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  • 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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  • 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.

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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.

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  • richardmitnick 3:27 pm on May 30, 2016 Permalink | Reply
    Tags: , , Quantum field theory, , ,   

    From PI: “Bridging Two Roads of Physics” Women in Science 

    Perimeter Institute
    Perimeter Institute

    May 30, 2016
    Rose Simone

    Recent Perimeter research based on the holographic principle seeks new connections between general relativity and quantum field theory.

    Imagine driving along a road that traverses a beautiful landscape. Around every corner, there is a new vista of natural beauty to explore. Suddenly you come to a chasm.

    You can see a road on the other side, but how do you get there to complete the journey? You need a bridge.

    That’s the state of physics today, and Bianca Dittrich, Perimeter Institute researcher in mathematical physics and quantum gravity, is one of the people trying to build that bridge.

    Bianca Dittrich

    On one side of the chasm is the road built by Albert Einstein’s theory of general relativity. It describes the force of gravity as the warping of spacetime by large masses such as planets and stars.

    On the other side is quantum field theory, our best description of interacting particles and the three other forces (the strong and weak nuclear forces and electromagnetism) operating at minuscule subatomic distances.

    The theories are incredibly successful in their respective realms, yet they are so different, both in formulation and conceptually, that it is difficult to bridge them.

    “Basically, we are trying to bridge all of the scales that we know,” Dittrich says. “That is what physics is about, but it is very hard. You need to bridge all of these scales by modelling the tiny scales, and show that this model actually does indeed describe reality as we know it at macroscopic scales.”

    In general relativity, spacetime is smooth and continuous. If you were to zoom in with a microscope to arbitrarily small distances, it should look the same as it does when you zoom out for the larger view. Quantum field theory, on the other hand, describes particles and forces that come as discrete “packets,” and spacetime would also have to be discrete and granular, like the pixels in a photograph.

    Scientists need a theory to describe the force of gravity at the quantum scale, and it must be consistent with the larger picture of general relativity. Building the bridge to a theory of quantum gravity is what occupies many physicists around the world today.

    It is easier said than done. If general relativity is scaled down to the quantum size, you start to get nonsensical “infinities” in the calculations. “Quantizing gravity sounds simple, in that it should be just the quantization of another force, besides the three forces (the non-gravitational forces) that were quantized decades ago,” Dittrich says. “But in fact it is a very hard and open problem.”

    There are many approaches to this longstanding problem. In loop quantum gravity, for example, physicists speak in terms of “spacetime atoms” linked together in a network like a fine mesh. This provides a model of what spacetime itself is made of.

    But in a recent paper*, “3D Holography: From Discretum to Continuum,” Dittrich and co-author Valentin Bonzom, now an assistant professor at Université Paris 13 who was previously a postdoctoral researcher at Perimeter Institute, tested a different approach, based on the holographic principle.

    The holographic principle says everything that happens in a given space can be explained in terms of information stored on the boundary of that space. (The principle takes its name from holograms, in which two-dimensional surfaces contain all the information needed to project a three-dimensional image.)

    A popular mathematical framework based on the holographic principle is known as the AdS/CFT correspondence. AdS is short for anti-de Sitter space, which describes a particular kind of geometry. Just like a bowling ball will stretch a rubber sheet, the elliptical shape of anti-de Sitter space can also stretch or contract, thus allowing it to describe gravity.

    CFT, meanwhile, is short for conformal field theory. Field theories are the language of quantum mechanics and can describe, for example, how an electrical field might change over space and time.

    The holographic principle applies because the AdS/CFT correspondence basically states that for every conformal field theory, there is a corresponding theory of gravity with one more dimension. So a two-dimensional CFT would correspond to a three-dimensional theory of gravity, for instance.

    But the holographic principle applies to infinitely large boundaries, and Dittrich and Bonzom wanted to see if it could also hold for finite boundaries, and for other types of geometries apart from AdS. This would then provide a more manageable way of describing a piece of spacetime, and understanding the microscopic details as they reconstruct the spacetime bulk.

    Working with a boundary without worrying too much about the bulk “very much simplifies the construction of a theory of quantum gravity,” Dittrich explains.

    They tested this in three spacetime dimensions, and “it turned out that the holographic principle indeed holds for finite boundaries, and we also obtained a very simple description of how to translate the boundary data into the geometry of the bulk,” she says.

    That this could be done in 3D was not too surprising, but the more challenging part will be extending this work into 4D space, Dittrich adds.

    Most theories of quantum gravity require the force of gravity to also be mediated by hypothetical particles called gravitons. If Dittrich can get her model to work in 4D, then she will have successfully taken it into a realm where gravitons exist. “Gravity can propagate through that spacetime,” Dittrich says.

    Dittrich has been on the physics road for some time. She grew up in Germany, reading a lot of popular books about science, as well as history and literature, and when she finished high school she considered various options, including areas such as geo-ecology.

    But she realized it was physics that could take her on the journey to the most complete understanding of nature. “If you want to understand why something works, the answer is in physics,” she says.

    Now, she is designing another bridge that will span that chasm between the two great roads and carry physicists to that more complete understanding of nature.

    *Science paper:
    3D holography: from discretum to continuum

    See the full article here .

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    About Perimeter

    Perimeter Institute is a leading centre for scientific research, training and educational outreach in foundational theoretical physics. Founded in 1999 in Waterloo, Ontario, Canada, its mission is to advance our understanding of the universe at the most fundamental level, stimulating the breakthroughs that could transform our future. Perimeter also trains the next generation of physicists through innovative programs, and shares the excitement and wonder of science with students, teachers and the general public.

  • richardmitnick 7:56 pm on January 15, 2016 Permalink | Reply
    Tags: , , , Quantum field theory   

    From FNAL: Don Lincoln on Quantum Field Theory 

    FNAL II photo

    Fermilab is an enduring source of strength for the US contribution to scientific research world wide.

    The subatomic world has long been known to be truly mind-bending, with particles that are waves and vice versa. Cats are alive and dead and everything is governed by probability.

    While this remains true, science has progressed since the invention of quantum mechanics and scientists currently use an extended form of quantum mechanics called quantum field theory or QFT. QFT teaches us that all particles are waves that interact with one another. If you thought the quantum world was weird before, modern ideas can give you a headache. In this video, Fermilab’s Dr. Don Lincoln tells us all about it.

    Watch, enjoy, learn.

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    Fermi National Accelerator Laboratory (Fermilab), located just outside Batavia, Illinois, near Chicago, is a US Department of Energy national laboratory specializing in high-energy particle physics. Fermilab is America’s premier laboratory for particle physics and accelerator research, funded by the U.S. Department of Energy. Thousands of scientists from universities and laboratories around the world
    collaborate at Fermilab on experiments at the frontiers of discovery.

  • richardmitnick 7:22 pm on September 28, 2015 Permalink | Reply
    Tags: Amplituhedrons, , , , , Quantum field theory   

    From Quanta: “A Jewel at the Heart of Quantum Physics” 

    Quanta Magazine
    Quanta Magazine

    September 17, 2013
    Natalie Wolchover

    Artist’s rendering of the amplituhedron, a newly discovered mathematical object resembling a multifaceted jewel in higher dimensions. Encoded in its volume are the most basic features of reality that can be calculated — the probabilities of outcomes of particle interactions. Illustration by Andy Gilmore

    Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality.

    “This is completely new and very much simpler than anything that has been done before,” said Andrew Hodges, a mathematical physicist at Oxford University who has been following the work.

    The revelation that particle interactions, the most basic events in nature, may be consequences of geometry significantly advances a decades-long effort to reformulate quantum field theory, the body of laws describing elementary particles and their interactions. Interactions that were previously calculated with mathematical formulas thousands of terms long can now be described by computing the volume of the corresponding jewel-like amplituhedron, which yields an equivalent one-term expression.

    “The degree of efficiency is mind-boggling,” said Jacob Bourjaily, a theoretical physicist at Harvard University and one of the researchers who developed the new idea. “You can easily do, on paper, computations that were infeasible even with a computer before.”

    The new geometric version of quantum field theory could also facilitate the search for a theory of quantum gravity that would seamlessly connect the large- and small-scale pictures of the universe. Attempts thus far to incorporate gravity into the laws of physics at the quantum scale have run up against nonsensical infinities and deep paradoxes. The amplituhedron, or a similar geometric object, could help by removing two deeply rooted principles of physics: locality and unitarity.

    “Both are hard-wired in the usual way we think about things,” said Nima Arkani-Hamed, a professor of physics at the Institute for Advanced Study in Princeton, N.J., and the lead author of the new work, which he is presenting in talks and in a forthcoming paper. “Both are suspect.”

    Nima Arkani-Hamed

    Locality is the notion that particles can interact only from adjoining positions in space and time. And unitarity holds that the probabilities of all possible outcomes of a quantum mechanical interaction must add up to one. The concepts are the central pillars of quantum field theory in its original form, but in certain situations involving gravity, both break down, suggesting neither is a fundamental aspect of nature.

    In keeping with this idea, the new geometric approach to particle interactions removes locality and unitarity from its starting assumptions. The amplituhedron is not built out of space-time and probabilities; these properties merely arise as consequences of the jewel’s geometry. The usual picture of space and time, and particles moving around in them, is a construct.

    “It’s a better formulation that makes you think about everything in a completely different way,” said David Skinner, a theoretical physicist at Cambridge University.

    The amplituhedron itself does not describe gravity. But Arkani-Hamed and his collaborators think there might be a related geometric object that does. Its properties would make it clear why particles appear to exist, and why they appear to move in three dimensions of space and to change over time.

    Because “we know that ultimately, we need to find a theory that doesn’t have” unitarity and locality, Bourjaily said, “it’s a starting point to ultimately describing a quantum theory of gravity.”

    Clunky Machinery

    The amplituhedron looks like an intricate, multifaceted jewel in higher dimensions. Encoded in its volume are the most basic features of reality that can be calculated, “scattering amplitudes,” which represent the likelihood that a certain set of particles will turn into certain other particles upon colliding. These numbers are what particle physicists calculate and test to high precision at particle accelerators like the Large Hadron Collider in Switzerland.

    CERN LHC Map
    CERN LHC Grand Tunnel
    CERN LHC particles
    LHC at CERN

    The iconic 20th century physicist Richard Feynman invented a method for calculating probabilities of particle interactions using depictions of all the different ways an interaction could occur. Examples of “Feynman diagrams” were included on a 2005 postage stamp honoring Feynman. United States Postal Service

    The 60-year-old method for calculating scattering amplitudes — a major innovation at the time — was pioneered by the Nobel Prize-winning physicist Richard Feynman. He sketched line drawings of all the ways a scattering process could occur and then summed the likelihoods of the different drawings. The simplest Feynman diagrams look like trees: The particles involved in a collision come together like roots, and the particles that result shoot out like branches. More complicated diagrams have loops, where colliding particles turn into unobservable “virtual particles” that interact with each other before branching out as real final products. There are diagrams with one loop, two loops, three loops and so on — increasingly baroque iterations of the scattering process that contribute progressively less to its total amplitude. Virtual particles are never observed in nature, but they were considered mathematically necessary for unitarity — the requirement that probabilities sum to one.

    “The number of Feynman diagrams is so explosively large that even computations of really simple processes weren’t done until the age of computers,” Bourjaily said. A seemingly simple event, such as two subatomic particles called gluons colliding to produce four less energetic gluons (which happens billions of times a second during collisions at the Large Hadron Collider), involves 220 diagrams, which collectively contribute thousands of terms to the calculation of the scattering amplitude.

    In 1986, it became apparent that Feynman’s apparatus was a Rube Goldberg machine.

    To prepare for the construction of the Superconducting Super Collider [SSC] in Texas (a project that was later canceled), theorists wanted to calculate the scattering amplitudes of known particle interactions to establish a background against which interesting or exotic signals would stand out. But even 2-gluon to 4-gluon processes were so complex, a group of physicists had written two years earlier, “that they may not be evaluated in the foreseeable future.”

    Ill fated SSC, killed by a myopic (Democratic)US Congress theat saw “no immediate economic benefit” in the finished project.

    Stephen Parke and Tomasz Taylor, theorists at Fermi National Accelerator Laboratory in Illinois, took that statement as a challenge. Using a few mathematical tricks, they managed to simplify the 2-gluon to 4-gluon amplitude calculation from several billion terms to a 9-page-long formula, which a 1980s supercomputer could handle. Then, based on a pattern they observed in the scattering amplitudes of other gluon interactions, Parke and Taylor guessed a simple one-term expression for the amplitude. It was, the computer verified, equivalent to the 9-page formula. In other words, the traditional machinery of quantum field theory, involving hundreds of Feynman diagrams worth thousands of mathematical terms, was obfuscating something much simpler. As Bourjaily put it: “Why are you summing up millions of things when the answer is just one function?”

    “We knew at the time that we had an important result,” Parke said. “We knew it instantly. But what to do with it?”

    The Amplituhedron

    The message of Parke and Taylor’s single-term result took decades to interpret. “That one-term, beautiful little function was like a beacon for the next 30 years,” Bourjaily said. It “really started this revolution.”

    Twistor diagrams depicting an interaction between six gluons, in the cases where two (left) and four (right) of the particles have negative helicity, a property similar to spin. The diagrams can be used to derive a simple formula for the 6-gluon scattering amplitude. Arkani-Hamed et al.

    In the mid-2000s, more patterns emerged in the scattering amplitudes of particle interactions, repeatedly hinting at an underlying, coherent mathematical structure behind quantum field theory. Most important was a set of formulas called the BCFW recursion relations, named for Ruth Britto, Freddy Cachazo, Bo Feng and Edward Witten. Instead of describing scattering processes in terms of familiar variables like position and time and depicting them in thousands of Feynman diagrams, the BCFW relations are best couched in terms of strange variables called “twistors,” and particle interactions can be captured in a handful of associated twistor diagrams. The relations gained rapid adoption as tools for computing scattering amplitudes relevant to experiments, such as collisions at the Large Hadron Collider. But their simplicity was mysterious.

    “The terms in these BCFW relations were coming from a different world, and we wanted to understand what that world was,” Arkani-Hamed said. “That’s what drew me into the subject five years ago.”

    With the help of leading mathematicians such as Pierre Deligne, Arkani-Hamed and his collaborators discovered that the recursion relations and associated twistor diagrams corresponded to a well-known geometric object. In fact, as detailed in a paper posted to arXiv.org in December by Arkani-Hamed, Bourjaily, Cachazo, Alexander Goncharov, Alexander Postnikov and Jaroslav Trnka, the twistor diagrams gave instructions for calculating the volume of pieces of this object, called the positive Grassmannian.

    Named for Hermann Grassmann, a 19th-century German linguist and mathematician who studied its properties, “the positive Grassmannian is the slightly more grown-up cousin of the inside of a triangle,” Arkani-Hamed explained. Just as the inside of a triangle is a region in a two-dimensional space bounded by intersecting lines, the simplest case of the positive Grassmannian is a region in an N-dimensional space bounded by intersecting planes. (N is the number of particles involved in a scattering process.)

    It was a geometric representation of real particle data, such as the likelihood that two colliding gluons will turn into four gluons. But something was still missing.

    The physicists hoped that the amplitude of a scattering process would emerge purely and inevitably from geometry, but locality and unitarity were dictating which pieces of the positive Grassmannian to add together to get it. They wondered whether the amplitude was “the answer to some particular mathematical question,” said Trnka, a post-doctoral researcher at the California Institute of Technology. “And it is,” he said.

    A sketch of the amplituhedron representing an 8-gluon particle interaction. Using Feynman diagrams, the same calculation would take roughly 500 pages of algebra. Nima Arkani-Hamed

    Arkani-Hamed and Trnka discovered that the scattering amplitude equals the volume of a brand-new mathematical object — the amplituhedron. The details of a particular scattering process dictate the dimensionality and facets of the corresponding amplituhedron. The pieces of the positive Grassmannian that were being calculated with twistor diagrams and then added together by hand were building blocks that fit together inside this jewel, just as triangles fit together to form a polygon.

    Like the twistor diagrams, the Feynman diagrams are another way of computing the volume of the amplituhedron piece by piece, but they are much less efficient. “They are local and unitary in space-time, but they are not necessarily very convenient or well-adapted to the shape of this jewel itself,” Skinner said. “Using Feynman diagrams is like taking a Ming vase and smashing it on the floor.”

    Arkani-Hamed and Trnka have been able to calculate the volume of the amplituhedron directly in some cases, without using twistor diagrams to compute the volumes of its pieces. They have also found a “master amplituhedron” with an infinite number of facets, analogous to a circle in 2-D, which has an infinite number of sides. Its volume represents, in theory, the total amplitude of all physical processes. Lower-dimensional amplituhedra, which correspond to interactions between finite numbers of particles, live on the faces of this master structure.

    “They are very powerful calculational techniques, but they are also incredibly suggestive,” Skinner said. “They suggest that thinking in terms of space-time was not the right way of going about this.”

    Quest for Quantum Gravity

    The seemingly irreconcilable conflict between gravity and quantum field theory enters crisis mode in black holes. Black holes pack a huge amount of mass into an extremely small space, making gravity a major player at the quantum scale, where it can usually be ignored. Inevitably, either locality or unitarity is the source of the conflict.


    Puzzling Thoughts

    Locality and unitarity are the central pillars of quantum field theory, but as the following thought experiments show, both break down in certain situations involving gravity. This suggests physics should be formulated without either principle.

    Locality says that particles interact at points in space-time. But suppose you want to inspect space-time very closely. Probing smaller and smaller distance scales requires ever higher energies, but at a certain scale, called the Planck length, the picture gets blurry: So much energy must be concentrated into such a small region that the energy collapses the region into a black hole, making it impossible to inspect. “There’s no way of measuring space and time separations once they are smaller than the Planck length,” said Arkani-Hamed. “So we imagine space-time is a continuous thing, but because it’s impossible to talk sharply about that thing, then that suggests it must not be fundamental — it must be emergent.”

    Unitarity says the quantum mechanical probabilities of all possible outcomes of a particle interaction must sum to one. To prove it, one would have to observe the same interaction over and over and count the frequencies of the different outcomes. Doing this to perfect accuracy would require an infinite number of observations using an infinitely large measuring apparatus, but the latter would again cause gravitational collapse into a black hole. In finite regions of the universe, unitarity can therefore only be approximately known.

    “We have indications that both ideas have got to go,” Arkani-Hamed said. “They can’t be fundamental features of the next description,” such as a theory of quantum gravity.

    String theory, a framework that treats particles as invisibly small, vibrating strings, is one candidate for a theory of quantum gravity that seems to hold up in black hole situations, but its relationship to reality is unproven — or at least confusing. Recently, a strange duality has been found between string theory and quantum field theory, indicating that the former (which includes gravity) is mathematically equivalent to the latter (which does not) when the two theories describe the same event as if it is taking place in different numbers of dimensions. No one knows quite what to make of this discovery. But the new amplituhedron research suggests space-time, and therefore dimensions, may be illusory anyway.

    “We can’t rely on the usual familiar quantum mechanical space-time pictures of describing physics,” Arkani-Hamed said. “We have to learn new ways of talking about it. This work is a baby step in that direction.”

    Even without unitarity and locality, the amplituhedron formulation of quantum field theory does not yet incorporate gravity. But researchers are working on it. They say scattering processes that include gravity particles may be possible to describe with the amplituhedron, or with a similar geometric object. “It might be closely related but slightly different and harder to find,” Skinner said.

    Nima Arkani-Hamed, a professor at the Institute for Advanced Study, and his former student and co-author Jaroslav Trnka, who finished his Ph.D. at Princeton University in July and is now a post-doctoral researcher at the California Institute of Technology. Courtesy of Jaroslav Trnka

    Physicists must also prove that the new geometric formulation applies to the exact particles that are known to exist in the universe, rather than to the idealized quantum field theory they used to develop it, called maximally supersymmetric Yang-Mills theory. This model, which includes a “superpartner” particle for every known particle and treats space-time as flat, “just happens to be the simplest test case for these new tools,” Bourjaily said. “The way to generalize these new tools to [other] theories is understood.”

    Beyond making calculations easier or possibly leading the way to quantum gravity, the discovery of the amplituhedron could cause an even more profound shift, Arkani-Hamed said. That is, giving up space and time as fundamental constituents of nature and figuring out how the Big Bang and cosmological evolution of the universe arose out of pure geometry.

    “In a sense, we would see that change arises from the structure of the object,” he said. “But it’s not from the object changing. The object is basically timeless.”

    While more work is needed, many theoretical physicists are paying close attention to the new ideas.

    The work is “very unexpected from several points of view,” said Witten, a theoretical physicist at the Institute for Advanced Study. “The field is still developing very fast, and it is difficult to guess what will happen or what the lessons will turn out to be.”

    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.

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