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'Smaller than the tiniest scale in nature': Physicists made a black hole out of light and used it to test Stephen Hawking's elusive radiation theory

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 β€ͺ—‬ the faint thermal emission that Stephen Hawking predicted should leak out of black holes β€ͺ—‬ 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" β€” 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.

Illustration of two theories by Einstein and Hawking regarding black holes (Graphic by AFP)

An infographic explaining how Hawking radiation works, contrary to the predictions of general relativity. (Image credit: ALAIN BOMMENEL,VALENTINA BRESCHI,WILLIAM ICKES via Getty Images)

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 β€” 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 β€ͺ—‬ 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.

A man in an electronic wheelchair stands in front of a projector screen with various space images on it

Physicist Stephen Hawking that black holes should be able to lose information through an elusive type of radiation. New research zooms in on the mechanism that makes it possible. (Image credit: Bryan Bedder / Stringer via Getty Images)

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 β€” space itself, in real life β€” 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 β€” in nonlinear optics, light acts like a material."

In practice, the researchers fired an intense, ultrashort "pump" pulse into a thin photonic-crystal fiber β€” 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 β€” 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 β€” 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 β€” 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 β€” 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 β€” 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" β€” 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!

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Was Einstein wrong about anything?

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," NicolΓ‘s 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."

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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.

An illustration of two dark spheres circling each other against a blue, grid-like surface.

Einstein originally thought that gravitational waves existed, then changed his mind when the math didn't work out. However, an anonymous peer reviewer named Howard Percy Robertson managed to secretly help Einstein fix his mathematical errors. (Image credit: MARK GARLICK/SCIENCE PHOTO LIBRARY via Getty Images)

Calculating "impossible infinities"

Remarkably, Einstein stumbled on the same error twice β€” at least, it seemed that way. When examining the mathematics around black holes, he once again calculated impossible infinities β€ͺ—‬ 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.

An illustration of a black sphere surrounded by glowing white gas in space

Einstein was skeptical of the existence of black holes (pictured here in a 3D render) because his math showed a breakdown in space-time at a black hole's edge. (Image credit: Cavan Images / Luca Pierro via Getty Images)

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!

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Science news this week: Time emerges inside a mini-universe, scientists thicken Arctic ice, and one of the oldest graves of a free Black person in the US found

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 β€” 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 β€” but there's a big catch

A person walking through snow toward an air defence radar station in Cambridge Bay, Nunavut.

Researchers conducted the first real-life sea ice thickening experiments in Cambridge Bay, Nunavut. (Image credit: Arctic-Images/Getty Images)

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

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

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

β€”'Uncharted territory': Record-high ocean temperatures confirmed for June as El NiΓ±o strengthens its grip

Life's Little Mysteries

Does fast charging damage your battery more than regular charging?

A close up of a phone showing 90% with a

Some types of batteries charge faster than others. (Image credit: Tfilm via Getty Images)

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?

β€”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

a grey gravestone in a barren landscape with a death's head decoration and inscription

The gravestone of "Boston," a formerly enslaved man who died in the 18th century in Boston, Massachusetts. (Image credit: Boston Parks and Recreation Department)

It was found amid photos of headstones during a restoration project at Boston's Granary Burying Ground β€” 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

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

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

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

Also in science news this week

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

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

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

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

β€”Malaria had nearly been eliminated around a giant dam in the Amazon β€” 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

A person puts a stethoscope on a stuffed toy

Decisions around antibiotic prescribing aren't driven only by medical knowledge β€” emotions also play a role, a medical sociologist explains. (Image credit: Angel Santana via Getty Images)

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.

β€”Superintelligent AI in space could explain the Fermi paradox [Opinion]

β€”'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]

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

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

Science photo of the week

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

A blurry photo of a grey asteroid in the vacuum of space with Chinse logos superimposed on top

China's Tianwen-2 spacecraft captured this photo of the quasi-moon Kamo'oalewa (a.k.a. 2016 HO3) at a distance of around 12.5 miles (20 kilometers) from the near-Earth asteroid. (Image credit: CNSA)

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" β€” 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 β€ͺ—‬ 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.

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NASA is creating a fifth state of matter on the ISS, thanks to an upgrade to a mini-fridge-sized quantum lab

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) β€” 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 β€” especially with this latest upgrade β€” 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 β€” which is the size of a mini-fridge β€” 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."

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'Complex numbers are not needed for quantum mechanics': Physicists develop quantum model that uses only 'real' numbers for first time ever

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

Complex numbers combine a regular "real" number with an "imaginary" one β€” a multiple of the square root of -1, represented by the symbol i β€” 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 DΓΌsseldorf, 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.

3d rendered image of quantum entanglement.

Entanglement is just one aspect of quantum mechanics that seems to defy reality. Now, the math behind such phenomena can be expressed with only "real" numbers for the first time. (Image credit: koto_feja/Getty Images)

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) β€” 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.

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