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.”

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.

Earth will warm 2.7 degrees Celsius based on current pledges to cut emissions

This year was supposed to be a turning point in addressing climate change. But the world’s nations are failing to meet the moment, states a new report by the United Nations Environment Programme.

The Emissions Gap Report 2021: The Heat Is On, released October 26, reveals that current pledges to reduce greenhouse gas emissions and rein in global warming still put the world on track to warm by 2.7 degrees Celsius above preindustrial levels by the end of the century.

Aiming for “net-zero emissions” by midcentury — a goal recently announced by China, the United States and other countries, but without clear plans on how to do so — could reduce that warming to 2.2 degrees C. But that still falls short of the mark, U.N. officials stated at a news event for the report’s release.

At a landmark meeting in Paris in 2015, 195 nations pledged to eventually reduce their emissions enough to hold global warming to well below 2 degrees C by 2100 (SN: 12/12/15). Restricting global warming further, to just 1.5 degrees C, would forestall many more devastating consequences of climate change, as the Intergovernmental Panel on Climate Change, or IPCC, reported in 2018 (SN: 12/17/18). In its latest report, released in August, the IPCC noted that extreme weather events, exacerbated by human-caused climate change, now occur in every part of the planet — and warned that the window to reverse some of these effects is closing (SN: 8/9/21).
Despite these dire warnings, “the parties to the Paris Agreement are utterly failing to keep [its] target in reach,” said U.N. Secretary-General António Guterres. “The era of half measures and hollow promises must end.”

The new U.N. report comes at a crucial time, just days before world leaders meet for the 2021 U.N. Climate Change Conference, or COP26, in Glasgow, Scotland. The COP26 meeting — postponed from 2020 to 2021 due to the COVID-19 pandemic — holds particular significance because it is the first COP meeting since the 2015 agreement in which signatories are expected to significantly ramp up their emissions reductions pledges.

The U.N. Environment Programme has kept annual tabs on the still-yawning gap between existing national pledges to reduce emissions and the Paris Agreement target (SN: 11/26/19). Ahead of the COP26 meeting, 120 countries, responsible for emitting just over half of the world’s greenhouse gas emissions, announced their new commitments to address climate change by 2030.

The 2021 report finds that new commitments bring the world only slightly closer to where emissions need to be by 2030 to reach warming targets. With the new pledges, total annual emissions in 2030 would be 7.5 percent lower (about 55 gigatons of carbon dioxide equivalent) than they would have been with pledges as of last year (about 59 gigatons). But to stay on track for 2 degrees C of warming, emissions would have to be about 30 percent lower than the new pledges, or about 39 gigatons each year. To hold warming to 1.5 degrees C requires a roughly 55 percent drop in emissions compared with the latest pledges, to about 25 gigatons a year.

“I’m hoping that the collision of the science and the statistics in the gap analysis, and the voices of the people will promote a greater sense of urgency,” says Gabriel Filippelli, a geochemist at Indiana University–Purdue University Indianapolis.

On October 26, Filippelli, the editor of the American Geophysical Union journal GeoHealth, and editors in chief of other journals published by the organization coauthored a statement in Geophysical Research Letters. Theyurged world leaders at COP26 to keep the “devastating impacts” of climate change in check by immediately reducing global carbon emissions and shifting to a green economy. “We are scientists, but we also have families and loved ones alongside our fellow citizens on this planet,” the letter states. “The time to bridge the divide between scientist and citizen, head and heart, is now.”

Publishing that plea was a departure for some of the scientists, Filippelli says. “We have been publishing papers for the last 20 to 30 years, documenting the train wreck of climate change,” he says. “As you can imagine, behind the scenes there were some people who were a little uncomfortable because it veered away from the true science. But ultimately, we felt it was more powerful to write a true statement that showed our hearts.”

From fair schools to vaccine distribution

Parag Pathak
Economist
MIT

Parag Pathak, featured in 2019, strives to make public education more equitable. He has used data and algorithms to overhaul school choice systems in Boston, New York and other U.S. cities. Now he’s applying his research to the question of how to equitably distribute vaccines and other medical resources.

What’s the most notable progress in your work since 2019?
Since we last talked, I released a paper on the effects of universal preschool. A lot of people are interested right now because [universal preschool, which is open to everyone with no income rule,] is part of the White House’s agenda. Because of the work we had done with Boston with their school choice algorithm over the years, we had some files on school admissions going back to the late 1990s. Boston was a leader nationwide in expanding slots for children in preschool. But, like many cities, there weren’t enough slots for demand, so they had to ration. And that’s where the lotteries come in.

Fast forward to now. We linked these applicant cohorts to standardized test scores and educational outcomes all the way into college. And what we found was pretty exciting: Those who won the [preschool] lottery are more likely to graduate high school, they score higher on SATs and they’re more likely to enroll in college. Boston has continued to refine and try to improve [the lottery system]. It’s a model for other cities that are expanding public preschool.

Are you pursuing any new questions or projects?
COVID-19 was this huge shock. We all were looking around for how we could be useful, using our respective toolboxes. Tayfun Sönmez, M. Utku Ünver and M. Bumin Yenmez, all of Boston College — the four of us — started to study how scarce medical resources are rationed. And it turns out, there are some parallels with the way school seats are rationed.

One of the ideas that we’ve explored is the idea of a reserve system. In cases where people can’t agree on what’s fair, who should get a vaccine first? It’s very similar to who should get into a school. And the way that [schools] have handled that is they set up more elaborate versions of priority systems. With a vaccine reserve system, you basically have a [supply] that’s reserved for cardiac communities, and one that’s reserved for frontline medical personnel, so on and so forth…. States like California and Massachusetts have used some of our ideas [for their reserve systems].

My wife [Ruma Rajbhandari] is a medical doctor, and my sister [Sapana Adhikari] is an emergency room physician. A big part of my interest in medical rationing guidelines was their having to go to the hospital in March 2020 not knowing what the risks were and not having personal protective equipment. That was something that got me really keen on this debate about frontline health care workers, do they get first priority or not?

How has the pandemic shifted how you view your work in the area of education?
I have a kindergartner who was virtual this past year. And he did an amazing job with it. I think what the pandemic has done is rip the Band-Aid off on these lingering problems in society — inequitable access to health care, inequitable access to education, inefficiencies in both of the systems — and has made them much more pronounced. That’s been the theme of our research throughout. We hope more people take these issues on, because the way COVID-19 played out was really a scarring event in terms of haves and the have-nots.

— Interview by Cassie Martin

Distant rocky planets may have exotic chemical makeups that don’t resemble Earth’s

If a real Captain Kirk ever blasts off for other stars in search of rocky planets like ours, he may find lots of strange new worlds whose innards actually bear no resemblance to Earth’s.

A smattering of heavy elements sprinkled on 23 white dwarf stars suggests that most of the rocky planets that once orbited the stars had unusual chemical makeups, researchers report online November 2 in Nature Communications. The elements, presumably debris from busted-up worlds, provide a possible peek at the planets’ mantles, the region between their crust and core.

“These planets could be just utterly alien to what we’re used to thinking of,” says geologist Keith Putirka of California State University, Fresno.

But deducing what a long-gone planet was made of from what it left behind is fraught with difficulties, cautions Caltech planetary scientist David Stevenson. Rocky worlds outside of the solar system may have exotic chemical compositions, he says. “It’s just that I don’t think this paper can be used to prove that.”

After a star like the sun expands into a red giant star, it ultimately blows off its atmosphere, leaving behind its small, dense core, which becomes a white dwarf. That star’s great gravity drags heavy chemical elements into its interior, so most white dwarfs have pristine surfaces of hydrogen and helium.

But more than a quarter of these stars sport surfaces with heavier elements such as silicon and iron, presumably from planets that once circled the star and met their ends when it expanded into a red giant (SN: 8/15/11). The heavy elements on these white dwarfs haven’t yet had time to sink beneath the stellar surface.

For that reason, Siyi Xu, an astronomer at the Gemini Observatory in Hilo, Hawaii, has long studied white dwarfs. Then she met Putirka. Because he’s a geologist, “he was like, ‘Oh! We can look at this problem from a new perspective,’” Xu says.

Xu had been measuring the abundances of chemical elements littered on white dwarfs by studying the wavelengths of light, or spectra, given off by the stars. Putirka realized that those measurements could indicate what rocks and minerals had made up the destroyed planets’ mantles, which constitute the bulk of a small planet’s rock, because different rocks and minerals contain different chemical elements.

By examining white dwarfs within 650 light-years of the sun, Putirka and Xu reached a startling conclusion about the ripped-apart rocky planets. Contrary to conventional wisdom, most of their planetary mantles didn’t resemble those of the sun’s rocky planets — Mercury, Venus, Earth and Mars, the researchers say.

For example, some of the white dwarfs have lots of silicon. That suggests that their planets’ mantles had quartz — a mineral that in its pure form consists solely of silicon and oxygen. But there’s little, if any, quartz in Earth’s mantle. A planet with a quartz-rich mantle would probably differ greatly from Earth, Putirka says.

Such exotic mineral compositions might affect, for example, volcanic eruptions, continental drift and the fraction of a planet’s surface that consists of oceans versus continents. And all those phenomena might affect the development of life.

Stevenson, however, is skeptical of the new finding. When you measure the elemental composition of a “polluted white dwarf,” he says, “you do not know how to connect those numbers to what you started with.”

That’s partly because the destruction of rocky worlds around sunlike stars is complicated, Stevenson says. The planets first get blasted by the red giant’s bright light. Then they may get engulfed by the star’s expanding atmosphere and may even crash into another planet.

Each of these traumatic events could alter a planet’s elemental makeup, as well as possibly send some elements toward the white dwarf ahead of others. As a result, the planetary remains that end up on the star’s surface at one snapshot in time may not reflect the world’s starting composition.

Xu agrees that astronomers don’t know precisely how the breakup plays out or which elements wind up falling onto the white dwarf. Future theoretical studies could provide insight into the matter, she says.

She also notes that astronomers have caught asteroids disintegrating around white dwarfs, which offer a small window into the actual breakup process. And future observations of these white dwarfs, she says, could help