is especially promising for such tests, Mitman said. Many "beyond-Einstein" theories predict slightly different vibration patterns during the ringdown phase — so measuring more than one tone, as his team did with GW250114, can help scientists place constraints on any possible deviations from general relativity.

If a discrepancy were to be found, researchers could compare the data with predictions from alternative theories of gravity to determine which, if any, matches reality.

"There has to be some way to resolve this paradox to make our theory of gravity consistent with our theory of quantum mechanics," Mitman said in the statement.

Next-generation detectors, including the proposed Einstein Telescope in Europe and the U.S.-based Cosmic Explorer, will be 10 times more sensitive than current facilities. In addition to detecting more events like GW250114, these detectors will be able to observe lower-frequency gravitational waves, which correspond to more massive black holes, thereby allowing scientists to probe entirely new classes of these cosmic behemoths.

Researchers are also looking ahead to the European Laser Interferometer Space Antenna (LISA), which is expected to observe gravitational waves from supermassive black holes at the centers of galaxies. Planned for launch in 2035, LISA is expected to detect a flood of events and could reveal dozens of distinct tones within a single black hole merger event, Mitman said.

"We're living in the regime where we don't have enough data, and we're kind of just twiddling our thumbs waiting for more data to come in," Mitman said. "Once LISA is online, we'll be overwhelmed."

If funding for gravitational-wave science continues, he added, "we're going to see more and more of these golden events and really start to learn wonderful things about the nature of gravity in our universe."

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An ice-bound "ghost particle" detector at the South Pole just got a major upgrade.

The IceCube Neutrino Observatory has expanded for the first time in its 15 years of service. Technicians have added more than 600 new instruments to the bottom of the detector, which now consists of 92 strings of neutrino detectors buried in a cubic kilometer of ice near Amundsen-Scott South Pole research station.

The observatory is designed to search for high-energy neutrinos — nicknamed "ghost particles" because they are nearly massless and chargeless subatomic particles that zip through space and matter at nearly the speed of light. Neutrinos are everywhere; about 100 trillion pass through every person on Earth every second. But because they rarely interact with the matter they pass through, they're hard to detect.

Scientists would like a better understanding of neutrinos because they're produced in important processes, like the Big Bang that kick-started the universe, the nuclear fusion that powers stars, and the supernova explosions that signal violent stellar deaths.

At IceCube, scientists detect tiny flashes of light that occur when neutrinos do interact with matter and produce secondary particles. This requires a remote and quiet environment, which is readily available at the South Pole, as well as a lot of transparent matter in which to detect the light — in this case, ice. IceCube scientists have already successfully traced the arrival of a single neutrino from a blazar, a distant galaxy surrounding a supermassive black hole. They've also used the particles to map all of the matter in the Milky Way.

In 2019, the U.S. National Science Foundation (NSF) approved funding to upgrade the detector from 86 to 92 strings of detectors. The six new strings hold new detector modules with multiple types of photosensors in each module. It took three 10-week field sessions from 2023 to 2026 to drill more than a mile into the Antarctic ice and place the sensors.

The new sensors will allow scientists to more precisely measure properties such as neutrino oscillations, which happen when neutrinos formed by cosmic rays in Earth's atmosphere change into different types. This will improve their ability to measure cosmic rays and to detect neutrinos from extraplanetary sources, such as supernovas, according to the IceCube Collaboration. Researchers will also be able to better calibrate the detector retrospectively, which will allow them to refine previously collected data from the past 15 years.

"This upgrade will secure the nation's continued leadership in neutrino physics for years to come, paving the way for new cosmic discoveries," Marion Dierickx, director of the NSF's Antarctic Astrophysics and Geospace Sciences Polar Cyberinfrastructure program, said in a statement.