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  • richardmitnick 11:12 am on July 9, 2021 Permalink | Reply
    Tags: "Mathematicians Prove Symmetry of Phase Transitions", , , Quanta Magazine(US)   

    From Quanta Magazine : “Mathematicians Prove Symmetry of Phase Transitions” 

    From Quanta Magazine

    July 8, 2021
    Allison Whitten


    A model of percolation through a porous medium that relates to important recent work
    on the symmetries of phase transitions. Vignette for Quanta Magazine.

    For more than 50 years, mathematicians have been searching for a rigorous way to prove that an unusually strong symmetry is universal across physical systems at the mysterious juncture where they’re changing from one state into another. The powerful symmetry, known as conformal invariance, is actually a package of three separate symmetries that are all wrapped up within it.

    Now, in a proof posted in December, a team of five mathematicians has come closer than ever before to proving that conformal invariance is a necessary feature of these physical systems as they transition between phases. The work establishes that rotational invariance — one of the three symmetries contained within conformal invariance — is present at the boundary between states in a wide range of physical systems.

    “It’s a major contribution. This was open for a long time,” said Gady Kozma of the Weizmann Institute of Science (IL).

    Rotational invariance is a symmetry exhibited by the circle: Rotate it any number of degrees and it looks the same. In the context of physical systems on the brink of phase changes, it means many properties of the system behave the same regardless of how a model of the system is rotated.

    Earlier results had established that rotational invariance holds for two specific models, but their methods were not flexible enough to be used for other models. The new proof breaks from this history and marks the first time that rotational invariance has been proved to be a universal phenomenon across a broad class of models.

    “This universality result is even more intriguing” because it means that the same patterns emerge regardless of the differences between models of physical systems, said Hugo Duminil-Copin of the Institute of Advanced Scientific Studies [Institut des Hautes Études Scientifiques] (FR) and the University of Geneva [Université de Genève](CH).

    Duminil-Copin is a co-author of the work along with Karol Kajetan Kozlowski of the Lyon Higher Normal School [École normale supérieure de Lyon] (FR), Dmitry Krachun of the University of Geneva, Ioan Manolescu of the University of Fribourg [Université de Fribourg; Universität Freiburg] (CH) and Mendes Oulamara of IHES and Paris-Saclay University [Université Paris-Saclay] (FR).

    The new work also raises hopes that mathematicians might be closing in on an even more ambitious result: proving that these physical models are conformally invariant. Over the last several decades mathematicians have proved that conformal invariance holds for a few particular models, but they’ve been unable to prove that it holds for all of them, as they suspect it does. This new proof lays the foundation for sweeping results along those lines.

    “It’s already a very big breakthrough,” said Stanislav Smirnov of the University of Geneva. “[Conformal invariance] now looks within reach.”

    Magic Moments

    Transitions between one state and another are some of the most mesmerizing events in the natural world. Some are abrupt, like the transformation of water when it heats into vapor or cools into ice. Others, like the phase transitions studied in the new work, evolve gradually, with a murky boundary between two states. It’s here, at these critical points, that the system hangs in the balance and is neither quite what it was nor what it’s about to become.

    Mathematicians try to bottle this magic in simplified models.

    Take, for example, what happens as you heat iron. Above a certain temperature it loses its magnetic attraction. The change occurs as millions of sizzling atoms acting as miniature magnets flip and no longer align with the magnetic positions of their neighbors. Around 1,000 degrees Fahrenheit, heat wins out and a magnet reduces to a mere piece of metal.

    Mathematicians study this process with the Ising model. It imagines a block of iron as a two-dimensional square lattice, much like the grid on a piece of graph paper. The model situates the iron atoms at the intersections of the lattice lines and represents them as arrows pointing up or down.

    The Ising model came into widespread use in the 1950s as a tool to represent physical systems near critical points. These included metals losing magnetism and also the gas-liquid transition in air and the switch between order and disorder in alloys. These are all very different types of systems that behave in very different ways at the microscopic level.

    Then, in 1970, the young physicist Alexander Polyakov predicted that despite their apparent differences, these systems all exhibit conformal invariance at their critical points. Decades of subsequent analysis convinced physicists that Polyakov was right. But mathematicians have been left with the difficult job of rigorously proving that it’s true.

    The Symmetry of Symmetries

    Conformal invariance consists of three types of symmetries rolled into one more extensive symmetry. You can shift objects that exhibit it (translational symmetry), rotate them by any number of degrees (rotational symmetry or invariance), or change their size (scale symmetry), all without changing any of their angles.

    “[Conformal invariance] is what sometimes I call ‘the symmetry to rule them all’ because it’s an overall symmetry, which is stronger than the three others,” said Duminil-Copin.

    Conformal invariance shows up in physical models in a more subtle way. In the Ising model, when magnetism is still intact and a phase transition hasn’t occurred yet, most arrows point up in one massive cluster. There are also some small clusters in which all arrows point down. But at the critical temperature, atoms can influence each other from greater distances than before. Suddenly, the alignment of atoms everywhere is unstable: Clusters of different sizes with arrows pointing either up or down appear all at once, and magnetism is about to be lost.

    At this critical point, mathematicians look at the model from very far away and study correlations between arrows, which characterize the likelihood that any given pair points in the same direction. In this setting, conformal invariance means that you can translate, rotate and rescale the grid without distorting those correlations. That is, if two arrows have a 50% chance of pointing in the same direction, and then you apply those symmetries, the arrows that come to occupy the same positions in the lattice will also have a 50% chance of aligning.

    The result is that if you compare your original lattice model with the new, transformed lattice, you won’t be able to tell which is which. Importantly, the same is not true of the Ising model before the phase transition. There, if you take the top corner of the lattice and blow it up to be the same size as the original (a scale transformation), you’ll also increase the typical size of the small islands of down arrows, making it obvious which lattice is the original.

    The presence of conformal invariance has a direct physical meaning: It indicates that the global behavior of the system won’t change even if you tweak the microscopic details of the substance. It also hints at a certain mathematical elegance that sets in, for a brief interlude, just as the entire system is breaking its overarching form and becoming something else.

    The First Proofs

    In 2001 Smirnov produced the first rigorous mathematical proof of conformal invariance in a physical model. It applied to a model of percolation, which is the process of liquid passing through a maze in a porous medium, like a stone.

    Smirnov looked at percolation on a triangular lattice, where water is allowed to flow only through vertices that are “open.” Initially, every vertex has the same probability of being open to the flow of water. When the probability is low, the chances of water having a path all the way through the stone is low.

    But as you slowly increase the probability, there comes a point where enough vertices are open to create the first path spanning the stone. Smirnov proved that at the critical threshold, the triangular lattice is conformally invariant, meaning percolation occurs regardless of how you transform it with conformal symmetries.

    Five years later, at the 2006 International Congress of Mathematicians, Smirnov announced that he had proved conformal invariance again, this time in the Ising model. Combined with his 2001 proof, this groundbreaking work earned him the Fields Medal, math’s highest honor.

    In the years since, other proofs have trickled in on a case-by-case basis, establishing conformal invariance for specific models. None have come close to proving the universality that Polyakov envisioned.

    “The previous proofs that worked were tailored to specific models,” said Federico Camia, a mathematical physicist at New York University Abu Dhabi (ABD). “You have a very specific tool to prove it for a very specific model.”

    Smirnov himself acknowledged that both of his proofs relied on some sort of “magic” that was present in the two models he worked with but isn’t usually available.

    “Since it used magic, it only works in situations where there is magic, and we weren’t able to find magic in other situations,” he said.

    The new work is the first to disrupt this pattern — proving that rotational invariance, a core feature of conformal invariance, exists widely.

    One at a Time

    Duminil-Copin first began to think about proving universal conformal invariance in the late 2000s, when he was Smirnov’s graduate student at the University of Geneva [Université de Genève](CH). He had a unique understanding of the brilliance of his mentor’s techniques — and also of their limitations. Smirnov bypassed the need to prove all three symmetries separately and instead found a direct route to establishing conformal invariance — like a shortcut to a summit.

    “He’s an amazing problem solver. He proved conformal invariance of two models of statistical physics by finding the entrance in this huge mountain, like this kind of crux that he went through,” said Duminil-Copin.

    For years after graduate school, Duminil-Copin worked on building up a set of proofs that might eventually allow him to go beyond Smirnov’s work. By the time he and his co-authors set to work in earnest on conformal invariance, they were ready to take a different approach than Smirnov had. Rather than take their chances with magic, they returned to the original hypotheses about conformal invariance made by Polyakov and later physicists.

    The physicists had required a proof in three steps, one for each symmetry present in conformal invariance: translational, rotational and scale invariance. Prove each of them separately, and you get conformal invariance as a consequence.

    With this in mind, the authors set out to prove scale invariance first, believing that rotational invariance would be the most difficult symmetry and knowing that translational invariance was simple enough and wouldn’t require its own proof. In attempting this, they realized instead that they could prove the existence of rotational invariance at the critical point in a large variety of percolation models on square and rectangular grids.

    They used a technique from probability theory, called coupling, that made it possible to directly compare the large-scale behavior of square lattices with rotated rectangular lattices. By combining this approach with ideas from another field of mathematics called integrability, which studies hidden structures in evolving systems, they were able to prove that the behavior at critical points was the same across the models — thus establishing rotational invariance. Then they proved that their results extended to other physical models where it’s possible to apply the same coupling.

    The end result is a powerful proof that rotational invariance is a universal property of a large subset of known two-dimensional models. They believe the success of their work indicates that a similarly eclectic set of techniques, melded from various fields of math, will be necessary to make additional progress on conformal invariance.

    “I think it’s going to be more and more true, in arguments of conformal invariance and the study of phase transitions, that you need a little bit of everything. You cannot just attack it with one angle of attack,” said Duminil-Copin.

    Last Steps

    For the first time since Smirnov’s 2001 result, mathematicians have new purchase on the long-standing challenge of proving the universality of conformal invariance. And unlike that earlier work, this new result opens new paths to follow. By following a bottom-up approach in which they aimed to prove one constituent symmetry at a time, the researchers hope they laid a foundation that will eventually support a universal set of results.

    Now, with rotational invariance down, Duminil-Copin and his colleagues have their sights set on scale invariance, their original target. A proof of scale invariance, given the recent work on rotational symmetry and the fact that translational symmetry doesn’t need its own proof, would put mathematicians on the cusp of proving full conformal invariance. And the flexibility of their methods makes the researchers optimistic it can be done.

    “I definitely think that step three is going to fall fairly soon,” said Duminil-Copin. “If it’s not us, it would be somebody smarter, but definitely, it’s going to happen very soon.”

    The proof of rotational invariance took five years, though, so the next results may yet take some time. Still, Smirnov is hopeful that two-dimensional conformal invariance may finally be within reach.

    “That might mean a week, or it might mean five years, but I’m much more optimistic than I was in November,” said Smirnov.

    See the full article here .


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    Please help promote STEM in your local schools.

    Stem Education Coalition

    Formerly known as Simons Science News, Quanta Magazine is an editorially independent online publication launched by the Simons Foundation to enhance public understanding of science. Why Quanta? Albert Einstein called photons “quanta of light.” Our goal is to “illuminate science.” At Quanta Magazine, scientific accuracy is every bit as important as telling a good story. All of our articles are meticulously researched, reported, edited, copy-edited and fact-checked.

     
  • richardmitnick 4:17 pm on June 25, 2021 Permalink | Reply
    Tags: "Nathan Seiberg on How Math Might Complete the Ultimate Physics Theory", , From the time of the ancient Babylonians and Greeks there hasn’t been a real distinction between math and physics., , Physicists and mathematicians are motivated by different questions. And different kinds of questions lead to different insights., , QFT: Quantum Field Theory, Quanta Magazine(US), Seiberg’s work has helped bring the study of quantum field theories closer to pure mathematics., The Standard Model of Particle Physics explains nearly every aspect of the physical world (except gravity)., We cannot yet formulate QFT in a rigorous way that would make mathematicians perfectly happy., [Isaac] Newton was motivated by physics when he invented calculus.   

    From Quanta Magazine : “Nathan Seiberg on How Math Might Complete the Ultimate Physics Theory” 

    From Quanta Magazine

    June 24, 2021
    Kevin Hartnett

    Even in an incomplete state, quantum field theory is the most successful physical theory ever discovered. Nathan Seiberg, one of its leading architects, talks about the gaps in QFT and how mathematicians could fill them.

    1
    Nathan Seiberg crosses a bridge over Stony Brook at the Institute for Advanced Study. Credit: Sasha Maslov for Quanta Magazine.

    Nathan Seiberg, 64, still does a lot of the electrical work and even some of the plumbing around his house in Princeton, New Jersey. It’s an interest he developed as a kid growing up in Israel, where he tinkered with his car and built a radio.

    “I was always fascinated by solving problems and understanding how things work,” he said.

    Seiberg’s professional career has been about problem solving, too, though nothing as straightforward as fixing radios. He’s a physicist at the Institute for Advanced Study (US), and over the course of a long and decorated career he has made many contributions to the development of Quantum Field Theory, or QFT.

    QFT refers broadly to the set of all possible quantum field theories. These are theories whose basic objects are “fields,” which stretch across space and time. There are fields associated with fundamental particles like electrons and quarks, and fields associated with fundamental forces, like gravity and electromagnetism. The most sweeping quantum field theory — and the most successful theory in the history of physics, period — is the Standard Model.

    It combines these fields into a single equation that explains nearly every aspect of the physical world (except gravity).

    By the time Seiberg started graduate school at the Weizmann Institute of Science (IL) in 1978, QFT was already well established as the principal perspective of physics. Its predictive power wasn’t in doubt, but many basic questions remained about how and why it worked so well.

    “It’s shocking that we have these techniques and sometimes they give beautiful answers, despite the fact that we don’t know how to formulate the problems rigorously,” said Seiberg.

    Much of Seiberg’s most important work has involved teasing apart how particular quantum field theories work the way they do. In the late 1980s he and Gregory Moore worked out mathematical details of types of quantum field theories called conformal field theories and topological field theories. Shortly after, partly in collaboration with Edward Witten, he focused on understanding features of three- and four-dimensional “supersymmetric” quantum field theories. This helped explain how quarks, the particles inside protons, are confined there.

    The work is complicated, but Seiberg retains an element of childlike fascination with it. Just as he once wanted to understand how a transistor radio produces sound, as a physicist he now seeks to explain how these quantum field theories yield often startlingly accurate predictions about the physical world.

    “You’re trying to figure out how something works and then you’re trying to use it,” he said.

    Seiberg’s work has also helped bring the study of quantum field theories closer to pure mathematics. In 1994, Witten discovered how to use physical phenomena that he and Seiberg had discovered to quantify basic characteristics of a space, like the number of holes it has. Their “Seiberg-Witten invariants” are now an essential tool in math. Seiberg believes quantum field theory and math must continue to grow closer if physicists are ever really going to understand the basic features underlying all quantum field theories.

    Quanta Magazine spoke with Seiberg about how physics and math are really two sides of the same coin, the ways in which QFT is incompletely understood today, and his own abandoned effort to write a textbook for the field. The interview has been condensed and edited for clarity.

    2
    Seiberg suspects that math and physics, which became separate fields of study only relatively recently, will one day merge together under the same deep intellectual structure. Credit: Sasha Maslov for Quanta Magazine.

    Math and physics have a long history together. What are some of the most important ways they have influenced each other over the centuries?

    From the time of the ancient Babylonians and Greeks there hasn’t been a real distinction between math and physics. They studied similar questions. There has been a lot of cross-fertilization between what today we call math and physics. [Isaac] Newton is a great example. He was motivated by physics when he invented calculus. Over the 20th century, things were a bit more complicated. People specialized in math or in physics.

    Physics usually offers very concrete questions and very concrete puzzles associated with reality and experiment. It’s also kind of grounded in reality. Math usually provides more generality, more powerful methods, and more rigor and precision. All of these elements are needed.

    Do you think they’ll continue to be increasingly separate fields?

    Given that they started as one field and lately diverged, but continue to influence each other, in the future I’d guess they’ll continue to influence each other to the point that there would be no clear separation between them. I think that there will be one deep, intellectual structure that encompasses math and physics.

    Why has QFT, and physics in general, been such a provocative stimulus for math?

    I think physicists and mathematicians are motivated by different questions. And different kinds of questions lead to different insights. There have been many examples where physicists came up with some ideas — which in most cases were not even rigorous — and mathematicians looked at them and said, “This is an equality between two different things; let’s try and prove it.” So the input from physics is another source of influence for the mathematicians. From this perspective, physics is like a machine that produces conjectures.

    And the track record with these conjectures has been quite amazing, so mathematicians have learned to take physics in general and quantum field theory in particular very seriously. But what is perhaps surprising for them is that they still can’t make QFT rigorous; they still can’t figure out where these insights come from.

    Let’s focus on the physics side for now, and that amazing track record. What are some of its biggest triumphs?

    QFT is by far the most successful theory ever created by mankind to explain anything. There are many [predictions] that agree perfectly with experiments to unprecedented accuracy. We’re talking about accuracy of up to the order of 12 digits between theory and experiment. And there are literally trillions and trillions of experiments that match the theory. I don’t think historically there has ever been any theory as successful as quantum field theory. And it includes as special cases all the previous discoveries, like Newton’s theory, [James Clerk] Maxwell’s theory of electromagnetism, and of course quantum mechanics and Albert Einstein’s special relativity. All these things are special cases of this one coherent intellectual structure. It’s an amazing, spectacular achievement.

    And yet we also think QFT is incomplete. What are its limitations?

    The biggest challenge is to merge it with Einstein’s general theory of relativity. There are many ideas how to do this. String theory is the main one. There has been a lot of progress, but we’re still not at the end of the story.

    You’ve referred to QFT as not yet “mature.” What do you mean by that?

    I have my preferred maturity test for a scientific field. That is to look at textbooks and at courses at universities that teach the topic. When you look at a mature field, most of the textbooks are more or less the same. They follow the same logical sequence of ideas. Similarly, most of the courses are more or less the same. When you learn calculus, you first learn one topic, then another, and then the third. It is the same sequence in all institutions. For me, this is a sign of a mature field.

    That’s not the case for QFT. There are several books with different perspectives from different points of view, with [ideas presented] in a different order. For me this means that we have not found the ultimate, streamlined version of presenting our understanding.

    You’ve also mentioned that it’s a sign of incompleteness that QFT doesn’t have its own place in mathematics. What does that mean?

    We cannot yet formulate QFT in a rigorous way that would make mathematicians perfectly happy. In special cases we can, but in general we cannot. In all the other theories in physics — in classical physics, in quantum mechanics — there is no such problem. Mathematicians have a rigorous description of it. They can prove theorems and make deep advances. That’s not yet the case in quantum field theory.

    I should emphasize that we do not look for rigor for the sake of rigor. That’s not our goal. But I think that the fact that we don’t yet have a rigorous description of it, the fact that mathematicians are not yet comfortable with it, is a clear reflection of the fact that we don’t yet fully understand what we’re doing.

    If we do have a rigorous description of QFT, it will give us new, deeper insights into the structure of the theory. It will give us new tools to perform calculations, and it will uncover new phenomena.

    Are we even close to doing this?

    Whatever approach we take, we get stuck somewhere. One approach that gets close to being rigorous is we imagine space as a lattice of points. Then we take the limit as the points approach each other and space becomes continuous. We describe space as a lattice, and as long as we’re on the lattice there is nothing non-rigorous about it. The challenge is to prove that the limit exists as the distance [between points on the lattice] becomes small and the number of points [on the lattice] becomes large. We assume this limit exists, but we cannot prove it.

    So if we do it, will a rigorous understanding of quantum field theory actually merge it with general relativity? That is, will it provide a long-sought theory of quantum gravity?

    It’s quite clear to me that there is one intellectual structure that includes everything. I think of quantum field theory as being the language of physics, simply because it already appears like the language of many different phenomena in many different fields. I expect it to encompass also quantum gravity. In fact, in special circumstances, quantum gravity is described by quantum field theory.

    It might take a century or two, even three centuries, to get there. But I personally don’t think it will take that long. This is not to say that in 200-300 years science will be over. There will still be many interesting questions to address. But with a better understanding of quantum field theory, I think [discovery] will be a lot faster.

    What could remain to be discovered after QFT is fully understood?

    Most physicists aren’t trying to find a more fundamental description of nature. [Instead they say,] “Given the rules, and given what we know, can we explain known phenomena and find new phenomena, like new materials that exhibit special properties?” I think this will continue for a long time. Nature is very rich, and once we fully understand the rules of nature we’ll be able to use these rules to predict new phenomena. This is not less exciting than finding the fundamental rules of nature.

    You mentioned that one indication the field of QFT is not complete is that it doesn’t yet have a canonical textbook. I mentioned this to another physicist recently, and he said a lot of people hope you’ll write it.

    I tried, actually, but I stopped. Around 2000, I took one summer, and at the end of the summer I had many pages written, and I realized I hated what I’d written.

    Honestly, my problem is that there are all these different ways of starting to write it, but I can’t find a preferred angle. I think it’s a reflection of the status of the field, a sign that it’s not yet mature enough. The fact that there isn’t a clear starting point, to me, is a sign that we haven’t yet found the ultimate way to think about it.

    See the full article here .


    five-ways-keep-your-child-safe-school-shootings

    Please help promote STEM in your local schools.

    Stem Education Coalition

    Formerly known as Simons Science News, Quanta Magazine is an editorially independent online publication launched by the Simons Foundation to enhance public understanding of science. Why Quanta? Albert Einstein called photons “quanta of light.” Our goal is to “illuminate science.” At Quanta Magazine, scientific accuracy is every bit as important as telling a good story. All of our articles are meticulously researched, reported, edited, copy-edited and fact-checked.

     
  • richardmitnick 10:03 am on June 23, 2021 Permalink | Reply
    Tags: "Gas Giants’ Energy Crisis Solved After 50 Years", Jupiter and Saturn should be freezing cold. Instead they’re hot. Researchers now know why., , Quanta Magazine(US)   

    From Quanta Magazine : “Gas Giants’ Energy Crisis Solved After 50 Years” 

    From Quanta Magazine

    June 22, 2021
    Robin George Andrews

    Cassini data solves Jupiter’s and Saturn’s energy mystery.

    Jupiter and Saturn should be freezing cold. Instead they’re hot. Researchers now know why.

    1
    Saturn’s auroras are clearly visible in this composite image made by NASA’s Cassini spacecraft. Blue light corresponds to reflected sunlight, red to the planet’s own heat, and green to emissions from hydrogen ions in the aurora.

    Living as they do in the distant, sun-forsaken reaches of the solar system, Jupiter and Saturn, the gas giants, and Uranus and Neptune, the ice giants, were always expected to be frosty realms. But when NASA’s Voyager spacecraft sailed past them in the late 1970s and 1980s, scientists found that all four worlds were running planetary fevers — a revelation as jarring as finding a bonfire inside your freezer.

    Follow-up observations by ground-based telescopes and the Galileo and Cassini spacecraft demonstrated that their planet-wide fevers have persisted through time.

    Their planetary pyrexias are acute: Jupiter’s lower latitudes, for example, should be a frigid −110 degrees Celsius. Instead, the atmosphere there cooks at 325 degrees. What incognito incinerator is behind this? And how is this unknown heat source warming not just a single spot on the planet, but the entire upper atmosphere?

    Scientists have tried to explain this “energy crisis,” but have remained “confused for about 50 years,” said James O’Donoghue, a planetary astronomer at the Japan Aerospace Exploration Agency [ (国立研究開発法人宇宙航空研究開発機構] (JP) JAXA. Now two papers have conclusively revealed where all that heat is coming from: Jupiter and Saturn’s northern and southern lights — their auroras.

    The results come from detailed measurements of both gas giants’ upper atmospheres. Saturn’s atmospheric temperature was taken by the Cassini spacecraft during the maneuvers that ultimately plunged it into the planet; Jupiter’s was stitched together using a telescope atop a giant Hawaiian volcano. Both show that the atmospheres are hottest near the auroral zones below both magnetic poles. As you approach the equator, the temperature drops off. Clearly, the aurora is bringing the heat — and, as with a radiator, that heat decreases with distance.


    This composite video shows Jupiter’s auroras as seen by the Hubble Space Telescope. The auroras were photographed in far-ultraviolet light and superimposed on images of the planet taken in visible light.
    Credit: NASA, ESA, J. Nichols (University of Leicester (UK)), and G. Bacon (Space Telescope Science Institute (US)); Acknowledgment: A. Simon (NASA Goddard Space Flight Center (US)) and the OPAL team.

    A solution to the energy crisis may have far-reaching ramifications. Planets — from those in our own solar system to those orbiting distant stars — don’t always keep their atmospheres. Many gassy envelopes are destroyed over time, in some cases turning giant worlds into tiny, uninhabitable husks. Researchers want to be able to distinguish these from habitable, Earth-like planets. If we hope to do so, said Zarah Brown, a researcher at the University of Arizona (UK), “one of the major parameters that you would want to know is the temperature of the outer atmosphere, since that’s where gas is lost to space.”

    Alien Auroras

    Earth’s northern and southern lights aren’t yet completely understood, but the basics are clear.

    The sun shoots volleys of magnetic fields and energetic particles into space. When these volleys — better known as the solar wind — reach our planet, they interact with Earth’s own magnetic bubble, which is known as the magnetosphere. The energetic particles then spiral down to the planet’s north and south magnetic poles. There, they ping off gas atoms and molecules in the upper atmosphere. Those impacts temporarily energize the gases, which emit visible flashes of light.

    In general, auroras require three ingredients: a source of energetic particles, a magnetic field and an atmosphere. Jupiter and Saturn have all three, but neither planet’s auroras are quite like Earth’s.


    Jupiter’s Magnetosphere. Jupiter’s magnetosphere is created by the movement of metallic hydrogen in the giant planet’s core. In this animation, magnetic field lines are seen in gold. The yellow arrow points to the sun. The light blue arrow marks the magnetic north, while the dark blue arrow marks the rotational axis. Red and green arrows define a coordinate system. Credit: NASA’s Scientific Visualization Studio/JPL-Caltech (US) Navigation and Ancillary Information Facility-NASA JPL (US).

    Earth’s magnetic field comes from the churning of liquid nickel-iron alloys deep below our feet. But the gas giants don’t have liquid-iron cores. Instead, the planets’ immense gravity squeezes colossal volumes of liquid hydrogen in their outer cores so hard that the hydrogen’s electrons pop free. The process turns the hydrogen into a magnetism-generating metal.

    Because these maelstroms of metal hydrogen are so immense, the gas giants’ magnetospheres make Earth’s look lilliputian.

    Jupiter’s magnetosphere “is the biggest structure in the solar system,” said O’Donoghue. “Its tail goes down to Saturn, and possibly beyond.”

    The gas giants also can’t rely on a plentiful supply of energetic particles, or plasma, from the solar wind, which dissipates with increasing distance from the sun. Instead, they rely on acts of volcanic alchemy.

    Jupiter gets most of its plasma from its moon Io, the most volcanic object known to science. Io’s near-constant magmatic eruptions jettison an abundance of volcanic material into space; there, it bathes in sunlight, becomes electrically excited, then showers down onto Jupiter. Most of Saturn’s plasma comes from Enceladus, a mirrorlike icy moon that fires spectacular jets of frigid watery matter into space.

    3
    4
    (2) Saturn’s icy moon Enceladus hides a global ocean of liquid salty water beneath its crust. Its geysers spray water ice and vapor hundreds of kilometers into space. Credit: NASA/JPL-Caltech/Space Science Institute – Boulder Colorado (US).

    These plasmas shoot into the planets’ expansive magnetospheres, which accelerate them into the poles. There, the charged particles in the plasma collide with gas molecules in the atmosphere.

    Auroras on Saturn emit mostly ultraviolet light; on Jupiter, they’re in both ultraviolet and infrared wavelengths. But the processes that make light aren’t the same as those that make heat. In this case, “it’s all about friction,” said O’Donoghue.

    Plasma flows to the planets’ magnetic poles via field lines — magnetized tendrils that stretch far into space. These tendrils and their streams rotate along with the planet. But they sometimes struggle to keep pace. Jupiter, for example, rotates once every 10 hours. When those streams of plasma lag behind the planet’s rotation, Jupiter’s powerful westerly winds push through them. The drag of these winds on the slow-moving plasma streams creates friction. And that friction makes heat — perhaps, in the case of Jupiter, 125 times more heat than the planet gets from the sun. “That’s kind of nuts,” said O’Donoghue.

    It’s not surprising, then, that astronomers have been wondering if the auroras are the source of those planetary fevers. “For decades, it was obvious that there was plenty of energy in the aurora,” said Luke Moore, a senior research scientist at Boston University (US). But in order to navigate from suspicion to certainty, astronomers needed a map: specifically, a heat map of the gas and ice giants’ upper atmospheres. With it, they could see if the highest temperatures could be superimposed on the auroras, and if this heat was diffusing over the entire planet.

    The first map came from a final act. In April 2017, after 13 years in orbit around Saturn, NASA’s Cassini spacecraft was commanded to do something remarkable: make 22 orbits of the planet while repeatedly diving between it and its rings. The so-called Grand Finale, which ended on September 15, 2017, when the spacecraft burned up in Saturn’s clouds, gave Cassini a close-up view of the world like no other.


    Cassini’s Grand Finale. During Cassini’s Grand Finale, the spacecraft dove between the rings and the planet 22 times. The maneuver began and ended with close flybys of Saturn’s moon Titan, whose orbit is shown in yellow.
    Credit: NASA/JPL-Caltech.

    As Cassini passed close to Saturn, it peered through the planet’s atmosphere at the bright stars beyond. The light from these stars appeared to change depending on the density of the atmosphere that the light passed through. A gas’s density and temperature are related, so researchers used dozens of these measurements, known as stellar occultations, to produce detailed heat maps for both the day and night sides of Saturn’s upper atmosphere.

    Published last year in Nature Astronomy, the heat maps showed a thermal spike around the auroras, and a gentle drop-off in temperatures toward the equator.

    It certainly seemed as if the auroras were responsible. But “if our theory of energy redistribution on Saturn is correct, it would have to work on Jupiter as well,” said Brown, who was the lead author on the Saturn study.

    Now, due to the work by O’Donoghue and his colleagues, it appears that it does.

    Attributing Jupiter’s upper atmospheric fever to its own auroras also required a heat map. But making such a map is far from easy. The planet’s chaotic upper atmosphere changes from week to week. You can’t just take a measurement near the poles on one night, then come back a few weeks later and compare it with a measurement near the equator. In time, the skies will shift significantly, and evidence of any heat flows will be lost.

    What researchers needed was a global heat map made during a relatively brief moment in time — one that showed the flow of heat over several hours.

    O’Donoghue, Moore and company turned to the Keck Observatory atop Hawai‘i’s dormant Mauna Kea volcano.

    They used it to observe Jupiter in infrared light over two nights — April 14, 2016, and January 25, 2017 — for five hours apiece. During the course of each night they created a high-resolution heat map of Jupiter’s day side. Both maps clearly showed temperatures peaking around the auroral zones, hitting a staggering 730 degrees Celsius. This thermal zenith gradually declined as you approached the equator, where the mercury still hit an impressive 325 degrees.

    6
    Jupiter’s moon Io is the most volcanically active place in the solar system. The constant gravitational tug of Jupiter and its planets distorts Io’s surface, leading to eruptions such as this one caught by NASA’s Galileo spacecraft. Credit: NASA/JPL/DLR German Aerospace Center [Deutsches Zentrum für Luft- und Raumfahrt e.V.](DE)

    Their results, accepted to Nature, harmonize with what Cassini saw at Saturn. The results have been taken as hard proof that the auroras can solve the energy crisis. “It’s a big step forward, seeing that it’s auroral heating,” said Rosie Johnson, a space physics researcher at Aberystwyth University [Prifysgol Aberystwyth] (WLS) who wasn’t involved with either paper.

    Licia Ray, a space and planetary physics researcher at Lancaster University (UK) who is also not involved with either paper, praises the Saturn study’s rigorous data set. But she is less convinced by the Jupiter paper. “They’re only using two nights of data, and I find that to be an issue,” she said. But despite her misgivings, “I think the temperature gradient result [at Jupiter] probably will hold, because they’ve seen it at Saturn,” she said.

    Having comparatively few observations is “a fair concern, because these are very dynamic places, these giant planets,” said Moore. Additional nights of Jupiter observations have been collected and are currently being processed.

    In any event, most independent researchers seem convinced that the planet-wide fevers are down to the auroras. These papers provide “a really nice confirmation that what we suspected was happening is actually happening,” said Leigh Fletcher, a planetary scientist at the University of Leicester in England who was not involved with the work. “Energy is leaking from the auroral domain down into the lower latitudes.” The question is: How?

    The Wicked Western Winds

    The majority of atmospheric circulation models struggle to move heat from the aurora through Jupiter and Saturn’s screeching westward winds to the equator — at yet, their heat maps show that these tempestuous hurdles are somehow being overcome.

    One potential solution [Geophysical Research Letters]was inspired by Cassini’s observations. Cassini discovered that, on occasion, a disturbance to a lower layer of Saturn’s atmosphere can cause that layer to migrate to the upper atmosphere. Such an inversion may disrupt and slow down the upper atmosphere’s powerful westward winds — perhaps enough to allow the auroral heat to leak through.

    7
    The aurora as seen over Saturn’s north pole. ESA/Hubble, NASA, A. Simon (GSFC) and the OPAL Team, J. DePasquale (STScI), L. Lamy (Observatoire de Paris (FR))

    In theory, this mechanism could apply to Jupiter too. But the upper atmospheres of gas giants lack clouds — clear markers of movement — which makes studying winds there “fiendishly challenging,” said Fletcher. For now, this part of the energy crisis remains a riddle without a resolution.

    O’Donoghue’s team suspects that a second process might help distribute heat around Jupiter. Occasionally, intense solar wind activity will exert pressure on Jupiter’s magnetosphere, squeezing it. Prior work indicated [Planetary and Space Science] that when this compression happens, Io’s plasma streams can get quickly pushed into the upper atmosphere. The additional plasma gives those powerful westward winds more to push through, which could produce a heating spike.

    Such a spike may have been seen during the recent surveys. Around the time of the January 25, 2017, observation, when solar wind activity was relatively high, the already hot upper atmosphere spiked in temperature. The team simultaneously spotted a curious high-temperature structure moving from the auroral zones toward the equator. These phenomena were not seen during the April 14, 2016, observation, when the solar wind activity was relatively quiet.

    The team speculates that a burst of solar wind activity in early 2017 may have pinched the planet’s magnetosphere. But other factors could also be in play. Ray speculates that an uptick in volcanic activity on Io may provide an alternative explanation. Without more observations, they can’t be certain one way or the other, said O’Donoghue.

    Despite these lingering quandaries, the conclusive identification of the auroras as Jupiter and Saturn’s atmospheric arsonists has significantly bolstered our understanding of these worlds. Uranus and Neptune, however, remain shrouded in a thick fog of uncertainty. They have different atmospheres, magnetic fields and rotational behaviors — “they’re wacky,” said Brown — meaning what works for the gas giants may not work for the ice giants. They’re so far away that we struggle to see either in detail using Earth’s telescopes, and it looks as though they won’t be visited by another spacecraft for the foreseeable future. Until that day comes, these distant realms will remain strangers, both afflicted with planetary fevers that we have yet to fathom.

    See the full article here .


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    Please help promote STEM in your local schools.

    Stem Education Coalition

    Formerly known as Simons Science News, Quanta Magazine is an editorially independent online publication launched by the Simons Foundation to enhance public understanding of science. Why Quanta? Albert Einstein called photons “quanta of light.” Our goal is to “illuminate science.” At Quanta Magazine, scientific accuracy is every bit as important as telling a good story. All of our articles are meticulously researched, reported, edited, copy-edited and fact-checked.

     
  • richardmitnick 1:52 pm on June 18, 2021 Permalink | Reply
    Tags: "Mathematicians Prove 2D Version of Quantum Gravity Really Works", A trilogy of landmark publications, , “Liouville field”- see the description in the full blog post., , DOZZ formula: a finding of Harald Dorn; Hans-Jörg Otto; Alexeif Zamolodchikov; Alexander Zamolodchikov, Fields are central to quantum physics too; however the situation here is more complicated due to the deep randomness of quantum theory., In classical physics for example a single field tells you everything about how a force pushes objects around., In physics today the main actors in the most successful theories are fields., , , QFT: Quantum Field Theory-a model of how one or more quantum fields each with their infinite variations act and interact., Quanta Magazine(US),   

    From Quanta Magazine : “Mathematicians Prove 2D Version of Quantum Gravity Really Works” 

    From Quanta Magazine

    June 17, 2021
    Charlie Wood

    In three towering papers, a team of mathematicians has worked out the details of Liouville quantum field theory, a two-dimensional model of quantum gravity.

    1
    Credit: Olena Shmahalo/Quanta Magazine.

    Alexander Polyakov, a theoretical physicist now at Princeton University (US), caught a glimpse of the future of quantum theory in 1981. A range of mysteries, from the wiggling of strings to the binding of quarks into protons, demanded a new mathematical tool whose silhouette he could just make out.

    “There are methods and formulae in science which serve as master keys to many apparently different problems,” he wrote in the introduction to a now famous four-page letter in Physics Letters B. “At the present time we have to develop an art of handling sums over random surfaces.”

    Polyakov’s proposal proved powerful. In his paper he sketched out a formula that roughly described how to calculate averages of a wildly chaotic type of surface, the “Liouville field.” His work brought physicists into a new mathematical arena, one essential for unlocking the behavior of theoretical objects called strings and building a simplified model of quantum gravity.

    Years of toil would lead Polyakov to breakthrough solutions for other theories in physics, but he never fully understood the mathematics behind the Liouville field.

    Over the last seven years, however, a group of mathematicians has done what many researchers thought impossible. In a trilogy of landmark publications, they have recast Polyakov’s formula using fully rigorous mathematical language and proved that the Liouville field flawlessly models the phenomena Polyakov thought it would.

    1
    Vincent Vargas of the National Centre for Scientific Research [Centre national de la recherche scientifique, [CNRS] (FR) and his collaborators have achieved a rare feat: a strongly interacting quantum field theory perfectly described by a brief mathematical formula.

    “It took us 40 years in math to make sense of four pages,” said Vincent Vargas, a mathematician at the French National Center for Scientific Research and co-author of the research with Rémi Rhodes of Aix-Marseille University [Aix-Marseille Université] (FR), Antti Kupiainen of the University of Helsinki [ Helsingin yliopisto; Helsingfors universitet] (FI), François David of the French National Centre for Scientific Research [Centre national de la recherche scientifique, [CNRS] (FR), and Colin Guillarmou of Paris-Saclay University [Université Paris-Saclay] (FR).

    The three papers forge a bridge between the pristine world of mathematics and the messy reality of physics — and they do so by breaking new ground in the mathematical field of probability theory. The work also touches on philosophical questions regarding the objects that take center stage in the leading theories of fundamental physics: quantum fields.

    “This is a masterpiece in mathematical physics,” said Xin Sun, a mathematician at the University of Pennsylvania (US).

    Infinite Fields

    In physics today the main actors in the most successful theories are fields — objects that fill space, taking on different values from place to place.

    In classical physics for example a single field tells you everything about how a force pushes objects around. Take Earth’s magnetic field: The twitches of a compass needle reveal the field’s influence (its strength and direction) at every point on the planet.

    Fields are central to quantum physics too; however the situation here is more complicated due to the deep randomness of quantum theory. From the quantum perspective, Earth doesn’t generate one magnetic field, but rather an infinite number of different ones. Some look almost like the field we observe in classical physics, but others are wildly different.

    But physicists still want to make predictions — predictions that ideally match, in this case, what a mountaineer reads on a compass. Assimilating the infinite forms of a quantum field into a single prediction is the formidable task of a “quantum field theory,” or QFT. This is a model of how one or more quantum fields each with their infinite variations act and interact.

    Driven by immense experimental support, QFTs have become the basic language of particle physics. The Standard Model is one such QFT, depicting fundamental particles like electrons as fuzzy bumps that emerge from an infinitude of electron fields. It has passed every experimental test to date (although various groups may be on the verge of finding the first holes).

    Physicists play with many different QFTs. Some, like the Standard Model, aspire to model real particles moving through the four dimensions of our universe (three spatial dimensions plus one dimension of time). Others describe exotic particles in strange universes, from two-dimensional flatlands to six-dimensional uber-worlds. Their connection to reality is remote, but physicists study them in the hopes of gaining insights they can carry back into our own world.

    Polyakov’s Liouville field theory is one such example.

    1

    Gravity’s Field

    The Liouville field, which is based on an equation from complex analysis developed in the 1800s by the French mathematician Joseph Liouville, describes a completely random two-dimensional surface — that is, a surface, like Earth’s crust, but one in which the height of every point is chosen randomly. Such a planet would erupt with mountain ranges of infinitely tall peaks, each assigned by rolling a die with infinite faces.

    Such an object might not seem like an informative model for physics, but randomness is not devoid of patterns. The bell curve, for example, tells you how likely you are to randomly pass a seven-foot basketball player on the street. Similarly, bulbous clouds and crinkly coastlines follow random patterns, but it’s nevertheless possible to discern consistent relationships between their large-scale and small-scale features.

    Liouville theory can be used to identify patterns in the endless landscape of all possible random, jagged surfaces. Polyakov realized this chaotic topography was essential for modeling strings, which trace out surfaces as they move. The theory has also been applied to describe quantum gravity in a two-dimensional world. Einstein defined gravity as space-time’s curvature, but translating his description into the language of quantum field theory creates an infinite number of space-times — much as the Earth produces an infinite collection of magnetic fields. Liouville theory packages all those surfaces together into one object. It gives physicists the tools to measure the curvature —and hence, gravitation — at every location on a random 2D surface.

    “Quantum gravity basically means random geometry, because quantum means random and gravity means geometry,” said Sun.

    Polyakov’s first step in exploring the world of random surfaces was to write down an expression defining the odds of finding a particular spiky planet, much as the bell curve defines the odds of meeting someone of a particular height. But his formula did not lead to useful numerical predictions.

    To solve a quantum field theory is to be able to use the field to predict observations. In practice, this means calculating a field’s “correlation functions,” which capture the field’s behavior by describing the extent to which a measurement of the field at one point relates, or correlates, to a measurement at another point. Calculating correlation functions in the photon field, for instance, can give you the textbook laws of quantum electromagnetism.

    Polyakov was after something more abstract: the essence of random surfaces, similar to the statistical relationships that make a cloud a cloud or a coastline a coastline. He needed the correlations between the haphazard heights of the Liouville field. Over the decades he tried two different ways of calculating them. He started with a technique called the Feynman path integral and ended up developing a workaround known as the bootstrap. Both methods came up short in different ways, until the mathematicians behind the new work united them in a more precise formulation.

    Add ’Em Up

    You might imagine that accounting for the infinitely many forms a quantum field can take is next to impossible. And you would be right. In the 1940s Richard Feynman, a quantum physics pioneer, developed one prescription for dealing with this bewildering situation, but the method proved severely limited.

    Take, again, Earth’s magnetic field. Your goal is to use quantum field theory to predict what you’ll observe when you take a compass reading at a particular location. To do this, Feynman proposed summing all the field’s forms together. He argued that your reading will represent some average of all the field’s possible forms. The procedure for adding up these infinite field configurations with the proper weighting is known as the Feynman path integral.

    It’s an elegant idea that yields concrete answers only for select quantum fields. No known mathematical procedure can meaningfully average an infinite number of objects covering an infinite expanse of space in general. The path integral is more of a physics philosophy than an exact mathematical recipe. Mathematicians question its very existence as a valid operation and are bothered by the way physicists rely on it.

    “I’m disturbed as a mathematician by something which is not defined,” said Eveliina Peltola, a mathematician at the University of Bonn [Rheinische Friedrich-Wilhelms-Universität Bonn](DE) in Germany.

    Physicists can harness Feynman’s path integral to calculate exact correlation functions for only the most boring of fields — free fields, which do not interact with other fields or even with themselves. Otherwise, they have to fudge it, pretending the fields are free and adding in mild interactions, or “perturbations.” This procedure, known as perturbation theory, gets them correlation functions for most of the fields in the Standard Model, because nature’s forces happen to be quite feeble.

    But it didn’t work for Polyakov. Although he initially speculated that the Liouville field might be amenable to the standard hack of adding mild perturbations, he found that it interacted with itself too strongly. Compared to a free field, the Liouville field seemed mathematically inscrutable, and its correlation functions appeared unattainable.

    Up by the Bootstraps

    Polyakov soon began looking for a workaround. In 1984, he teamed up with Alexander Belavin and Alexander Zamolodchikov to develop a technique called the bootstrap — a mathematical ladder that gradually leads to a field’s correlation functions.

    To start climbing the ladder, you need a function which expresses the correlations between measurements at a mere three points in the field. This “three-point correlation function,” plus some additional information about the energies a particle of the field can take, forms the bottom rung of the bootstrap ladder.

    From there you climb one point at a time: Use the three-point function to construct the four-point function, use the four-point function to construct the five-point function, and so on. But the procedure generates conflicting results if you start with the wrong three-point correlation function in the first rung.

    Polyakov, Belavin and Zamolodchikov used the bootstrap to successfully solve a variety of simple QFT theories, but just as with the Feynman path integral, they couldn’t make it work for the Liouville field.

    Then in the 1990s two pairs of physicists — Harald Dorn and Hans-Jörg Otto, and Zamolodchikov and his brother Alexei — managed to hit on the three-point correlation function that made it possible to scale the ladder, completely solving the Liouville field (and its simple description of quantum gravity). Their result, known by their initials as the DOZZ formula, let physicists make any prediction involving the Liouville field. But even the authors knew they had arrived at it partially by chance, not through sound mathematics.

    “They were these kind of geniuses who guessed formulas,” said Vargas.

    Educated guesses are useful in physics, but they don’t satisfy mathematicians, who afterward wanted to know where the DOZZ formula came from. The equation that solved the Liouville field should have come from some description of the field itself, even if no one had the faintest idea how to get it.

    “It looked to me like science fiction,” said Kupiainen. “This is never going to be proven by anybody.”

    Taming Wild Surfaces

    In the early 2010s, Vargas and Kupiainen joined forces with the probability theorist Rémi Rhodes and the physicist François David. Their goal was to tie up the mathematical loose ends of the Liouville field — to formalize the Feynman path integral that Polyakov had abandoned and, just maybe, demystify the DOZZ formula.

    As they began, they realized that a French mathematician named Jean-Pierre Kahane had discovered, decades earlier, what would turn out to be the key to Polyakov’s master theory.

    “In some sense it’s completely crazy that Liouville was not defined before us,” Vargas said. “All the ingredients were there.”

    The insight led to three milestone papers in mathematical physics completed between 2014 and 2020.

    2

    They first polished off the path integral, which had failed Polyakov because the Liouville field interacts strongly with itself, making it incompatible with Feynman’s perturbative tools. So instead, the mathematicians used Kahane’s ideas to recast the wild Liouville field as a somewhat milder random object known as the Gaussian free field. The peaks in the Gaussian free field don’t fluctuate to the same random extremes as the peaks in the Liouville field, making it possible for the mathematicians to calculate averages and other statistical measures in sensible ways.

    “Somehow it’s all just using the Gaussian free field,” Peltola said. “From that they can construct everything in the theory.”

    In 2014, they unveiled their result: a new and improved version of the path integral Polyakov had written down in 1981, but fully defined in terms of the trusted Gaussian free field. It’s a rare instance in which Feynman’s path integral philosophy has found a solid mathematical execution.

    “Path integrals can exist, do exist,” said Jörg Teschner, a physicist at the German Electron Synchrotron.

    With a rigorously defined path integral in hand, the researchers then tried to see if they could use it to get answers from the Liouville field and to derive its correlation functions. The target was the mythical DOZZ formula — but the gulf between it and the path integral seemed vast.

    “We’d write in our papers, just for propaganda reasons, that we want to understand the DOZZ formula,” said Kupiainen.

    The team spent years prodding their probabilistic path integral, confirming that it truly had all the features needed to make the bootstrap work. As they did so, they built on earlier work by Teschner. Eventually, Vargas, Kupiainen and Rhodes succeeded with a paper posted in 2017 [Annals of Mathematics] and another in October 2020, with Colin Guillarmou. They derived DOZZ and other correlation functions from the path integral and showed that these formulas perfectly matched the equations physicists had reached using the bootstrap.

    “Now we’re done,” Vargas said. “Both objects are the same.”

    The work explains the origins of the DOZZ formula and connects the bootstrap procedure —which mathematicians had considered sketchy — with verified mathematical objects. Altogether, it resolves the final mysteries of the Liouville field.

    “It’s somehow the end of an era,” said Peltola. “But I hope it’s also the beginning of some new, interesting things.”

    New Hope for QFTs

    Vargas and his collaborators now have a unicorn on their hands, a strongly interacting QFT perfectly described in a nonperturbative way by a brief mathematical formula that also makes numerical predictions.

    Now the literal million-dollar question is: How far can these probabilistic methods go? Can they generate tidy formulas for all QFTs? Vargas is quick to dash such hopes, insisting that their tools are specific to the two-dimensional environment of Liouville theory. In higher dimensions, even free fields are too irregular, so he doubts the group’s methods will ever be able to handle the quantum behavior of gravitational fields in our universe.

    But the fresh minting of Polyakov’s “master key” will open other doors. Its effects are already being felt in probability theory, where mathematicians can now wield previously dodgy physics formulas with impunity. Emboldened by the Liouville work, Sun and his collaborators have already imported equations from physics to solve two problems regarding random curves.

    Physicists await tangible benefits too, further down the road. The rigorous construction of the Liouville field could inspire mathematicians to try their hand at proving features of other seemingly intractable QFTs — not just toy theories of gravity but descriptions of real particles and forces that bear directly on the deepest physical secrets of reality.

    “[Mathematicians] will do things that we can’t even imagine,” said Davide Gaiotto, a theoretical physicist at the Perimeter Institute for Theoretical Physics (CA).

    See the full article here .


    five-ways-keep-your-child-safe-school-shootings

    Please help promote STEM in your local schools.

    Stem Education Coalition

    Formerly known as Simons Science News, Quanta Magazine is an editorially independent online publication launched by the Simons Foundation to enhance public understanding of science. Why Quanta? Albert Einstein called photons “quanta of light.” Our goal is to “illuminate science.” At Quanta Magazine, scientific accuracy is every bit as important as telling a good story. All of our articles are meticulously researched, reported, edited, copy-edited and fact-checked.

     
  • richardmitnick 12:38 pm on June 11, 2021 Permalink | Reply
    Tags: "The Mystery at the Heart of Physics That Only Math Can Solve", Even in this incomplete state QFT has prompted a number of important mathematical discoveries., Every idea that’s been used in physics over the past centuries had its natural place in mathematics., For millennia the physical world has been mathematics’ greatest muse., Mathematics does not admit new subjects lightly., Physicists realized in the 1930s that physics based on fields rather than particles resolved some of their most pressing inconsistencies., Quanta Magazine(US), , Quantum field theory emerged as an almost universal language of physical phenomena but it’s in bad math shape., The accelerating effort to understand the mathematics of quantum field theory will have profound consequences for both math and physics., The distant relationship with math is a sign that there’s a lot more they need to understand about the theory they birthed., While QFT has been successful at generating leads for mathematics to follow its core ideas still exist almost entirely outside of mathematics.   

    From Quanta Magazine : “The Mystery at the Heart of Physics That Only Math Can Solve” 

    From Quanta Magazine

    June 10, 2021
    Kevin Hartnett

    1
    Olena Shmahalo/Quanta Magazine.

    The accelerating effort to understand the mathematics of quantum field theory will have profound consequences for both math and physics.

    Over the past century, quantum field theory has proved to be the single most sweeping and successful physical theory ever invented. It is an umbrella term that encompasses many specific quantum field theories — the way “shape” covers specific examples like the square and the circle. The most prominent of these theories is known as the Standard Model, and it is this framework of physics that has been so successful.

    “It can explain at a fundamental level literally every single experiment that we’ve ever done,” said David Tong, a physicist at the University of Cambridge (UK).

    But quantum field theory, or QFT, is indisputably incomplete. Neither physicists nor mathematicians know exactly what makes a quantum field theory a quantum field theory. They have glimpses of the full picture, but they can’t yet make it out.

    “There are various indications that there could be a better way of thinking about QFT,” said Nathan Seiberg, a physicist at the Institute for Advanced Study (US). “It feels like it’s an animal you can touch from many places, but you don’t quite see the whole animal.”

    Mathematics, which requires internal consistency and attention to every last detail, is the language that might make QFT whole. If mathematics can learn how to describe QFT with the same rigor with which it characterizes well-established mathematical objects, a more complete picture of the physical world will likely come along for the ride.

    “If you really understood quantum field theory in a proper mathematical way, this would give us answers to many open physics problems, perhaps even including the quantization of gravity,” said Robbert Dijkgraaf, director of the Institute for Advanced Study (and a regular columnist for Quanta).

    Nor is this a one-way street. For millennia the physical world has been mathematics’ greatest muse. The ancient Greeks invented trigonometry to study the motion of the stars. Mathematics turned it into a discipline with definitions and rules that students now learn without any reference to the topic’s celestial origins. Almost 2,000 years later, Isaac Newton wanted to understand Kepler’s laws of planetary motion and attempted to find a rigorous way of thinking about infinitesimal change. This impulse (along with revelations from Gottfried Leibniz) birthed the field of calculus, which mathematics appropriated and improved — and today could hardly exist without.

    Now mathematicians want to do the same for QFT, taking the ideas, objects and techniques that physicists have developed to study fundamental particles and incorporating them into the main body of mathematics. This means defining the basic traits of QFT so that future mathematicians won’t have to think about the physical context in which the theory first arose.

    The rewards are likely to be great: Mathematics grows when it finds new objects to explore and new structures that capture some of the most important relationships — between numbers, equations and shapes. QFT offers both.

    “Physics itself, as a structure, is extremely deep and often a better way to think about mathematical things we’re already interested in. It’s just a better way to organize them,” said David Ben-Zvi, a mathematician at the University of Texas-Austin (US).

    For 40 years at least, QFT has tempted mathematicians with ideas to pursue. In recent years, they’ve finally begun to understand some of the basic objects in QFT itself — abstracting them from the world of particle physics and turning them into mathematical objects in their own right.

    Yet it’s still early days in the effort.

    “We won’t know until we get there, but it’s certainly my expectation that we’re just seeing the tip of the iceberg,” said Greg Moore, a physicist at Rutgers University (US). “If mathematicians really understood [QFT], that would lead to profound advances in mathematics.”

    Fields Forever

    It’s common to think of the universe as being built from fundamental particles: electrons, quarks, photons and the like. But physics long ago moved beyond this view. Instead of particles, physicists now talk about things called “quantum fields” as the real warp and woof of reality.

    These fields stretch across the space-time of the universe. They come in many varieties and fluctuate like a rolling ocean. As the fields ripple and interact with each other, particles emerge out of them and then vanish back into them, like the fleeting crests of a wave.

    “Particles are not objects that are there forever,” said Tong. “It’s a dance of fields.”

    To understand quantum fields, it’s easiest to start with an ordinary, or classical, field. Imagine, for example, measuring the temperature at every point on Earth’s surface. Combining the infinitely many points at which you can make these measurements forms a geometric object, called a field, that packages together all this temperature information.

    In general, fields emerge whenever you have some quantity that can be measured uniquely at infinitely fine resolution across a space.

    2

    “You’re sort of able to ask independent questions about each point of space-time, like, what’s the electric field here versus over there,” said Davide Gaiotto, a physicist at the Perimeter Institute for Theoretical Physics (CA).

    Quantum fields come about when you’re observing quantum phenomena, like the energy of an electron, at every point in space and time. But quantum fields are fundamentally different from classical ones.

    While the temperature at a point on Earth is what it is, regardless of whether you measure it, electrons have no definite position until the moment you observe them. Prior to that, their positions can only be described probabilistically, by assigning values to every point in a quantum field that captures the likelihood you’ll find an electron there versus somewhere else. Prior to observation, electrons essentially exist nowhere — and everywhere.

    “Most things in physics aren’t just objects; they’re something that lives in every point in space and time,” said Dijkgraaf.

    A quantum field theory comes with a set of rules called correlation functions that explain how measurements at one point in a field relate to — or correlate with — measurements taken at another point.

    Each quantum field theory describes physics in a specific number of dimensions. Two-dimensional quantum field theories are often useful for describing the behavior of materials, like insulators; six-dimensional quantum field theories are especially relevant to string theory; and four-dimensional quantum field theories describe physics in our actual four-dimensional universe. The Standard Model is one of these; it’s the single most important quantum field theory because it’s the one that best describes the universe.

    There are 12 known fundamental particles that make up the universe. Each has its own unique quantum field. To these 12 particle fields the Standard Model adds four force fields, representing the four fundamental forces: gravity, electromagnetism, the strong nuclear force and the weak nuclear force.

    It combines these 16 fields in a single equation that describes how they interact with each other. Through these interactions, fundamental particles are understood as fluctuations of their respective quantum fields, and the physical world emerges before our eyes.

    It might sound strange, but physicists realized in the 1930s that physics based on fields rather than particles resolved some of their most pressing inconsistencies, ranging from issues regarding causality to the fact that particles don’t live forever. It also explained what otherwise appeared to be an improbable consistency in the physical world.

    “All particles of the same type everywhere in the universe are the same,” said Tong. “If we go to the Large Hadron Collider and make a freshly minted proton, it’s exactly the same as one that’s been traveling for 10 billion years.

    That deserves some explanation.” QFT provides it: All protons are just fluctuations in the same underlying proton field (or, if you could look more closely, the underlying quark fields).

    But the explanatory power of QFT comes at a high mathematical cost.

    “Quantum field theories are by far the most complicated objects in mathematics, to the point where mathematicians have no idea how to make sense of them,” said Tong. “Quantum field theory is mathematics that has not yet been invented by mathematicians.”

    3

    Too Much Infinity

    What makes it so complicated for mathematicians? In a word, infinity.

    When you measure a quantum field at a point, the result isn’t a few numbers like coordinates and temperature. Instead, it’s a matrix, which is an array of numbers. And not just any matrix — a big one, called an operator, with infinitely many columns and rows. This reflects how a quantum field envelops all the possibilities of a particle emerging from the field.

    “There are infinitely many positions that a particle can have, and this leads to the fact that the matrix that describes the measurement of position, of momentum, also has to be infinite-dimensional,” said Kasia Rejzner of the University of York (UK).

    And when theories produce infinities, it calls their physical relevance into question, because infinity exists as a concept, not as anything experiments can ever measure. It also makes the theories hard to work with mathematically.

    “We don’t like having a framework that spells out infinity. That’s why you start realizing you need a better mathematical understanding of what’s going on,” said Alejandra Castro, a physicist at the University of Amsterdam [Universiteit van Amsterdam] (NL).

    The problems with infinity get worse when physicists start thinking about how two quantum fields interact, as they might, for instance, when particle collisions are modeled at the Large Hadron Collider outside Geneva. In classical mechanics this type of calculation is easy: To model what happens when two billiard balls collide, just use the numbers specifying the momentum of each ball at the point of collision.

    When two quantum fields interact, you’d like to do a similar thing: multiply the infinite-dimensional operator for one field by the infinite-dimensional operator for the other at exactly the point in space-time where they meet. But this calculation — multiplying two infinite-dimensional objects that are infinitely close together — is difficult.

    “This is where things go terribly wrong,” said Rejzner.

    Smashing Success

    Physicists and mathematicians can’t calculate using infinities, but they have developed workarounds — ways of approximating quantities that dodge the problem. These workarounds yield approximate predictions, which are good enough, because experiments aren’t infinitely precise either.

    “We can do experiments and measure things to 13 decimal places and they agree to all 13 decimal places. It’s the most astonishing thing in all of science,” said Tong.

    One workaround starts by imagining that you have a quantum field in which nothing is happening. In this setting — called a “free” theory because it’s free of interactions — you don’t have to worry about multiplying infinite-dimensional matrices because nothing’s in motion and nothing ever collides. It’s a situation that’s easy to describe in full mathematical detail, though that description isn’t worth a whole lot.

    “It’s totally boring, because you’ve described a lonely field with nothing to interact with, so it’s a bit of an academic exercise,” said Rejzner.

    But you can make it more interesting. Physicists dial up the interactions, trying to maintain mathematical control of the picture as they make the interactions stronger.

    This approach is called perturbative QFT, in the sense that you allow for small changes, or perturbations, in a free field. You can apply the perturbative perspective to quantum field theories that are similar to a free theory. It’s also extremely useful for verifying experiments. “You get amazing accuracy, amazing experimental agreement,” said Rejzner.

    But if you keep making the interactions stronger, the perturbative approach eventually overheats. Instead of producing increasingly accurate calculations that approach the real physical universe, it becomes less and less accurate. This suggests that while the perturbation method is a useful guide for experiments, ultimately it’s not the right way to try and describe the universe: It’s practically useful, but theoretically shaky.

    “We do not know how to add everything up and get something sensible,” said Gaiotto.

    Another approximation scheme tries to sneak up on a full-fledged quantum field theory by other means. In theory, a quantum field contains infinitely fine-grained information. To cook up these fields, physicists start with a grid, or lattice, and restrict measurements to places where the lines of the lattice cross each other. So instead of being able to measure the quantum field everywhere, at first you can only measure it at select places a fixed distance apart.

    From there, physicists enhance the resolution of the lattice, drawing the threads closer together to create a finer and finer weave. As it tightens, the number of points at which you can take measurements increases, approaching the idealized notion of a field where you can take measurements everywhere.

    “The distance between the points becomes very small, and such a thing becomes a continuous field,” said Seiberg. In mathematical terms, they say the continuum quantum field is the limit of the tightening lattice.

    Mathematicians are accustomed to working with limits and know how to establish that certain ones really exist. For example, they’ve proved that the limit of the infinite sequence 1/2 + 1/4 +1/8 +1/16 … is 1. Physicists would like to prove that quantum fields are the limit of this lattice procedure. They just don’t know how.

    “It’s not so clear how to take that limit and what it means mathematically,” said Moore.

    Physicists don’t doubt that the tightening lattice is moving toward the idealized notion of a quantum field. The close fit between the predictions of QFT and experimental results strongly suggests that’s the case.

    “There is no question that all these limits really exist, because the success of quantum field theory has been really stunning,” said Seiberg. But having strong evidence that something is correct and proving conclusively that it is are two different things.

    It’s a degree of imprecision that’s out of step with the other great physical theories that QFT aspires to supersede. Isaac Newton’s laws of motion, quantum mechanics, Albert Einstein’s theories of special and general relativity — they’re all just pieces of the bigger story QFT wants to tell, but unlike QFT, they can all be written down in exact mathematical terms.

    “Quantum field theory emerged as an almost universal language of physical phenomena but it’s in bad math shape,” said Dijkgraaf. And for some physicists, that’s a reason for pause.

    “If the full house is resting on this core concept that itself isn’t understood in a mathematical way, why are you so confident this is describing the world? That sharpens the whole issue,” said Dijkgraaf.

    Outside Agitator

    Even in this incomplete state QFT has prompted a number of important mathematical discoveries. The general pattern of interaction has been that physicists using QFT stumble onto surprising calculations that mathematicians then try to explain.

    “It’s an idea-generating machine,” said Tong.

    At a basic level, physical phenomena have a tight relationship with geometry. To take a simple example, if you set a ball in motion on a smooth surface, its trajectory will illuminate the shortest path between any two points, a property known as a geodesic. In this way, physical phenomena can detect geometric features of a shape.

    Now replace the billiard ball with an electron. The electron exists probabilistically everywhere on a surface. By studying the quantum field that captures those probabilities, you can learn something about the overall nature of that surface (or manifold, to use the mathematicians’ term), like how many holes it has. That’s a fundamental question that mathematicians working in geometry, and the related field of topology, want to answer.

    “One particle even sitting there, doing nothing, will start to know about the topology of a manifold,” said Tong.

    4

    In the late 1970s, physicists and mathematicians began applying this perspective to solve basic questions in geometry. By the early 1990s, Seiberg and his collaborator Edward Witten figured out how to use it to create a new mathematical tool — now called the Seiberg-Witten invariants — that turns quantum phenomena into an index for purely mathematical traits of a shape: Count the number of times quantum particles behave in a certain way, and you’ve effectively counted the number of holes in a shape.

    “Witten showed that quantum field theory gives completely unexpected but completely precise insights into geometrical questions, making intractable problems soluble,” said Graeme Segal, a mathematician at the University of Oxford (UK).

    Another example of this exchange also occurred in the early 1990s, when physicists were doing calculations related to string theory. They performed them in two different geometric spaces based on fundamentally different mathematical rules and kept producing long sets of numbers that matched each other exactly. Mathematicians picked up the thread and elaborated it into a whole new field of inquiry, called mirror symmetry, that investigates the concurrence — and many others like it.

    “Physics would come up with these amazing predictions, and mathematicians would try to prove them by our own means,” said Ben-Zvi. “The predictions were strange and wonderful, and they turned out to be pretty much always correct.”

    But while QFT has been successful at generating leads for mathematics to follow its core ideas still exist almost entirely outside of mathematics. Quantum field theories are not objects that mathematicians understand well enough to use the way they can use polynomials, groups, manifolds and other pillars of the discipline (many of which also originated in physics).

    For physicists, this distant relationship with math is a sign that there’s a lot more they need to understand about the theory they birthed. “Every other idea that’s been used in physics over the past centuries had its natural place in mathematics,” said Seiberg. “This is clearly not the case with quantum field theory.”

    And for mathematicians, it seems as if the relationship between QFT and math should be deeper than the occasional interaction. That’s because quantum field theories contain many symmetries, or underlying structures, that dictate how points in different parts of a field relate to each other. These symmetries have a physical significance — they embody how quantities like energy are conserved as quantum fields evolve over time. But they’re also mathematically interesting objects in their own right.

    “A mathematician might care about a certain symmetry, and we can put it in a physical context. It creates this beautiful bridge between these two fields,” said Castro.

    Mathematicians already use symmetries and other aspects of geometry to investigate everything from solutions to different types of equations to the distribution of prime numbers. Often, geometry encodes answers to questions about numbers. QFT offers mathematicians a rich new type of geometric object to play with — if they can get their hands on it directly, there’s no telling what they’ll be able to do.

    “We’re to some extent playing with QFT,” said Dan Freed, a mathematician at the University of Texas, Austin. “We’ve been using QFT as an outside stimulus, but it would be nice if it were an inside stimulus.”

    Make Way for QFT

    Mathematics does not admit new subjects lightly. Many basic concepts went through long trials before they settled into their proper, canonical places in the field.

    Take the real numbers — all the infinitely many tick marks on the number line. It took math nearly 2,000 years of practice to agree on a way of defining them. Finally, in the 1850s, mathematicians settled on a precise three-word statement describing the real numbers as a “complete ordered field.” They’re complete because they contain no gaps, they’re ordered because there’s always a way of determining whether one real number is greater or less than another, and they form a “field,” which to mathematicians means they follow the rules of arithmetic.

    “Those three words are historically hard fought,” said Freed.

    In order to turn QFT into an inside stimulus — a tool they can use for their own purposes — mathematicians would like to give the same treatment to QFT they gave to the real numbers: a sharp list of characteristics that any specific quantum field theory needs to satisfy.

    A lot of the work of translating parts of QFT into mathematics has come from a mathematician named Kevin Costello at the Perimeter Institute. In 2016 he coauthored a textbook that puts perturbative QFT on firm mathematical footing, including formalizing how to work with the infinite quantities that crop up as you increase the number of interactions. The work follows an earlier effort from the 2000s called algebraic quantum field theory that sought similar ends, and which Rejzner reviewed in a 2016 book. So now, while perturbative QFT still doesn’t really describe the universe, mathematicians know how to deal with the physically non-sensical infinities it produces.

    “His contributions are extremely ingenious and insightful. He put [perturbative] theory in a nice new framework that is suitable for rigorous mathematics,” said Moore.

    Costello explains he wrote the book out of a desire to make perturbative quantum field theory more coherent. “I just found certain physicists’ methods unmotivated and ad hoc. I wanted something more self-contained that a mathematician could go work with,” he said.

    By specifying exactly how perturbation theory works, Costello has created a basis upon which physicists and mathematicians can construct novel quantum field theories that satisfy the dictates of his perturbation approach. It’s been quickly embraced by others in the field.

    “He certainly has a lot of young people working in that framework. [His book] has had its influence,” said Freed.

    Costello has also been working on defining just what a quantum field theory is. In stripped-down form, a quantum field theory requires a geometric space in which you can make observations at every point, combined with correlation functions that express how observations at different points relate to each other. Costello’s work describes the properties a collection of correlation functions needs to have in order to serve as a workable basis for a quantum field theory.

    The most familiar quantum field theories, like the Standard Model, contain additional features that may not be present in all quantum field theories. Quantum field theories that lack these features likely describe other, still undiscovered properties that could help physicists explain physical phenomena the Standard Model can’t account for. If your idea of a quantum field theory is fixed too closely to the versions we already know about, you’ll have a hard time even envisioning the other, necessary possibilities.

    “There is a big lamppost under which you can find theories of fields [like the Standard Model], and around it is a big darkness of [quantum field theories] we don’t know how to define, but we know they’re there,” said Gaiotto.

    Costello has illuminated some of that dark space with his definitions of quantum fields. From these definitions, he’s discovered two surprising new quantum field theories. Neither describes our four-dimensional universe, but they do satisfy the core demands of a geometric space equipped with correlation functions. Their discovery through pure thought is similar to how the first shapes you might discover are ones present in the physical world, but once you have a general definition of a shape, you can think your way to examples with no physical relevance at all.

    And if mathematics can determine the full space of possibilities for quantum field theories — all the many different possibilities for satisfying a general definition involving correlation functions — physicists can use that to find their way to the specific theories that explain the important physical questions they care most about.

    “I want to know the space of all QFTs because I want to know what quantum gravity is,” said Castro.

    A Multi-Generational Challenge

    There’s a long way to go. So far, all of the quantum field theories that have been described in full mathematical terms rely on various simplifications, which make them easier to work with mathematically.

    One way to simplify the problem, going back decades, is to study simpler two-dimensional QFTs rather than four-dimensional ones. A team in France recently nailed down all the mathematical details of a prominent two-dimensional QFT.

    Other simplifications assume quantum fields are symmetrical in ways that don’t match physical reality, but that make them more tractable from a mathematical perspective. These include “supersymmetric” and “topological” QFTs.

    The next, and much more difficult, step will be to remove the crutches and provide a mathematical description of a quantum field theory that better suits the physical world physicists most want to describe: the four-dimensional, continuous universe in which all interactions are possible at once.

    “This is [a] very embarrassing thing that we don’t have a single quantum field theory we can describe in four dimensions, nonperturbatively,” said Rejzner. “It’s a hard problem, and apparently it needs more than one or two generations of mathematicians and physicists to solve it.”

    But that doesn’t stop mathematicians and physicists from eyeing it greedily. For mathematicians, QFT is as rich a type of object as they could hope for. Defining the characteristic properties shared by all quantum field theories will almost certainly require merging two of the pillars of mathematics: analysis, which explains how to control infinities, and geometry, which provides a language for talking about symmetry.

    “It’s a fascinating problem just in math itself, because it combines two great ideas,” said Dijkgraaf.

    If mathematicians can understand QFT, there’s no telling what mathematical discoveries await in its unlocking. Mathematicians defined the characteristic properties of other objects, like manifolds and groups, long ago, and those objects now permeate virtually every corner of mathematics. When they were first defined, it would have been impossible to anticipate all their mathematical ramifications. QFT holds at least as much promise for math.

    “I like to say the physicists don’t necessarily know everything, but the physics does,” said Ben-Zvi. “If you ask it the right questions, it already has the phenomena mathematicians are looking for.”

    And for physicists, a complete mathematical description of QFT is the flip side of their field’s overriding goal: a complete description of physical reality.

    “I feel there is one intellectual structure that covers all of it, and maybe it will encompass all of physics,” said Seiberg.

    Now mathematicians just have to uncover it.

    See the full article here .


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    Formerly known as Simons Science News, Quanta Magazine is an editorially independent online publication launched by the Simons Foundation to enhance public understanding of science. Why Quanta? Albert Einstein called photons “quanta of light.” Our goal is to “illuminate science.” At Quanta Magazine, scientific accuracy is every bit as important as telling a good story. All of our articles are meticulously researched, reported, edited, copy-edited and fact-checked.

     
  • richardmitnick 12:16 pm on March 26, 2021 Permalink | Reply
    Tags: "The Near-Magical Mystery of Quasiparticles", , Everlasting Magnons, Majoranas, , , , Quanta Magazine(US)   

    From Quanta Magazine: “The Near-Magical Mystery of Quasiparticles” 

    From Quanta Magazine

    March 24, 2021
    Thomas Lewton

    1
    Polaritons, which are half-light, half-matter quasiparticles, emerge in a simulated lattice of particles cooled to a few degrees above absolute zero. Credit: Kirill Kalinin.

    Waking up in an alternate reality, Harry Kim, an officer aboard the starship USS Voyager, creates a distortion in the space-time continuum with a beam of polarons. Sounds like science fiction? Well, yes, but only in part.

    “Star Trek used to love taking the names of real quasiparticles and ascribing magical properties to them,” said Douglas Natelson, a physicist at Rice University (US) in Texas whose job involves creating actual quasiparticles with near-magical properties.

    Quasiparticles are kind of particles. Barred entry from the exclusive club of 17 “fundamental” particles that are thought to be the building blocks of all material reality, quasiparticles emerge out of the complicated interactions between huge numbers of those fundamental particles. Physicists can take a solid, liquid or plasma made of a vast number of particles, subject it to extreme temperatures and pressures, and describe the resulting system as a few robust, particlelike entities. The emerging quasiparticles can be quite stable with well-defined properties like mass and charge.

    Polarons, for instance, discovered by Lev Landau in 1933 and given a cameo on Star Trek: Voyager in 1995, materialize when many electrons are trapped inside a crystal. The push and pull between each electron and all the particles in its environment “dress” the electron so that it acts like a quasiparticle with a larger mass.

    In other types of condensed matter that have dominated research over the last few decades, things get a whole lot weirder. Researchers can create quasiparticles that have a precise fraction of the electron’s charge or spin (a kind of intrinsic angular momentum). How these exotic properties emerge is still not understood. “It’s literally like magic,” said Sankar Das Sarma, a condensed matter physicist at the University of Maryland (US).

    Using intuition, educated guesswork and computer simulations, condensed matter physicists have become better at figuring out which quasiparticles are theoretically possible. Meanwhile in the lab, as physicists push novel materials to new extremes, the quasiparticle zoo has grown quickly and become more and more exotic. “It really is a towering intellectual achievement,” said Natelson.

    Recent discoveries include pi-tons, immovable fractons and warped wrinklons. “We now think about quasiparticles with properties that we never really dreamt of before,” said Steve Simon, a theoretical condensed matter physicist at the University of Oxford (UK).

    Here are a few of the most curious and potentially useful quasiparticles.

    Quantum Computing With Majoranas

    One of the earliest quasiparticles discovered was a “hole”: simply the absence of an electron in a place where one should exist. Physicists in the 1940s discovered that holes hop around inside solids like positively charged particles. Weirder still — and potentially very useful — are hypothesized Majorana quasiparticles, which have a split personality: They are half an electron and half a hole at the same time. “It’s such a crazy thing,” Das Sarma said.

    In 2010, Das Sarma and his collaborators argued that Majorana quasiparticles could be used to create quantum computers. When you move the electron and the hole around each other, they store information, like a pattern braided into two ropes. Different twists correspond to the 1s, 0s and superpositions of 1s and 0s that are the bits of quantum computation.

    Efforts to build effective quantum computers have so far stumbled because quantum superpositions of most types of particles fall apart when they get too hot or when they collide with other particles. Not so for Majorana quasiparticles. Their unusual composition endows them with zero energy and zero charge, and this theoretically allows them to exist deep inside a certain type of superconductor, a material that conducts electricity without resistance. No other particles can exist there, creating a “gap” that makes it impossible for the Majorana to decay. “The superconducting gap protects the Majorana,” said Das Sarma — at least in theory.

    Since 2010, experimentalists have been racing to build actual Majorana quasiparticles from an intricate assembly of a superconductor, a nanowire and a magnetic field. In 2018, one group of researchers reported in Nature that they’d observed key signatures of Majoranas. But outside experts questioned aspects of the data analysis, and earlier this month the paper was retracted.

    It’s one thing to think up a possible quasiparticle, and another to observe it in an experiment where temperatures are close to absolute zero, samples are constructed atom by atom, and tiny impurities can derail everything.

    Das Sarma is undeterred. “I guarantee you the Majorana will be seen, because its theory is pristine. This is an engineering problem; this is not a physics problem,” he said.

    A Black Hole Made of Polaritons

    The growing quasiparticle zoo, with its array of unusual characters, offers physicists a toolkit with which they can build analogues of other systems that are hard or impossible to access, such as black holes.

    “With these analogues we want to go and probe physics that we cannot touch with our hands,” said Maxime Jacquet of the Kastler–Brossel Laboratory at Sorbonne University [Sorbonne Université] (FR) .

    Black holes form in the cosmos wherever gravity becomes so strong that even light cannot escape. You can make a simple analogue of a black hole by pulling out the plug in your bathtub and watching water swirl down the drain: Water waves that come too close to the drain are inescapably sucked into the vortex. You can make an even better analogue — as Jacquet and his collaborators are doing — with the quasiparticles called polaritons.

    2
    4
    A rotating polariton fluid serves as an analogue of a rotating black hole. The image to the left shows the fluid’s density in different places, where the edge of the dark center is like a black hole’s event horizon. At right, a map of the fluid’s phase reveals its vortex flow. Credit: Maxime Jacquet.

    Polaritons are mixtures of matter and light. Researchers use two mirrors to trap a photon inside a cage that also contains an exciton, itself a kind of quasiparticle made of an electron and a hole that orbit each other. (An exciton is distinct from a Majorana quasiparticle, which is half an electron and half a hole in the same place at the same time.) The photon bounces back and forth between the mirrors roughly a million times before it escapes, and as it bounces the photon blends with the exciton to form a polariton. Many photons and excitons are caged and combined in this way, and these polaritons behave en masse like liquid light, which is frictionless and doesn’t scatter. Researchers have engineered the flow of these polaritons to mimic how light moves around a black hole.

    Liquid light isn’t stable, and eventually the photon escapes. It’s this leaky cage that allows Jacquet to study how black holes evolve with time. The Nobel Prize-winning mathematical physicist Roger Penrose [Oxford University] theorized that rotating black holes can lose energy and gradually slow down; Jacquet plans to test this idea with polaritons.

    “No one can tell you that with astrophysics, but we can,” said Jacquet, acknowledging that it is a “leap” from these laboratory experiments to the goings-on of actual black holes.

    Everlasting Magnons

    If a quasiparticle can decay, it ultimately will decay. A magnon, for example — a quasiparticle made from bits of magnetic field in motion across a material —can decay into two other magnons so long as the energy of these products isn’t greater than the original magnon’s.

    Yet quasiparticles are fairly stable, supposedly for two reasons: They emerge out of systems that are held at very low temperatures, so they possess little energy to begin with, and they only interact with each other weakly, so there are few disturbances triggering them to decay. “When there’s a lot of push and pull, the naive expectation was that decay will only happen quicker,” said Ruben Verresen, a condensed matter physicist at Harvard University (US).

    But Verresen’s research has flipped that picture on its head. In a paper published in 2019 Nature Physics, he and his colleagues described how they theoretically modeled decaying quasiparticles and then gradually cranked up the strength of the interactions between them to see what happened. At first the quasiparticles decayed more quickly, as expected. But then — to Verresen’s surprise — when the strength of the interaction became very strong, the quasiparticles bounced back. “Suddenly you have a quasiparticle again that’s infinitely long-lived,” he said.

    The team then ran a computer simulation exploring the behavior of an ultra-cold magnet, and they saw magnons emerge that didn’t decay. They showed that their new understanding of strongly interacting quasiparticles could explain some puzzling features seen in magnon experiments from 2017 [Nature Communications]. More than a neat theory, these everlasting magnons are realized in nature.

    The findings suggest that quasiparticles can be far more robust than researchers once thought. The line between particle and quasiparticle is becoming blurred. “I don’t see a fundamental difference,” Verresen said.

    Quasiparticles arise out of arrangements of many particles. But what we term fundamental particles, such as quarks, photons and electrons, may not be as elementary as we think. Some physicists suspect that these apparently fundamental particles are emergent as well — though from what exactly, no one can say.

    “We don’t know the fundamental theory from which electrons, photons and so on actually emerge. We believe there is some unifying framework,” said Leon Balents, a theorist who researches quantum states of matter at the University of California, Santa Barbara (US). “The things we think of as fundamental particles probably aren’t fundamental; they’re quasiparticles of some other theory.”

    See the full article here .


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    Formerly known as Simons Science News, Quanta Magazine is an editorially independent online publication launched by the Simons Foundation to enhance public understanding of science. Why Quanta? Albert Einstein called photons “quanta of light.” Our goal is to “illuminate science.” At Quanta Magazine, scientific accuracy is every bit as important as telling a good story. All of our articles are meticulously researched, reported, edited, copy-edited and fact-checked.

     
  • richardmitnick 1:59 pm on March 14, 2021 Permalink | Reply
    Tags: "New Kind of Space Explosion Reveals the Birth of a Black Hole", , , , , , Quanta Magazine(US)   

    From Northwestern UniversityUS) via Quanta Magazine(US): “New Kind of Space Explosion Reveals the Birth of a Black Hole” 

    Northwestern U bloc

    From From Northwestern UniversityUS)

    via

    Quanta Magazine(US)

    March 10, 2021
    Jonathan O’Callaghan

    1
    The new explosion, illustrated here, is bluer than an ordinary supernova and more than 100 times as bright. Credit: SAKKMESTERKE / Science Source.

    In 2018, astronomers were shocked to find a bizarre explosion in a galaxy 200 million light-years away. It wasn’t like any normal supernova seen before — it was both briefer and brighter. The event was given an official designation, AT2018cow, but soon went by a more jovial nickname: the Cow.

    The short-lived event — known as a transient — defied explanation. Some thought it might be a star being torn apart by a nearby black hole, but others favored a “failed supernova” scenario, where a black hole quite literally eats a star from the inside out. To find out for sure, they needed to find more Cow-like events.

    More than two years later, they got one.

    Beginning on October 12, 2020, telescopes watched as something in a galaxy 3 billion light-years away became incredibly bright, then disappeared from view. It behaved almost identically to the Cow, astronomers reported in a paper posted to appear in MNRAS, leading them to conclude that it must be the same type of episode. In keeping with tradition, it was given its own animal-inspired name: the Camel.

    “It’s really exciting,” said Deanne Coppejans, an astrophysicist at Northwestern University. “The discovery of a new transient like AT2018cow shows that it’s not a complete oddball. This is a new type of transient that we’re looking at.”

    The Cow was a complete surprise, and astronomers weren’t really sure what they were looking at when it appeared. The Camel, in contrast, was like a burglar tripping the new alarm system. “We were able to realize what it was within a few days of it going off,” said Daniel Perley, an astrophysicist at Liverpool John Moores University(UK) who led the new study. “And we got lots of follow-up data.”

    Four days later, the team used telescopes in the Canary Islands and Hawaii to obtain vital data on its properties.

    2-metre Liverpool Telescope at the Roque de los Muchachos Observatory | Instituto de Astrofísica de Canarias • IAC, at La Palma (ES) altitude 2,363 m (7,753 ft)

    Caltech Palomar(US) 1.5 meter 60 inch telescope, located in San Diego County, California, U.S.A., Altitude 1,712 m (5,617 ft) 1.5 meter 60 inch telescope, located in San Diego County, California, U.S.A.,

    3
    0.7m GROWTH-India Telescope (GIT) locatedatthe Indian Astronomical Observatory (IAO),Hanle-Ladakh (India).

    ESO/NTT at Cerro La Silla, Chile, at an altitude of 2400 metres.

    ESO FORS2 VLT mounted on Unit Telescope 1 (Antu).


    ESO VLT at Cerro Paranal in the Atacama Desert, •ANTU (UT1; The Sun ),
    •KUEYEN (UT2; The Moon ),
    •MELIPAL (UT3; The Southern Cross ), and
    •YEPUN (UT4; Venus – as evening star).
    elevation 2,635 m (8,645 ft) from above Credit J.L. Dauvergne & G. Hüdepohl atacama photo.

    UCO Keck LRIS on Keck 1.


    Discovery Channel Telescope(US), operated by the Lowell Observatory)US) in partnership with University of Maryland(US), Boston University(US), the University of Toledo(US) and Northern Arizona University, at Lowell Observatory(US), Happy Jack AZ, USA, Altitude 2,360 m (7,740 ft)

    They later put out an alert to other astronomers on a service called the Astronomer’s Telegram.

    The event was given two designations. One, AT2020xnd, came from a global catalog of all transients, and the other, ZTF20acigmel, came from the Zwicky Transient Facility, the telescope where it was discovered.

    Zwicky Transient Facility (ZTF) instrument installed on the 1.2m diameter Samuel Oschin Telescope at Palomar Observatory in California. Credit: Caltech Optical Observatories.

    The team twisted the latter into its “Camel” nickname. “Xnd didn’t quite have the same ring to it,” said Perley.

    Like its predecessor, the Camel became very bright in a short time, reaching its peak in two or three days. It grew about 100 times brighter than any normal type of supernova. Then it rapidly dimmed in a process that lasted just days, rather than weeks. “It fades very fast, and while it’s fading it stays hot,” Perley said.

    Prior to this discovery, astronomers had sifted through historical data to find two additional Cow-like events, the “Koala” and CSS161010, but the Camel is the first to be seen in real time and thus studied in detail since the Cow.

    The four events have similar properties. They quickly get bright, then fade fast. They’re also hot, which makes them look blue. But these “fast blue optical transients” are not identical.

    “The explosion itself and the sort of zombie afterlife behavior, those are quite similar,” said Anna Ho, an astrophysicist at the University of California, Berkeley(US) who discovered the Koala and was part of the Camel discovery team. The events all appear to be some sort of explosion from a star that collides with nearby gas and dust. “But the collision stage where you’re seeing the explosion collide with ambient material, that has shown some variation in the amount of material lying around and the speed in which the shock wave from the explosion is plowing through the material.”

    The leading idea at the moment is the failed-supernova hypothesis. The process begins when a massive star around 20 times the mass of our sun reaches the end of its life and exhausts its fuel. Its core then collapses, beginning what would normally be a regular supernova, where infalling material rebounds back out, leaving behind a dense object called a neutron star.

    But in cases like the Camel and the Cow, “something unusual happens in the process to core collapse,” said Perley. “What we claim is that instead of collapsing to a neutron star, it collapsed straight into a black hole, and most of the star fell into the black hole.”

    As the black hole eats the star’s outer layers, it begins to spin rapidly, producing powerful jets that fire out from the poles. We’re seeing the explosion of light caused by the jets as they burst through the outer layers.

    Other ideas have also been proposed, such as an event where a black hole of intermediate mass rips material from an orbiting star, but that idea isn’t widely accepted. “That was an exotic idea,” said Brian Metzger, a theoretical astrophysicist at Columbia University(US). “I’m less inclined to believe more exotic things.”

    The exciting thing about the Camel is that astronomers were able to rapidly collect more data, including radio and X-ray data. That could prove very useful in working out what causes these events, said Stephen Smartt, an astronomer at Queen’s University Belfast who was the first to spot the Cow back in 2018.

    “The data we have [from the Camel] almost mimics the object in 2018,” he said. “It gives us some confidence that we could pick out [more of] these objects and work out what they might be.”

    Ho said that this should now be possible, thanks to improvements in observational techniques that make these events easier to spot. “Initially we were just looking for events that brightened very quickly,” she said. “Since then, we’ve learned that Cow-like objects not only brighten very quickly, they also fade very quickly.”

    The hope now is that more of these objects will spring up, so they can be studied in greater detail. “It’s an example of how, when we observe the sky, we find things that are utterly unexpected,” said Ho.

    See the full article here .

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    Please help promote STEM in your local schools.

    Stem Education Coalition

    Northwestern South Campus
    South Campus

    Northwestern University(US) is a private research university in Evanston, Illinois. Founded in 1851 to serve the former Northwest Territory, the university is a founding member of the Big Ten Conference.

    On May 31, 1850, nine men gathered to begin planning a university that would serve the Northwest Territory.

    Given that they had little money, no land and limited higher education experience, their vision was ambitious. But through a combination of creative financing, shrewd politicking, religious inspiration and an abundance of hard work, the founders of Northwestern University were able to make that dream a reality.

    In 1853, the founders purchased a 379-acre tract of land on the shore of Lake Michigan 12 miles north of Chicago. They established a campus and developed the land near it, naming the surrounding town Evanston in honor of one of the University’s founders, John Evans. After completing its first building in 1855, Northwestern began classes that fall with two faculty members and 10 students.
    Twenty-one presidents have presided over Northwestern in the years since. The University has grown to include 12 schools and colleges, with additional campuses in Chicago and Doha, Qatar.

    Northwestern is known for its focus on interdisciplinary education, extensive research output, and student traditions. The university provides instruction in over 200 formal academic concentrations, including various dual degree programs. The university is composed of eleven undergraduate, graduate, and professional schools, which include the Kellogg School of Management, the Pritzker School of Law, the Feinberg School of Medicine, the Weinberg College of Arts and Sciences, the Bienen School of Music, the McCormick School of Engineering and Applied Science, the Medill School of Journalism, the School of Communication, the School of Professional Studies, the School of Education and Social Policy, and The Graduate School. As of fall 2019, the university had 21,946 enrolled students, including 8,327 undergraduates and 13,619 graduate students.

    Valued at $12.2 billion, Northwestern’s endowment is among the largest university endowments in the United States. Its numerous research programs bring in nearly $900 million in sponsored research each year.

    Northwestern’s main 240-acre (97 ha) campus lies along the shores of Lake Michigan in Evanston, 12 miles north of Downtown Chicago. The university’s law, medical, and professional schools, along with its nationally ranked Northwestern Memorial Hospital, are located on a 25-acre (10 ha) campus in Chicago’s Streeterville neighborhood. The university also maintains a campus in Doha, Qatar and locations in San Francisco, California, Washington, D.C. and Miami, Florida.

    As of October 2020, Northwestern’s faculty and alumni have included 1 Fields Medalist, 22 Nobel Prize laureates, 40 Pulitzer Prize winners, 6 MacArthur Fellows, 17 Rhodes Scholars, 27 Marshall Scholars, 23 National Medal of Science winners, 11 National Humanities Medal recipients, 84 members of the American Academy of Arts and Sciences, 10 living billionaires, 16 Olympic medalists, and 2 U.S. Supreme Court Justices. Northwestern alumni have founded notable companies and organizations such as the Mayo Clinic, The Blackstone Group, Kirkland & Ellis, U.S. Steel, Guggenheim Partners, Accenture, Aon Corporation, AQR Capital, Booz Allen Hamilton, and Melvin Capital.

    The foundation of Northwestern University can be traced to a meeting on May 31, 1850, of nine prominent Chicago businessmen, Methodist leaders, and attorneys who had formed the idea of establishing a university to serve what had been known from 1787 to 1803 as the Northwest Territory. On January 28, 1851, the Illinois General Assembly granted a charter to the Trustees of the North-Western University, making it the first chartered university in Illinois. The school’s nine founders, all of whom were Methodists (three of them ministers), knelt in prayer and worship before launching their first organizational meeting. Although they affiliated the university with the Methodist Episcopal Church, they favored a non-sectarian admissions policy, believing that Northwestern should serve all people in the newly developing territory by bettering the economy in Evanston.

    John Evans, for whom Evanston is named, bought 379 acres (153 ha) of land along Lake Michigan in 1853, and Philo Judson developed plans for what would become the city of Evanston, Illinois. The first building, Old College, opened on November 5, 1855. To raise funds for its construction, Northwestern sold $100 “perpetual scholarships” entitling the purchaser and his heirs to free tuition. Another building, University Hall, was built in 1869 of the same Joliet limestone as the Chicago Water Tower, also built in 1869, one of the few buildings in the heart of Chicago to survive the Great Chicago Fire of 1871. In 1873 the Evanston College for Ladies merged with Northwestern, and Frances Willard, who later gained fame as a suffragette and as one of the founders of the Woman’s Christian Temperance Union (WCTU), became the school’s first dean of women (Willard Residential College, built in 1938, honors her name). Northwestern admitted its first female students in 1869, and the first woman was graduated in 1874.

    Northwestern fielded its first intercollegiate football team in 1882, later becoming a founding member of the Big Ten Conference. In the 1870s and 1880s, Northwestern affiliated itself with already existing schools of law, medicine, and dentistry in Chicago. Northwestern University Pritzker School of Law is the oldest law school in Chicago. As the university’s enrollments grew, these professional schools were integrated with the undergraduate college in Evanston; the result was a modern research university combining professional, graduate, and undergraduate programs, which gave equal weight to teaching and research. By the turn of the century, Northwestern had grown in stature to become the third largest university in the United States after Harvard University(US) and the University of Michigan(US).

    Under Walter Dill Scott’s presidency from 1920 to 1939, Northwestern began construction of an integrated campus in Chicago designed by James Gamble Rogers, noted for his design of the Yale University(US) campus, to house the professional schools. The university also established the Kellogg School of Management and built several prominent buildings on the Evanston campus, including Dyche Stadium, now named Ryan Field, and Deering Library among others. In the 1920s, Northwestern became one of the first six universities in the United States to establish a Naval Reserve Officers Training Corps (NROTC). In 1939, Northwestern hosted the first-ever NCAA Men’s Division I Basketball Championship game in the original Patten Gymnasium, which was later demolished and relocated farther north, along with the Dearborn Observatory, to make room for the Technological Institute.

    After the golden years of the 1920s, the Great Depression in the United States (1929–1941) had a severe impact on the university’s finances. Its annual income dropped 25 percent from $4.8 million in 1930-31 to $3.6 million in 1933-34. Investment income shrank, fewer people could pay full tuition, and annual giving from alumni and philanthropists fell from $870,000 in 1932 to a low of $331,000 in 1935. The university responded with two salary cuts of 10 percent each for all employees. It imposed hiring and building freezes and slashed appropriations for maintenance, books, and research. Having had a balanced budget in 1930-31, the university now faced deficits of roughly $100,000 for the next four years. Enrollments fell in most schools, with law and music suffering the biggest declines. However, the movement toward state certification of school teachers prompted Northwestern to start a new graduate program in education, thereby bringing in new students and much needed income. In June 1933, Robert Maynard Hutchins, president of the University of Chicago(US), proposed a merger of the two universities, estimating annual savings of $1.7 million. The two presidents were enthusiastic, and the faculty liked the idea; many Northwestern alumni, however, opposed it, fearing the loss of their Alma Mater and its many traditions that distinguished Northwestern from Chicago. The medical school, for example, was oriented toward training practitioners, and alumni feared it would lose its mission if it were merged into the more research-oriented University of Chicago Medical School. The merger plan was ultimately dropped. In 1935, the Deering family rescued the university budget with an unrestricted gift of $6 million, bringing the budget up to $5.4 million in 1938-39. This allowed many of the previous spending cuts to be restored, including half of the salary reductions.

    Like other American research universities, Northwestern was transformed by World War II (1939–1945). Regular enrollment fell dramatically, but the school opened high-intensity, short-term programs that trained over 50,000 military personnel, including future president John F. Kennedy. Northwestern’s existing NROTC program proved to be a boon to the university as it trained over 36,000 sailors over the course of the war, leading Northwestern to be called the “Annapolis of the Midwest.” Franklyn B. Snyder led the university from 1939 to 1949, and after the war, surging enrollments under the G.I. Bill drove dramatic expansion of both campuses. In 1948, prominent anthropologist Melville J. Herskovits founded the Program of African Studies at Northwestern, the first center of its kind at an American academic institution. J. Roscoe Miller’s tenure as president from 1949 to 1970 saw an expansion of the Evanston campus, with the construction of the Lakefill on Lake Michigan, growth of the faculty and new academic programs, and polarizing Vietnam-era student protests. In 1978, the first and second Unabomber attacks occurred at Northwestern University. Relations between Evanston and Northwestern became strained throughout much of the post-war era because of episodes of disruptive student activism, disputes over municipal zoning, building codes, and law enforcement, as well as restrictions on the sale of alcohol near campus until 1972. Northwestern’s exemption from state and municipal property-tax obligations under its original charter has historically been a source of town-and-gown tension.

    Although government support for universities declined in the 1970s and 1980s, President Arnold R. Weber was able to stabilize university finances, leading to a revitalization of its campuses. As admissions to colleges and universities grew increasingly competitive in the 1990s and 2000s, President Henry S. Bienen’s tenure saw a notable increase in the number and quality of undergraduate applicants, continued expansion of the facilities and faculty, and renewed athletic competitiveness. In 1999, Northwestern student journalists uncovered information exonerating Illinois death-row inmate Anthony Porter two days before his scheduled execution. The Innocence Project has since exonerated 10 more men. On January 11, 2003, in a speech at Northwestern School of Law’s Lincoln Hall, then Governor of Illinois George Ryan announced that he would commute the sentences of more than 150 death-row inmates.

    In the 2010s, a 5-year capital campaign resulted in a new music center, a replacement building for the business school, and a $270 million athletic complex. In 2014, President Barack Obama delivered a seminal economics speech at the Evanston campus.

    Organization and administration

    Governance

    Northwestern is privately owned and governed by an appointed Board of Trustees, which is composed of 70 members and, as of 2011, has been chaired by William A. Osborn ’69. The board delegates its power to an elected president who serves as the chief executive officer of the university. Northwestern has had sixteen presidents in its history (excluding interim presidents). The current president, economist Morton O. Schapiro, succeeded Henry Bienen whose 14-year tenure ended on August 31, 2009. The president maintains a staff of vice presidents, directors, and other assistants for administrative, financial, faculty, and student matters. Kathleen Haggerty assumed the role of interim provost for the university in April 2020.

    Students are formally involved in the university’s administration through the Associated Student Government, elected representatives of the undergraduate students, and the Graduate Student Association, which represents the university’s graduate students.

    The admission requirements, degree requirements, courses of study, and disciplinary and degree recommendations for each of Northwestern’s 12 schools are determined by the voting members of that school’s faculty (assistant professor and above).

    Undergraduate and graduate schools

    Evanston Campus:

    Weinberg College of Arts and Sciences (1851)
    School of Communication (1878)
    Bienen School of Music (1895)
    McCormick School of Engineering and Applied Science (1909)
    Medill School of Journalism (1921)
    School of Education and Social Policy (1926)
    School of Professional Studies (1933)

    Graduate and professional

    Evanston Campus

    Kellogg School of Management (1908)
    The Graduate School

    Chicago Campus

    Feinberg School of Medicine (1859)
    Kellogg School of Management (1908)
    Pritzker School of Law (1859)
    School of Professional Studies (1933)

    Northwestern University had a dental school from 1891 to May 31, 2001, when it closed.

    Endowment

    In 1996, Princess Diana made a trip to Evanston to raise money for the university hospital’s Robert H. Lurie Comprehensive Cancer Center at the invitation of then President Bienen. Her visit raised a total of $1.5 million for cancer research.

    In 2003, Northwestern finished a five-year capital campaign that raised $1.55 billion, exceeding its fundraising goal by $550 million.

    In 2014, Northwestern launched the “We Will” campaign with a fundraising goal of $3.75 billion. As of December 31, 2019, the university has received $4.78 billion from 164,026 donors.

    Sustainability

    In January 2009, the Green Power Partnership (sponsored by the EPA) listed Northwestern as one of the top 10 universities in the country in purchasing energy from renewable sources. The university matches 74 million kilowatt hours (kWh) of its annual energy use with Green-e Certified Renewable Energy Certificates (RECs). This green power commitment represents 30 percent of the university’s total annual electricity use and places Northwestern in the EPA’s Green Power Leadership Club. The Initiative for Sustainability and Energy at Northwestern (ISEN), supporting research, teaching and outreach in these themes, was launched in 2008.

    Northwestern requires that all new buildings be LEED-certified. Silverman Hall on the Evanston campus was awarded Gold LEED Certification in 2010; Wieboldt Hall on the Chicago campus was awarded Gold LEED Certification in 2007, and the Ford Motor Company Engineering Design Center on the Evanston campus was awarded Silver LEED Certification in 2006. New construction and renovation projects will be designed to provide at least a 20% improvement over energy code requirements where feasible. At the beginning of the 2008–09 academic year, the university also released the Evanston Campus Framework Plan, which outlines plans for future development of the university’s Evanston campus. The plan not only emphasizes sustainable building construction, but also focuses on reducing the energy costs of transportation by optimizing pedestrian and bicycle access. Northwestern has had a comprehensive recycling program in place since 1990. The university recycles over 1,500 tons of waste, or 30% of all waste produced on campus, each year. All landscape waste at the university is composted.

    Academics

    Education and rankings

    Northwestern is a large, residential research university, and is frequently ranked among the top universities in the United States. The university is a leading institution in the fields of materials engineering, chemistry, business, economics, education, journalism, and communications. It is also prominent in law and medicine. Accredited by the Higher Learning Commission and the respective national professional organizations for chemistry, psychology, business, education, journalism, music, engineering, law, and medicine, the university offers 124 undergraduate programs and 145 graduate and professional programs. Northwestern conferred 2,190 bachelor’s degrees, 3,272 master’s degrees, 565 doctoral degrees, and 444 professional degrees in 2012–2013. Since 1951, Northwestern has awarded 520 honorary degrees. Northwestern also has chapters of academic honor societies such as Phi Beta Kappa (Alpha of Illinois), Eta Kappa Nu, Tau Beta Pi, Eta Sigma Phi (Beta Chapter), Lambda Pi Eta, and Alpha Sigma Lambda (Alpha Chapter).

    The four-year, full-time undergraduate program comprises the majority of enrollments at the university. Although there is no university-wide core curriculum, a foundation in the liberal arts and sciences is required for all majors; individual degree requirements are set by the faculty of each school. The university heavily emphasizes interdisciplinary learning, with 72% of undergrads combining two or more areas of study. Northwestern’s full-time undergraduate and graduate programs operate on an approximately 10-week academic quarter system with the academic year beginning in late September and ending in early June. Undergraduates typically take four courses each quarter and twelve courses in an academic year and are required to complete at least twelve quarters on campus to graduate. Northwestern offers honors, accelerated, and joint degree programs in medicine, science, mathematics, engineering, and journalism. The comprehensive doctoral graduate program has high coexistence with undergraduate programs.

    Despite being a mid-sized university, Northwestern maintains a relatively low student to faculty ratio of 6:1.

    Research

    Northwestern was elected to the Association of American Universities in 1917 and is classified as an R1 university, denoting “very high” research activity. Northwestern’s schools of management, engineering, and communication are among the most academically productive in the nation. The university received $887.3 million in research funding in 2019 and houses over 90 school-based and 40 university-wide research institutes and centers. Northwestern also supports nearly 1,500 research laboratories across two campuses, predominately in the medical and biological sciences.

    Northwestern is home to the Center for Interdisciplinary Exploration and Research in Astrophysics, Northwestern Institute for Complex Systems, Nanoscale Science and Engineering Center, Materials Research Center, Center for Quantum Devices, Institute for Policy Research, International Institute for Nanotechnology, Center for Catalysis and Surface Science, Buffet Center for International and Comparative Studies, the Initiative for Sustainability and Energy at Northwestern, and the Argonne/Northwestern Solar Energy Research Center among other centers for interdisciplinary research.

    Student body

    Northwestern enrolled 8,186 full-time undergraduate, 9,904 full-time graduate, and 3,856 part-time students in the 2019–2020 academic year. The freshman retention rate for that year was 98%. 86% of students graduated after four years and 92% graduated after five years. These numbers can largely be attributed to the university’s various specialized degree programs, such as those that allow students to earn master’s degrees with a one or two year extension of their undergraduate program.

    The undergraduate population is drawn from all 50 states and over 75 foreign countries. 20% of students in the Class of 2024 were Pell Grant recipients and 12.56% were first-generation college students. Northwestern also enrolls the 9th-most National Merit Scholars of any university in the nation.

    In Fall 2014, 40.6% of undergraduate students were enrolled in the Weinberg College of Arts and Sciences, 21.3% in the McCormick School of Engineering and Applied Science, 14.3% in the School of Communication, 11.7% in the Medill School of Journalism, 5.7% in the Bienen School of Music, and 6.4% in the School of Education and Social Policy. The five most commonly awarded undergraduate degrees are economics, journalism, communication studies, psychology, and political science. The Kellogg School of Management’s MBA, the School of Law’s JD, and the Feinberg School of Medicine’s MD are the three largest professional degree programs by enrollment. With 2,446 students enrolled in science, engineering, and health fields, the largest graduate programs by enrollment include chemistry, integrated biology, material sciences, electrical and computer engineering, neuroscience, and economics.

    Athletics

    Northwestern is a charter member of the Big Ten Conference. It is the conference’s only private university and possesses the smallest undergraduate enrollment (the next-smallest member, the University of Iowa, is roughly three times as large, with almost 22,000 undergraduates).

    Northwestern fields 19 intercollegiate athletic teams (8 men’s and 11 women’s) in addition to numerous club sports. 12 of Northwestern’s varsity programs have had NCAA or bowl postseason appearances. Northwestern is one of five private AAU members to compete in NCAA Power Five conferences (the other four being Duke, Stanford, USC, and Vanderbilt) and maintains a 98% NCAA Graduation Success Rate, the highest among Football Bowl Subdivision schools.

    In 2018, the school opened the Walter Athletics Center, a $270 million state of the art lakefront facility for its athletics teams.

    Nickname and mascot

    Before 1924, Northwestern teams were known as “The Purple” and unofficially as “The Fighting Methodists.” The name Wildcats was bestowed upon the university in 1924 by Wallace Abbey, a writer for the Chicago Daily Tribune, who wrote that even in a loss to the University of Chicago, “Football players had not come down from Evanston; wildcats would be a name better suited to “[Coach Glenn] Thistletwaite’s boys.” The name was so popular that university board members made “Wildcats” the official nickname just months later. In 1972, the student body voted to change the official nickname to “Purple Haze,” but the new name never stuck.

    The mascot of Northwestern Athletics is “Willie the Wildcat”. Prior to Willie, the team mascot had been a live, caged bear cub from the Lincoln Park Zoo named Furpaw, who was brought to the playing field on game days to greet the fans. After a losing season however, the team decided that Furpaw was to blame for its misfortune and decided to select a new mascot. “Willie the Wildcat” made his debut in 1933, first as a logo and then in three dimensions in 1947, when members of the Alpha Delta fraternity dressed as wildcats during a Homecoming Parade.

    Traditions

    Northwestern’s official motto, “Quaecumque sunt vera,” was adopted by the university in 1890. The Latin phrase translates to “Whatsoever things are true” and comes from the Epistle of Paul to the Philippians (Philippians 4:8), in which St. Paul admonishes the Christians in the Greek city of Philippi. In addition to this motto, the university crest features a Greek phrase taken from the Gospel of John inscribed on the pages of an open book, ήρης χάριτος και αληθείας or “the word full of grace and truth” (John 1:14).
    Alma Mater is the Northwestern Hymn. The original Latin version of the hymn was written in 1907 by Peter Christian Lutkin, the first dean of the School of Music from 1883 to 1931. In 1953, then Director-of-Bands John Paynter recruited an undergraduate music student, Thomas Tyra (’54), to write an English version of the song, which today is performed by the Marching Band during halftime at Wildcat football games and by the orchestra during ceremonies and other special occasions.
    Purple became Northwestern’s official color in 1892, replacing black and gold after a university committee concluded that too many other universities had used these colors. Today, Northwestern’s official color is purple, although white is something of an official color as well, being mentioned in both the university’s earliest song, Alma Mater (1907) (“Hail to purple, hail to white”) and in many university guidelines.
    The Rock, a 6-foot high quartzite boulder donated by the Class of 1902, originally served as a water fountain. It was painted over by students in the 1940s as a prank and has since become a popular vehicle of self-expression on campus.
    Armadillo Day, commonly known as Dillo Day, is the largest student-run music festival in the country. The festival is hosted every Spring on Northwestern’s Lakefront.
    Primal Scream is held every quarter at 9 p.m. on the Sunday before finals week. Students lean out of windows or gather in courtyards and scream to help relieve stress.
    In the past, students would throw marshmallows during football games, but this tradition has since been discontinued.

    Philanthropy

    One of Northwestern’s most notable student charity events is Dance Marathon, the most established and largest student-run philanthropy in the nation. The annual 30-hour event is among the most widely-attended events on campus. It has raised over $1 million for charity ever year since 2011 and has donated a total of $13 million to children’s charities since its conception.

    The Northwestern Community Development Corps (NCDC) is a student-run organization that connects hundreds of student volunteers to community development projects in Evanston and Chicago throughout the year. The group also holds a number of annual community events, including Project Pumpkin, a Halloween celebration that provides over 800 local children with carnival events and a safe venue to trick-or-treat each year.

    Many Northwestern students participate in the Freshman Urban Program, an initiative for students interested in community service to work on addressing social issues facing the city of Chicago, and the university’s Global Engagement Studies Institute (GESI) programs, including group service-learning expeditions in Asia, Africa, or Latin America in conjunction with the Foundation for Sustainable Development.

    Several internationally recognized non-profit organizations were established at Northwestern, including the World Health Imaging, Informatics and Telemedicine Alliance, a spin-off from an engineering student’s honors thesis.

    Media
    Print

    Established in 1881, The Daily Northwestern is the university’s main student newspaper and is published on weekdays during the academic year. It is directed entirely by undergraduate students and owned by the Students Publishing Company. Although it serves the Northwestern community, the Daily has no business ties to the university and is supported wholly by advertisers.
    North by Northwestern is an online undergraduate magazine established in September 2006 by students at the Medill School of Journalism. Published on weekdays, it consists of updates on news stories and special events throughout the year. It also publishes a quarterly print magazine.
    Syllabus is the university’s undergraduate yearbook. It is distributed in late May and features a culmination of the year’s events at Northwestern. First published in 1885, the yearbook is published by Students Publishing Company and edited by Northwestern students.
    Northwestern Flipside is an undergraduate satirical magazine. Founded in 2009, it publishes a weekly issue both in print and online.
    Helicon is the university’s undergraduate literary magazine. Established in 1979, it is published twice a year: a web issue is released in the winter and a print issue with a web complement is released in the spring.
    The Protest is Northwestern’s quarterly social justice magazine.
    The Northwestern division of Student Multicultural Affairs supports a number of publications for particular cultural groups including Ahora, a magazine about Hispanic and Latino/a culture and campus life; Al Bayan, published by the Northwestern Muslim-cultural Student Association; BlackBoard Magazine, a magazine centered around African-American student life; and NUAsian, a magazine and blog on Asian and Asian-American culture and issues.
    The Northwestern University Law Review is a scholarly legal publication and student organization at Northwestern University School of Law. Its primary purpose is to publish a journal of broad legal scholarship. The Law Review publishes six issues each year. Student editors make the editorial and organizational decisions and select articles submitted by professors, judges, and practitioners, as well as student pieces. The Law Review also publishes scholarly pieces weekly on the Colloquy.
    The Northwestern Journal of Technology and Intellectual Property is a law review published by an independent student organization at Northwestern University School of Law.
    The Northwestern Interdisciplinary Law Review is a scholarly legal publication published annually by an editorial board of Northwestern undergraduates. Its mission is to publish interdisciplinary legal research, drawing from fields such as history, literature, economics, philosophy, and art. Founded in 2008, the journal features articles by professors, law students, practitioners, and undergraduates. It is funded by the Buffett Center for International and Comparative Studies and the Office of the Provost.

    Web-based

    Established in January 2011, Sherman Ave is a humor website that often publishes content on Northwestern student life. Most of its staff writers are current Northwestern undergraduates writing under various pseudonyms. The website is popular among students for its interviews of prominent campus figures, Freshman Guide, and live-tweeting coverage of football games. In Fall 2012, the website promoted a satiric campaign to end the Vanderbilt University football team’s custom of clubbing baby seals.
    Politics & Policy is dedicated to the analysis of current events and public policy. Established in 2010 by students at the Weinberg College of Arts and Sciences, School of Communication, and Medill School of Journalism, the publication reaches students on more than 250 college campuses around the world. Run entirely by undergraduates, it is published several times a week and features material ranging from short summaries of events to extended research pieces. The publication is financed in part by the Buffett Center.
    Northwestern Business Review is a campus source for business news. Founded in 2005, it has an online presence as well as a quarterly print schedule.
    TriQuarterly Online (formerly TriQuarterly) is a literary magazine published twice a year featuring poetry, fiction, nonfiction, drama, literary essays, reviews, blog posts, and art.
    The Queer Reader is Northwestern’s first radical feminist and LGBTQ+ publication.

    Radio, film, and television

    WNUR (89.3 FM) is a 7,200-watt radio station that broadcasts to the city of Chicago and its northern suburbs. WNUR’s programming consists of music (jazz, classical, and rock), literature, politics, current events, varsity sports (football, men’s and women’s basketball, baseball, softball, and women’s lacrosse), and breaking news on weekdays.
    Studio 22 is a student-run production company that produces roughly ten films each year. The organization financed the first film Zach Braff directed, and many of its films have featured students who would later go into professional acting, including Zach Gilford of Friday Night Lights.
    Applause for a Cause is currently the only student-run production company in the nation to create feature-length films for charity. It was founded in 2010 and has raised over $5,000 to date for various local and national organizations across the United States.
    Northwestern News Network is a student television news and sports network, serving the Northwestern and Evanston communities. Its studios and newsroom are located on the fourth floor of the McCormick Tribune Center on Northwestern’s Evanston campus. NNN is funded by the Medill School of Journalism.

     
  • richardmitnick 11:43 pm on February 17, 2021 Permalink | Reply
    Tags: "Growing Inventory of Black Holes Offers a Radical Probe of the Cosmos", , , , , Before black holes can be used to study the cosmos as a whole astrophysicists must first figure out how they are made., Black hole astrophysics, , , Masses in the Stellar Graveyard, , Quanta Magazine(US)   

    From Quanta Magazine(US): “Growing Inventory of Black Holes Offers a Radical Probe of the Cosmos” 

    From Quanta Magazine(US)

    February 17, 2021
    Thomas Lewton

    1
    The dozens of black hole collisions observed by the LIGO and Virgo gravitational wave detectors are changing our view of the universe. Credit: Sakkmesterke/Science Source.

    When the first black hole collision was detected in 2015, it was a watershed moment in the history of astronomy. With gravitational waves, astronomers were observing the universe in an entirely new way.

    Gravitational waves. Credit: MPG Institute for Gravitational Physics [Max-Planck-Institut für Gravitationsphysik] (Albert Einstein Institute) (DE)/Werner Benger.

    But this first event didn’t revolutionize our understanding of black holes — nor could it. This collision would be the first of many, astronomers knew, and only with that bounty would answers come.

    “The first discovery was the thrill of our lives,” said Vicky Kalogera, an astrophysicist at Northwestern University and part of the Laser Interferometer Gravitational-Wave Observatory (LIGO) collaboration that made the 2015 detection.

    MIT/Caltech Advanced aLigo .

    “But you cannot do astrophysics with one source.”

    Now, gravitational wave physicists like Kalogera say they are entering a new era of black hole astronomy, driven by a rapid increase in the number of black holes they are observing.

    The latest catalog of these so-called black hole binary mergers — the result of two black holes spiraling inward toward each other and colliding — has quadrupled the black hole merger data available to study.

    Masses in the Stellar Graveyard GWTC-2 plot v1.0 BY LIGO-Virgo. Credit: Frank Elavsky and Aaron Geller at Northwestern University.

    There are now almost 50 mergers for astrophysicists to scrutinize, with dozens more expected in the next few months and hundreds more in the coming years.

    “Black hole astrophysics is being revolutionized by gravitational waves because the numbers are so big. And the numbers are allowing us to ask qualitatively different questions,” said Kalogera. “We’ve opened a treasure trove.”

    On the strength of this data, new statistically driven studies are beginning to reveal the secrets of these enigmatic objects: how black holes form, and why they merge. This growing black hole inventory could also offer a novel way to probe cosmological evolution — from the Big Bang through the birth of the first stars and the growth of galaxies.

    “I definitely didn’t expect that we’d be looking at these questions so soon after the first detection,” said Maya Fishbach, an astrophysicist at Northwestern. “The field has exploded.”

    Where Do Black Holes Come From?

    Before black holes can be used to study the cosmos as a whole, astrophysicists must first figure out how they are made. Two theories have dominated the debate so far.

    Some astronomers suggest that most black holes originate inside crowded clusters of stars — regions that are sometimes a million times denser than our own galactic backyard. Each time a very massive star explodes, it leaves behind a black hole that sinks to the middle of the star cluster. The center of the cluster becomes thick with black holes, which become entwined by gravity into a fateful cosmic dance. Astronomers call this “dynamical” black hole formation.

    Others suggest that black hole binaries start out as pairs of stars in comparatively desolate areas of galaxies. After a long and chaotic life together, they too explode, creating a pair of “isolated” black holes that continue to orbit each other.

    “There’s been this perception that it’s a fight between the dynamical and the isolated models,” said Daniel Holz, an astrophysicist at the University of Chicago.

    The tendency of many theorists to advocate for just one black hole binary formation channel partly stems from the practicalities of working with very little data. “Each event was lovingly analyzed, obsessed over and fussed over,” said Holz. “We would make a detection and people would try to abstract very broad statements from a sample size of one or two black holes.”

    Indeed, astrophysicists used that first detection to argue for opposing conclusions. LIGO found its first black hole merger extremely quickly — before the official start of observation, in fact — which suggested that black hole binary systems are very common in the universe.

    Artist’s by now iconic conception of two merging black holes similar to those detected by LIGO Credit LIGO-Caltech/MIT/Sonoma State /Aurore Simonnet.

    Since isolated black holes can form in a broad range of astrophysical environments, theories that favor isolated black holes predict that we’ll see a lot of mergers.

    Others pointed out that the first merger featured unusually large black holes, and that the existence of these giants supported the dynamical theory. Such large black holes, they reasoned, could only be made in the early universe, when star clusters are also thought to have formed.

    Yet with a sample size of one, such assertions could only be an “educated guess,” said Carl Rodriguez, an astrophysicist at Carnegie Mellon University.

    Now data from LIGO’s latest catalog shows that black hole binaries are far less common than expected. In fact, the rate of merging black holes now observed could be “entirely explained” by star clusters, according to a paper posted by Rodriguez and his collaborators for RNAAS late last month. (The paper’s conclusion is more measured and suggests that both the dynamical and isolated processes are important.)

    In addition, the new mergers have enabled a fresh approach to the puzzle of where black holes come from. Despite their elusive nature, black holes are very simple. Aside from mass and charge, the only trait a black hole can have is spin — a measure of how quickly it rotates. If a pair of black holes, and the stars from which they form, live their whole lives together, the constant push and pull will align their spins. But if two black holes happen to encounter each other later in life, their spins will be random.

    After measuring the spin of the black holes in the LIGO data set, astronomers now suggest that the dynamic and isolated scenarios are almost equally likely. There is no “one channel to rule them all,” wrote the astrophysicist Michael Zevin and collaborators in a recent AAS paper outlining an array of different pathways that together can explain this new and growing population of black hole binaries.

    “The simplest answer is not always the correct one,” said Zevin. “It’s a more complicated landscape, and it’s certainly a bigger challenge. But I think it’s a more fun problem to address as well.”

    Young Black Holes

    LIGO and its sister observatory Virgo have also grown more sensitive over time, which means they can now see colliding black holes that are much farther away from Earth and much further back in time.

    MIT /Caltech Advanced aLigo at Hanford, WA (US), Livingston, LA, (US) and VIRGO Gravitational Wave interferometer, near Pisa, Italy.

    “We’re listening to a really big chunk of the universe, out to when the universe was much younger than it is today,” said Fishbach.

    In a recent paper, Fishbach and her collaborators found indications of differences in the types of black holes observed at different points in cosmic history. In particular, heavier black holes seem to be more common earlier in the universe’s history.

    This came as no surprise to many astrophysicists; they expect that the first stars in the universe formed from huge clouds of hydrogen and helium, which would make them much bigger than later stars. Black holes created from these stars should then also be huge.

    But it’s one thing to predict what happened in the early universe, and another to observe it. “You can really start to use [black holes] as a tracer of how the universe formed stars over cosmic time and how the galaxies that form those stars and star clusters are assembled. And that starts to get really cool,” said Rodriguez.

    The study is a first step toward using large data sets of black holes as a radical tool to explore the cosmos. Astronomers have created an astonishingly accurate model of how the universe evolved, known as Lambda-CDM.

    Lamda Cold Dark Matter Accerated Expansion of The universe http scinotions.com the-cosmic-inflation-suggests-the-existence-of-parallel-universes. Credit: Alex Mittelmann, Coldcreation.

    But no model is perfect. Gravitational waves offer a way to measure the universe that is completely independent of every other method in the history of cosmology, said Salvatore Vitale, an astrophysicist at the Massachusetts Institute of Technology. “If you get the same results, you’ll sleep better at night. If you don’t, that points to a potential misunderstanding.”

    Theorists are now building models that include multiple black hole formation scenarios and unscrambling how each one evolves across the universe’s history. Gravitational wave physicists are hopeful that in the coming months and years they’ll be able to answer these questions with confidence.

    “We’re just scratching the surface,” said Kalogera. “The sample is still too small to give us a robust answer, but when we have 100 or 200 of these [mergers], then I think we’ll have clear answers.

    “We’re not that far away.”

    See the full article here .


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    Formerly known as Simons Science News, Quanta Magazine (US) is an editorially independent online publication launched by the Simons Foundation to enhance public understanding of science. Why Quanta? Albert Einstein called photons “quanta of light.” Our goal is to “illuminate science.” At Quanta Magazine, scientific accuracy is every bit as important as telling a good story. All of our articles are meticulously researched, reported, edited, copy-edited and fact-checked.

     
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