Quantum physics requires imaginary numbers to explain reality

Imaginary numbers might seem like unicorns and goblins — interesting but irrelevant to reality.

But for describing matter at its roots, imaginary numbers turn out to be essential. They seem to be woven into the fabric of quantum mechanics, the math describing the realm of molecules, atoms and subatomic particles. A theory obeying the rules of quantum physics needs imaginary numbers to describe the real world, two new experiments suggest.

Imaginary numbers result from taking the square root of a negative number. They often pop up in equations as a mathematical tool to make calculations easier. But everything we can actually measure about the world is described by real numbers, the normal, nonimaginary figures we’re used to (SN: 5/8/18). That’s true in quantum physics too. Although imaginary numbers appear in the inner workings of the theory, all possible measurements generate real numbers.

Quantum theory’s prominent use of complex numbers — sums of imaginary and real numbers — was disconcerting to its founders, including physicist Erwin Schrödinger. “From the early days of quantum theory, complex numbers were treated more as a mathematical convenience than a fundamental building block,” says physicist Jingyun Fan of the Southern University of Science and Technology in Shenzhen, China.
Some physicists have attempted to build quantum theory using real numbers only, avoiding the imaginary realm with versions called “real quantum mechanics.” But without an experimental test of such theories, the question remained whether imaginary numbers were truly necessary in quantum physics, or just a useful computational tool.

A type of experiment known as a Bell test resolved a different quantum quandary, proving that quantum mechanics really requires strange quantum linkages between particles called entanglement (SN: 8/28/15). “We started thinking about whether an experiment of this sort could also refute real quantum mechanics,” says theoretical physicist Miguel Navascués of the Institute for Quantum Optics and Quantum Information Vienna. He and colleagues laid out a plan for an experiment in a paper posted online at arXiv.org in January 2021 and published December 15 in Nature.

In this plan, researchers would send pairs of entangled particles from two different sources to three different people, named according to conventional physics lingo as Alice, Bob and Charlie. Alice receives one particle, and can measure it using various settings that she chooses. Charlie does the same. Bob receives two particles and performs a special type of measurement to entangle the particles that Alice and Charlie receive. A real quantum theory, with no imaginary numbers, would predict different results than standard quantum physics, allowing the experiment to distinguish which one is correct.

Fan and colleagues performed such an experiment using photons, or particles of light, they report in a paper to be published in Physical Review Letters. By studying how Alice, Charlie and Bob’s results compare across many measurements, Fan, Navascués and colleagues show that the data could be described only by a quantum theory with complex numbers.

Another team of physicists conducted an experiment based on the same concept using a quantum computer made with superconductors, materials which conduct electricity without resistance. Those researchers, too, found that quantum physics requires complex numbers, they report in another paper to be published in Physical Review Letters. “We are curious about why complex numbers are necessary and play a fundamental role in quantum mechanics,” says quantum physicist Chao-Yang Lu of the University of Science and Technology of China in Hefei, a coauthor of the study.

But the results don’t rule out all theories that eschew imaginary numbers, notes theoretical physicist Jerry Finkelstein of Lawrence Berkeley National Laboratory in California, who was not involved with the new studies. The study eliminated certain theories based on real numbers, namely those that still follow the conventions of quantum mechanics. It’s still possible to explain the results without imaginary numbers by using a theory that breaks standard quantum rules. But those theories run into other conceptual issues, making them “ugly,” he says. But “if you’re willing to put up with the ugliness, then you can have a real quantum theory.”

Despite the caveat, other physicists agree that the quandaries raised by the new findings are compelling. “I find it intriguing when you ask questions about why is quantum mechanics the way it is,” says physicist Krister Shalm of the National Institute of Standards and Technology in Boulder, Colo. Asking whether quantum theory could be simpler or if it contains anything unnecessary, “these are very interesting and thought-provoking questions.”

Neandertals were the first hominids to turn forest into grassland 125,000 years ago

Neandertals took Stone Age landscaping to a previously unrecognized level.

Around 125,000 years ago, these close human relatives transformed a largely forested area bordering two central European lakes into a relatively open landscape, say archaeologist Wil Roebroeks of Leiden University in the Netherlands, and his colleagues. Analyses of pollen, charcoal, animal fossils and other material previously unearthed at two ancient lake basins in Germany provide the oldest known evidence of hominids reshaping their environments, the scientists report December 15 in Science Advances.

The excavated areas are located within a site called Neumark-Nord. Neandertals’ daily activities there, apparently ongoing throughout the year, had a big environmental impact, the researchers suspect. Those pursuits, which occurred over a span of about 2,000 years, included setting campfires, butchering game, collecting wood, making tools and constructing shelters, they say.

“We might be dealing with larger and less mobile groups of [Neandertals] than commonly acknowledged,” Roebroeks says, thanks in part to warming temperatures after around 150,000 years ago that cleared ice sheets from resource-rich locations such as Neumark-Nord.
His team can’t say whether Neandertals set fires to clear large tracts of land at Neumark-Nord, a practice that has been observed among some modern hunter-gatherers. The geological remnants of many small campfires may look much like those of a small number of large fires, Roebroeks says.

Finds at Neumark-Nord play into an ongoing debate about when humans began to have a dominating influence on the natural world. Some scientists regard this period as a new geological epoch, the Anthropocene (SN: 4/1/13). It’s unclear when the Anthropocene began and whether its roots extend back to the Stone Age.

Regular fire use by members of the Homo genus began around 400,000 years ago (SN: 4/2/12). Evidence of human occupations associated with increased fire setting and shifts to open habitats date to around 40,000 years ago in Australia; 45,000 years ago in highland New Guinea; and 50,000 years ago in Borneo.

Analyses of lake cores and stone-tool sites in southern-central Africa indicate that fires set by increasing numbers of humans kept the landscape open even as rainy conditions conducive to forest growth developed around 85,000 years ago. Open environments still predominate in this part of Africa, Yale University paleoanthropologist Jessica Thompson and her colleagues reported May 5 in Science Advances. “Humans and close human relatives like Neandertals have likely been [modifying] their ecosystems for a very long time,” Thompson says.

A large coal mining operation revealed ancient Neumark-Nord sediments in 1985. German scientists then excavated a large lakeside site, wrapping up that project in the mid-1990s. The same team excavated a smaller site at a lake basin located about 100 meters from the first site between 2004 and 2008.

Pollen from these sites indicates that grasses and herbs, hallmarks of an open landscape, appeared in a brief window of time around 125,000 years ago, Roebroeks and his colleagues say. Large numbers of stone artifacts — some showing signs of having been heated, possibly to make finished edges sharper — and animal bones displaying butchery marks date to the same time at Neumark-Nord, when Neandertals but not Homo sapiens inhabited Europe.
Stone tools and bone fragments displaying signs of heating, burned wood, charred seeds and dense patches of charcoal particles suggested that Neandertals had frequently set fires near the Neumark-Nord lakes.

Pollen from two other sites in the same mountainous part of Germany, where researchers previously found small numbers of stone tools suggesting a limited Neandertal presence, show that forests dominated there when Neandertals inhabited Neumark-Nord’s grasslands. That strengthens the view that Neandertals altered the Neumark-Nord landscape rather than settling there after forests had shrunk, Roebroeks says.

Archaeologist Manuel Will of Eberhard Karls University of Tübingen in Germany agrees. “Neandertal evidence from Neumark-Nord should be a wake-up call for the international scientific community to include archaeologists [studying] the Paleolithic record as part of any team trying to define and identify the beginning of the Anthropocene,” says Will, who did not participate in the new study.

The Parker Solar Probe is the first spacecraft to visit the sun’s atmosphere

For the first time, a spacecraft has made contact with the sun. During a recent flyby, NASA’s Parker Solar Probe entered the sun’s atmosphere.

“We have finally arrived,” Nicola Fox, director of NASA’s Heliophysics Science Division in Washington, D.C., said December 14 in a news briefing at the fall meeting of the American Geophysical Union. “Humanity has touched the sun.”

Parker left interplanetary space and crossed into solar territory on April 28, 2021, during one of its close encounters with the sun. While there, the probe took the first measurements of exactly where this boundary, called the Alfvén critical surface, lies. It was about 13 million kilometers above the sun’s surface, physicists reported at the meeting, held online and in New Orleans, and in Physical Review Letters on December 14.

“We knew the Alfvén critical surface had to exist,” solar physicist Justin Kasper of the University of Michigan in Ann Arbor said at the news briefing. “We just didn’t know where it was.”
Finding this crucial layer was one of Parker’s main goals when it launched in 2018 (SN: 7/5/18). The Alfvén critical surface is important because it marks where packets of plasma can separate from the sun and become part of the solar wind, the speedy stream of charged particles that constantly emanates from the sun (SN: 8/18/17). The solar wind and other, more dramatic forms of space weather can wreak havoc on Earth’s satellites and even on life (SN: 2/26/21). Scientists want to pinpoint exactly how the wind gets started to better understand how it can impact Earth.

The Alfvén critical surface also may hold the key to one of the biggest solar mysteries: why the sun’s corona, its wispy outer atmosphere, is so much hotter than the sun’s surface (SN: 8/20/17). With most heat sources, temperatures drop as you move farther away. But the sun’s corona sizzles at more than a million degrees Celsius, while the surface is only a few thousand degrees.

In 1942, physicist Hannes Alfvén proposed a solution to the mystery: A type of magnetic wave might carry energy from the solar surface and heat up the corona. It took until 2009 to directly observe such waves, in the lower corona, but they didn’t carry enough energy there to explain all the heat (SN: 3/19/09). Solar physicists have suspected that what happens as those waves climb higher and meet the Alfvén critical surface might play a role in heating the corona. But until now, scientists didn’t know where this frontier began.

With the boundary identified, “we’ll now be able to witness directly how coronal heating happens,” Kasper said.

As Parker crossed the invisible boundary, its instruments recorded a marked increase in the strength of the local magnetic field and a drop in the density of charged material. Out in the solar wind, waves of charged particles gush away from the sun. But below the Alfvén critical surface, some of those waves bend back toward the surface of the sun.
Surprisingly, Parker’s measurements showed that the Alfvén critical surface is wrinkly. “That was one of the big outstanding questions,” says solar physicist Craig DeForest of the Southwest Research Institute in Boulder, Colo., who is a member of the Parker probe team but was not part of this measurement.

“There was some debate in the community about whether the Alfvén surface would exist as a surface at all,” he says. Decades ago, scientists imagined the boundary as a smooth sphere surrounding the sun like a snow globe. More recently, some thought it would be so ragged that it wouldn’t be apparent when the spacecraft crossed it.

Neither of those images turned out to be correct. The surface is smooth enough that the moment of crossing was noticeable, Kasper said. But during the spacecraft’s close approach to the sun in April, it crossed in and out of the boundary three times. The first dip lasted about five hours, the last only half an hour.

“The surface clearly has some structure and warp to it,” Kasper said.

That structure could influence everything from the way solar eruptions leave the sun to the way the solar wind interacts with itself farther out from the sun, DeForest says. “That has consequences that we don’t know yet, but are likely to be profound,” he says. “This is very exciting. It’s terra incognita.”

Parker is still orbiting the sun and planning to make several more close approaches over the next few years, eventually getting within 6 million kilometers of the solar surface. That should bring Parker into the solar corona again and again, solar physicist Nour Raouafi of the Johns Hopkins Applied Physics Laboratory in Laurel, Md., said in the news briefing. The spacecraft may have made another journey past the Alfvén critical surface in August and will have another opportunity in January.

“The expectation is that as we fly closer and closer to the sun, we’ll keep crossing this boundary,” Raouafi said. But the boundary might not be in the same place every time. As the sun’s activity changes, the level of the Alfvén critical surface is expected to rise and fall as if the corona is breathing in and out, he said.

That’s another thing that scientists hope to observe for the first time.

Nostalgia may have bona fide benefits in hard times, like the pandemic

Over 300 years ago, Swiss physician Johannes Hofer observed disturbing behaviors among Swiss mercenaries fighting in far-flung lands. The soldiers were prone to anorexia, despondency and bouts of weeping. Many attempted suicide. Hofer determined that the mercenaries suffered from what he called “nostalgia,” which he concluded was “a cerebral disease of essentially demonic cause.”

Nowadays, nostalgia’s reputation is much improved. Social psychologists define the emotion — which Hofer saw as synonymous with “homesickness” — as a sentimental longing for meaningful events from one’s past. And research suggests that nostalgia can help people cope with dementia, grief and even the disorientation experienced by immigrants and refugees (SN: 3/1/21).

Nostalgia may even help people cope with the COVID-19 pandemic. In a study published September 8 in Social, Psychological and Personality Science, researchers found when some lonely, unhappy people reminisced about better, pre-pandemic moments, they felt happier. The results suggest that nostalgia can serve as an antidote to loneliness during the pandemic, the researchers conclude.

“A good analogy is the immune system,” says social psychologist Tim Wildschut of the University of Southampton in England. “A viral infection may make you ill, but it also activates your immune system and your immune system makes you better. Loneliness reduces happiness but also triggers nostalgia, and nostalgia increases happiness.”

In the new study, Wildschut and colleagues first surveyed over 3,700 participants in the United States, United Kingdom and China to assess people’s levels of loneliness, nostalgia and happiness during the early days of the pandemic. Surveys varied slightly by country, but for most questions or statements, participants responded on a scale from 1 to 7, with 1 for “not at all” and 7 for “very much.” For instance, participants in the United States rated how isolated they felt from the rest of the world in the week prior to the survey, how happy they felt compared with their peers and their overall feelings of nostalgia.

The researchers found that across the three countries, people who scored relatively high in loneliness also, not surprisingly, scored lower in happiness. But when the team drilled down on the role nostalgia plays, they found people who didn’t indulge in those memories were the least happy.

“Loneliness [triggers] unhappiness and nostalgia. Then unhappiness and nostalgia fight with each other,” says coauthor Constantine Sedikides, a social psychologist also at the University of Southampton.

Meanwhile, in three experiments with new sets of U.S. participants, the researchers manipulated people’s nostalgia levels, using the spring 2020 lockdown as a proxy for heightened loneliness. For example, in one experiment conducted in April 2020, the researchers recruited just over 200 online participants. The team induced nostalgia in half the participants by having them write four words describing a specific nostalgic event from their past. Participants were then prompted to write freely for three minutes about how that past experience made them feel. People in the control group completed the same tasks but about ordinary past experiences.

Those experiments revealed that, compared with the control group, participants in the nostalgia group reported slight but statistically significant higher happiness levels, as measured by the same 1-7 scale used in the earlier surveys. For instance, in the experiment with the 200-plus participants, the researchers found that happiness scores in the nostalgia group averaged 5.64 compared with 5.3 in the control group. Statistical analysis suggests that nostalgia can explain about 2 percent of the variation in happiness, the researchers say.

Those results may sound trivial, but even small variations can yield large results when viewed across large populations or across time, says personality psychologist Friedrich Götz of the University of British Columbia in Vancouver.

“Let’s say you are a happy person every day of your life. Chances are you will have a more fulfilled life than if you are a less happy person,” Götz says. “So 2 percent can make a difference because our happiness influences how we act, feel and think every day of our lives.”
The hope that nostalgia-induced happiness could build up over time underpins some researchers’ long-term goal of harnessing and deploying techniques to trigger nostalgic memories as a form of therapy. Nostalgia can connect people to their past, present and even desired future selves, these researchers say. And since many nostalgic memories often involve other people, they can also help people feel linked to a wider community.

In one study, for example, existential psychologist Clay Routledge and colleagues tapped nostalgia’s social side. Participants first completed an established “nostalgia inventory,” where they rated on a scale from 1 to 5 how nostalgic they felt about 20 aspects of their past lives, such as family and vacations. The researchers then asked people about the types of studies that they might want to participate in later on. Two of those potential studies involved meeting other participants while two others did not.

Participants reporting high levels of nostalgia, especially those nostalgic for social experiences, were more likely than other participants to select the studies that involved meeting new people, the researchers reported in the December 2015 Journal of Personality and Social Psychology. That suggests that proneness to remembering meaningful past social experiences engenders future social experiences, the team says.

“Nostalgia isn’t just people remembering time with loved ones,” says Routledge, of North Dakota State University in Fargo. “It’s orienting them toward building new social experiences.”

A key question, though, is if nostalgia’s benefits can persist beyond that fleeting moment of remembrance. Wildschut’s team found that nostalgia’s benefits, in terms of happiness, faded after just a day or two. But nostalgia-induced happiness persisted for a couple days when the researchers reminded people to think about that special memory.

Crucially, nostalgia therapy may not be for everyone. Researchers reported in October 2019 in Personality and Individual Differences that invoking nostalgia in individuals who viewed relationships as a source of comfort and security increased those people’s intention to engage with others. The reverse, however, held true for individuals who saw relationships as a source of pain.

“For these types of avoidant people … nostalgia pushed them in the opposite direction. They were even less likely to want to connect with others on a deeper level,” says existential and social psychologist Andrew Abeyta of Rutgers University–Camden in New Jersey.
Wildschut and colleagues found a similar result when investigating whether invoking nostalgia among Syrian refugees living in Saudi Arabia could increase self-esteem, sense of meaning in life, feelings of social belonging and optimism.

In that study, refugees in an experimental group wrote about meaningful events from their past, while refugees in a control group wrote about ordinary events. The experiment showed that triggering nostalgia in refugees high in resilience — a trait defined by a capacity to withstand and recover from adversity — resulted in more positive emotions than those reported by resilient refugees in a control group, the team concluded in the December 2019 European Journal of Social Psychology. But while inducing nostalgia in refugees low in resilience did help them feel a greater sense of continuity in life and more socially connected compared with a low-resilience control group, nostalgic memories also made them feel less optimistic about the future.

“When you push the test of nostalgia to those extremes, it’s a very, very tough test,” Wildschut says.

Caveats aside, Wildschut remains optimistic about developing some form of nostalgia therapy. He recalls a conversation with his young daughter many years ago. When he asked her how long nostalgia lasts, she replied “forever,” Wildschut says. “What she meant is that the memory is there, and you can recall it any time.” Ultimately, he and other nostalgia researchers hope to one day identify suitable candidates for nostalgia therapy and then train those people to recall special memories whenever they feel blue.

A Jupiter-like planet orbiting a white dwarf hints at our solar system’s future

A glimpse of our solar system’s future has appeared thousands of light-years away in the constellation Sagittarius. There a giant planet like Jupiter orbits a white dwarf, a dim, dense star that once resembled the sun.

In 2010, that star passed in front of a much more distant star. Like a magnifying glass, the white dwarf’s gravity bent the more distant star’s light rays so that they converged on Earth and made the distant star look hundreds of times brighter. A giant planet orbiting the white dwarf star also “microlensed” the distant star’s light, revealing the planet’s presence.

In 2015, 2016 and again in 2018 astrophysicist Joshua Blackman of the University of Tasmania in Hobart, Australia and colleagues pointed the Keck II telescope in Hawaii at the far-off system, which lies some 5,000 to 8,000 light-years from Earth. The team was in search of the giant planet’s star, but saw, well, nothing.

“We expected that we’d see a star similar to the sun,” Blackman says. “And so we spent quite a few years trying to figure out why on Earth we didn’t see the star which we expected to see.”
After failing to detect any light from the spot where the planet’s star should be, Blackman’s team concluded that the object can’t be a typical star like the sun — also known as a main sequence star, which generates energy by converting hydrogen into helium at its center. Instead, the star must be something much fainter. The microlensing data indicate that the star is roughly half as massive as the sun, so the object isn’t massive enough to be a neutron star or black hole. But a white dwarf star fits the bill perfectly, the researchers report online October 13 in Nature.

“They’ve carefully ruled out the other possible lens stars — neutron stars and black holes and main sequence stars and whatnot,” says Ben Zuckerman, an astronomer at UCLA, who was not involved with the work. He notes that only a handful of planets have ever been found orbiting white dwarfs.

The new planet is the first ever discovered that is orbiting a white dwarf and resembles Jupiter in both its mass and its distance from its star. Blackman’s team estimates that the planet is one to two times as massive as Jupiter and probably lies 2.5 to six times farther from the white dwarf star than Earth does from the sun. For comparison, Jupiter is 5.2 times farther out from the sun than Earth is. The white dwarf is somewhat larger than Earth, which means the planet is much bigger than its host star.

The white dwarf formed after a sunlike star expanded and became a red giant star. Then the red giant ejected its outer layers, exposing its hot core. That former core is the white dwarf star.

Our sun will turn into a white dwarf about 7.8 billion years from now, so the new discovery is “a snapshot into the future of our solar system,” Blackman says. As the sun becomes a red giant, it will engulf and destroy its innermost planet, Mercury, and perhaps Venus too. But Mars, Jupiter and more distant planets should survive.

And Earth? No one yet knows what will happen to it.