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  • richardmitnick 3:30 pm on March 21, 2022 Permalink | Reply
    Tags: "The Evolving Quest for a Grand Unified Theory of Mathematics", , , , Quantum field theory,   

    From Scientific American: “The Evolving Quest for a Grand Unified Theory of Mathematics” 

    From Scientific American

    March 21, 2022
    Rachel Crowell

    Credit: Boris SV/Getty Images.

    More than 50 years after the seeds of a vast collection of mathematical ideas called the Langlands program began to sprout, surprising new findings are emerging.

    Within mathematics, there is a vast and ever expanding web of conjectures, theorems and ideas called the Langlands program. That program links seemingly disconnected subfields. It is such a force that some mathematicians say it—or some aspect of it—belongs in the esteemed ranks of the Millennium Prize Problems, a list of the top open questions in math. Edward Frenkel, a mathematician at the University of California-Berkeley, has even dubbed the Langlands program “a Grand Unified Theory of Mathematics.”

    The program is named after Robert Langlands, a mathematician at the Institute for Advanced Study in Princeton, N.J. Four years ago, he was awarded the Abel Prize, one of the most prestigious awards in mathematics, for his program, which was described as “visionary.”

    Langlands is retired, but in recent years the project has sprouted into “almost its own mathematical field, with many disparate parts,” which are united by “a common wellspring of inspiration,” says Steven Rayan, a mathematician and mathematical physicist at the University of Saskatchewan. It has “many avatars, some of which are still open, some of which have been resolved in beautiful ways.”

    Increasingly mathematicians are finding links between the original program—and its offshoot, geometric Langlands—and other fields of science. Researchers have already discovered strong links to physics, and Rayan and other scientists continue to explore new ones. He has a hunch that, with time, links will be found between these programs and other areas as well. “I think we’re only at the tip of the iceberg there,” he says. “I think that some of the most fascinating work that will come out of the next few decades is seeing consequences and manifestations of Langlands within parts of science where the interaction with this kind of pure mathematics may have been marginal up until now.” Overall Langlands remains mysterious, Rayan adds, and to know where it is headed, he wants to “see an understanding emerge of where these programs really come from.”

    A Puzzling Web

    The Langlands program has always been a tantalizing dance with the unexpected, according to James Arthur, a mathematician at the University of Toronto (CA). Langlands was Arthur’s adviser at Yale University, where Arthur earned his Ph.D. in 1970. (Langlands declined to be interviewed for this story.)

    “I was essentially his first student, and I was very fortunate to have encountered him at that time,” Arthur says. “He was unlike any mathematician I had ever met. Any question I had, especially about the broader side of mathematics, he would answer clearly, often in a way that was more inspiring than anything I could have imagined.”

    During that time, Langlands laid the foundation for what eventually became his namesake program. In 1969 Langlands famously handwrote a 17-page letter to French mathematician André Weil. In that letter, Langlands shared new ideas that later became known as the “Langlands conjectures.”

    In 1969 Langlands delivered conference lectures in which he shared the seven conjectures that ultimately grew into the Langlands program, Arthur notes. One day Arthur asked his adviser for a copy of a preprint paper based on those lectures.

    “He willingly gave me one, no doubt knowing that it was beyond me,” Arthur says. “But it was also beyond everybody else for many years. I could, however, tell that it was based on some truly extraordinary ideas, even if just about everything in it was unfamiliar to me.”

    The Conjectures at the Heart of It All

    Two conjectures are central to the Langlands program. “Just about everything in the Langlands program comes in one way or another from those,” Arthur says.

    The reciprocity conjecture connects to the work of Alexander Grothendieck, famous for his research in algebraic geometry, including his prediction of “motives.” “I think Grothendieck chose the word [motive] because he saw it as a mathematical analogue of motifs that you have in art, music or literature: hidden ideas that are not explicitly made clear in the art, but things that are behind it that somehow govern how it all fits together,” Arthur says.

    The reciprocity conjecture supposes these motives come from a different type of analytical mathematical object discovered by Langlands called automorphic representations, Arthur notes. “‘Automorphic representation’ is just a buzzword for the objects that satisfy analogues of the Schrödinger equation” from quantum physics, he adds. The Schrödinger equation predicts the likelihood of finding a particle in a certain state.

    The second important conjecture is the functoriality conjecture, also simply called functoriality. It involves classifying number fields. Imagine starting with an equation of one variable whose coefficients are integers—such as x2 + 2x + 3 = 0—and looking for the roots of that equation. The conjecture predicts that the corresponding field will be “the smallest field that you get by taking sums, products and rational number multiples of these roots,” Arthur says.

    Exploring Different Mathematical “Worlds”

    With the original program, Langlands “discovered a whole new world,” Arthur says.

    The offshoot, geometric Langlands, expanded the territory this mathematics covers. Rayan explains the different perspectives the original and geometric programs provide. “Ordinary Langlands is a package of ideas, correspondences, dualities and observations about the world at a point,” he says. “Your world is going to be described by some sequence of relevant numbers. You can measure the temperature where you are; you could measure the strength of gravity at that point,” he adds.

    With the geometric program, however, your environment becomes more complex, with its own geometry. You are free to move about, collecting data at each point you visit. “You might not be so concerned with the individual numbers but more how they are varying as you move around in your world,” Rayan says. The data you gather are “going to be influenced by the geometry,” he says. Therefore, the geometric program “is essentially replacing numbers with functions.”

    Number theory and representation theory are connected by the geometric Langlands program. “Broadly speaking, representation theory is the study of symmetries in mathematics,” says Chris Elliott, a mathematician at the University of Massachusetts Amherst.

    Using geometric tools and ideas, geometric representation theory expands mathematicians’ understanding of abstract notions connected to symmetry, Elliot notes. That area of representation theory is where the geometric Langlands program “lives,” he says.

    Intersections with Physics

    The geometric program has already been linked to physics, foreshadowing possible connections to other scientific fields.

    In 2018 Kazuki Ikeda, a postdoctoral researcher in Rayan’s group, published a Journal of Mathematical Physics study that he says is connected to an electromagnetic duality that is “a long-known concept in physics” and that is seen in error-correcting codes in quantum computers, for instance. Ikeda says his results “were the first in the world to suggest that the Langlands program is an extremely important and powerful concept that can be applied not only to mathematics but also to condensed-matter physics”—the study of substances in their solid state—“and quantum computation.”

    Connections between condensed-matter physics and the geometric program have recently strengthened, according to Rayan. “In the last year the stage has been set with various kinds of investigations,” he says, including his own work involving the use of algebraic geometry and number theory in the context of quantum matter.

    Other work established links between the geometric program and high-energy physics. In 2007 Anton Kapustin, a theoretical physicist at the California Institute of Technology, and Edward Witten, a mathematical and theoretical physicist at the Institute for Advanced Study, published what Rayan calls “a beautiful landmark paper” that “paved the way for an active life for geometric Langlands in theoretical high-energy physics.” In the paper, Kapustin and Witten wrote that they aimed to “show how this program can be understood as a chapter in quantum field theory.”

    Elliott notes that viewing quantum field theory from a mathematical perspective can help glean new information about the structures that are foundational to it. For instance, Langlands may help physicists devise theories for worlds with different numbers of dimensions than our own.

    Besides the geometric program, the original Langlands program is also thought to be fundamental to physics, Arthur says. But exploring that connection “may require first finding an overarching theory that links the original and geometric programs,” he says.

    The reaches of these programs may not stop at math and physics. “I believe, without a doubt, that [they] have interpretations across science,” Rayan says. “The condensed-matter part of the story will lead naturally to forays into chemistry.” Furthermore, he adds, “pure mathematics always makes its way into every other area of science. It’s only a matter of time.”

    See the full article here .

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    Scientific American, the oldest continuously published magazine in the U.S., has been bringing its readers unique insights about developments in science and technology for more than 160 years.

  • richardmitnick 9:45 am on January 24, 2022 Permalink | Reply
    Tags: "At the interface of physics and mathematics", , , Integrable model: equation that can be solved exactly., , , , Quantum field theory, String Theory-which scientists hope will eventually provide a unified description of particle physics and gravity., ,   

    From The Swiss Federal Institute of Technology in Zürich [ETH Zürich] [Eidgenössische Technische Hochschule Zürich] (CH): “At the interface of physics and mathematics” 

    From The Swiss Federal Institute of Technology in Zürich [ETH Zürich] [Eidgenössische Technische Hochschule Zürich] (CH)

    Barbara Vonarburg

    Sylvain Lacroix is a theoretical physicist who conducts research into fundamental concepts of physics – an exciting but intellectually challenging field of science. As an Advanced Fellow at ETH Zürich’s Institute for Theoretical Studies (ITS), he works on complex equations that can be solved exactly only thanks to their large number of symmetries.

    “It was fascinating to learn abstract mathematical concepts and see them neatly applied in the realm of physics,” says Sylvain Lacroix, Advanced Fellow at the Institute for Theoretical Studies. Photo: Nicola Pitaro/ETH Zürich.

    “I got hooked on the interplay of physics and mathematics while I was still at secondary school,” says 30-​year-old Sylvain Lacroix, who was born and grew up near Paris. “It was fascinating to learn abstract mathematical concepts and see them neatly applied in the realm of physics.” During his studies at The University of Lyon [Université Claude Bernard Lyon 1] (FR), he devoted much of his energy and enthusiasm to physics problems that had highly complex underlying mathematical structures. So when it came to selecting a topic for his doctoral thesis, this area of research seemed like the obvious choice. He decided to explore the theory of what are known as integrable models – a subject he has continued to pursue up to the present day.

    Lacroix readily acknowledges that most people outside his line of work find the term “integrable models” completely incomprehensible: “I have to admit that it’s probably not the simplest or most accessible field of physics,” he says, almost apologetically. That’s why he takes pains to explain it in layman’s terms: “We define a model as a body of laws, a set of equations that describe the behaviour of certain quantities, for example how the position of an object changes over time.” An integrable model is characterised by equations that can be solved exactly, which is by no means a given.

    Symmetry is the key

    Many of the equations used in modern physics – such as that practised at The European Organization for Nuclear Research [Organización Europea para la Investigación Nuclear][Organisation européenne pour la recherche nucléaire] [Europäische Organisation für Kernforschung](CH) [CERN] – are so complex that they can be solved only approximately. These approximation methods often serve their purpose well, for instance if there is only a weak interaction between two particles. However, other cases require exact calculations – and that’s where integrable models come in. But what makes them so exact? “That’s another aspect that is tricky to explain,” Lacroix says, “but it ultimately comes down to symmetry.” Take, for example, the symmetry of time or space: a physics experiment will produce the same results whether you perform it today or – under identical conditions – ten days from now, and whether it takes place in Zürich or New York. Consequently, the equation that describes the experiment must remain invariant even if the time or location changes. This is reflected in the mathematical structure of the equation, which contains the corresponding constraints. “If we have enough symmetries, this results in so many constraints that we can simplify the equation to the point where we get exact results,” says the physicist.

    Integrable models and their exact solutions are actually very rare in mathematics. “If I chose a random equation, it would be extremely unlikely to have this property of exact solvability,” Lacroix says. “But equations of this kind really do exist in nature.” Some describe the movement of waves propagating in a channel, for example, while others describe the behaviour of a hydrogen atom. “But it’s important to note that my work doesn’t have any practical applications of that kind,” Lacroix says. “I don’t examine concrete physical models; instead, I study mathematical structures and attempt to find general approaches that will allow us to construct new exactly solvable equations.” Although some of these formulas may eventually find a real-​world application, others probably won’t.

    After completing his doctoral thesis, Lacroix spent three years working as a postdoc at The University of Hamburg [Universität Hamburg](DE), before finally moving to Zürich in September 2021. “I don’t have a family, so I had no problem making the switch,” he says. He is relieved that he can now spend five years at the ITS as an Advanced Fellow and focus entirely on his research without having to worry about the future. He admits it was a pleasure getting to know different countries as a postdoc and that he enjoyed moving from place to place. “But it makes it very hard to have any kind of stability in your life.”

    A beautiful setting

    Lacroix spends most of his time working in his office at the ITS, which is located in a stately building dating from 1882 not far from the ETH Main Building. “It’s a lovely place,” he says, glancing out the window at the green surroundings and the city beyond. “I feel very much at home here. Living in Zürich is wonderful, it’s such a great feeling being here.” In his spare time, he likes watching movies, reading books and socialising. “I love meeting up with friends in restaurants or cafés,” he says. He also feels fortunate that he didn’t start working in Zürich until after the Covid measures had been relaxed.

    “I’m vaccinated and everyone’s very careful at ETH. We still have restrictions in place, but life is slowly getting back to normal – and that made it much easier to get to know my colleagues from day one,” he says. One of the greatest privileges of working at the ITS, Lacroix says, is that it offers an international environment that brings together researchers from all over the world. As well as offering a space for experts to exchange ideas and holding seminars where Fellows can present their work, the Institute also has a tradition of organising joint excursions. In the autumn of 2021, Lacroix joined his colleagues on a hike in the Flumserberg mountain resort for the first time: “I love hiking and it’s incredible to have the mountains so close.”

    Normally, however, he can be found sitting at his desk jotting down a series of mostly abstract equations on a sheet of paper. Occasionally his computer comes in handy, he says, because it has become so much more than just a calculating device; today’s computers can also handle abstract mathematical concepts, which can be very useful. Most people don’t really understand much of what Lacroix puts down on paper, but that doesn’t bother him: “I’ve learned to live with that,” he says; “I don’t feel isolated in my research at all – at least not in the academic sphere.”

    A better understanding of quantum field theory

    Integrable models are extremely symmetrical models, Lacroix explains. The basic principle of symmetry plays an important role in modern physics, for example in quantum field theory – the theoretical basis of particle physics – as well as in string theory, which scientists hope will eventually provide a unified description of particle physics and gravity. So could such an all-​encompassing unified field theory turn out to be an integrable model? “That would obviously be great, especially for me!” Lacroix says with a wry smile. “But it’s a bit optimistic to believe that whatever unified theory of physics finally emerges will have enough symmetries to make it completely exact.”

    Even if the equations he studies don’t explain the world directly, he still believes they can help us achieve a better understanding of theoretical physics. For example, we can take advantage of so-​called “toy models”, which have a particularly large number of symmetries, to simplify extremely complex equations in quantum field theory. “This gives us a better understanding of how the theory works, even if these models are too simplistic for the real world,” Lacroix says. Yet his primary interest lies in the purely mathematical questions that integrable models pose, and he admits that the equations they involve sometimes even appear in his dreams: “It’s hard to shake off what I’ve been thinking about the entire day. But I’ve never managed to solve a mathematical problem in my dreams – at least not so far!”

    See the full article here .


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    ETH Zurich campus

    The Swiss Federal Institute of Technology in Zürich [ETH Zürich] [Eidgenössische Technische Hochschule Zürich] (CH) is a public research university in the city of Zürich, Switzerland. Founded by the Swiss Federal Government in 1854 with the stated mission to educate engineers and scientists, the school focuses exclusively on science, technology, engineering and mathematics. Like its sister institution The Swiss Federal Institute of Technology in Lausanne [EPFL-École Polytechnique Fédérale de Lausanne](CH) , it is part of The Swiss Federal Institutes of Technology Domain (ETH Domain)) , part of the The Swiss Federal Department of Economic Affairs, Education and Research [EAER][Eidgenössisches Departement für Wirtschaft, Bildung und Forschung] [Département fédéral de l’économie, de la formation et de la recherche] (CH).

    The university is an attractive destination for international students thanks to low tuition fees of 809 CHF per semester, PhD and graduate salaries that are amongst the world’s highest, and a world-class reputation in academia and industry. There are currently 22,200 students from over 120 countries, of which 4,180 are pursuing doctoral degrees. In the 2021 edition of the QS World University Rankings ETH Zürich is ranked 6th in the world and 8th by the Times Higher Education World Rankings 2020. In the 2020 QS World University Rankings by subject it is ranked 4th in the world for engineering and technology (2nd in Europe) and 1st for earth & marine science.

    As of November 2019, 21 Nobel laureates, 2 Fields Medalists, 2 Pritzker Prize winners, and 1 Turing Award winner have been affiliated with the Institute, including Albert Einstein. Other notable alumni include John von Neumann and Santiago Calatrava. It is a founding member of the IDEA League and the International Alliance of Research Universities (IARU) and a member of the CESAER network.

    ETH Zürich was founded on 7 February 1854 by the Swiss Confederation and began giving its first lectures on 16 October 1855 as a polytechnic institute (eidgenössische polytechnische Schule) at various sites throughout the city of Zurich. It was initially composed of six faculties: architecture, civil engineering, mechanical engineering, chemistry, forestry, and an integrated department for the fields of mathematics, natural sciences, literature, and social and political sciences.

    It is locally still known as Polytechnikum, or simply as Poly, derived from the original name eidgenössische polytechnische Schule, which translates to “federal polytechnic school”.

    ETH Zürich is a federal institute (i.e., under direct administration by the Swiss government), whereas The University of Zürich [Universität Zürich ] (CH) is a cantonal institution. The decision for a new federal university was heavily disputed at the time; the liberals pressed for a “federal university”, while the conservative forces wanted all universities to remain under cantonal control, worried that the liberals would gain more political power than they already had. In the beginning, both universities were co-located in the buildings of the University of Zürich.

    From 1905 to 1908, under the presidency of Jérôme Franel, the course program of ETH Zürich was restructured to that of a real university and ETH Zürich was granted the right to award doctorates. In 1909 the first doctorates were awarded. In 1911, it was given its current name, Eidgenössische Technische Hochschule. In 1924, another reorganization structured the university in 12 departments. However, it now has 16 departments.

    ETH Zürich, EPFL (Swiss Federal Institute of Technology in Lausanne) [École polytechnique fédérale de Lausanne](CH), and four associated research institutes form The Domain of the Swiss Federal Institutes of Technology (ETH Domain) [ETH-Bereich; Domaine des Écoles polytechniques fédérales] (CH) with the aim of collaborating on scientific projects.

    Reputation and ranking

    ETH Zürich is ranked among the top universities in the world. Typically, popular rankings place the institution as the best university in continental Europe and ETH Zürich is consistently ranked among the top 1-5 universities in Europe, and among the top 3-10 best universities of the world.

    Historically, ETH Zürich has achieved its reputation particularly in the fields of chemistry, mathematics and physics. There are 32 Nobel laureates who are associated with ETH Zürich, the most recent of whom is Richard F. Heck, awarded the Nobel Prize in chemistry in 2010. Albert Einstein is perhaps its most famous alumnus.

    In 2018, the QS World University Rankings placed ETH Zürich at 7th overall in the world. In 2015, ETH Zürich was ranked 5th in the world in Engineering, Science and Technology, just behind the Massachusetts Institute of Technology(US), Stanford University(US) and University of Cambridge(UK). In 2015, ETH Zürich also ranked 6th in the world in Natural Sciences, and in 2016 ranked 1st in the world for Earth & Marine Sciences for the second consecutive year.

    In 2016, Times Higher Education World University Rankings ranked ETH Zürich 9th overall in the world and 8th in the world in the field of Engineering & Technology, just behind the Massachusetts Institute of Technology(US), Stanford University(US), California Institute of Technology(US), Princeton University(US), University of Cambridge(UK), Imperial College London(UK) and University of Oxford(UK) .

    In a comparison of Swiss universities by swissUP Ranking and in rankings published by CHE comparing the universities of German-speaking countries, ETH Zürich traditionally is ranked first in natural sciences, computer science and engineering sciences.

    In the survey CHE ExcellenceRanking on the quality of Western European graduate school programs in the fields of biology, chemistry, physics and mathematics, ETH Zürich was assessed as one of the three institutions to have excellent programs in all the considered fields, the other two being Imperial College London(UK) and The University of Cambridge(UK), respectively.

  • richardmitnick 12:13 pm on July 20, 2021 Permalink | Reply
    Tags: "A Video Tour of the Standard Model", , , , , Quantum field theory,   

    From Quanta Magazine (US) via Symmetry: “A Video Tour of the Standard Model” 

    From Quanta Magazine


    Symmetry Mag


    July 16, 2021
    Kevin Hartnett

    Standard Model of Particle Physics. Credit: Quanta Magazine.

    The Standard Model: The Most Successful Scientific Theory Ever.
    Video: The Standard Model of particle physics is the most successful scientific theory of all time. In this explainer, Cambridge University physicist David Tong recreates the model, piece by piece, to provide some intuition for how the fundamental building blocks of our universe fit together.
    Emily Buder/Quanta Magazine.
    Kristina Armitage and Rui Braz for Quanta Magazine.

    Recently, Quanta has explored the collaboration between physics and mathematics on one of the most important ideas in science: quantum field theory. The basic objects of a quantum field theory are quantum fields, which spread across the universe and, through their fluctuations, give rise to the most fundamental phenomena in the physical world. We’ve emphasized the unfinished business in both physics and mathematics — the ways in which physicists still don’t fully understand a theory they wield so effectively, and the grand rewards that await mathematicians if they can provide a full description of what quantum field theory actually is.

    This incompleteness, however, does not mean the work has been unsatisfying so far.

    For our final entry in this “Math Meets QFT” series, we’re exploring the most prominent quantum field theory of them all: the Standard Model. As the University of Cambridge (UK) physicist David Tong puts it in the accompanying video, it’s “the most successful scientific theory of all time” despite being saddled with a “rubbish name.”

    The Standard Model describes physics in the three spatial dimensions and one time dimension of our universe. It captures the interplay between a dozen quantum fields representing fundamental particles and a handful of additional fields representing forces. The Standard Model ties them all together into a single equation that scientists have confirmed countless times, often with astonishing accuracy. In the video, Professor Tong walks us through that equation term by term, introducing us to all the pieces of the theory and how they fit together. The Standard Model is complicated, but it is easier to work with than many other quantum field theories. That’s because sometimes the fields of the Standard Model interact with each other quite feebly, as writer Charlie Wood described in the second piece in our series.

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

    The Standard Model has been a boon for physics, but it’s also had a bit of a hangover effect. It’s been extraordinarily effective at explaining experiments we can do here on Earth, but it can’t account for several major features of the wider universe, including the action of gravity at short distances and the presence of dark matter and dark energy. Physicists would like to move beyond the Standard Model to an even more encompassing physical theory. But, as the physicist Davide Gaiotto put it in the first piece in our series, the glow of the Standard Model is so strong that it’s hard to see beyond it.

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

    And that, maybe, is where math comes in. Mathematicians will have to develop a fresh perspective on quantum field theory if they want to understand it in a self-consistent and rigorous way. There’s reason to hope that this new vantage will resolve many of the biggest open questions in physics.

    The process of bringing QFT into math may take some time — maybe even centuries, as the physicist Nathan Seiberg speculated in the third piece in our series — but it’s also already well underway. By now, math and quantum field theory have indisputably met. It remains to be seen what happens as they really get to know each other.

    From Quanta Magazine : “Nathan Seiberg on How Math Might Complete the Ultimate Physics 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 9:50 am on June 18, 2021 Permalink | Reply
    Tags: "Brookhaven Lab Intern Returns to Continue Theoretical Physics Pursuit", Co-design Center for Quantum Advantage (C2QA), DOE Science Undergraduate Laboratory Internships, National Quantum Information Science Research Centers, , , , Quantum field theory, , Wenjie Gong recently received a Barry Goldwater Scholarship., Women in STEM-Wenjie Gong   

    From DOE’s Brookhaven National Laboratory (US) : Women in STEM-Wenjie Gong “Brookhaven Lab Intern Returns to Continue Theoretical Physics Pursuit” 

    From DOE’s Brookhaven National Laboratory (US)

    June 14, 2021
    Kelly Zegers

    Wenjie Gong virtually visits Brookhaven for an internship to perform theory research on quantum information science in nuclear physics.

    Wenjie Gong, who recently received a Barry Goldwater Scholarship. (Courtesy photo.)

    Internships often help students nail down the direction they’d like to take their scientific pursuits. For Wenjie Gong, who just completed her junior year at Harvard University (US), a first look into theoretical physics last summer as an intern with the U.S. Department of Energy’s (DOE) Brookhaven National Laboratory made her want to dive further into the field.

    Gong returns to Brookhaven Lab this summer for her second experience as a virtual DOE Science Undergraduate Laboratory Internships (SULI) participant to continue collaborating with Raju Venugopalan, a senior physicist and Nuclear Theory Group leader. Together, they will explore the connections between nuclear physics theory—which explores the interactions of fundamental particles—and quantum computing.

    “I find theoretical physics fascinating as there are so many different avenues to explore and so many different angles from which to approach a problem,” Gong said. “Even though it can be difficult to parse through the technical underpinnings of different physical situations, any progress made is all the more exciting and rewarding.”

    Last year, Gong collaborated with Venugopalan on a project exploring possible ways to measure a quantum phenomenon known as “entanglement” in the matter produced at high-energy collisions.

    The physical properties of entangled particles are inextricably linked, even when the particles are separated by a great distance. Albert Einstein referred to entanglement as “spooky action at distance.”

    Studying this phenomenon is an important part of setting up long-distance quantum computing networks—the topic of many of the experiments at Co-design Center for Quantum Advantage (C2QA). The center led by Brookhaven Lab is one of five National Quantum Information Science Research Centers and applies quantum principles to materials, devices and software co-design efforts to lay the foundation for a new generation of quantum computers.

    “Usually, entanglement requires very precise measurements that are found in optics laboratories, but we wanted to look at how we could understand entanglement in high-energy particle collisions, which have much less of a controlled environment,” Gong said.

    Venugopalan said the motivation behind thinking of ways to detect entanglement in high-energy collisions is two-fold, first asking the question: “Can we think of experimental measures in collider experiments that have comparable ability to extract quantum action-at-a distance just as the carefully designed tabletop experiments?”

    “That would be interesting in itself because one might be inclined to think it unlikely,” he said.

    Venugopalan said scientists have identified sub-atomic particle correlations of so-called Lambda hyperons, which have particular properties that may allow such an experiment. Those experiments would open up the question of whether entanglement persists if scientists change the conditions of the collisions, he said.

    “If we made the collisions more violent, say, by increasing the number of particles produced, would the quantum action-at-a-distance correlation go away, just as you, and I, as macroscopic quantum states, don’t exhibit any spooky action-at-a-distance nonsense,” Venugopalan said. “When does such a quantum-to-classical transition take place?”

    In addition, can such measurements teach us about the nature of the interactions of the building blocks of matter–quarks and gluons?

    There may be more questions than answers at this stage, “but these questions force us to refine our experimental and computational tools,” Venugopalan said.

    Gong will continue collaborating with Venugopalan to develop the project on entanglement this summer. She may also start a new project exploring quirky features of soft particles in the quantum theory of electromagnetism that also apply to the strong force of nuclear physics, Venugopalan said. While her internship is virtual again this year, she said she learned last summer that collaborating remotely can be productive and rewarding.

    “Wenjie is the real deal,” Venugopalan said. “Even as a rising junior, she was functioning at the level of a postdoc. It’s a great joy to exchange ‘crazy’ ideas with her and work out the consequences. She shows great promise for an outstanding career in theoretical physics.”

    Others have noticed Gong’s scientific talent. She was recently honored with a Barry M. Goldwater Scholarship. The prestigious award supports impressive undergraduates who plan to pursue a PhD in the natural sciences, mathematics, and engineering.

    “I feel really honored and also very grateful to Raju, the Department of Energy (US) , and Brookhaven for providing me the opportunity to do this research—which I wrote about in my Goldwater essay,” Gong said.

    Gong said she’s looking forward to applying concepts from courses she took at Harvard over the past year, including quantum field theory, which she found challenging but also rewarding.

    Gong’s interest in physics started when she took Advanced Placement (AP) Physics in high school. The topic drew her in because it requires a way of thinking that’s different compared to other sciences because it explores the laws governing the motion of matter and existence, she said.

    In addition to further exploring high energy theoretical physics research, Gong said she hopes to one day teach as a university professor. She’s currently a peer tutor at Harvard.

    “I love teaching physics,” she said. “It’s really cool to see the ‘Ah-ha!’ moment when students go from not really understanding something to grasping a concept.”

    The SULI program at Brookhaven is managed by the Lab’s Office of Educational Programs and sponsored by DOE’s Office of Workforce Development for Teachers and Scientists (WDTS) within the Department’s Office of Science.

    See the full article here .


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    Stem Education Coalition

    One of ten national laboratories overseen and primarily funded by the DOE(US) Office of Science, DOE’s Brookhaven National Laboratory (US) conducts research in the physical, biomedical, and environmental sciences, as well as in energy technologies and national security. Brookhaven Lab also builds and operates major scientific facilities available to university, industry and government researchers. The Laboratory’s almost 3,000 scientists, engineers, and support staff are joined each year by more than 5,000 visiting researchers from around the world. Brookhaven is operated and managed for DOE’s Office of Science by Brookhaven Science Associates, a limited-liability company founded by Stony Brook University(US), the largest academic user of Laboratory facilities, and Battelle(US), a nonprofit, applied science and technology organization.

    Research at BNL specializes in nuclear and high energy physics, energy science and technology, environmental and bioscience, nanoscience and national security. The 5,300 acre campus contains several large research facilities, including the Relativistic Heavy Ion Collider [below] and National Synchrotron Light Source II [below]. Seven Nobel prizes have been awarded for work conducted at Brookhaven lab.

    BNL is staffed by approximately 2,750 scientists, engineers, technicians, and support personnel, and hosts 4,000 guest investigators every year. The laboratory has its own police station, fire department, and ZIP code (11973). In total, the lab spans a 5,265-acre (21 km^2) area that is mostly coterminous with the hamlet of Upton, New York. BNL is served by a rail spur operated as-needed by the New York and Atlantic Railway. Co-located with the laboratory is the Upton, New York, forecast office of the National Weather Service.

    Major programs

    Although originally conceived as a nuclear research facility, Brookhaven Lab’s mission has greatly expanded. Its foci are now:

    Nuclear and high-energy physics
    Physics and chemistry of materials
    Environmental and climate research
    Energy research
    Structural biology
    Accelerator physics


    Brookhaven National Lab was originally owned by the Atomic Energy Commission(US) and is now owned by that agency’s successor, the United States Department of Energy (DOE). DOE subcontracts the research and operation to universities and research organizations. It is currently operated by Brookhaven Science Associates LLC, which is an equal partnership of Stony Brook University(US) and Battelle Memorial Institute(US). From 1947 to 1998, it was operated by Associated Universities, Inc. (AUI) (US), but AUI lost its contract in the wake of two incidents: a 1994 fire at the facility’s high-beam flux reactor that exposed several workers to radiation and reports in 1997 of a tritium leak into the groundwater of the Long Island Central Pine Barrens on which the facility sits.


    Following World War II, the US Atomic Energy Commission was created to support government-sponsored peacetime research on atomic energy. The effort to build a nuclear reactor in the American northeast was fostered largely by physicists Isidor Isaac Rabi and Norman Foster Ramsey Jr., who during the war witnessed many of their colleagues at Columbia University leave for new remote research sites following the departure of the Manhattan Project from its campus. Their effort to house this reactor near New York City was rivalled by a similar effort at the Massachusetts Institute of Technology (US) to have a facility near Boston, Massachusettes(US). Involvement was quickly solicited from representatives of northeastern universities to the south and west of New York City such that this city would be at their geographic center. In March 1946 a nonprofit corporation was established that consisted of representatives from nine major research universities — Columbia University(US), Cornell University(US), Harvard University(US), Johns Hopkins University(US), Massachusetts Institute of Technology(US), Princeton University(US), University of Pennsylvania(US), University of Rochester(US), and Yale University(US).

    Out of 17 considered sites in the Boston-Washington corridor, Camp Upton on Long Island was eventually chosen as the most suitable in consideration of space, transportation, and availability. The camp had been a training center from the US Army during both World War I and World War II. After the latter war, Camp Upton was deemed no longer necessary and became available for reuse. A plan was conceived to convert the military camp into a research facility.

    On March 21, 1947, the Camp Upton site was officially transferred from the U.S. War Department to the new U.S. Atomic Energy Commission (AEC), predecessor to the U.S. Department of Energy (DOE).

    Research and facilities

    Reactor history

    In 1947 construction began on the first nuclear reactor at Brookhaven, the Brookhaven Graphite Research Reactor. This reactor, which opened in 1950, was the first reactor to be constructed in the United States after World War II. The High Flux Beam Reactor operated from 1965 to 1999. In 1959 Brookhaven built the first US reactor specifically tailored to medical research, the Brookhaven Medical Research Reactor, which operated until 2000.

    Accelerator history

    In 1952 Brookhaven began using its first particle accelerator, the Cosmotron. At the time the Cosmotron was the world’s highest energy accelerator, being the first to impart more than 1 GeV of energy to a particle.

    The Cosmotron was retired in 1966, after it was superseded in 1960 by the new Alternating Gradient Synchrotron (AGS).

    The AGS was used in research that resulted in 3 Nobel prizes, including the discovery of the muon neutrino, the charm quark, and CP violation.

    In 1970 in BNL started the ISABELLE project to develop and build two proton intersecting storage rings.

    The groundbreaking for the project was in October 1978. In 1981, with the tunnel for the accelerator already excavated, problems with the superconducting magnets needed for the ISABELLE accelerator brought the project to a halt, and the project was eventually cancelled in 1983.

    The National Synchrotron Light Source (US) operated from 1982 to 2014 and was involved with two Nobel Prize-winning discoveries. It has since been replaced by the National Synchrotron Light Source II (US) [below].

    After ISABELLE’S cancellation, physicist at BNL proposed that the excavated tunnel and parts of the magnet assembly be used in another accelerator. In 1984 the first proposal for the accelerator now known as the Relativistic Heavy Ion Collider (RHIC)[below] was put forward. The construction got funded in 1991 and RHIC has been operational since 2000. One of the world’s only two operating heavy-ion colliders, RHIC is as of 2010 the second-highest-energy collider after the Large Hadron Collider(CH). RHIC is housed in a tunnel 2.4 miles (3.9 km) long and is visible from space.

    On January 9, 2020, It was announced by Paul Dabbar, undersecretary of the US Department of Energy Office of Science, that the BNL eRHIC design has been selected over the conceptual design put forward by DOE’s Thomas Jefferson National Accelerator Facility [Jlab] (US) as the future Electron–ion collider (EIC) in the United States.

    In addition to the site selection, it was announced that the BNL EIC had acquired CD-0 (mission need) from the Department of Energy. BNL’s eRHIC design proposes upgrading the existing Relativistic Heavy Ion Collider, which collides beams light to heavy ions including polarized protons, with a polarized electron facility, to be housed in the same tunnel.

    Other discoveries

    In 1958, Brookhaven scientists created one of the world’s first video games, Tennis for Two. In 1968 Brookhaven scientists patented Maglev, a transportation technology that utilizes magnetic levitation.

    Major facilities

    Relativistic Heavy Ion Collider (RHIC), which was designed to research quark–gluon plasma and the sources of proton spin. Until 2009 it was the world’s most powerful heavy ion collider. It is the only collider of spin-polarized protons.
    Center for Functional Nanomaterials (CFN), used for the study of nanoscale materials.
    BNL National Synchrotron Light Source II(US), Brookhaven’s newest user facility, opened in 2015 to replace the National Synchrotron Light Source (NSLS), which had operated for 30 years.[19] NSLS was involved in the work that won the 2003 and 2009 Nobel Prize in Chemistry.
    Alternating Gradient Synchrotron, a particle accelerator that was used in three of the lab’s Nobel prizes.
    Accelerator Test Facility, generates, accelerates and monitors particle beams.
    Tandem Van de Graaff, once the world’s largest electrostatic accelerator.
    Computational Science resources, including access to a massively parallel Blue Gene series supercomputer that is among the fastest in the world for scientific research, run jointly by Brookhaven National Laboratory and Stony Brook University.
    Interdisciplinary Science Building, with unique laboratories for studying high-temperature superconductors and other materials important for addressing energy challenges.
    NASA Space Radiation Laboratory, where scientists use beams of ions to simulate cosmic rays and assess the risks of space radiation to human space travelers and equipment.

    Off-site contributions

    It is a contributing partner to ATLAS experiment, one of the four detectors located at the Large Hadron Collider (LHC).

    It is currently operating at CERN near Geneva, Switzerland.

    Brookhaven was also responsible for the design of the SNS accumulator ring in partnership with Spallation Neutron Source at DOE’s Oak Ridge National Laboratory (US), Tennessee.

    Brookhaven plays a role in a range of neutrino research projects around the world, including the Daya Bay Neutrino Experiment (CN) nuclear power plant, approximately 52 kilometers northeast of Hong Kong and 45 kilometers east of Shenzhen, China.

  • 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., , Quantum field theory, 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

    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.


    “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.”


    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.


    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 .


    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 10:54 am on July 27, 2019 Permalink | Reply
    Tags: "Ask Ethan: Can We Really Get A Universe From Nothing?", , , , , Because dark energy is a property of space itself when the Universe expands the dark energy density must remain constant., , , , , Galaxies that are gravitationally bound will merge together into groups and clusters while the unbound groups and clusters will accelerate away from one another., , , Negative gravity?, , Quantum field theory   

    From Ethan Siegel: “Ask Ethan: Can We Really Get A Universe From Nothing?” 

    From Ethan Siegel
    July 27, 2019

    Our entire cosmic history is theoretically well-understood in terms of the frameworks and rules that govern it. It’s only by observationally confirming and revealing various stages in our Universe’s past that must have occurred, like when the first stars and galaxies formed, and how the Universe expanded over time, that we can truly come to understand what makes up our Universe and how it expands and gravitates in a quantitative fashion. The relic signatures imprinted on our Universe from an inflationary state before the hot Big Bang give us a unique way to test our cosmic history, subject to the same fundamental limitations that all frameworks possess. (NICOLE RAGER FULLER / NATIONAL SCIENCE FOUNDATION)

    And does it require the idea of ‘negative gravity’ in order to work?

    The biggest question that we’re even capable of asking, with our present knowledge and understanding of the Universe, is where did everything we can observe come from? If it came from some sort of pre-existing state, we’ll want to know exactly what that state was like and how our Universe came from it. If it emerged out of nothingness, we’d want to know how we went from nothing to the entire Universe, and what if anything caused it. At least, that’s what our Patreon supporter Charles Buchanan wants to know, asking:

    “One concept bothers me. Perhaps you can help. I see it in used many places, but never really explained. “A universe from Nothing” and the concept of negative gravity. As I learned my Newtonian physics, you could put the zero point of the gravitational potential anywhere, only differences mattered. However Newtonian physics never deals with situations where matter is created… Can you help solidify this for me, preferably on [a] conceptual level, maybe with a little calculation detail?”

    Gravitation might seem like a straightforward force, but an incredible number of aspects are anything but intuitive. Let’s take a deeper look.

    Countless scientific tests of Einstein’s general theory of relativity have been performed, subjecting the idea to some of the most stringent constraints ever obtained by humanity. Einstein’s first solution was for the weak-field limit around a single mass, like the Sun; he applied these results to our Solar System with dramatic success. We can view this orbit as Earth (or any planet) being in free-fall around the Sun, traveling in a straight-line path in its own frame of reference. All masses and all sources of energy contribute to the curvature of spacetime. (LIGO SCIENTIFIC COLLABORATION / T. PYLE / CALTECH / MIT)

    MIT /Caltech Advanced aLigo

    VIRGO Gravitational Wave interferometer, near Pisa, Italy

    Caltech/MIT Advanced aLigo Hanford, WA, USA installation

    Caltech/MIT Advanced aLigo detector installation Livingston, LA, USA

    LSC LIGO Scientific Collaboration

    Cornell SXS, the Simulating eXtreme Spacetimes (SXS) project

    Gravitational waves. Credit: MPI for Gravitational Physics/W.Benger

    Gravity is talking. Lisa will listen. Dialogos of Eide

    ESA/eLISA the future of gravitational wave research

    Localizations of gravitational-wave signals detected by LIGO in 2015 (GW150914, LVT151012, GW151226, GW170104), more recently, by the LIGO-Virgo network (GW170814, GW170817). After Virgo came online in August 2018

    Skymap showing how adding Virgo to LIGO helps in reducing the size of the source-likely region in the sky. (Credit: Giuseppe Greco (Virgo Urbino group)

    If you have two point masses located some distance apart in your Universe, they’ll experience an attractive force that compels them to gravitate towards one another. But this attractive force that you perceive, in the context of relativity, comes with two caveats.

    The first caveat is simple and straightforward: these two masses will experience an acceleration towards one another, but whether they wind up moving closer to one another or not is entirely dependent on how the space between them evolves. Unlike in Newtonian gravity, where space is a fixed quantity and only the masses within that space can evolve, everything is changeable in General Relativity. Not only does matter and energy move and accelerate due to gravitation, but the very fabric of space itself can expand, contract, or otherwise flow. All masses still move through space, but space itself is no longer stationary.

    The ‘raisin bread’ model of the expanding Universe, where relative distances increase as the space (dough) expands. The farther away any two raisin are from one another, the greater the observed redshift will be by time the light is received. The redshift-distance relation predicted by the expanding Universe is borne out in observations, and has been consistent with what’s been known going all the way back to the 1920s. (NASA / WMAP SCIENCE TEAM)

    NASA/WMAP 2001 to 2010

    The second caveat is that the two masses you’re considering, even if you’re extremely careful about accounting for what’s in your Universe, are most likely not the only forms of energy around. There are bound to be other masses in the form of normal matter, dark matter, and neutrinos. There’s the presence of radiation, from both electromagnetic and gravitational waves. There’s even dark energy: a type of energy inherent to the fabric of space itself.

    Now, here’s a scenario that might exemplify where your intuition leads you astray: what happens if these masses, for the volume they occupy, have less total energy than the average energy density of the surrounding space?

    The gravitational attraction (blue) of overdense regions and the relative repulsion (red) of the underdense regions, as they act on the Milky Way. Even though gravity is always attractive, there is an average amount of attraction throughout the Universe, and regions with lower energy densities than that will experience (and cause) an effective repulsion with respect to the average. (YEHUDA HOFFMAN, DANIEL POMARÈDE, R. BRENT TULLY, AND HÉLÈNE COURTOIS, NATURE ASTRONOMY 1, 0036 (2017))

    You can imagine three different scenarios:

    1.The first mass has a below-average energy density while the second has an above-average value.
    2.The first mass has an above-average energy density while the second has a below-average value.
    3.Both the first and second masses have a below-average energy density compared to the rest of space.

    In the first two scenarios, the above-average mass will begin growing as it pulls on the matter/energy all around it, while the below-average mass will start shrinking, as it’s less able to hold onto its own mass in the face of its surroundings. These two masses will effectively repel one another; even though gravitation is always attractive, the intervening matter is preferentially attracted to the heavier-than-average mass. This causes the lower-mass object to act like it’s both repelling and being repelled by the heavier-mass object, the same way a balloon held underwater will still be attracted to Earth’s center, but will be forced away from it owing to the (buoyant) effects of the water.

    The Earth’s crust is thinnest over the ocean and thickest over mountains and plateaus, as the principle of buoyancy dictates and as gravitational experiments confirm. Just as a balloon submerged in water will accelerate away from the center of the Earth, a region with below-average energy density will accelerate away from an overdense region, as average-density regions will be more preferentially attracted to the overdense region than the underdense region will. (USGS)

    So what’s going to happen if you have two regions of space with below-average densities, surrounded by regions of just average density? They’ll both shrink, giving up their remaining matter to the denser regions around them. But as far as motions go, they’ll accelerate towards one another, with exactly the same magnitude they’d accelerate at if they were both overdense regions that exceeded the average density by equivalent amounts.

    You might be wondering why it’s important to think about these concerns when talking about a Universe from nothing. After all, if your Universe is full of matter and energy, it’s pretty hard to understand how that’s relevant to making sense of the concept of something coming from nothing. But just as our intuition can lead us astray when thinking about matter and energy on the spacetime playing field of General Relativity, it’s a comparable situation when we think about nothingness.

    A representation of flat, empty space with no matter, energy or curvature of any type. With the exception of small quantum fluctuations, space in an inflationary Universe becomes incredibly flat like this, except in a 3D grid rather than a 2D sheet. Space is stretched flat, and particles are rapidly driven away. (AMBER STUVER / LIVING LIGO)

    You very likely think about nothingness as a philosopher would: the complete absence of everything. Zero matter, zero energy, an absolutely zero value for all the quantum fields in the Universe, etc. You think of space that’s completely flat, with nothing around to cause its curvature anywhere.

    If you think this way, you’re not alone: there are many different ways to conceive of “nothing.” You might even be tempted to take away space, time, and the laws of physics themselves, too. The problem, if you start doing that, is that you lose your ability to predict anything at all. The type of nothingness you’re thinking about, in this context, is what we call unphysical.

    If we want to think about nothing in a physical sense, you have to keep certain things. You need spacetime and the laws of physics, for example; you cannot have a Universe without them.

    A visualization of QCD illustrates how particle/antiparticle pairs pop out of the quantum vacuum for very small amounts of time as a consequence of Heisenberg uncertainty.

    The quantum vacuum is interesting because it demands that empty space itself isn’t so empty, but is filled with all the particles, antiparticles and fields in various states that are demanded by the quantum field theory that describes our Universe. Put this all together, and you find that empty space has a zero-point energy that’s actually greater than zero. (DEREK B. LEINWEBER)

    But here’s the kicker: if you have spacetime and the laws of physics, then by definition you have quantum fields permeating the Universe everywhere you go. You have a fundamental “jitter” to the energy inherent to space, due to the quantum nature of the Universe. (And the Heisenberg uncertainty principle, which is unavoidable.)

    Put these ingredients together — because you can’t have a physically sensible “nothing” without them — and you’ll find that space itself doesn’t have zero energy inherent to it, but energy with a finite, non-zero value. Just as there’s a finite zero-point energy (that’s greater than zero) for an electron bound to an atom, the same is true for space itself. Empty space, even with zero curvature, even devoid of particles and external fields, still has a finite energy density to it.

    The four possible fates of the Universe with only matter, radiation, curvature and a cosmological constant allowed. The top three possibilities are for a Universe whose fate is determined by the balance of matter/radiation with spatial curvature alone; the bottom one includes dark energy. Only the bottom “fate” aligns with the evidence. (E. SIEGEL / BEYOND THE GALAXY)

    From the perspective of quantum field theory, this is conceptualized as the zero-point energy of the quantum vacuum: the lowest-energy state of empty space. In the framework of General Relativity, however, it appears in a different sense: as the value of a cosmological constant, which itself is the energy of empty space, independent of curvature or any other form of energy density.

    Although we do not know how to calculate the value of this energy density from first principles, we can calculate the effects it has on the expanding Universe. As your Universe expands, every form of energy that exists within it contributes to not only how your Universe expands, but how that expansion rate changes over time. From multiple independent lines of evidence — including the Universe’s large-scale structure, the cosmic microwave background, and distant supernovae — we have been able to determine how much energy is inherent to space itself.

    Constraints on dark energy from three independent sources: supernovae, the CMB (cosmic microwave background) and BAO (which is a wiggly feature seen in the correlations of large-scale structure). Note that even without supernovae, we’d need dark energy for certain, and also that there are uncertainties and degeneracies between the amount of dark matter and dark energy that we’d need to accurately describe our Universe. (SUPERNOVA COSMOLOGY PROJECT, AMANULLAH, ET AL., AP.J. (2010))

    This form of energy is what we presently call dark energy, and it’s responsible for the observed accelerated expansion of the Universe. Although it’s been a part of our conceptions of reality for more than two decades now, we don’t fully understand its true nature. All we can say is that when we measure the expansion rate of the Universe, our observations are consistent with dark energy being a cosmological constant with a specific magnitude, and not with any of the alternatives that evolve significantly over cosmic time.

    Because dark energy causes distant galaxies to appear to recede from one another more and more quickly as time goes on — since the space between those galaxies is expanding — it’s often called negative gravity. This is not only highly informal, but incorrect. Gravity is only positive, never negative. But even positive gravity, as we saw earlier, can have effects that look very much like negative repulsion.

    Dark Energy Survey

    Dark Energy Camera [DECam], built at FNAL

    NOAO/CTIO Victor M Blanco 4m Telescope which houses the DECam at Cerro Tololo, Chile, housing DECam at an altitude of 7200 feet

    Timeline of the Inflationary Universe WMAP

    The Dark Energy Survey (DES) is an international, collaborative effort to map hundreds of millions of galaxies, detect thousands of supernovae, and find patterns of cosmic structure that will reveal the nature of the mysterious dark energy that is accelerating the expansion of our Universe. DES began searching the Southern skies on August 31, 2013.

    According to Einstein’s theory of General Relativity, gravity should lead to a slowing of the cosmic expansion. Yet, in 1998, two teams of astronomers studying distant supernovae made the remarkable discovery that the expansion of the universe is speeding up. To explain cosmic acceleration, cosmologists are faced with two possibilities: either 70% of the universe exists in an exotic form, now called dark energy, that exhibits a gravitational force opposite to the attractive gravity of ordinary matter, or General Relativity must be replaced by a new theory of gravity on cosmic scales.

    DES is designed to probe the origin of the accelerating universe and help uncover the nature of dark energy by measuring the 14-billion-year history of cosmic expansion with high precision. More than 400 scientists from over 25 institutions in the United States, Spain, the United Kingdom, Brazil, Germany, Switzerland, and Australia are working on the project. The collaboration built and is using an extremely sensitive 570-Megapixel digital camera, DECam, mounted on the Blanco 4-meter telescope at Cerro Tololo Inter-American Observatory, high in the Chilean Andes, to carry out the project.

    Over six years (2013-2019), the DES collaboration used 758 nights of observation to carry out a deep, wide-area survey to record information from 300 million galaxies that are billions of light-years from Earth. The survey imaged 5000 square degrees of the southern sky in five optical filters to obtain detailed information about each galaxy. A fraction of the survey time is used to observe smaller patches of sky roughly once a week to discover and study thousands of supernovae and other astrophysical transients.

    How energy density changes over time in a Universe dominated by matter (top), radiation (middle), and a cosmological constant (bottom). Note that dark energy doesn’t change in density as the Universe expands, which is why it comes to dominate the Universe at late times. (E. SIEGEL)

    If there were greater amounts of dark energy present within our spatially flat Universe, the expansion rate would be greater. But this is true for all forms of energy in a spatially flat Universe: dark energy is no exception. The only different between dark energy and the more commonly encountered forms of energy, like matter and radiation, is that as the Universe expands, the densities of matter and radiation decrease.

    But because dark energy is a property of space itself, when the Universe expands, the dark energy density must remain constant. As time goes on, galaxies that are gravitationally bound will merge together into groups and clusters, while the unbound groups and clusters will accelerate away from one another. That’s the ultimate fate of the Universe if dark energy is real.

    Laniakea supercluster. From Nature The Laniakea supercluster of galaxies R. Brent Tully, Hélène Courtois, Yehuda Hoffman & Daniel Pomarède at http://www.nature.com/nature/journal/v513/n7516/full/nature13674.html. Milky Way is the red dot.

    So why do we say we have a Universe that came from nothing? Because the value of dark energy may have been much higher in the distant past: before the hot Big Bang. A Universe with a very large amount of dark energy in it will behave identically to a Universe undergoing cosmic inflation. In order for inflation to end, that energy has to get converted into matter and radiation. The evidence strongly points to that happening some 13.8 billion years ago.

    When it did, though, a small amount of dark energy remained behind. Why? Because the zero-point energy of the quantum fields in our Universe isn’t zero, but a finite, greater-than-zero value. Our intuition may not be reliable when we consider the physical concepts of nothing and negative/positive gravity, but that’s why we have science. When we do it right, we wind up with physical theories that accurately describe the Universe we measure and observe.

    See the full article here .


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    “Starts With A Bang! is a blog/video blog about cosmology, physics, astronomy, and anything else I find interesting enough to write about. I am a firm believer that the highest good in life is learning, and the greatest evil is willful ignorance. The goal of everything on this site is to help inform you about our world, how we came to be here, and to understand how it all works. As I write these pages for you, I hope to not only explain to you what we know, think, and believe, but how we know it, and why we draw the conclusions we do. It is my hope that you find this interesting, informative, and accessible,” says Ethan

  • richardmitnick 8:41 am on June 5, 2019 Permalink | Reply
    Tags: "Stanford joins collaboration to explore 'ultra-quantum matter'", , , Quantum field theory, , The Simons Collaboration on Ultra-Quantum Matter   

    From Stanford University: “Stanford joins collaboration to explore ‘ultra-quantum matter'” 

    Stanford University Name
    From Stanford University

    June 3, 2019
    Ker Than


    The Simons Collaboration on Ultra-Quantum Matter brings together physicists from 12 institutions to “understand, classify and realize” new forms of ultra-quantum matter in the lab.

    Stanford physicist Shamit Kachru is a member of a new collaboration that aims to unravel the mystery of entangled quantum matter — macroscopic assemblages of atoms and electrons that seem to share the same seemingly telepathic link as entangled subatomic particles.

    The Simons Collaboration on Ultra-Quantum Matter is funded by the Simons Foundation and led by Harvard physics Professor Ashvin Vishwanath. It is part of the Simons Collaborations in Mathematics and Physical Sciences program, which aims to “stimulate progress on fundamental scientific questions of major importance in mathematics, theoretical physics and theoretical computer science.” The Simons Collaboration on Ultra-Quantum Matter will be one of 12 such collaborations ranging across these fields.

    Ultra-quantum matter, or UQM, exhibit non-intuitive quantum properties that were once thought to arise only in very small systems. One key property is “non-local entanglement,” in which two physically separated groups of atoms can share joint properties, so that measuring one affects the measurement outcome of the other. UQM should exhibit entirely new physical properties, a better understanding of which could lead to new types of quantum information storage systems and quantum materials.

    The Simons Collaboration on Ultra-Quantum Matter brings together physicists from 12 institutions to “understand, classify and realize” new forms of ultra-quantum matter in the lab. To achieve this, the collaboration includes physicists working in different domains, including condensed matter and high energy theorists, as well as atomic and quantum information experts. Kachru’s own background is in string theory, theoretical cosmology, and condensed matter physics.

    A confluence of factors makes this a particularly exciting time to study UQM, said Kachru, who is the Wells Family Director of the Stanford Institute for Theoretical Physics (SITP) and the chair of the physics department.

    “Many of the cutting-edge questions in quantum field theory now seem to involve highly quantum condensed matter systems,” Kachru said. “These systems are often best studied using elegant and clean mathematical techniques, and there is a promise of genuine contact between high level theory and experiment. I can’t imagine better people to teach me about issues and opportunities here than the collaboration members, who are leading experts in all aspects of UQM.”

    Kachru also looks forward to working again with former Stanford graduate student and collaboration member, John McGreevy, who was Kachru’s first PhD advisee and is now a professor of physics at the University of California, San Diego.

    Ultra-Quantum Matter is an $8M four-year award funded by the Simons Foundation and renewable for three additional years. It will support researchers from the following institutions: Caltech, Harvard, the Institute for Advanced Study, MIT, Stanford, University of California Santa Barbara, University of California San Diego, the University of Chicago, the University of Colorado Boulder, the University of Innsbruck, University of Maryland and University of Washington.

    A UQM meeting of the new collaboration is scheduled to take place at Stanford in May of 2020.

    See the full article here .

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    Stanford University campus. No image credit

    Stanford University

    Leland and Jane Stanford founded the University to “promote the public welfare by exercising an influence on behalf of humanity and civilization.” Stanford opened its doors in 1891, and more than a century later, it remains dedicated to finding solutions to the great challenges of the day and to preparing our students for leadership in today’s complex world. Stanford, is an American private research university located in Stanford, California on an 8,180-acre (3,310 ha) campus near Palo Alto. Since 1952, more than 54 Stanford faculty, staff, and alumni have won the Nobel Prize, including 19 current faculty members

    Stanford University Seal

  • richardmitnick 7:14 am on March 20, 2018 Permalink | Reply
    Tags: , , , , Cosmological-constant problem, , , In 1998 astronomers discovered that the expansion of the cosmos is in fact gradually accelerating, , , Quantum field theory, , Saul Perlmutter UC Berkeley Nobel laureate, , Why Does the Universe Need to Be So Empty?, Zero-point energy of the field   

    From The Atlantic Magazine and Quanta: “Why Does the Universe Need to Be So Empty?” 

    Quanta Magazine
    Quanta Magazine

    Atlantic Magazine

    The Atlantic Magazine

    Mar 19, 2018
    Natalie Wolchover

    Physicists have long grappled with the perplexingly small weight of empty space.

    The controversial idea that our universe is just a random bubble in an endless, frothing multiverse arises logically from nature’s most innocuous-seeming feature: empty space. Specifically, the seed of the multiverse hypothesis is the inexplicably tiny amount of energy infused in empty space—energy known as the vacuum energy, dark energy, or the cosmological constant. Each cubic meter of empty space contains only enough of this energy to light a light bulb for 11 trillionths of a second. “The bone in our throat,” as the Nobel laureate Steven Weinberg once put it [http://hetdex.org/dark_energy.html
    ], is that the vacuum ought to be at least a trillion trillion trillion trillion trillion times more energetic, because of all the matter and force fields coursing through it.


    Somehow the effects of all these fields on the vacuum almost equalize, producing placid stillness. Why is empty space so empty?

    While we don’t know the answer to this question—the infamous “cosmological-constant problem”—the extreme vacuity of our vacuum appears necessary for our existence. In a universe imbued with even slightly more of this gravitationally repulsive energy, space would expand too quickly for structures like galaxies, planets, or people to form. This fine-tuned situation suggests that there might be a huge number of universes, all with different doses of vacuum energy, and that we happen to inhabit an extraordinarily low-energy universe because we couldn’t possibly find ourselves anywhere else.

    Some scientists bristle at the tautology of “anthropic reasoning” and dislike the multiverse for being untestable. Even those open to the multiverse idea would love to have alternative solutions to the cosmological constant problem to explore. But so far it has proved nearly impossible to solve without a multiverse. “The problem of dark energy [is] so thorny, so difficult, that people have not got one or two solutions,” says Raman Sundrum, a theoretical physicist at the University of Maryland.

    To understand why, consider what the vacuum energy actually is. Albert Einstein’s general theory of relativity says that matter and energy tell space-time how to curve, and space-time curvature tells matter and energy how to move. An automatic feature of the equations is that space-time can possess its own energy—the constant amount that remains when nothing else is there, which Einstein dubbed the cosmological constant. For decades, cosmologists assumed its value was exactly zero, given the universe’s reasonably steady rate of expansion, and they wondered why. But then, in 1998, astronomers discovered that the expansion of the cosmos is in fact gradually accelerating, implying the presence of a repulsive energy permeating space. Dubbed dark energy by the astronomers, it’s almost certainly equivalent to Einstein’s cosmological constant. Its presence causes the cosmos to expand ever more quickly, since, as it expands, new space forms, and the total amount of repulsive energy in the cosmos increases.

    However, the inferred density of this vacuum energy contradicts what quantum-field theory, the language of particle physics, has to say about empty space. A quantum field is empty when there are no particle excitations rippling through it. But because of the uncertainty principle in quantum physics, the state of a quantum field is never certain, so its energy can never be exactly zero. Think of a quantum field as consisting of little springs at each point in space. The springs are always wiggling, because they’re only ever within some uncertain range of their most relaxed length. They’re always a bit too compressed or stretched, and therefore always in motion, possessing energy. This is called the zero-point energy of the field. Force fields have positive zero-point energies while matter fields have negative ones, and these energies add to and subtract from the total energy of the vacuum.

    The total vacuum energy should roughly equal the largest of these contributing factors. (Say you receive a gift of $10,000; even after spending $100, or finding $3 in the couch, you’ll still have about $10,000.) Yet the observed rate of cosmic expansion indicates that its value is between 60 and 120 orders of magnitude smaller than some of the zero-point energy contributions to it, as if all the different positive and negative terms have somehow canceled out. Coming up with a physical mechanism for this equalization is extremely difficult for two main reasons.

    First, the vacuum energy’s only effect is gravitational, and so dialing it down would seem to require a gravitational mechanism. But in the universe’s first few moments, when such a mechanism might have operated, the universe was so physically small that its total vacuum energy was negligible compared to the amount of matter and radiation. The gravitational effect of the vacuum energy would have been completely dwarfed by the gravity of everything else. “This is one of the greatest difficulties in solving the cosmological-constant problem,” the physicist Raphael Bousso wrote in 2007. A gravitational feedback mechanism precisely adjusting the vacuum energy amid the conditions of the early universe, he said, “can be roughly compared to an airplane following a prescribed flight path to atomic precision, in a storm.”

    Compounding the difficulty, quantum-field theory calculations indicate that the vacuum energy would have shifted in value in response to phase changes in the cooling universe shortly after the Big Bang. This raises the question of whether the hypothetical mechanism that equalized the vacuum energy kicked in before or after these shifts took place. And how could the mechanism know how big their effects would be, to compensate for them?

    So far, these obstacles have thwarted attempts to explain the tiny weight of empty space without resorting to a multiverse lottery. But recently, some researchers have been exploring one possible avenue: If the universe did not bang into existence, but bounced instead, following an earlier contraction phase, then the contracting universe in the distant past would have been huge and dominated by vacuum energy. Perhaps some gravitational mechanism could have acted on the plentiful vacuum energy then, diluting it in a natural way over time. This idea motivated the physicists Peter Graham, David Kaplan, and Surjeet Rajendran to discover a new cosmic bounce model, though they’ve yet to show how the vacuum dilution in the contracting universe might have worked.

    In an email, Bousso called their approach “a very worthy attempt” and “an informed and honest struggle with a significant problem.” But he added that huge gaps in the model remain, and “the technical obstacles to filling in these gaps and making it work are significant. The construction is already a Rube Goldberg machine, and it will at best get even more convoluted by the time these gaps are filled.” He and other multiverse adherents see their answer as simpler by comparison.

    See the full article here .

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  • richardmitnick 4:49 pm on July 1, 2017 Permalink | Reply
    Tags: , , Quantum field theory   

    From PBS: Quantum Field Theory 

    Quantum Field Theory

    Watch for Don Lincoln of FNAL

    Watch, enjoy learn.

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  • richardmitnick 4:58 pm on August 1, 2016 Permalink | Reply
    Tags: , , Quantum field theory   

    From PPPL via Princeton Journal Watch: “PPPL researchers combine quantum mechanics and Einstein’s theory of special relativity to clear up puzzles in plasma physics (Phys. Rev. A)” 

    Princeton University
    Princeton University

    PPPL Large

    Princeton Plasma Physics Laboratory

    August 1, 2016
    John Greenwald

    Sketch of a pulsar, center, in binary star system (Photo credit: NASA Goddard Space Flight Center)

    Among the intriguing issues in plasma physics are those surrounding X-ray pulsars — collapsed stars that orbit around a cosmic companion and beam light at regular intervals, like lighthouses in the sky. Physicists want to know the strength of the magnetic field and density of the plasma that surrounds these pulsars, which can be millions of times greater than the density of plasma in stars like the sun.

    Researchers at the U.S. Department of Energy’s (DOE) Princeton Plasma Physics Laboratory (PPPL) have developed a theory of plasma waves that can infer these properties in greater detail than in standard approaches. The new research analyzes the plasma surrounding the pulsar by coupling Einstein’s theory of relativity with quantum mechanics, which describes the motion of subatomic particles such as the atomic nuclei — or ions — and electrons in plasma. Supporting this work is the DOE Office of Science.

    Quantum field theory

    The key insight comes from quantum field theory, which describes charged particles that are relativistic, meaning that they travel at near the speed of light. “Quantum theory can describe certain details of the propagation of waves in plasma,” said Yuan Shi, a graduate student at Princeton University in the Department of Astrophysics’ Princeton Program in Plasma Physics, and lead author of a paper published July 29 in the journal Physical Review A. Understanding the interactions behind the propagation can then reveal the composition of the plasma.

    Shi developed the paper with assistance from co-authors Nathaniel Fisch, director of the Princeton Program in Plasma Physics and professor and associate chair of astrophysical sciences at Princeton University, and Hong Qin, a physicist at PPPL and executive dean of the School of Nuclear Science and Technology at the University of Science and Technology of China. “When I worked out the mathematics they showed me how to apply it,” said Shi.

    In pulsars, relativistic particles in the magnetosphere, which is the magnetized atmosphere surrounding the pulsar, absorb light waves, and this absorption displays peaks. “The question is, what do these peaks mean?” asks Shi. Analysis of the peaks with equations from special relativity and quantum field theory, he found, can determine the density and field strength of the magnetosphere.

    Combining physics techniques

    The process combines the techniques of high-energy physics, condensed matter physics, and plasma physics. In high-energy physics, researchers use quantum field theory to describe the interaction of a handful of particles. In condensed matter physics, people use quantum mechanics to describe the states of a large collection of particles. Plasma physics uses model equations to explain the collective movement of millions of particles. The new method utilizes aspects of all three techniques to analyze the plasma waves in pulsars.

    The same technique can be used to infer the density of the plasma and strength of the magnetic field created by inertial confinement fusion experiments. Such experiments use lasers to ablate — or vaporize —a target that contains plasma fuel. The ablation then causes an implosion that compresses the fuel into plasma and produces fusion reactions.

    Standard formulas give inconsistent answers

    Researchers want to know the precise density, temperature and field strength of the plasma that this process creates. Standard mathematical formulas give inconsistent answers when lasers of different color are used to measure the plasma parameters. This is because the extreme density of the plasma gives rise to quantum effects, while the high energy density of the magnetic field gives rise to relativistic effects, says Shi. So formulations that draw upon both fields are needed to reconcile the results.

    For Shi, the new technique shows the benefits of combining physics disciplines that don’t often interact. Says he: “Putting fields together gives tremendous power to explain things that we couldn’t understand before.”

    Yuan Shi, Nathaniel J. Fisch, and Hong Qin. Effective-action approach to wave propagation in scalar QED plasmas. Phys. Rev. A 94, 012124 – Published 29 July 2016.

    See the full article here .

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