This article is the first in a series on the biggest problems in physics.

A successful scientific theory is one that makes precise and accurate predictions. Scientists are even happier when two distinct theories make predictions that agree with one another. Thus, physicists are a bit chagrined when they use their two best theories to predict the simplest possible quantity, and the result is that they disagree spectacularly enough that it is often called the worst prediction in the history of science.

Empty space is, well, empty. Containing nothing, it would seem that calculating the energy of empty space would be simple and the prediction would be zero. However, that expectation is not correct.

The two theories that, when combined, underlie all of modern physics are called the theory of general relativity and the standard model of particle physics. General relativity describes the behavior of the force of gravity and applies to large structures in the Universe. In contrast, the standard model of particle physics is used to explain all other forces and governs the quantum world of the very small.

Both theories can be applied to empty space. So, what happens when the two theories are used to calculate the energy density of a true vacuum?

Einsteins theory of general relativity discusses the shape and motion of space itself. We have known for a century that the Universe is expanding, and the theory that describes the evolution of the Universe is called the Big Bang. Basically, the theory says that the Universe was once smaller, and something caused the expansion to begin.

Given that gravity is an attractive force, this implies that after the expansion began, this expansion would slow down. Why? Because all the matter of the Universe attracted all of the other matter.

Thus, it was very surprising when, in 1998, researchers studying the evolution of the Universe found that not only was the Universe expanding, but that the expansion was speeding up. The only way this could happen is if space had a small and distinct energy associated with it. If the energy was of the right kind, it would result in a repulsive form of gravity. Researchers call this repulsive gravity dark energy, and they can calculate just how much dark energy is required to explain the observed evolution of the Universe. This energy is very small equivalent to about the energy of four hydrogen atoms per cubic meter of space.

So, does the standard model predict an energy of space and, if so, how?

The standard model says that all of space is filled with a variety of fields. When those fields vibrate in certain ways, the particles of the quantum world appear electrons, quarks, etc. However, even when the fields are quiescent nominally at rest there remains an ongoing residual hum, with tiny transient vibrations in the fields with an array of wavelengths. Because in the quantum world particles and waves are the same thing, this implies that empty space contains a chaotic mix of ephemeral particles that appear and disappear essentially instantly. This lowest energy state of the various fields is called the zero point, and the energy they contain is called the zero-point energy.

To calculate the zero-point energy of the quantum world, add up the effect of all the quantum waves. In principle, there is no minimum wavelength, so you add up shorter and shorter waves. Because short wavelength means high energy, this means adding higher and higher energies. Taken to the extreme, you could add up near-zero wavelengths with near-infinite energy but we know that the standard model eventually fails at very high energies, so you only add up energies to a certain maximum (and, hence, only to a certain minimum wavelength).

Just what exactly the maximum energy should be used in the calculations is a matter of theoretical dispute, but most scientists agree that the absolute highest possible energy for which the standard model applies is called the Planck energy. If you use that energy as the cutoff in your calculation, you calculate the zero-point energy to be very high. The energy density is equivalent to having the mass of a 100 quintillion times more than the entire visible Universe compacted down into a cubic meter.

Indeed, by this simple calculation, the energy density predicted by the standard model is about 10120 times that predicted by general relativity.That is a one followed by 120 zeros.This discrepancy certainly earns the title the worst prediction in all of science.

The factor 10120 is a worst-case scenario. Unproven theories have been proposed that improve the situation. For example, if a theory called supersymmetry turns out to be true, the disagreement is only a factor of 1060.

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When such a large disagreement occurs, something is very wrong with one or both theories. It remains possible that our current theoretical understanding is wrong, but general relativity describes the cosmos well and the standard model does a good job at the quantum level. Its only when the two are compared that a problem arises.

What are some of the proposed solutions? Well, there are many. For example, one explanation arises from the fact that the standard model assumes that there is no smallest unit of space. This means that the smallest volume you can imagine can be split into even smaller units in a never-ending series. But what if there is a smallest unit of space effectively an atom of space? If thats true, then this changes the calculations, and in such a scenario, the disagreement between cosmic and quantum energy can disappear.

Another idea is that we have been fooled by our senses. As we experience the world around us, we seem to move in three spatial dimensions. If there were additional dimensions of space, then this would radically change our theory of gravity, which would mean that the quantum calculations (which are currently performed in three-dimensional space) are wrong.

While the final answer is unknown, it seems more likely that the problem arises in our understanding of the world of the very small. After all, if the standard model prediction was correct, the Universe would have expanded so fast that stars, galaxies, and humans never would have existed.

But a mystery is a mystery. The simple fact is that researchers dont know why our theories of the cosmic and quantum worlds make such different predictions. Despite decades of effort, the answer has eluded some of the brightest minds of science. We will simply have to wait until that future day when someone solves this cosmic conundrum and enters the pantheon of physics legends.

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The worst prediction in all of science - Big Think

A couple of years ago, the library of the University of Groningen in the Netherlands was subject to a massive reclassification. Hundreds of books were provisionally placed higgledy-piggledy on the shelves, atlases leaning against poetry collections, folios of sheet music wedged between a tome on malaria treatments and a study of birds in the Arctic. In the midst of this jumble, one of us was preparing the valedictory lecture that would mark her official retirement as professor of philosophy.

After two hours of thinking and writing, it was time for a break and a leisurely look at the miscellany of intellectual effort on the shelves. A bright blue book drew attention. It was the fourth volume (the rest were nowhere to be seen) of A History of Women Philosophers (1995) edited by Mary Ellen Waithe, which deals with female philosophers in the 20th century. Upon inspection, it contained not only essays on thinkers such as Simone de Beauvoir and Hannah Arendt, but also a chapter on a completely unknown English philosopher, E E Constance Jones (1848-1922). The authors of this chapter, Waithe and Samantha Cicero, argued that Jones had solved Freges Puzzle two years before Gottlob Frege himself had done so.

Emily Elizabeth Constance Jones (1916) by John Lavery. Courtesy Girton College Cambridge/Wikipedia

This was by all accounts a spectacular claim. Frege, the German mathematician and philosopher born in the same year as Jones, had been the major inspiration for Principia Mathematica, the bible of modern logic that Alfred North Whitehead and Bertrand Russell published between 1910 and 1913. Freges grand aim was to find a foundation from which the whole of number theory could be derived. In carrying out this project, however, he encountered a philosophical problem. How to account for the fact that an equation like 2 x 2 = 1 + 3 is informative, whereas 4 = 4 is not? It is not just that the symbols on both sides of the identity sign are different. After all, in 7 = VII the symbols on either side of the identity sign differ, but the statement is not informative in the way that 2 x 2 = 1 + 3 is; it simply represents the number seven in two different symbol systems. In later work, Frege used a non-mathematical example to illustrate his problem. Why is the statement The morning star is the evening star informative, whereas The morning star is the morning star is not? Since both the morning star and the evening star refer to the planet Venus, both sentences seem to say nothing more than that Venus is Venus.

Frege solved the problem in his paper On Sense and Reference (1892). He argued that the meaning of a term like morning star is not just its reference (Venus), but also contains another component the sense which is the way in which the reference is given to us, in this case as a star that appears in the morning. The morning star is the evening star is informative because the references of morning star and evening star are the same, while their senses are different. In fact, it took the Babylonians quite some time to discover that this star that appears in the morning is the same heavenly body as the star that appears in the evening. The morning star is the morning star, on the other hand, is trivially true for the Babylonians as well as for us.

Waithe and Cicero discovered that Constance Jones was struggling with a problem similar to that of Frege, for she wanted to know: why is the statement A is B significant while A is A is trivial? Waithe and Cicero argued that in 1890 two years before Frege wrote his classic paper Jones had published a solution that was basically the same as Freges.

For any scholar in analytic philosophy, this was breaking news. Both of us have long been teaching the history of analytic philosophy, one of us for more than 30 years. We have taught countless students how, at the University of Cambridge, Bertrand Russell and George Edward Moore revolted against traditional logic and traditional philosophy, thereby founding what became known as analytic philosophy. We have described how, in the 20th century, analytic philosophy branched out in two different directions, a formal one that led to Ludwig Wittgensteins Tractatus Logico-Philosophicus (1922), the Vienna Circle, and W V Quines naturalised philosophy; and an informal one consisting of the ordinary language philosophy associated with J L Austin, Gilbert Ryle, and the later work of Wittgenstein. Nowhere did we mention Constance Jones. We simply did not know about her, much less did we suspect that she could have anticipated that crucial building block of analytic philosophy, Freges distinction between sense and reference.

When we subsequently read Joness work ourselves, we found that the story is a bit more nuanced than what we had gathered from the chapter by Waithe and Cicero. There are similarities between Jones and Frege, but also some salient differences. It is not just that Joness approach is simpler than Freges, dealing only with elementary sentences such as A is B there are differences that cut much deeper than this. Freges distinction between sense and reference (in German: Sinn and Bedeutung) does not coincide with Joness more traditional distinction between what she calls determination and denomination, and later connotation and denotation, or intension and extension. The extension of the predicate term is red, for example, is simply the class of all red things in the world. The Fregean Bedeutung of this term is, however, a concept, more particularly a mathematical function. And while Joness intensions are properties of real or imagined things, Fregean Sinne (senses) constitute an objective realm separate from any actual or fictional world. (For details on the differences, see the chapter E E Constance Jones and the Law of Significant Assertion by Jeanne Peijnenburg and Maria van der Schaar, forthcoming in the Oxford Handbook of British and American Women Philosophers in the Nineteenth Century, edited by Lydia Moland and Alison Stone.)

By their choices, they influence our ideas about who are and who are not important philosophers

None of this alters the fact that Jones was completely forgotten, even though she had been a very active and respected member of the philosophical community. From 1884 to 1916, Jones taught Moral Sciences at Girton, the first residential college for female students in the UK, where she became Vice-Mistress and later Mistress. Her specialisation was logic: she wrote four books on the subject and many articles in leading philosophical journals such as Mind and Proceedings of the Aristotelian Society. Although her work is firmly rooted in the old Aristotelian syllogistics, it is in some respects surprisingly modern. At a time when logic was generally seen as being about subjective laws of thought, Jones anticipated later developments by staunchly asserting that logic was objective. Moreover, her problem-driven approach and remarkably clear style make her work different from the florid prose of some of her contemporaries and more akin to the later analytic tradition. In 1892, she became a member of the Aristotelian Society. Four years later, she was the first woman to address the Cambridge Moral Sciences Club, and established philosophers such as F C S Schiller, W E Johnson and Bernard Bosanquet engaged in public discussions of her work.

Then why was she forgotten? The history of 20th-century philosophy is largely shaped by handbooks, textbooks, companions or anthologies. By the choices they make, by the texts they rely on, historians, editors and educators influence our ideas about who are and who are not important philosophers. Joness name is not in the handbooks. Why not? Perhaps it was due to the supremacy of modern mathematical logic, which reduced the old Aristotelian logic that Jones uses to a mere special case. The fact that Russell was personally exasperated by Jones and her Victorian mindset, describing her in a letter to Ottoline Morrell as motherly and prissy, may not have helped either. But, whatever the precise causes, Jones does not deserve to be consigned to oblivion.

The case of Constance Jones is one of what we may call historiographical marginalisation: although she was a prolific and respected writer during her lifetime, her work never entered the canon because historians and textbook authors for some reason chose not to include it in their overviews. There are also cases where the marginalisation is historical: a philosophers significance is insufficiently recognised by her contemporaries. An example of historical marginalisation is the reception of work by the German philosopher, physicist and mathematician Grete Hermann (1901-84). After the dawn of quantum mechanics at the beginning of the 20th century, physicists and philosophers were baffled by its spectacular empirical successes. How could an essentially indeterministic and counterintuitive theory be so effective? Was the world really that weird? Following Albert Einstein, many people suspected the existence of hidden variables that, once discovered, would reveal that quantum mechanics was deterministic after all. Their hopes were dashed in 1932, when the mathematician John von Neumann seemingly proved that any theory about hidden variables is incompatible with quantum mechanics. The quantum mechanical structure, he argued, is such that it simply does not allow the addition of variables that would enable us to identify deterministic causes, on pain of becoming inconsistent.

But he had a challenger. In a paper of 1935, Hermann showed that von Neumanns argument was flawed. The source of difficulty is an assumption he makes about a sum of noncommuting operators. Von Neumann was right that this assumption holds in quantum mechanics, but he failed to see that it may well be false in an extended theory, encompassing both quantum mechanics and the new or hidden variables. Hermann explained that this failure made his proof essentially circular. Her voice, however, was not heard. Thirty years later, the Irish physicist John Bell independently criticised von Neumann on similar grounds, and the subsequent experimental check of his findings earned Alain Aspect, John Clauser and Anton Zeilinger the Nobel Prize in 2022.

The causes of marginalisation are strong and manifold, ranging from the political, social, cultural or even personal

Although Hermanns argument against von Neumann was mentioned by Max Jammer in his standard work The Philosophy of Quantum Mechanics (1974), and by David Mermin in a paper of 1993, it received little attention at the time. This changed in 2016, when Guido Bacciagaluppi and Elise Crull discovered an unpublished manuscript by Hermann in the archives of the English theoretical physicist Paul Dirac. As it turned out, in 1933, one year after von Neumanns book, Hermann had sent a paper of 25 pages to Dirac, explaining the flaw in von Neumanns argument. Dirac never responded. It is, however, no exaggeration to say that the history of 20th-century physics would have been different if he had, and if the papers by Hermann had been noted earlier.

Historical and historiographical marginalisation are of all times and places: they arise in arts, sciences, and in all corners of philosophy. While generally lacking justification, the causes of marginalisation are strong and manifold, ranging from the political, social, cultural or even personal. More women than men were affected by it, and the history of analytic philosophy is in this respect no exception.

In our recent book Women in the History of Analytic Philosophy (2022), we collected the metadata of articles published in main outlets for analytic philosophers in the first half of the 20th century. In particular, we looked at all the 3,288 articles that appeared in six philosophy journals between 1896 and 1960: Mind, The Monist, Erkenntnis, Analysis, Journal of Symbolic Logic, and Philosophical Studies. In 99.6 per cent of the cases, that is, in 3,274 articles, we were able to identify the gender of the authors. We found that, on average, only 4 per cent of these 3,274 articles were authored by women. Most of these women, 70 in number, are presently forgotten, as is illustrated by recent meetings of the Society for the Study of the History of Analytical Philosophy. Only four of the 246 papers presented at meetings of this society in the period 2015 to 2019 were about female philosophers less than 2 per cent.

In practice, it is often hard to separate historical and historiographical marginalisation, for they typically go hand in hand. If work by female authors is not much read or cited by contemporaries, historians will be disinclined to include it in their textbooks. And if these female philosophers views are not discussed in textbooks, anthologies or introductions, they are less likely to be studied by the next generation of philosophers.

Susanne K Langer photographed by Richard Avedon. Courtesy the Smithsonian National Museum of American History

A prominent example of the interplay between the two types of marginalisation is the reception of work by Susanne K Langer (1895-1985), one of the first to use the term analytic philosophy in print. Langer was an American logician and a student of Whitehead, the co-author of the aforementioned Principia Mathematica. Whitehead had worked at the University of Cambridge in the UK his entire career but had taken up a position at Harvard University in Massachusetts in his 60s. This move greatly stimulated the dissemination of logical analysis in US philosophy, and Langer was among the most active proponents of the new approach. In 1964, she recalled having been part of a small group of students who looked forward to a new philosophical era, that was to grow from logic and semantics. After completing her PhD, Langer actively contributed to the spread of the new analytic philosophy. She published a number of papers on Principia Mathematica, wrote one of the first American logic textbooks, and co-founded the Association for Symbolic Logic, the first international society for logicians.

Langers book sold more than half a million copies and was cited in the academic literature c10,000 times

In the beginning, Langers work was much respected by her colleagues. Her first books and papers were frequently discussed by analytic philosophers, both in print and in private discussion groups. Members of the celebrated Vienna Circle studied her work in the early 1930s and saw her as one of the major representatives of the analytic approach in the US. (For details, see the chapter Susanne Langer and the American Development of Analytic Philosophy by Sander Verhaegh in our book.)

Then, Langer published what would become her most influential work: Philosophy in a New Key (1942). It sold more than half a million copies and has been cited in the academic literature almost 10,000 times. The book is a plea to expand the scope of logical analysis. Until then, analytic philosophers had used the new logic to analyse science, philosophy and language in general. But Langer suggested to apply it to a broader range of phenomena: abstract paintings, sculptures, symphonies, rituals, dreams and myths. All these things, Langer argued, are complex symbols with an internal structure and are therefore suitable subjects for logical analysis. Much as we can investigate the logical form of propositions such as 2 x 2 = 1 + 3 and The morning star is the evening star, we can analyse the logical structure of J S Bachs Air on the G String and Piet Mondrians Composition with Red, Blue, and Yellow.

In the years that Philosophy in a New Key went through reprint after reprint, Langers work began to be ignored by her former analytic companions. In advocating the study of art, myths and rituals, Langer had proposed research topics that many analytic philosophers relegated to the realm of the irrational. While her colleagues were reconstructing the foundations of probability, arithmetic and quantum mechanics, Langer was studying subjects that were taken to be expressions of emotions and feelings. As a result, there was hardly any discussion of her book within the analytic community, despite her rising fame outside it. Even analytic colleagues who were demonstrably influenced by her book, such as Quine, failed to cite it. By the time that analytic philosophers started to compile anthologies and took the first steps towards documenting the history of their own discipline in the late 1940s, Langers work was pushed into the background: it was not mentioned, not even her contributions to the development of logic and analysis in the first phase of her career. Today, Langer is well-known among philosophers of art, but her role in analytic philosophy has been forgotten.

In recent years, quite a lot of attention has been given to the ways in which sociopolitical and other external factors shaped the development of analytic philosophy. Were it not for the grim political situation in the 1930s, members of the Vienna Circle would not have immigrated en masse to England and the US. And were it not for the amenable climate at US universities, where rigour and clarity had become key virtues across the humanities and social sciences, their logical positivism would not so quickly have caught on. Even demographic factors played a role. When the first baby boomers started to enter college, in the 1960s and 70s, many departments had turned analytic, and profited from the explosive growth of higher education, creating more and more jobs for analytically minded philosophers.

Textbooks on analytic philosophy tend to present its development as a more-or-less continuous line, where key figures respond to one another: Russell reacting to Frege, Wittgenstein and Rudolf Carnap to Russell, Quine to Carnap, and so on. This way of telling the history has been very effective: it is no exception to find that, at a conference on the history of analytic philosophy, more than half of the papers are about Frege, Russell, Wittgenstein or Carnap. But the actual spread and growth of analytic philosophy is of course richer, more varied and more complex than is suggested by the stylised and regimented narratives that authors of textbooks are necessarily bound to relate. Like the development of any other historical movement, the development of analytic philosophy is full of interesting details that not only fail to match, but even contradict and undermine the general textbook outline. Had scholars given these details more attention, we might have enjoyed a broader and intellectually more diverse canon. For then we might have seen that the development of analytic philosophy was not only driven by purely philosophical arguments, but also by political, sociological and cultural circumstances, some of which made it difficult for particular academics, such as women, to be heard.

Historians can play a role in correcting the omissions, oversights and downright mistakes of our predecessors

We are not suggesting that a broader recognition of the consequences of historical and historiographical marginalisation will lead to a completely novel canon or a radically new history of the tradition. What happened happened: we cannot go back in time and undo the processes that pushed female philosophers into the periphery. We will have to deal with the facts, even if we do not like them and believe they were preventable. It is a fact that only a small percentage of the publications in analytic philosophy were written by women. And it is also a fact that most of them were junior academics and therefore relatively young. Even if women were allowed to get a degree and were able to make it to the vanguard in a male-dominated intellectual climate, they often stopped publishing when they got married. This is why the 70 female authors we identified were responsible for just 131 publications in the journals we investigated, less than two articles per person on average. Only a very small number of women, such as Jones and Langer, had the time and the opportunity to build a comprehensive philosophical research programme.

What we are saying is that historians can play a role in correcting the omissions, oversights and even downright mistakes our predecessors made in writing about (or worse, not writing about) the contributions of female philosophers. For there is an internal, purely philosophical point to be made. Although external factors influenced its development, analytic philosophy is more than the product of sociopolitical and cultural circumstances. In documenting the history of analytic philosophy, there is something to be right or wrong about. Hermanns discovery really was a significant contribution to the debate about the existence of hidden variables, even if her colleagues and later historians failed to see it. And Langer really did play a major role in the development of US analytic philosophy, even though her name is missing in companions and anthologies on the subject. It is true that, until the 1960s, only a few women actively contributed to the development of analytic philosophy, but many of them had ideas that are worth studying. In examining and re-assessing their work, we will be able to discover interesting but forgotten theories, proofs and arguments, shed new light on the development of the tradition, and contribute to a richer, more diverse and philosophically more fertile canon.

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The lost women of early analytic philosophy - Aeon

The passionate but troubled romance between the young scientists Albert Einstein and Mileva Maric, who met in Switzerland in the early years of the Twentieth Century, is the subject of the world premiere QUANTUM LOVERS: THE MUSICAL, by Hasan Padamsee, a Cornell University Professor of Physics and playwright with three previously produced plays to his credit. This intense and tragic romance, a musicalization of a previous play by Padamsee, was inspired by the books EINSTEIN IN LOVE: A SCIENTIFIC ROMANCE by Dennis Overbye, EINSTEIN IN BERLIN by Thomas Levenson, and ALBERT EINSTEIN/MILEVA MARIC: THE LOVE LETTERS by Albert Einstein, Jurgen Renn, Robert Schulmann and Shawn Smith. Padamsee wrote the musicals book and the lyrics for its 22 musical numbers, with music by Athena Antiporda (Ainna), Roberto Flora, Michaela Catapano, Anshu Jha, Umuk oro Fortune (El Doxa).QUANTUM LOVERS: THE MUSICAL will be performed three times only on Friday, August 11 and Saturday, August 12 at 7:30 each night; and on Sunday, August 13 at 2:30 pm.The fully staged performances will be at City Lit Theater, located on the second floor of the Edgewater Presbyterian Church at 1020 W. Bryn Mawr Avenue, Chicago.Albert Einstein, known as the father of relativity who transformed space, time and gravity, also played a major role in discovering Quantum Physics, a concept mysterious, full of apparent contradictions, difficult to understand, and yet captivating. Like quantum physics, true love is magical but enigmatic, deceptively familiar but incomprehensible. Can the man with dramatic success in revolutionizing space, time and gravity succeed in taming the Quantum? CanEinstein find true love in the whirlpool of his personal experiences?Padamsees cast of eight includes Carson Carter (Albert Einstein), Mikaela May (Mileva Maric), Peter Stielstra (Max Planck and Professor Weber), Carleigh Ray (Elsa Lowenthal Einstein), Eliana Tirona (Milana Bota and Young Mileva), Ronnie Lyall (Marcel Grossman), Patricia Lomden (Ruzica Drazic), and Erick Heyer-Fogelberg. The production team is Rachel Fox (Stage Manager), Dominic Dom Bonelli (Sound Engineer), Autumn Thielander (Choreographer), Zole Morack (Lighting Designer), and Mario Gallego (Production Assistant).

Padamsee began writing plays as a device to teach physics to his Cornell students. He wrote short plays about fascinating characters and the adventure of their discoveries, and gave his students the option to perform the plays in lieu of writing papers. Since those days he has written the full-length plays CREATIONS BIRTHDAY, QUANTUM LOVERS, QUANTUM WONDERLAND, in addition to QUANTUM LOVERS - THE MUSICAL. Padamsee says of QUANTUM LOVERS, By exploring two less charted dimensions of Einsteins character, passionate lover, and staunch anti-nationalist, the play is transporting, timely and true. It moves the audience to Europe into the time that led to the First World War, strongly connecting to the dominant events of today.

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World Premiere of QUANTUM LOVERS: THE MUSICAL to Explore ... - Broadway World

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Some of our most important everyday items, such as computers, medical equipment, stereos, generators, and more, work because of magnets. We know what happens when computers become more powerful, but what might be possible if magnets became more versatile? What if one could change a physical property that defined their usability? What innovation might that catalyze?

It's a question that MIT Plasma Science and Fusion Center (PSFC) research scientists Hang Chi, Yunbo Ou, Jagadeesh Moodera, and their co-authors explore in a new, open-access Nature Communications paper, "Strain-tunable Berry curvature in quasi-two-dimensional chromium telluride."

Understanding the magnitude of the authors' discovery requires a brief trip back in time: In 1879, a 23-year-old graduate student named Edwin Hall discovered that when he put a magnet at right angles to a strip of metal that had a current running through it, one side of the strip would have a greater charge than the other. The magnetic field was deflecting the current's electrons toward the edge of the metal, a phenomenon that would be named the Hall effect in his honor.

In Hall's time, the classical system of physics was the only kind, and forces like gravity and magnetism acted on matter in predictable and immutable ways: Just like dropping an apple would result in it falling, making a "T" with a strip of electrified metal and magnet resulted in the Hall effect, full stop. Except it wasn't, really; now we know quantum mechanics plays a role, too.

Think of classical physics as a map of Arizona, and quantum mechanics as a car trip through the desert. The map provides a macro view and generalized information about the area, but it can't prepare the driver for all the random events one might encounter, like an armadillo running across the road. Quantum spaces, like the journey the driver is on, are governed by a different set of local traffic rules. So, while the Hall effect is induced by an applied magnetic field in a classical system, in a quantum case the Hall effect may occur even without the external field, at which point it becomes the anomalous Hall effect.

When cruising in the quantum realm, one is equipped with the knowledge of the so-called "Berry phase," named after British physicist Michael Berry. It serves as a GPS logger for the car: It's as if the driver has recorded their entire trip from start to finish, and by analyzing the GPS history, one can better plot the ups and downs, or "curvature" of the space. This "Berry curvature" of the quantum landscape can naturally shift electrons to one side, inducing the Hall effect without a magnetic field, just as the hills and valleys dictate the path of the car.

While many have observed the anomalous Hall effect in magnetic materials, none had been able to manipulate it by squeezing and/or stretchinguntil the paper's authors developed a method to demonstrate the change in the anomalous Hall effect and Berry curvature in an unusual magnet.

First, they took half-millimeter-thick bases made of either aluminum oxide or strontium titanate, both of which are crystals, and grew an incredibly thin layer of chromium telluride, a magnetic compound, on top of the bases. On their own, these materials wouldn't do much; however, when combined, film's magnetism and the interface it created with the bases onto which it was grown caused the layers to stretch or squeeze.

To deepen their understanding of how these materials were working together, the researchers partnered with Oak Ridge National Laboratory (ORNL)'s Spallation Neutron Source to perform neutron scattering experimentsessentially blasting the material with shots of particles and studying what bounced backto learn more about the film's chemical and magnetic properties.

Neutrons were an ideal tool for the study because they are magnetic but have no electrical charge. The neutron experiments allowed the researchers to build a profile that revealed how the chemical elements and magnetic behaviors changed at different levels as they probed deeper into the material.

The researchers witnessed the anomalous Hall effect and Berry curvature responding to the degree of squeezing or stretching occurring on the base after the film was applied, an observation later verified by modeling and data simulations.

Though this breakthrough occurred at the tiniest molecular level, the scientists' discovery has significant, real-world ramifications. For example, hard drives store data in tiny magnetic regions, and if they were built using "strain-tunable" materials like the film, they could store additional data in regions that have been stretched different ways.

In robotics, strain-tunable materials could be used as sensors able to provide precise feedback on robots' movements and positioning. Such materials would be especially useful for "soft robots," which use soft and flexible components that better imitate biological organisms. Or, a magnetic device that changed its behavior when flexed or bent could be used to detect minute changes in the environment, or to make incredibly sensitive health monitoring equipment.

More information: Hang Chi et al, Strain-tunable Berry curvature in quasi-two-dimensional chromium telluride, Nature Communications (2023). DOI: 10.1038/s41467-023-38995-4

Journal information: Nature Communications

This story is republished courtesy of MIT News (web.mit.edu/newsoffice/), a popular site that covers news about MIT research, innovation and teaching.

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Researchers control the anomalous Hall effect and Berry curvature to create flexible quantum magnets - Phys.org