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  • richardmitnick 7:02 pm on December 2, 2016 Permalink | Reply
    Tags: , , String Theory   

    From Ethan Siegel: “What every layperson should know about string theory” 

    From Ethan Siegel

    12.2.16

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    The idea that instead of 0-dimensional particles, it’s 1-dimensional strings that fundamentally make up the Universe is at the core of string theory. Image credit: flickr user Trailfan, via https://www.flickr.com/photos/7725050@N06/631503428.

    If you’ve ever wondered just why it has piqued the interest of so many, have a look inside.

    “I just think too many nice things have happened in string theory for it to be all wrong. Humans do not understand it very well, but I just don’t believe there is a big cosmic conspiracy that created this incredible thing that has nothing to do with the real world.” -Edward Witten

    It’s one of the most brilliant, controversial and unproven ideas in all of physics: string theory. At the heart of string theory is the thread of an idea that’s run through physics for centuries, that at some fundamental level, all the different forces, particles, interactions and manifestations of reality are tied together as part of the same framework. Instead of four independent fundamental forces — strong, electromagnetic, weak and gravitational — there’s one unified theory that encompasses all of them. In many regards, string theory is the best contender for a quantum theory of gravitation, which just happens to unify at the highest-energy scales. Although there’s no experimental evidence for it, there are compelling theoretical reasons to think it might be true. A year ago, the top living string theorist, Ed Witten, wrote a piece on what every physicist should know about string theory. Here’s what that means, translated for non-physicists.

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    The difference between standard quantum field theory interactions (L), for point-like particles, and string theory interactions (R), for closed strings. Image credit: Wikimedia Commons user Kurochka.

    When it comes to the laws of nature, it’s remarkable how many similarities there are between seemingly unrelated phenomena. The way that two massive bodies gravitate, according to Newton’s laws, is almost identical to the way that electrically charged particles attract-or-repel. The way a pendulum oscillates is completely analogous to the way a mass on a spring moves back-and-forth, or the way a planet orbits a star. Gravitational waves, water waves and light waves all share remarkably similar features, despite arising from fundamentally different physical origins. And in the same vein, although most don’t realize it, the quantum theory of a single particle and how you’d approach a quantum theory of gravity are similarly analogous.

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    A Feynman diagram representing electron-electron scattering, which requires summing over all the possible histories of the particle-particle interactions. Image credit: Dmitri Fedorov.

    he way quantum field theory works is that you take a particle and you perform a mathematical “sum over histories.” You can’t just calculate where the particle was and where it is and how it got to be there, since there’s an inherent, fundamental quantum uncertainty to nature. Instead, you add up all the possible ways it could have arrived at its present state, appropriately weighted probabilistically, and that’s how you calculate the state of a single particle. Because Einstein’s General Relativity isn’t concerned with particles but rather the curvature of spacetime, you don’t average over all possible histories of a particle, but rather over all possible spacetime geometries.

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    Gravity, governed by Einstein, and everything else (strong, weak and electromagnetic interactions), governed by quantum physics, are the two independent rules known to govern everything in our Universe. Image credit: SLAC National Accelerator Laboratory.

    Working in three spatial dimensions is very difficult, but if you go down to one dimension, things become very simple. The only possible one-dimensional surfaces are an open string, where there are two separate, unattached ends, or a closed string, where the two ends are attached to form a loop. In addition, the spatial curvature — so complicated in three dimensions — becomes trivial. So what we’re left with, if we want to add in matter, is a set of scalar fields (just like certain types of particles) and the cosmological constant (which acts just like a mass term): a beautiful analogy.

    The extra degrees of freedom a particle gains from being in multiple dimensions don’t play much of a role; so long as you can define a momentum vector, that’s the main dimension that matters. In one dimension, therefore, quantum gravity looks just like a free quantum particle in any arbitrary number of dimensions. The next step is to incorporate interactions, and to go from a free particle with no scattering amplitudes or cross-sections to one that can play a physical role, coupled to the Universe.

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    A graph with trivalent vertices is a key component of constructing the path integral relevant for 1-D quantum gravity. Image credit: Phys. Today 68, 11, 38 (2015).

    Graphs, like the one above, allow us to describe the physical concept of action in quantum gravity. If we write down all the possible combinations of such graphs and sum over them — applying the same laws like conservation of momentum that we always enforce — we can complete the analogy. Quantum gravity in one dimension is very much like a single particle interacting in any number of dimensions.

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    The probability of finding a quantum particle at any particular location is never 100%; the probability is spread out over both space and time. Image credit: Wikimedia Commons user Maschen.

    The next step would be to move from one spatial dimension to 3+1 dimensions: where the Universe has three spatial dimensions and one time dimension. But doing it for gravity may be very challenging. Instead, there might be a better approach in working in the opposite direction. Instead of calculating how a single particle (a zero-dimensional entity) behaves in any number of dimensions, maybe we could calculate how a string, whether open or closed (a one-dimensional entity) behaves. And then, from that, we can look for analogies to a more complete theory of quantum gravity in a more realistic number of dimensions.

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    Feynman diagrams (top) are based off of point particles and their interactions. Converting them into their string theory analogues (bottom) gives rise to surfaces which can have non-trivial curvature. Image credit: Phys. Today 68, 11, 38 (2015).

    Instead of points and interactions, we immediately start working with surfaces. And once you have a true, multi-dimensional surface, that surface can be curved in non-trivial ways. You start getting very interesting behavior out; behavior that just might be at the root of the spacetime curvature we experience in our Universe as General Relativity. While 1D quantum gravity gave us quantum field theory for particles in a possibly curved spacetime, it didn’t describe gravitation itself. The subtle piece of the puzzle that was missing? There was no correspondence between operators, or the functions that represent quantum mechanical forces and properties, and states, or how the particles and their properties evolve over time. But if we move from point-like particles to string-like entities, that correspondence shows up.

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    Deforming the spacetime metric can be represented by the fluctuation (labelled ‘p’), and if you apply it to the string analogues, it describes a spacetime fluctuation and corresponds to a quantum state of the string. Image credit: Phys. Today 68, 11, 38 (2015).

    There’s a real operator-state correspondence, where a fluctuation in the spacetime metric (i.e., an operator) automatically represents a state in the quantum mechanical description of a string’s properties. So you can get a quantum theory of gravity in spacetime from string theory. But that’s not all you get: you also get quantum gravity unified with the other particles and forces in spacetime, the ones that correspond to the other operators in the field theory of the string. There’s also the operator that describes the spacetime geometry’s fluctuations, and the other quantum states of the string. The biggest news about string theory is that it can give you a working quantum theory of gravity.

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    Brian Greene presenting on String Theory. Image credit: NASA/Goddard/Wade Sisler.

    That doesn’t mean it’s a foregone conclusion, however, that string theory is the path to quantum gravity. The great hope of string theory is that these analogies will hold up at all scales, and that there will be an unambiguous, one-to-one mapping of the string picture onto the Universe we observe around us. Right now, there are only a few sets of dimensions that the string/superstring picture is self-consistent in, and the most promising one doesn’t give us the four-dimensional gravity of Einstein, but rather a 10-dimensional Brans-Dicke theory of gravity. In order to recover the gravity of our Universe, you must “get rid of” six dimensions and take the Brans-Dicke coupling constant, ω, to infinity. How this happens remains an open challenge for string theory.

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    A 2-D projection of a Calabi-Yau manifold, one popular method of compactifying the extra, unwanted dimensions of String Theory. Image credit: Wikimedia Commons user Lunch.

    But string theory offers a path to quantum gravity, and if we make the judicious choices of “the math works out this way,” we can get both General Relativity and the Standard Model out of it. It’s the only idea, to date, that gives us this, and that’s why it’s so hotly pursued. No matter whether you tout string theory’s successes or failure, or how you feel about its lack of verifiable predictions, it will no doubt remain one of the most active areas of theoretical physics research, and at the core of a great many physicists’ dreams of an ultimate theory.

    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 7:18 am on September 16, 2016 Permalink | Reply
    Tags: , , String Theory   

    From Quanta: “The Strange Second Life of String Theory” 

    Quanta Magazine
    Quanta Magazine

    September 15, 2016
    K.C. Cole

    String theory has so far failed to live up to its promise as a way to unite gravity and quantum mechanics.
    At the same time, it has blossomed into one of the most useful sets of tools in science.

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    Renee Rominger/Moonrise Whims for Quanta Magazine

    String theory strutted onto the scene some 30 years ago as perfection itself, a promise of elegant simplicity that would solve knotty problems in fundamental physics — including the notoriously intractable mismatch between Einstein’s smoothly warped space-time and the inherently jittery, quantized bits of stuff that made up everything in it.

    It seemed, to paraphrase Michael Faraday, much too wonderful not to be true: Simply replace infinitely small particles with tiny (but finite) vibrating loops of string. The vibrations would sing out quarks, electrons, gluons and photons, as well as their extended families, producing in harmony every ingredient needed to cook up the knowable world. Avoiding the infinitely small meant avoiding a variety of catastrophes. For one, quantum uncertainty couldn’t rip space-time to shreds. At last, it seemed, here was a workable theory of quantum gravity.

    Even more beautiful than the story told in words was the elegance of the math behind it, which had the power to make some physicists ecstatic.

    To be sure, the theory came with unsettling implications. The strings were too small to be probed by experiment and lived in as many as 11 dimensions of space. These dimensions were folded in on themselves — or “compactified” — into complex origami shapes. No one knew just how the dimensions were compactified — the possibilities for doing so appeared to be endless — but surely some configuration would turn out to be just what was needed to produce familiar forces and particles.

    For a time, many physicists believed that string theory would yield a unique way to combine quantum mechanics and gravity. “There was a hope. A moment,” said David Gross, an original player in the so-called Princeton String Quartet, a Nobel Prize winner and permanent member of the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara. “We even thought for a while in the mid-’80s that it was a unique theory.”

    And then physicists began to realize that the dream of one singular theory was an illusion. The complexities of string theory, all the possible permutations, refused to reduce to a single one that described our world. “After a certain point in the early ’90s, people gave up on trying to connect to the real world,” Gross said. “The last 20 years have really been a great extension of theoretical tools, but very little progress on understanding what’s actually out there.”

    Many, in retrospect, realized they had raised the bar too high. Coming off the momentum of completing the solid and powerful “standard model” of particle physics in the 1970s, they hoped the story would repeat — only this time on a mammoth, all-embracing scale. “We’ve been trying to aim for the successes of the past where we had a very simple equation that captured everything,” said Robbert Dijkgraaf, the director of the Institute for Advanced Study in Princeton, New Jersey. “But now we have this big mess.”

    Like many a maturing beauty, string theory has gotten rich in relationships, complicated, hard to handle and widely influential. Its tentacles have reached so deeply into so many areas in theoretical physics, it’s become almost unrecognizable, even to string theorists. “Things have gotten almost postmodern,” said Dijkgraaf, who is a painter as well as mathematical physicist.

    The mathematics that have come out of string theory have been put to use in fields such as cosmology and condensed matter physics — the study of materials and their properties. It’s so ubiquitous that “even if you shut down all the string theory groups, people in condensed matter, people in cosmology, people in quantum gravity will do it,” Dijkgraaf said.

    “It’s hard to say really where you should draw the boundary around and say: This is string theory; this is not string theory,” said Douglas Stanford, a physicist at the IAS. “Nobody knows whether to say they’re a string theorist anymore,” said Chris Beem, a mathematical physicist at the University of Oxford. “It’s become very confusing.”

    String theory today looks almost fractal. The more closely people explore any one corner, the more structure they find. Some dig deep into particular crevices; others zoom out to try to make sense of grander patterns. The upshot is that string theory today includes much that no longer seems stringy. Those tiny loops of string whose harmonics were thought to breathe form into every particle and force known to nature (including elusive gravity) hardly even appear anymore on chalkboards at conferences. At last year’s big annual string theory meeting, the Stanford University string theorist Eva Silverstein was amused to find she was one of the few giving a talk “on string theory proper,” she said. A lot of the time she works on questions related to cosmology.

    Even as string theory’s mathematical tools get adopted across the physical sciences, physicists have been struggling with how to deal with the central tension of string theory: Can it ever live up to its initial promise? Could it ever give researchers insight into how gravity and quantum mechanics might be reconciled — not in a toy universe, but in our own?

    “The problem is that string theory exists in the landscape of theoretical physics,” said Juan Maldacena, a mathematical physicist at the IAS and perhaps the most prominent figure in the field today. “But we still don’t know yet how it connects to nature as a theory of gravity.” Maldacena now acknowledges the breadth of string theory, and its importance to many fields of physics — even those that don’t require “strings” to be the fundamental stuff of the universe — when he defines string theory as “Solid Theoretical Research in Natural Geometric Structures.”

    An Explosion of Quantum Fields

    One high point for string theory as a theory of everything came in the late 1990s, when Maldacena revealed that a string theory including gravity in five dimensions was equivalent to a quantum field theory in four dimensions. This “AdS/CFT” duality appeared to provide a map for getting a handle on gravity — the most intransigent piece of the puzzle — by relating it to good old well-understood quantum field theory.

    This correspondence was never thought to be a perfect real-world model. The five-dimensional space in which it works has an “anti-de Sitter” geometry, a strange M.C. Escher-ish landscape that is not remotely like our universe.

    But researchers were surprised when they dug deep into the other side of the duality. Most people took for granted that quantum field theories — “bread and butter physics,” Dijkgraaf calls them — were well understood and had been for half a century. As it turned out, Dijkgraaf said, “we only understand them in a very limited way.”

    These quantum field theories were developed in the 1950s to unify special relativity and quantum mechanics. They worked well enough for long enough that it didn’t much matter that they broke down at very small scales and high energies. But today, when physicists revisit “the part you thought you understood 60 years ago,” said Nima Arkani-Hamed, a physicist at the IAS, you find “stunning structures” that came as a complete surprise. “Every aspect of the idea that we understood quantum field theory turns out to be wrong. It’s a vastly bigger beast.”

    Researchers have developed a huge number of quantum field theories in the past decade or so, each used to study different physical systems. Beem suspects there are quantum field theories that can’t be described even in terms of quantum fields. “We have opinions that sound as crazy as that, in large part, because of string theory.”

    This virtual explosion of new kinds of quantum field theories is eerily reminiscent of physics in the 1930s, when the unexpected appearance of a new kind of particle — the muon — led a frustrated I.I. Rabi to ask: “Who ordered that?” The flood of new particles was so overwhelming by the 1950s that it led Enrico Fermi to grumble: “If I could remember the names of all these particles, I would have been a botanist.”

    Physicists began to see their way through the thicket of new particles only when they found the more fundamental building blocks making them up, like quarks and gluons. Now many physicists are attempting to do the same with quantum field theory. In their attempts to make sense of the zoo, many learn all they can about certain exotic species.

    Conformal field theories (the right hand of AdS/CFT) are a starting point. In the simplest type of conformal field theory, you start with a version of quantum field theory where “the interactions between the particles are turned off,” said David Simmons-Duffin, a physicist at the IAS. If these specific kinds of field theories could be understood perfectly, answers to deep questions might become clear. “The idea is that if you understand the elephant’s feet really, really well, you can interpolate in between and figure out what the whole thing looks like.”

    Like many of his colleagues, Simmons-Duffin says he’s a string theorist mostly in the sense that it’s become an umbrella term for anyone doing fundamental physics in underdeveloped corners. He’s currently focusing on a physical system that’s described by a conformal field theory but has nothing to do with strings. In fact, the system is water at its “critical point,” where the distinction between gas and liquid disappears. It’s interesting because water’s behavior at the critical point is a complicated emergent system that arises from something simpler. As such, it could hint at dynamics behind the emergence of quantum field theories.

    Beem focuses on supersymmetric field theories, another toy model, as physicists call these deliberate simplifications. “We’re putting in some unrealistic features to make them easier to handle,” he said. Specifically, they are amenable to tractable mathematics, which “makes it so a lot of things are calculable.”

    Toy models are standard tools in most kinds of research. But there’s always the fear that what one learns from a simplified scenario does not apply to the real world. “It’s a bit of a deal with the devil,” Beem said. “String theory is a much less rigorously constructed set of ideas than quantum field theory, so you have to be willing to relax your standards a bit,” he said. “But you’re rewarded for that. It gives you a nice, bigger context in which to work.”

    It’s the kind of work that makes people such as Sean Carroll, a theoretical physicist at the California Institute of Technology, wonder if the field has strayed too far from its early ambitions — to find, if not a “theory of everything,” at least a theory of quantum gravity. “Answering deep questions about quantum gravity has not really happened,” he said. “They have all these hammers and they go looking for nails.” That’s fine, he said, even acknowledging that generations might be needed to develop a new theory of quantum gravity. “But it isn’t fine if you forget that, ultimately, your goal is describing the real world.”

    It’s a question he has asked his friends. Why are they investigating detailed quantum field theories? “What’s the aspiration?” he asks. Their answers are logical, he says, but steps removed from developing a true description of our universe.

    nstead, he’s looking for a way to “find gravity inside quantum mechanics.” A paper he recently wrote with colleagues claims to take steps toward just that. It does not involve string theory.

    The Broad Power of Strings

    Perhaps the field that has gained the most from the flowering of string theory is mathematics itself. Sitting on a bench beside the IAS pond while watching a blue heron saunter in the reeds, Clay Córdova, a researcher there, explained how what seemed like intractable problems in mathematics were solved by imagining how the question might look to a string. For example, how many spheres could fit inside a Calabi-Yau manifold — the complex folded shape expected to describe how spacetime is compactified? Mathematicians had been stuck. But a two-dimensional string can wiggle around in such a complex space. As it wiggled, it could grasp new insights, like a mathematical multidimensional lasso. This was the kind of physical thinking Einstein was famous for: thought experiments about riding along with a light beam revealed E=mc2. Imagining falling off a building led to his biggest eureka moment of all: Gravity is not a force; it’s a property of space-time.

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    The amplituhedron is a multi-dimensional object that can be used to calculate particle interactions. Physicists such as Chris Beem are applying techniques from string theory in special geometries where “the amplituhedron is its best self,” he says. Nima Arkani-Hamed

    Using the physical intuition offered by strings, physicists produced a powerful formula for getting the answer to the embedded sphere question, and much more. “They got at these formulas using tools that mathematicians don’t allow,” Córdova said. Then, after string theorists found an answer, the mathematicians proved it on their own terms. “This is a kind of experiment,” he explained. “It’s an internal mathematical experiment.” Not only was the stringy solution not wrong, it led to Fields Medal-winning mathematics. “This keeps happening,” he said.

    String theory has also made essential contributions to cosmology. The role that string theory has played in thinking about mechanisms behind the inflationary expansion of the universe — the moments immediately after the Big Bang, where quantum effects met gravity head on — is “surprisingly strong,” said Silverstein, even though no strings are attached.

    Still, Silverstein and colleagues have used string theory to discover, among other things, ways to see potentially observable signatures of various inflationary ideas. The same insights could have been found using quantum field theory, she said, but they weren’t. “It’s much more natural in string theory, with its extra structure.”

    Inflationary models get tangled in string theory in multiple ways, not least of which is the multiverse — the idea that ours is one of a perhaps infinite number of universes, each created by the same mechanism that begat our own. Between string theory and cosmology, the idea of an infinite landscape of possible universes became not just acceptable, but even taken for granted by a large number of physicists. The selection effect, Silverstein said, would be one quite natural explanation for why our world is the way it is: In a very different universe, we wouldn’t be here to tell the story.

    This effect could be one answer to a big problem string theory was supposed to solve. As Gross put it: “What picks out this particular theory” — the Standard Model — from the “plethora of infinite possibilities?”

    Silverstein thinks the selection effect is actually a good argument for string theory. The infinite landscape of possible universes can be directly linked to “the rich structure that we find in string theory,” she said — the innumerable ways that string theory’s multidimensional space-time can be folded in upon itself.

    Building the New Atlas

    At the very least, the mature version of string theory — with its mathematical tools that let researchers view problems in new ways — has provided powerful new methods for seeing how seemingly incompatible descriptions of nature can both be true. The discovery of dual descriptions of the same phenomenon pretty much sums up the history of physics. A century and a half ago, James Clerk Maxwell saw that electricity and magnetism were two sides of a coin. Quantum theory revealed the connection between particles and waves. Now physicists have strings.

    “Once the elementary things we’re probing spaces with are strings instead of particles,” said Beem, the strings “see things differently.” If it’s too hard to get from A to B using quantum field theory, reimagine the problem in string theory, and “there’s a path,” Beem said.

    In cosmology, string theory “packages physical models in a way that’s easier to think about,” Silverstein said. It may take centuries to tie together all these loose strings to weave a coherent picture, but young researchers like Beem aren’t bothered a bit. His generation never thought string theory was going to solve everything. “We’re not stuck,” he said. “It doesn’t feel like we’re on the verge of getting it all sorted, but I know more each day than I did the day before – and so presumably we’re getting somewhere.”

    Stanford thinks of it as a big crossword puzzle. “It’s not finished, but as you start solving, you can tell that it’s a valid puzzle,” he said. “It’s passing consistency checks all the time.”

    “Maybe it’s not even possible to capture the universe in one easily defined, self-contained form, like a globe,” Dijkgraaf said, sitting in Robert Oppenheimer’s many windowed office from when he was Einstein’s boss, looking over the vast lawn at the IAS, the pond and the woods in the distance. Einstein, too, tried and failed to find a theory of everything, and it takes nothing away from his genius.

    “Perhaps the true picture is more like the maps in an atlas, each offering very different kinds of information, each spotty,” Dijkgraaf said. “Using the atlas will require that physics be fluent in many languages, many approaches, all at the same time. Their work will come from many different directions, perhaps far-flung.”

    He finds it “totally disorienting” and also “fantastic.”

    Arkani-Hamed believes we are in the most exciting epoch of physics since quantum mechanics appeared in the 1920s. But nothing will happen quickly. “If you’re excited about responsibly attacking the very biggest existential physics questions ever, then you should be excited,” he said. “But if you want a ticket to Stockholm for sure in the next 15 years, then probably not.”

    See the full article here .

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

     
  • richardmitnick 1:37 pm on August 4, 2016 Permalink | Reply
    Tags: , Miranda Cheng, Monstrous moonshine, , String Theory   

    From Quanta: “Moonshine Master Toys With String Theory” 

    Quanta Magazine
    Quanta Magazine

    August 4, 2016
    Natalie Wolchover

    The physicist-mathematician Miranda Cheng is working to harness a mysterious connection between string theory, algebra and number theory.

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    Ilvy Njiokiktjien for Quanta Magazine

    After the Eyjafjallajökull volcano erupted in Iceland in 2010, flight cancellations left Miranda Cheng stranded in Paris. While waiting for the ash to clear, Cheng, then a postdoctoral researcher at Harvard University studying string theory, got to thinking about a paper that had recently been posted online. Its three coauthors had pointed out a numerical coincidence connecting far-flung mathematical objects. “That smells like another moonshine,” Cheng recalled thinking. “Could it be another moonshine?”

    She happened to have read a book about the “monstrous moonshine,” a mathematical structure that unfolded out of a similar bit of numerology: In the late 1970s, the mathematician John McKay noticed that 196,884, the first important coefficient of an object called the j-function, was the sum of one and 196,883, the first two dimensions in which a giant collection of symmetries called the monster group could be represented. By 1992, researchers had traced this farfetched (hence “moonshine”) correspondence to its unlikely source: string theory, a candidate for the fundamental theory of physics that casts elementary particles as tiny oscillating strings. The j-function describes the strings’ oscillations in a particular string theory model, and the monster group captures the symmetries of the space-time fabric that these strings inhabit.

    By the time of Eyjafjallajökull’s eruption, “this was ancient stuff,” Cheng said — a mathematical volcano that, as far as physicists were concerned, had gone dormant. The string theory model underlying monstrous moonshine was nothing like the particles or space-time geometry of the real world. But Cheng sensed that the new moonshine, if it was one, might be different. It involved K3 surfaces — the geometric objects that she and many other string theorists study as possible toy models of real space-time.

    By the time she flew home from Paris, Cheng had uncovered more evidence that the new moonshine existed. She and collaborators John Duncan and Jeff Harvey gradually teased out evidence of not one but 23 new moonshines: mathematical structures that connect symmetry groups on the one hand and fundamental objects in number theory called mock modular forms (a class that includes the j-function) on the other. The existence of these 23 moonshines, posited in their Umbral Moonshine Conjecture in 2012, was proved by Duncan and coworkers late last year.

    Meanwhile, Cheng, 37, is on the trail of the K3 string theory underlying the 23 moonshines — a particular version of the theory in which space-time has the geometry of a K3 surface. She and other string theorists hope to be able to use the mathematical ideas of umbral moonshine to study the properties of the K3 model in detail. This in turn could be a powerful means for understanding the physics of the real world where it can’t be probed directly — such as inside black holes. An assistant professor at the University of Amsterdam on leave from France’s National Center for Scientific Research, Cheng spoke with Quanta Magazine about the mysteries of moonshines, her hopes for string theory, and her improbable path from punk-rock high school dropout to a researcher who explores some of the most abstruse ideas in math and physics. An edited and condensed version of the conversation follows.

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    Ilvy Njiokiktjien for Quanta Magazine

    QUANTA MAGAZINE: You do string theory on so-called K3 surfaces. What are they, and why are they important?

    MIRANDA CHENG: String theory says there are 10 space-time dimensions. Since we only perceive four, the other six must be curled up or “compactified” too small to see, like the circumference of a very thin wire. There’s a plethora of possibilities — something like 10^500 — for how the extra dimensions might be compactified, and it’s almost impossible to say which compactification is more likely to describe reality than the rest. We can’t possibly study the physical properties of all of them. So you look for a toy model. And if you like having exact results instead of approximated results, which I like, then you often end up with a K3 compactification, which is a middle ground for compactifications between too simple and too complicated. It also captures the key properties of Calabi-Yau manifolds [the most highly studied class of compactifications] and how string theory behaves when it’s compactified on them. K3 also has the feature that you can often do direct and exact computations with it.

    What does K3 actually look like?

    You can think of a flat torus, then you fold it so that there’s a line or corner of sharp edges. Mathematicians have a way to smooth it, and the result of smoothing a folded flat torus is a K3 surface.

    So you can figure out what the physics is in this setup, with strings moving through this space-time geometry?

    Yes. In the context of my Ph.D., I explored how black holes behave in this theory. Once you have the curled-up dimensions being K3-related Calabi-Yaus, black holes can form. How do these black holes behave — especially their quantum properties?

    So you could try to solve the information paradox—the long-standing puzzle of what happens to quantum information when it falls inside a black hole.

    Absolutely. You can ask about the information paradox or properties of various types of black holes, like realistic astrophysical black holes or supersymmetric black holes that come out of string theory. Studying the second type can shed light on your realistic problems because they share the same paradox. That’s why trying to understand string theory in K3 and the black holes that arise in that compactification should also shed light on other problems. At least, that’s the hope, and I think it’s a reasonable hope.

    Do you think string theory definitely describes reality? Or is it something you study purely for its own sake?

    I personally always have the real world at the back of my mind — but really, really, really back. I use it as sort of an inspiration for determining roughly the big directions I’m going in. But my day-to-day research is not aimed at solving the real world. I see it as differences in taste and style and personal capabilities. New ideas are needed in fundamental high-energy physics, and it’s hard to say where those new ideas will come from. Understanding the basic, fundamental structures of string theory is needed and helpful. You’ve got to start somewhere where you can compute things, and that leads, often, to very mathematical corners. The payoff to understanding the real world might be really long term, but that’s necessary at this stage.

    Have you always had a knack for physics and math?

    As a child in Taiwan I was more into literature — that was my big thing. And then I got into music when I was 12 or so — pop music, rock, punk. I was always very good at math and physics, but I wasn’t really interested in it. And I always found school insufferable and was always trying to find a way around it. I tried to make a deal with the teacher that I wouldn’t need to go into the class. Or I had months of sick leave while I wasn’t sick at all. Or I skipped a year here and there. I just don’t know how to deal with authority, I guess.

    And the material was probably too easy. I skipped two years, but that didn’t help. So then they moved me to a special class and that made it even worse, because everybody was very competitive, and I just couldn’t deal with the competition at all. Eventually I was super depressed, and I decided either I would kill myself or not go to school. So I stopped going to school when I was 16, and I also left home because I was convinced that my parents would ask me to go back to school and I really didn’t want to do that. So I started working in a record shop, and by that time I also played in a band, and I loved it.

    How did you get from there to string theory?

    Long story short, I got a little bit discouraged or bored. I wanted to do something else aside from music. So I tried to go back to university, but then I had the problem that I hadn’t graduated from high school. But before I quit school I was in a special class for kids who are really good in science. I could get in the university with this. So I thought, OK, great, I’ll just get into university first by majoring in physics or math, and then I can switch to literature. So I enrolled in the physics department, having a very on- and off-again relationship to it, going to class every now and then, and then trying to study literature, while still playing in the band. Then I realized I’m not good enough in literature. And also there was a very good teacher teaching quantum mechanics. Just once I went to his class and thought, that’s actually pretty cool. I started paying a bit more attention to my studies of math and physics, and I started to find peace in it. That’s what started to attract me about math and physics, because my other life in the band playing music was more chaotic somehow. It sucks a lot of emotions out of you. You’re always working with people, and the music is too much about life, about emotions — you have to give a lot of yourself to it. Math and physics seems to have this peaceful quiet beauty. This space of serenity.

    Then at the end of university I thought, well, let me just have one more year to study physics, then I’m really done with it and can move on with my life. So I decided to go to Holland to see the world and study some physics, and I got really into it there.

    You got your master’s at Utrecht under Nobel Prize-winning physicist Gerard ’t Hooft, and then you did your Ph.D. in Amsterdam. What drew you in?

    Working with [’t Hooft] was a big factor. But just learning more is also a big factor — to realize that there are so many interesting questions. That’s the big-picture part. But for me the day-to-day part is also important. The learning process, the thinking process, really the beauty of it. Every day you encounter some equations or some way of thinking, or this fact leads to that fact — I thought, well, this is pretty. Gerard is not a string theorist — he’s very open-minded about what the correct area of quantum gravity should be — so I got exposed to a few different options. I got attracted by string theory because it’s mathematically rigorous, and pretty.

    With the work you’re doing now, aside from the beauty, are you also drawn to the mystery of these connections between seemingly different parts of math and physics?

    The mystery part connects to the bad side of my character, which is the obsessive side. That’s one of the driving forces that I would call slightly negative from the human point of view, though not the scientist point of view. But there’s also the positive driving force, which is that I really enjoy learning different stuff and feeling how ignorant I am. I enjoy that frustration, like, “I know nothing about this subject; I really want to learn!” So that’s one motivation — to be at this boundary place between math and physics. Moonshine is a puzzle that might require inspirations from everywhere and knowledge from everywhere. And the beauty, certainly — it’s a beautiful story. It’s kind of hard to say why it is beautiful. It’s beautiful not the same way as a song is beautiful or a picture is beautiful.

    What’s the difference?

    Typically a song is beautiful because it triggers certain emotions. It resonates with part of your life. Mathematical beauty is not that. It’s something much more structured. It gives you a feeling of something much more permanent, and independent of you. It makes me feel small, and I like that.

    What is a moonshine, exactly?

    A moonshine relates representations of a finite symmetry group to a function with special symmetries [ways that you can transform the function without affecting its output]. Underlying this relationship, at least in the case of monstrous moonshine, is a string theory. String theory has two geometries. One is the “worldsheet” geometry. If you have a string — essentially a circle — moving in time, then you get a cylinder. That’s what we call the worldsheet geometry; it’s the geometry of the string itself. If you roll the cylinder and connect the two ends, you get a torus. The torus gives you the symmetry of the j-function. The other geometry in string theory is space-time itself, and its symmetry gives you the monster group.

    We don’t know yet, but these are educated guesses: To have a moonshine tells you that this theory has to have an algebraic structure [you have to be able to do algebra with its elements]. If you look at a theory and you ask what kind of particles you have at a certain energy level, this question is infinite, because you can go to higher and higher energies, and then this question goes on and on. In monstrous moonshine, this is manifested in the fact that if you look at the j-function, there are infinitely many terms that basically capture the energy of the particles. But we know there’s an algebraic structure underlying it — there’s a mechanism for how the lower energy states can be related to higher energy states. So this infinite question has a structure; it’s not just random.

    As you can imagine, having an algebraic structure helps you understand what the structure is that captures a theory — how, if you look at the lower energy states, they will tell you something about the higher energy states. And then it also gives you more tools to do computations. If you want to understand something at a high-energy level [such as inside black holes], then I have more information about it. I can compute what I want to compute for high-energy states using this low-energy data I already have in hand. That’s the hope.

    Umbral moonshine tells you that there should be a structure like this that we don’t understand yet. Understanding it more generally will force us to understand this algebraic structure. And that will lead to a much deeper understanding of the theory. That’s the hope.

    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 5:14 pm on June 20, 2016 Permalink | Reply
    Tags: , Joseph Conlon, , , String Theory   

    From Physics Today: “Questions and answers with Joseph Conlon” String Theory 

    Physics Today bloc

    Physics Today

    17 June 2016
    Jermey N. A. Matthews

    1
    Joseph Conlon. NO image credit.

    The apple didn’t fall far from the tree,” says University of Oxford theoretical physicist Joseph Conlon. The author of Why String Theory?, reviewed in this month’s issue of Physics Today, says that from an early age he was good at math—a critical skill for a string theorist—thanks to the influence of his father and uncle, both PhD mathematicians, and his mother, a physics teacher.

    2

    By age 18 Conlon had earned a bachelor’s degree in mathematics from the local University of Reading in the UK; he did it part-time, while still in secondary school. Conlon followed that up by obtaining his bachelor’s and PhD degrees in physics at the University of Cambridge. At Oxford, he now focuses on phenomenological applications of string theory to particle physics and cosmology. “One thing I certainly benefited from is that if you [pursue] a physics undergraduate degree, having already done a math undergraduate degree, then you don’t need to concentrate on the math; you can just concentrate on understanding the physics concepts,” says Conlon.

    For those who would question string theory’s validity because it can’t be experimentally tested, Conlon “presents a set of compelling arguments for the value of string theory while acknowledging its weaknesses and open challenges,” writes Gary Shiu in his Physics Today review. “Like courtroom juries, readers are encouraged to draw their own logical conclusions.” Conlon is also a cocreator of the public outreach website http://whystringtheory.com, which aims to be “a layman’s journey to the frontiers of physics.”

    Physics Today books editor Jermey Matthews and senior editor Steven Blau, a theoretical physicist by training, recently caught up with Conlon to discuss the book.

    PT: Why did you write the book?

    CONLON: It’s to answer the question I think lots of people are asking: Why are so many people working on string theory if this is something you can’t directly say is the true theory of the universe at the smallest possible scales?

    PT: So how would you answer the question “Why string theory?” for a nonexpert?

    CONLON: String theory has brought ideas and insights and results to so many different areas beyond its supposedly core area of quantum gravity. The analogy I use in the book is it’s like in a gold rush, you get rich by selling spades, rather than by finding nuggets. String theory has … been able to provide spades to lots of people across mathematics and theoretical physics in so many different topics. And this is why so many people are interested in it.

    PT: What inspired you to study string theory?

    CONLON: I guess it was a fairly natural thing for me to do, given my interests and inclinations at the time. When I was in Cambridge, I was training in particle theory, and I was trying to learn as much particle theory as I could. You take courses on quantum field theory, you take courses on the standard model, you take a course in string theory.

    The reason I wanted to carry on with the PhD in string theory was the feeling that lots of the standard model was carved out and understood in the 1970s and 1980s. String theory seemed more like something where I could get in and feel it wasn’t already done by the generation that came before.

    The Standard Model of elementary particles (more schematic depiction), with the three generations of matter, gauge bosons in the fourth column, and the Higgs boson in the fifth.
    The Standard Model of elementary particles (more schematic depiction), with the three generations of matter, gauge bosons in the fourth column, and the Higgs boson in the fifth

    PT: Were you ever tempted by any of the other alternative approaches to quantum gravity like loop quantum gravity or dynamic causal histories?

    CONLON: Not really. I was never really exposed to them. As an undergraduate, it wasn’t something I learned or particularly had the option of learning then. And I haven’t been particularly tempted since then. From quite early on in my work on string theory I’ve been more interested in connecting it to experiments and observation. It’s great that people work on the formal problems of quantum gravity, but it’s not really my style of physics.

    PT: As you were writing the book, was there something that you were hoping to be able to convey but said, “this is just too tough a nut to crack”? Did you have to leave anything on the table?

    CONLON: Yes. There was a series of results around 1995 that were very important, involving D-branes. I ended up covering this less than I thought I would. And it partly was because I felt it was hard to try and convey to a general reader what was important about them without just dropping into buzz words.

    PT: And, conversely, is there anything that you were particularly proud you were able to get across in simple language?

    CONLON: I guess you have to ask the readers that. There are things I learned about—for example, the monstrous moonshine [a mathematical theory involving symmetries and related to conformal field theories] is a topic which I learned more about in the process of writing the book. I enjoyed writing about that because I learned about it at a slightly more technical level. It was a discovery process for me, too.

    PT: According to the Physics Today review, your book also touches on “the sociology of string theory.” Was that your intention?

    CONLON: Yes. Science is always more interesting when it’s done by humans, rather than [being] just abstract results. There’s also [a danger] you can get in if you look at someone very big [successful] and you say, “Gosh, they’ve gotten all these fantastic results. I can never possibly be like them. I’ll never be smart enough.”

    But people are good at different things. Even though you might not be able to get the results that person did, you’ve got skills that they don’t have. I tried to convey that there are many, many different ways of being a good theoretical physicist. And part of that was by talking about the sociology, the different types of people who do the subject and do it successfully.

    PT: Was explaining string theory to the general public a particular itch you wanted to scratch, or are you interested in writing other popular books?

    CONLON: A bit of both. I thought string theory was being misrepresented, particularly in the general press, that there was this [notion] that string theory primarily was a theory of quantum gravity. And so string theory would then … compete with other theories of quantum gravity. And this is something I wanted to argue against because most people who work on string theory don’t focus on quantum gravity. That was the itch I wanted to scratch.

    The book was also a chance to kind of let go the other side of my brain [used to write research papers] … and just write freely.

    PT: What is your next project?

    CONLON: In the process of finishing the book, basically I stopped doing research for six to nine months. So for the next two or three years I just want to do research because I enjoy doing research. And then I think I would like to write another book. I don’t know yet what it would be on.

    PT: What books are you currently reading?

    CONLON: I’ve got two on the go. The longer one, which I’m about halfway through, is [Winston] Churchill’s series The Second World War (Houghton Mifflin, ca. 1948–ca. 1953). And then the sort of more easy reading is one by Apollo astronaut (and physicist) Walter Cunningham, The All-American Boys: An Insider’s Look at the U.S. Space Program (revised edition, iPicturebooks, 2010).

    See the full article here .

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    “Our mission

    The mission of Physics Today is to be a unifying influence for the diverse areas of physics and the physics-related sciences.

    It does that in three ways:

    • by providing authoritative, engaging coverage of physical science research and its applications without regard to disciplinary boundaries;
    • by providing authoritative, engaging coverage of the often complex interactions of the physical sciences with each other and with other spheres of human endeavor; and
    • by providing a forum for the exchange of ideas within the scientific community.”

     
  • richardmitnick 7:54 am on June 5, 2016 Permalink | Reply
    Tags: , , , , String Theory   

    From Science Alert: “Gravitational waves could reveal a stringy universe, say physicists” 

    ScienceAlert

    Science Alert

    3 JUN 2016
    DAVID NIELD

    1
    AbstractUniverse/Shutterstock.com

    Time to brush up on your string theory?

    Back in February, physicists gave us one of the most exciting scientific discoveries of the century – the first direct evidence of gravitational waves.

    Gravitational wave Henze NASA
    Gravitational wave Henze NASA

    These waves are like ripples that expand after a major event in space, such as two black holes merging or the explosion of a massive star.

    The discovery gave us a whole new way of looking at the Universe, and that’s something two physicists in Spain are taking advantage of, by testing out another scientific hypothesis: string theory. And if their ideas are correct, it could fundamentally change our thinking about the nature of the Universe.

    First off, it’s important to understand how gravitational waves work. In the very early Universe, everything was much denser than it is now, which resulted in a great deal of light scattering. Those photon signals can be a big problem when it comes to peering deep into the Universe to look back in time, because there’s so much background noise to take into account.

    What makes gravitational waves special is that their movements don’t appear to be affected by interfering electrons and protons. In fact, gravitational waves might allow us to observe objects and events that don’t emit any light at all, including the cosmic ‘strings’ that underlie the famous string theory hypothesis.

    String theory aims to provide a unified approach to explaining the fundamental structure of the Universe. It suggests that cosmic strings – incredibly long and thin defects in the curvature of space and time – formed right after the Big Bang. Unfortunately, these cosmic strings are thought to have been obliterated many aeons ago, so find a large number of them, we’d have to go back to the earliest moments of the Universe.

    And that brings us back to gravitational waves. Physicists Isabel Fernandez-Nunez and Oleg Bulashenko of the University of Barcelona think that one could lead us to the other – gravitational waves could help us find cosmic strings.

    Fernandez-Nunez and Bulashenko started off by picturing a string as a sharp crease in space-time, and then calculated how a gravitational wave would pass through that crease. If we can find wave ripples that match these calculations, then we might have evidence of a cosmic string, they suggest.

    There are hurdles to overcome before we can test out their hypothesis, because right now, we don’t have the kind of technology to measure gravitational waves in the way that the pair’s hypothesis requires.

    [Here is what we have:
    LIGO map
    LIGO map

    Caltech/MIT Advanced aLigo detector in Livingston, LA, USA
    Caltech/MIT   Advanced Ligo Hanford, WA, USA installation
    Caltech/MIT Advanced aLigo detector in Livingston, LA, USA and Caltech/MIT Advanced Ligo Hanford, WA, USA, which work in tandem.

    ESA/LISA Pathfinder
    ESA/LISA Pathfinder spacecraft, prelude to ESA/LISA

    ESA/eLISA
    Future ESA/eLISA

    NASA/Fermi Telescope
    NASA/Fermi Telescope

    Event Horizon Telescope Array

    Event Horizon Telescope map
    Event Horizon Telescope map

    Arizona Radio Observatory
    Arizona Radio Observatory/Submillimeter-wave Astronomy (ARO/SMT)

    ESO/APEX
    Atacama Pathfinder EXperiment (APEX)

    CARMA Array no longer in service
    Combined Array for Research in Millimeter-wave Astronomy (CARMA)

    Atacama Submillimeter Telescope Experiment (ASTE)
    Atacama Submillimeter Telescope Experiment (ASTE)

    Caltech Submillimeter Observatory
    Caltech Submillimeter Observatory (CSO)

    IRAM NOEMA interferometer
    Institut de Radioastronomie Millimetrique (IRAM) 30m

    James Clerk Maxwell Telescope interior, Mauna Kea, Hawaii, USA
    James Clerk Maxwell Telescope interior, Mauna Kea, Hawaii, USA

    Large Millimeter Telescope Alfonso Serrano
    Large Millimeter Telescope Alfonso Serrano

    CfA Submillimeter Array Hawaii SAO
    Submillimeter Array Hawaii SAO

    Future Array/Telescopes

    ESO/NRAO/NAOJ ALMA Array
    ESO/NRAO/NAOJ ALMA Array, Chile

    Plateau de Bure interferometer
    Plateau de Bure interferometer

    South Pole Telescope SPTPOL
    South Pole Telescope SPTPOL]

    But these are still early days for gravitational wave astronomy, so scientists are still sharing ideas about how we might be able to make the most of this discovery.

    The researchers’ paper is available on pre-print website, arXiv.org, but has yet to be peer-reviewed by other astrophysicists, so we’ll have to wait and see what the community makes of their hypothesis before we can get too excited. That said, this isn’t the first time that scientists have speculated that gravitational waves could lead us to cosmic strings.

    B.S. Sathyaprakash from Cardiff University in the UK, who works at the observatory where gravitational waves were first measured, thinks a lot of new such discoveries could be just around the corner. “I am pretty confident that within the next three or four years we will be making detections one by one and ticking the boxes,” he told Tim Radford at The Guardian.

    Plus we’d also have to be very lucky to find a pattern of just the right intensity from our position on Earth.

    See the full article here .

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  • richardmitnick 5:09 pm on February 5, 2016 Permalink | Reply
    Tags: , , , String Theory,   

    From SA: “Taming Superconductors with String Theory” 

    Scientific American

    Scientific American

    February 4, 2016
    Kevin Hartnett, Quanta Magazine

    The physicist Subir Sachdev borrows tools from string theory to understand the puzzling behavior of superconductors.

    String theory was devised as a way to unite the laws of quantum mechanics with those of gravity [General Relativity], with the goal of creating the vaunted theory of everything.

    Subir Sachdev is taking the “everything” literally. He’s applying the mathematics of string theory to a major problem at the other end of physics — the behavior of a potentially revolutionary class of materials known as high-temperature superconductors.

    Superconductivity
    Superconductivity

    These materials are among the most promising and the most perplexing. Unlike regular superconductors, which need to be cooled almost to absolute zero (–273.15 degrees Celsius) to pass a frictionless current of electricity, high-temperature superconductors yield the same remarkable performance under more accommodating conditions. Since the first high-temperature superconductor was discovered in 1986, physicists have found other materials that exhibit superconductivity at successively higher temperatures, with the current record standing at –70 degrees Celsius.

    This progress has occurred despite the fact that physicists don’t understand how these superconductors work. Broadly speaking, many condensed-matter physicists study how electrons — the carriers of electrical current — move through a given material. In an ordinary conductor like copper or gold, the electrons flow through a lattice formed by the copper or gold atoms. In an insulator like diamond, electrons tend to stay put. In superconductors, electrons move through the underlying atomic lattice with no energy loss at all. For three decades, physicists have been unable to develop a comprehensive theory that explains how electrons in high-temperature superconductors behave.

    A particularly interesting question is how the behavior of the material changes with temperature — in particular, how conductors transition from ordinary to super as the temperature drops. Scientists call this a “quantum phase change,” with the two phases being the property of the material on either side of the transition temperature.

    Sachdev, a condensed-matter physicist at Harvard University, explains that the challenge is one of scale. A typical chunk of material has trillions upon trillions of electrons. When those electrons interact with one another — as they do in superconductors — they become impossible to keep track of. In some phases of matter, physicists have been able to overcome this scale issue by modeling swarms of electrons as quasiparticles, quantum excitations that behave a lot like individual particles. But the quasiparticle strategy doesn’t work in high-temperature superconductors, forcing physicists to look for another way to impose collective order on the behavior of electrons in these materials.

    In 2007 Sachdev had a startling insight: He realized that certain features of string theory correspond to the electron soup found in high-temperature superconductors. In the years since, Sachdev has developed models in string theory that offer ways to think about the electron behavior in high-temperature superconductors. He’s used these ideas to design real-world experiments with materials like graphene — a flat sheet of carbon atoms — which have properties in common with the materials that interest him.

    In a forthcoming paper in Science, he and his collaborators use methods borrowed from string theory to correctly predict experimental results related to the flow of heat and electrical charge in graphene. Now he hopes to apply his insights to high-temperature superconductors themselves.

    Quanta Magazine spoke with Sachdev about how the electrons in high-temperature superconductors are related to black holes, his recent success with graphene, and why the biggest name in condensed-matter physics is skeptical that the string-theory approach works at all. An edited and condensed version of the interview follows.

    QUANTA MAGAZINE: What’s going on inside a high-temperature superconductor?
    SUBIR SACHDEV: The difference between old materials and the new materials is that in older materials, electrons conduct electricity independent of one another. They obey the exclusion principle, which says electrons can’t occupy the same quantum state at the same time and that they move independently of one another. In the new materials that I, and many others, have been studying, it’s clear that this independent-electron model fails. The general picture is that they move cooperatively and, in particular, they’re entangled — their quantum properties are linked.

    This entanglement makes high-temperature superconductors much more complicated to model than regular superconductors. How have you been looking at the problem?
    Generally I approach this through the classification of the quantum phases of matter. Examples of simple quantum phases are simple metals like silver and gold, or simple insulators like diamonds. Many of these phases are well-understood and appear everywhere in our daily lives. Since we discovered high-temperature superconductors, and many other new materials, we’ve been trying to understand the other physical properties that can emerge when you have trillions of electrons obeying quantum principles and also interacting with each other. At the back of my mind is the hope that this broad attack on classifying quantum phases of matter will lead to a deeper understanding of high-temperature superconductors.

    How far have you gotten?
    There has been great progress in understanding the theory of quantum phase transitions, which involves taking two phases of quantum matter that are very different from each other and adjusting some parameter — say, pressure on a crystal — and asking what happens when the material goes from one phase to the other. There has been a huge amount of progress for a wide class of quantum phase transitions. We now understand many different kinds of phases we didn’t know existed before.

    But a full theory of how electrons behave in high-temperature superconductors has been difficult to develop. Why?
    If you have a single electron moving through a lattice, then you really only need to worry about the different positions that electron can occupy. Even though the number of positions is large, that pretty much is something you can handle on a computer.

    But once you start talking about many electrons, you have to think about it very differently. One way to think about it is to imagine that each site on the lattice can be either empty or full. With N sites it’s 2N, so the possibilities are unimaginably vast. In this vast set of possibilities, you have to classify what are reasonable things an electron would tend to do. That in a nutshell is why it’s a difficult problem.

    Returning to phase transitions, you’ve spent a lot of time studying what happens to a high-temperature superconductor when it grows too warm. At this point, it becomes a so-called “strange metal.” Why would understanding strange metals help you to understand high-temperature superconductors?
    If you start with a superconductor and raise the temperature, there’s a critical temperature at which the superconductivity disappears. Right above this temperature you get a type of metal that we call a strange metal because many of its properties are very different from ordinary metals. Now imagine reversing the path, so that the phase of a system is changing from a strange-metal state to a superconducting state as it goes below the critical temperature. If we’re going to determine the temperature at which this happens, we need to compare the energies of the quantum states on either side of the critical temperature. But strange metals look strange in every respect, and we have only the simplest models for their physical properties.

    What makes strange metals so different from other unique quantum phases?
    In certain phases, [quantum] excitations generally behave like new emergent particles. They are quasiparticles. Their inner structure is very complicated, but from the outside they look like ordinary particles. The quasiparticle theory of many-body states pretty much applies to all states we’ve discovered in the older materials.

    Strange metals are one of the most prominent cases we know where quasiparticle theory fails. That’s why it’s so much harder to study them, because this basic tool of many-body theory doesn’t apply.

    You had the idea that string theory might be useful for understanding quantum phases that lack quasiparticles, like strange metals. How is string theory useful in this setting?
    From my point of view, string theory was another powerful mathematical tool for understanding large numbers of quantum-entangled particles. In particular, there are certain phases of string theory in which you can imagine that the ends of strings are sticking to a surface. If you are an ant moving on the surface, you only see the ends of the string. To you, these ends look like particles, but really the particles are connected by a string that goes to an extra dimension. To you, these particles sitting on the surface will appear entangled, and it is the string in the extra dimension which is entangling the particles. It’s a different way of describing entanglement.

    Now you could imagine continuing that process, not just with two electrons, but with four, six, infinitely many electrons, looking at the different entangled states the electrons can form. This is closely connected to the classification of phases of matter. It’s a hierarchical description of entanglement, where each electron finds a partner, and then the pairs entangle with other pairs, and so on. You can build this hierarchical structure using the stringy description. So it is one approach to talking about the entanglement of trillions of electrons.

    This application of string theory to strange metals has some interesting implications. For instance, it’s led you to draw connections between strange metals and the properties of black holes. How do you get from one to the other?
    In the string-theory picture, [changing the density of electrons] corresponds to putting a charge on a black hole. Many people have been studying this in the last five years or so — trying to understand things about strange metals from the properties of charged black holes. I have a recent paper in which I actually found a certain artificial model of electrons moving on a lattice where many properties precisely match the properties of charged black holes.

    I’ve read that Philip Anderson, considered by many people to be the most-influential living condensed-matter physicist, is skeptical that string theory is really useful for understanding strange metals. Do you know if that’s true?
    I think that’s correct. He’s told me himself that he doesn’t believe any of this, but, you know, what can I say, he’s a brilliant man with his own point of view. I would say that when we first proposed the idea in 2007, it certainly sounded crazy. A lot of progress has been made since then. I have a new paper with Philip Kim and others where it turns out that with graphene, which is a slightly less-strange metal, many of the methods inspired by string theory have led to quantitative predictions that have been verified by experiments.

    I think that’s been one of the best successes of the string-theory methods so far. It literally works; you can get the numbers right. But graphene is a simple system, and whether these methods are going to work for high-temperature superconductors hasn’t yet been proven.

    Could you say more about why Anderson might be skeptical of the approach you’ve taken?
    If you go back and actually look at string-theory models, on the surface they look very different from the kinds of models you need for high-temperature superconductors. You look at the stringy models and their constituents, and it appears absurd that these are connected to the constituents of the high-temperature superconductors. But if you take the point of view that, OK, I’m not literally saying this model is going to be found in [high-temperature superconductors], this is just a model that helps me make progress on difficult issues, like how do materials without quasiparticles behave, string theory gives you examples of one of these materials that’s reliably solvable.

    How literally are you using string theory? Is it a direct application, or are you drawing inspiration from it?
    It’s closer to the inspiration side of things. Once you’ve solved the model, it gives you a lot of insight into other models that you may not be able to solve. After six or seven years of work closer to the string-theory side, we think we’ve learned a lot. For us the next step appears to be working in more realistic systems using inspiration we got from more solvable models.

    How might the string-theory models, plus the work on graphene, put you in a position to understand the properties of high-temperature superconductors?
    As you change the density of electrons in high-temperature superconductors, there’s a much more dramatic change in which the electrons go from a regime where it seems only a few electrons are mobile to one where all electrons are mobile. We’re understanding that there’s a special point called the optimal density where there seems to be a dramatic change in the quantum state of electrons. And right near this point is where the strange metal is also observed. We’re trying to work out microscopic theories of this special point where the quantum state changes, and stringy models can teach us a lot about such quantum-critical points. Once we have the full framework, we’re hopeful and optimistic that we can take many of the insights from graphene and apply them to this more complicated model. That’s where we are.

    See the full article here .

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  • richardmitnick 4:31 pm on January 13, 2016 Permalink | Reply
    Tags: , , , String Theory   

    From Quanta: “String Theory Meets Loop Quantum Gravity” 

    Quanta Magazine
    Quanta Magazine

    January 12, 2016
    Sabine Hossenfelder

    Temp 1

    Eight decades have passed since physicists realized that the theories of quantum mechanics and gravity [Albert Einstein’s Theory of General Relativity] don’t fit together, and the puzzle of how to combine the two remains unsolved. In the last few decades, researchers have pursued the problem in two separate programs — string theory and loop quantum gravity — that are widely considered incompatible by their practitioners. But now some scientists argue that joining forces is the way forward.

    Among the attempts to unify quantum theory and gravity, string theory has attracted the most attention. Its premise is simple: Everything is made of tiny strings. The strings may be closed unto themselves or have loose ends; they can vibrate, stretch, join or split. And in these manifold appearances lie the explanations for all phenomena we observe, both matter and space-time included.

    Loop quantum gravity, by contrast, is concerned less with the matter that inhabits space-time than with the quantum properties of space-time itself. In loop quantum gravity, or LQG, space-time is a network. The smooth background of Einstein’s theory of gravity is replaced by nodes and links to which quantum properties are assigned. In this way, space is built up of discrete chunks. LQG is in large part a study of these chunks.

    This approach has long been thought incompatible with string theory. Indeed, the conceptual differences are obvious and profound. For starters, LQG studies bits of space-time, whereas string theory investigates the behavior of objects within space-time. Specific technical problems separate the fields. String theory requires that space-time have 10 dimensions; LQG doesn’t work in higher dimensions. String theory also implies the existence of supersymmetry, in which all known particles have yet-undiscovered partners.

    Supersymmetry standard model
    Standard Model of Supersymmetry

    Supersymmetry isn’t a feature of LQG.

    These and other differences have split the theoretical physics community into deeply divergent camps. “Conferences have segregated,” said Jorge Pullin, a physicist at Louisiana State University and co-author of an LQG textbook. “Loopy people go to loopy conferences. Stringy people go to stringy conferences. They don’t even go to ‘physics’ conferences anymore. I think it’s unfortunate that it developed this way.”

    But a number of factors may be pushing the camps closer together. New theoretical findings have revealed potential similarities between LQG and string theory. A young generation of string theorists has begun to look outside string theory for methods and tools that might be useful in the quest to understand how to create a “theory of everything.” And a still-raw paradox involving black holes and information loss has given everyone a fresh dose of humility.

    Moreover, in the absence of experimental evidence for either string theory or LQG, mathematical proof that the two are in fact opposite sides of the same coin would bolster the argument that physicists are progressing toward the correct theory of everything. Combining LQG and string theory would truly make it the only game in town.

    An Unexpected Link

    An effort to solve some of LQG’s own internal problems has led to the first surprising link with string theory. Physicists who study LQG lack a clear understanding of how to zoom out from their network of space-time chunks and arrive at a large-scale description of space-time that dovetails with Einstein’s general theory of relativity — our best theory of gravity. More worrying still, their theory can’t reconcile the special case in which gravity can be neglected. It’s a malaise that befalls any approach reliant on chunking-up space-time: In Einstein’s theory of special relativity, an object will appear to contract depending on how fast an observer is moving relative to it. This contraction also affects the size of space-time chunks, which are then perceived differently by observers with different velocities. The discrepancy leads to problems with the central tenet of Einstein’s theory — that the laws of physics should be the same no matter what the observer’s velocity.

    “It’s difficult to introduce discrete structures without running into difficulties with special relativity,” said Pullin. In a brief paper he wrote in 2014 with frequent collaborator Rodolfo Gambini, a physicist at the University of the Republic in Montevideo, Uruguay, Pullin argued that making LQG compatible with special relativity necessitates interactions that are similar to those found in string theory.

    That the two approaches have something in common seemed likely to Pullin since a seminal discovery in the late 1990s by Juan Maldacena, a physicist at the Institute for Advanced Study in Princeton, N.J. Maldacena matched up a gravitational theory in a so-called anti-de Sitter (AdS) space-time with a field theory (CFT — the “C” is for “conformal”) on the boundary of the space-time. By using this AdS/CFT identification, the gravitational theory can be described by the better-understood field theory.

    The full version of the duality is a conjecture, but it has a well-understood limiting case that string theory plays no role in. Because strings don’t matter in this limiting case, it should be shared by any theory of quantum gravity. Pullin sees this as a contact point.

    Herman Verlinde, a theoretical physicist at Princeton University who frequently works on string theory, finds it plausible that methods from LQG can help illuminate the gravity side of the duality. In a recent paper, Verlinde looked at AdS/CFT in a simplified model with only two dimensions of space and one of time, or “2+1” as physicists say. He found that the AdS space can be described by a network like those used in LQG. Even though the construction presently only works in 2+1, it offers a new way to think about gravity. Verlinde hopes to generalize the model to higher dimensions. “Loop quantum gravity has been seen too narrowly. My approach is to be inclusive. It’s much more intellectually forward-looking,” he said.

    But even having successfully combined LQG methods with string theory to make headway in anti-de Sitter space, the question remains: How useful is that combination? Anti-de Sitter space-times have a negative cosmological constant (a number that describes the large-scale geometry of the universe); our universe has a positive one. We just don’t inhabit the mathematical construct that is AdS space.

    Verlinde is pragmatic. “One idea is that [for a positive cosmological constant] one needs a totally new theory,” he said. “Then the question is how different that theory is going to look. AdS is at the moment the best hint for the structure we are looking for, and then we have to find the twist to get a positive cosmological constant.” He thinks it’s time well spent: “Though [AdS] doesn’t describe our world, it will teach us some lessons that will guide us where to go.”

    Coming Together in a Black Hole

    Verlinde and Pullin both point to another chance for the string theory and loop quantum gravity communities to come together: the mysterious fate of information that falls into a black hole. In 2012, four researchers based at the University of California, Santa Barbara, highlighted an internal contradiction in the prevailing theory. They argued that requiring a black hole to let information escape would destroy the delicate structure of empty space around the black hole’s horizon, thereby creating a highly energetic barrier — a black hole “firewall.” This firewall, however, is incompatible with the equivalence principle that underlies general relativity, which holds that observers can’t tell whether they’ve crossed the horizon. The incompatibility roiled string theorists, who thought they understood black hole information and now must revisit their notebooks.

    But this isn’t a conundrum only for string theorists. “This whole discussion about the black hole firewalls took place mostly within the string theory community, which I don’t understand,” Verlinde said. “These questions about quantum information, and entanglement, and how to construct a [mathematical] Hilbert space – that’s exactly what people in loop quantum gravity have been working on for a long time.”

    Meanwhile, in a development that went unnoted by much of the string community, the barrier once posed by supersymmetry and extra dimensions has fallen as well. A group around Thomas Thiemann at Friedrich-Alexander University in Erlangen, Germany, has extended LQG to higher dimensions and included supersymmetry, both of which were formerly the territory of string theory.

    More recently, Norbert Bodendorfer, a former student of Thiemann’s who is now at the University of Warsaw, has applied methods of LQG’s loop quantization to anti-de Sitter space. He argues that LQG can be useful for the AdS/CFT duality in situations where string theorists don’t know how to perform gravitational computations. Bodendorfer feels that the former chasm between string theory and LQG is fading away. “On some occasions I’ve had the impression that string theorists knew very little about LQG and didn’t want to talk about it,” he said. “But [the] younger people in string theory, they are very open-minded. They are very interested what is going on at the interface.”

    “The biggest difference is in how we define our questions,” said Verlinde. “It’s more sociological than scientific, unfortunately.” He doesn’t think the two approaches are in conflict: “I’ve always viewed [string theory and loop quantum gravity] as parts of the same description. LQG is a method, it’s not a theory. It’s a method to think of quantum mechanics and geometry. It’s a method that string theorists can use and are actually using. These things are not incompatible.”

    Not everyone is so convinced. Moshe Rozali, a string theorist at the University of British Columbia, remains skeptical of LQG: “The reason why I personally don’t work on LQG is the issue with special relativity,” he said. “If your approach does not respect the symmetries of special relativity from the outset, then you basically need a miracle to happen at one of your intermediate steps.” Still, Rozali said, some of the mathematical tools developed in LQG might come in handy. “I don’t think that there is any likelihood that string theory and LQG are going to converge to some middle ground,” he said. “But the methods are what people normally care about, and these are similar enough; the mathematical methods could have some overlap.”

    Not everyone on the LQG side expects the two will merge either. Carlo Rovelli, a physicist at the University of Marseille and a founding father of LQG, believes his field ascendant. “The string planet is infinitely less arrogant than ten years ago, especially after the bitter disappointment of the non-appearance of supersymmetric particles,” he said. “It is possible that the two theories could be parts of a common solution … but I myself think it is unlikely. String theory seems to me to have failed to deliver what it had promised in the ’80s, and is one of the many ‘nice-idea-but-nature-is-not-like-that’ that dot the history of science. I do not really understand how can people still have hope in it.”

    For Pullin, declaring victory seems premature: “There are LQG people now saying, ‘We are the only game in town.’ I don’t subscribe to this way of arguing. I think both theories are vastly incomplete.”

    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 9:22 pm on December 30, 2015 Permalink | Reply
    Tags: , , , String Theory   

    From Ethan Siegel: “Why String Theory Is Not A Scientific Theory” 

    Starts with a bang
    Starts with a Bang

    12.30.15
    Ethan Siegel

    Temp 1
    Image credit: flickr user Trailfan, via https://www.flickr.com/photos/7725050@N06/631503428.

    Scientists work on it, it’s consistent with science, and it hopes to be the biggest scientific breakthrough of all. But it’s missing one key ingredient.

    “As of now, string theorists have no explanation of why there are three large dimensions as well as time, and the other dimensions are microscopic. Proposals about that have been all over the map.” -Edward Witten

    There are a lot of different ways to define science, but perhaps one that everyone can agree on is that it’s a process by which:

    knowledge about the natural world or a particular phenomenon is gathered,
    a testable hypothesis is put forth concerning a natural, physical explanation for that phenomenon,
    that hypothesis is then tested and either validated or falsified,
    and an overarching framework — or scientific theory — is constructed to explain the hypothesis and that makes predictions about other phenomena,
    which is then tested further, and either validated, in which case new phenomena to test are sought (back to step 3), or falsified, in which case a new testable hypothesis is put forth (back to step 2)…

    and so on. This scientific process always involves the continued gathering of more data, the continued refining or outright replacing of hypotheses when the realm of validity of the theory is exceeded, and testing that subjects that theory to either further validation or potential falsification.

    That’s how science has always progressed, whether we’ve recognized it or not. Heliocentrism replaced geocentrism because it explained phenomena that geocentrism couldn’t, including:

    Jupiter’s moons,
    the phases and relative sizes of Venus and Mars at different times of year,
    and the periodicity of cometary orbits.

    2
    Image credit: public domain work by Wikimedia Commons users Nichalp and Sagredo, of the phases (and angular size) of Venus in the heliocentric model.

    Newtonian gravity superseded Kepler’s laws because of its additional predictive power, combining terrestrial and celestial mechanics. Even Einstein’s relativity, both special and general, came about because of the failures of Newtonian mechanics to account for behavior close to the speed of light and in strong gravitational fields. It took observations well beyond what was capable of in Newton’s time, such as the measurements of the lifetimes of particles produced in radioactive decays and the orbit of Mercury around the Sun over the course of centuries. The continued gathering of data — in new regimes, at higher precision and over longer timescales — allowed us to see the cracks in the scientific theories du jour, as well as where the potential to expand beyond them were.

    Now, we come to the present day. [Albert] Einstein’s general relativity is still our leading theory of gravity, having passed every experimental and observational test tossed its way, from gravitational lensing to relativistic frame dragging to the decay of binary pulsar orbits, while three other fundamental forces — electromagnetism and the strong and weak nuclear forces — are described by quantum field theories. These two classes of theories are fundamentally incompatible and incomplete on their own, and indicate that there is more to the Universe than we currently understand, despite the success of the Standard Model and the need for a quantum theory of gravity.

    10
    The Standard Model of elementary particles (more schematic depiction), with the three generations of matter, gauge bosons in the fourth column, and the Higgs boson in the fifth.

    3
    Image credit: NASA, of an artist’s concept of Gravity Probe B orbiting the Earth to measure space-time curvature.

    NASA Gravity Probe B
    NASA/Gravity Probe B

    One option for a solution to this conundrum is string theory., or the idea that everything we perceive as a particle or force is simply an excitation of a closed or open string, vibrating at specific but unique frequencies.

    It may seem that, by calling it “string theory” and presenting it as a possible solution to a scientific question, we’ve already answered in the affirmative: yes, string theory is a scientific theory. But it’s only a theory in the mathematical sense, which means it has its own set of axioms, postulates, elements, as well as the theorems and corollaries that can be derived from them. Set theory, group theory and number theory are all examples of mathematical theories, and string theory is another such example.

    4
    Image credit: Wikimedia Commons user Lunch, of a 2-D projection of a Calabi-Yau manifold, one popular method of compactifying the extra, unwanted dimensions of String Theory.

    But is it a physical theory?

    It makes physical predictions, such as:

    the existence of ten dimensions,
    that the fundamental constants are determined by the “vacuum” of string theory,
    the existence of supersymmetric particles,

    Supersymmetry standard model
    Standard Model of Supersymmetry

    and that there is a mathematically equivalent relation between a theory of quantum gravity in, say, five-dimensional space and a field theory without gravity on the boundary (and hence, in four dimensions) of that space.

    These are, no doubt, predictions about the physical Universe. But can we test any of these predictions?

    5
    Image credit: public domain work by Wikimedia Commons user Rogilbert.

    The answer, so far, is no. The first one is a huge problem: we need to get rid of six dimensions to get back the Universe we see, and there are more ways to do it than there are atoms in the Universe. What’s worse, is that each way you do it gives a different “vacuum” for string theory, with no clear way to get the fundamental constants that describe the Universe we inhabit, which is the second prediction. The third prediction has come up empty, but we would need to achieve energies that are ~1015 times higher than what the LHC can produce to rule out string theory entirely and falsify it.

    CERN LHC Map
    CERN LHC Grand Tunnel
    CERN LHC particles
    LHC at CERN, the most powerful particle accelerator ever built.

    Moreover, supersymmetric particles is not a unique prediction of string theory; finding them would only mean that string theory isn’t ruled out, not that it’s right. And the last prediction is only a mathematical one, not a physical one. It doesn’t give us anything specific to look for or test about our Universe.

    Although there was an entire conference on it earlier this month, spurred by a controversial opinion piece written a year ago by George Ellis and Joe Silk, the answer is very clear: no, string theory is not a scientific theory. The way people are trying to turn it into science is — as Sabine Hossenfelder and Davide Castelvecchi report — by redefining what “science” is.

    6
    Image credit: Gideon Pisanty, of Tulipa agenensis sharonensis (Dinsm.) Feinbrun, Dor-Habonim Beach, Israel, February 26, 2012.

    How absurd! If I showed you a tulip and said, “this is a rose,” you could show me all the roses in the world and say, “no, these are roses, that is a tulip.” If I then changed the definition of a rose to include tulips, would that cause a tulip to become a rose? Or would I merely be turning a useful definition and distinction into a less useful one?

    7
    Image credit: public domain, retrieved from https://pixabay.com/en/globe-earth-country-continents-73397/.

    If you want to rise to the level of a scientific theory, you have to make a testable — and hence, falsifiable or validatable — predictions. Even a physical state that arises as a consequence of an established theory, such as the multiverse, isn’t a scientific theory until we have a way to confirm or refute it; it’s only a hypothesis, even if it’s a good hypothesis. What’s interesting about string theory is that when it was first proposed, it was called the string hypothesis, as it was recognized this idea hadn’t yet risen to the status of a full-fledged theory. (Of course, at that time, it hypothesized that strings were the fundamental entity inside of atomic nuclei, rather than quarks and gluons.)

    8
    Image credit: G.S. Sharov (Tver State U.), 2013, via http://inspirehep.net/record/1233875.

    It’s still a physical hypothesis, and perhaps someday it will become a physically interesting scientific theory. When that day comes, we’ll all proudly welcome string theory into the fold as science. Until then, we can all agree that string theory is interesting for the possibilities it holds. Whether those possibilities are relevant or meaningful for our Universe, however, is a question science is unable to address today.

    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 4:24 pm on December 24, 2015 Permalink | Reply
    Tags: , , , , , String Theory   

    From Ethan Siegel: “What Are Quantum Gravity’s Alternatives To String Theory?” 

    Starts with a bang
    Starts with a Bang

    12.24.15
    Ethan Siegel

    1
    Image credit: CPEP (Contemporary Physics Education Project), NSF/DOE/LBNL.

    If there is a quantum theory of gravity, is String Theory the only game in town?

    “I just think too many nice things have happened in string theory for it to be all wrong. Humans do not understand it very well, but I just don’t believe there is a big cosmic conspiracy that created this incredible thing that has nothing to do with the real world.” –Edward Witten

    The Universe we know and love — with [Albert] Einstein’s General Relativity as our theory of gravity and quantum field theories of the other three forces — has a problem that we don’t often talk about: it’s incomplete, and we know it. Einstein’s theory on its own is just fine, describing how matter-and-energy relate to the curvature of space-and-time. Quantum field theories on their own are fine as well, describing how particles interact and experience forces. Normally, the quantum field theory calculations are done in flat space, where spacetime isn’t curved. We can do them in the curved space described by Einstein’s theory of gravity as well (although they’re harder — but not impossible — to do), which is known as semi-classical gravity. This is how we calculate things like Hawking radiation and black hole decay.

    2
    Image credit: NASA, via http://www.nasa.gov/topics/universe/features/smallest_blackhole.html

    But even that semi-classical treatment is only valid near and outside the black hole’s event horizon, not at the location where gravity is truly at its strongest: at the singularities (or the mathematically nonsensical predictions) theorized to be at the center. There are multiple physical instances where we need a quantum theory of gravity, all having to do with strong gravitational physics on the smallest of scales: at tiny, quantum distances. Important questions, such as:

    What happens to the gravitational field of an electron when it passes through a double slit?
    What happens to the information of the particles that form a black hole, if the black hole’s eventual state is thermal radiation?
    And what is the behavior of a gravitational field/force at and around a singularity?

    3
    Image credit: Nature 496, 20–23 (04 April 2013) doi:10.1038/496020a, via http://www.nature.com/news/astrophysics-fire-in-the-hole-1.12726.

    In order to explain what happens at short distances in the presence of gravitational sources — or masses — we need a quantum, discrete, and hence particle-based theory of gravity. The known quantum forces are mediated by particles known as bosons, or particles with integer spin. The photon mediates the electromagnetic force, the W-and-Z bosons mediate the weak force, while the gluons mediate the strong force. All these types of particles have a spin of 1, which for massive (W-and-Z) particles mean they can take on spin values of -1, 0, or +1, while for massless ones (like gluons and photons), they can take on values of -1 or +1 only.

    The Higgs boson is also a boson, although it doesn’t mediate any forces, and has a spin of 0. Because of what we know about gravitation — General Relativity is a tensor theory of gravity — it must be mediated by a massless particle with a spin of 2, meaning it can take on a spin value of -2 or +2 only.

    This is fantastic! It means that we already know a few things about a quantum theory of gravity before we even try to formulate one! We know this because whatever the true quantum theory of gravity turns out to be, it must be consistent with General Relativity when we’re not at very small distances from a massive particle or object, just as — 100 years ago — we knew that General Relativity needed to reduce to Newtonian gravity in the weak-field regime.

    4
    Image credit: NASA, of an artist’s concept of Gravity Probe B orbiting the Earth to measure space-time curvature.

    NASA Gravity Probe B
    Gravity Probe B

    The big question, of course is how? How do you quantize gravity in a way that’s correct (at describing reality), consistent (with both GR and QFT), and hopefully leads to calculable predictions for new phenomena that might be observed, measured or somehow tested. The leading contender, of course, is something you’ve long heard of: String Theory.

    String Theory is an interesting framework — it can include all of the standard model fields and particles, both the fermions and the bosons.

    0
    The Standard Model of elementary particles (more schematic depiction), with the three generations of matter, gauge bosons in the fourth column, and the Higgs boson in the fifth.

    It includes also a 10-dimensional Tensor-Scalar theory of gravity: with 9 space and 1 time dimensions, and a scalar field parameter. If we erase six of those spatial dimensions (through an incompletely defined process that people just call compactification) and let the parameter (ω) that defines the scalar interaction go to infinity, we can recover General Relativity.

    5
    Image credit: NASA/Goddard/Wade Sisler, of Brian Greene presenting on String Theory.

    But there are a whole host of phenomenological problems with String Theory. One is that it predicts a large number of new particles, including all the supersymmetric ones, none of which have been found.

    Supersymmetry standard model
    Standard Model of Supersymmetry

    It claims to not need to need “free parameters” like the standard model has (for the masses of the particles), but it replaces that problem with an even worse one. String theory refers to “10⁵⁰⁰ possible solutions,” where these solutions refer to the vacuum expectation values of the string fields, and there’s no mechanism to recover them; if you want String Theory to work, you need to give up on dynamics, and simply say, “well, it must’ve been anthropically selected.” There are frustrations, drawbacks, and problems with the very idea of String Theory. But the biggest problem with it may not be these mathematical ones. Instead, it may be that there are four other alternatives that may lead us to quantum gravity instead; approaches that are completely independent of String Theory.

    6
    Image credit: Wikimedia Commons user Linfoxman, of an illustration of a quantized “fabric of space.”

    1.) Loop Quantum Gravity [reader, please take the time to visit this link and read the article]. LQG is an interesting take on the problem: rather than trying to quantize particles, LQG has as one of its central features that space itself is discrete. Imagine a common analogy for gravity: a bedsheet pulled taut, with a bowling ball in the center. Rather than a continuous fabric, though, we know that the bedsheet itself is really quantized, in that it’s made up of molecules, which in turn are made of atoms, which in turn are made of nuclei (quarks and gluons) and electrons.

    Space might be the same way! Perhaps it acts like a fabric, but perhaps it’s made up of finite, quantized entities. And perhaps it’s woven out of “loops,” which is where the theory gets it name from. Weave these loops together and you get a spin network, which represents a quantum state of the gravitational field. In this picture, not just the matter itself but space itself is quantized. The way to go from this idea of a spin network to a perhaps realistic way of doing gravitational computations is an active area of research, one that saw a tremendous leap forward made in just 2007/8, so this is still actively advancing.

    7
    Image credit: Wikimedia Commons user & reasNink, generated with Wolfram Mathematica 8.0.

    2.) Asymptotically Safe Gravity. This is my personal favorite of the attempts at a quantum theory of gravity. Asymptotic freedom was developed in the 1970s to explain the unusual nature of the strong interaction: it was a very weak force at extremely short distances, then got stronger as (color) charged particles got farther and farther apart. Unlike electromagnetism, which had a very small coupling constant, the strong force has a large one. Due to some interesting properties of QCD, if you wound up with a (color) neutral system, the strength of the interaction fell off rapidly. This was able to account for properties like the physical sizes of baryons (protons and neutrons, for example) and mesons (pions, for example).

    Asymptotic safety, on the other hand, looks to solve a fundamental problem that’s related to this: you don’t need small couplings (or couplings that tend to zero), but rather for the couplings to simply be finite in the high-energy limit. All coupling constants change with energy, so what asymptotic safety does is pick a high-energy fixed point for the constant (technically, for the renormalization group, from which the coupling constant is derived), and then everything else can be calculated at lower energies.

    At least, that’s the idea! We’ve figured out how to do this in 1+1 dimensions (one space and one time), but not yet in 3+1 dimensions. Still, progress has been made, most notably by Christof Wetterich, who had two ground breaking papers in the 1990s. More recently, Wetterich used asymptotic safety — just six years ago — to calculate a prediction for the mass of the Higgs boson before the LHC found it. The result?

    9
    Image credit: Mikhail Shaposhnikov & Christof Wetterich.

    Amazingly, what it indicated was perfectly in line with what the LHC wound up finding.

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

    It’s such an amazing prediction that if asymptotic safety is correct, and — when the error bars are beaten down further — the masses of the top quark, the W-boson and the Higgs boson are finalized, there may not even be a need for any other fundamental particles (like SUSY particles) for physics to be stable all the way up to the Planck scale. It’s not only very promising, it has many of the same appealing properties of string theory: quantizes gravity successfully, reduces to GR in the low energy limit, and is UV-finite. In addition, it beats string theory on at least one account: it doesn’t need the addition of new particles or parameters that we have no evidence for! Of all the string theory alternatives, this one is my favorite.

    3.) Causal Dynamical Triangulations. This idea, CDT, is one of the new kids in town, first developed only in 2000 by Renate Loll and expanded on by others since. It’s similar to LQG in that space itself is discrete, but is primarily concerned with how that space itself evolves. One interesting property of this idea is that time must be discrete as well! As an interesting feature, it gives us a 4-dimensional spacetime (not even something put in a priori, but something that the theory gives us) at the present time, but at very, very high energies and small distances (like the Planck scale), it displays a 2-dimensional structure. It’s based on a mathematical structure called a simplex, which is a multi-dimensional analogue of a triangle.

    10
    Image credit: screenshot from the Wikipedia page for Simplex, via https://en.wikipedia.org/wiki/Simplex.

    A 2-simplex is a triangle, a 3-simplex is a tetrahedron, and so on. One of the “nice” features of this option is that causality — a notion held sacred by most human beings — is explicitly preserved in CDT. (Sabine has some words on CDT here, and its possible relation to asymptotically safe gravity.) It might be able to explain gravity, but it isn’t 100% certain that the standard model of elementary particles can fit suitably into this framework. It’s only major advances in computation that have enabled this to become a fairly well-studied alternative of late, and so work in this is both ongoing and relatively young.

    4.) Emergent gravity. And finally, we come to what’s probably the most speculative, recent of the quantum gravity possibilities. Emergent gravity only gained prominence in 2009, when Erik Verlinde proposed entropic gravity, a model where gravity was not a fundamental force, but rather emerged as a phenomenon linked to entropy. In fact, the seeds of emergent gravity go back to the discoverer of the conditions for generating a matter-antimatter asymmetry, Andrei Sakharov, who proposed the concept back in 1967. This research is still in its infancy, but as far as developments in the last 5–10 years go, it’s hard to ask for more than this.

    11
    Image credit: flickr gallery of J. Gabas Esteban.

    We’re sure we need a quantum theory of gravity to make the Universe work at a fundamental level, but we’re not sure what that theory looks like or whether any of these five avenues (string theory included) are going to prove fruitful or not. String Theory is the best studied of all the options, but Loop Quantum Gravity is a rising second, with the others being given serious consideration at long last. They say the answer’s always in the last place you look, and perhaps that’s motivation enough to start looking, seriously, in newer places.

    See the full article here .

    Please help promote STEM in your local schools.

    STEM Icon

    Stem Education Coalition

    “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 2:12 pm on August 27, 2015 Permalink | Reply
    Tags: , , String Theory,   

    From Symmetry: “Looking for strings inside inflation” 

    Symmetry

    August 27, 2015
    Troy Rummler

    1

    Theorists from the Institute for Advanced Study have proposed a way forward in the quest to test string theory.

    Two theorists recently proposed a way to find evidence for an idea famous for being untestable: string theory. It involves looking for particles that were around 14 billion years ago, when a very tiny universe hit a growth spurt that used 15 billion times more energy than a collision in the Large Hadron Collider.

    Scientists can’t crank the LHC up that high, not even close. But they could possibly observe evidence of these particles through cosmological studies, with the right technological advances.
    Unknown particles

    During inflation—the flash of hyperexpansion that happened 10-33 seconds after the big bang— particles were colliding with astronomical power. We see remnants of that time in tiny fluctuations in the haze of leftover energy called the cosmic microwave background [CMB].

    Cosmic Background Radiation Planck
    CMB per Planck

    ESA Planck
    ESA/Planck

    Scientists might be able to find remnants of any prehistoric particles that were around during that time as well.

    “If new particles existed during inflation, they can imprint a signature on the primordial fluctuations, which can be seen through specific patterns,” says theorist Juan Maldacena of the Institute for Advanced Study at Princeton University.

    Maldacena and his IAS collaborator, theorist Nima Arkani-Hamed, have used quantum field theory calculations to figure out what these patterns might look like. The pair presented their findings at an annual string theory conference held this year in Bengaluru, India, in June.

    The probable, impossible string

    String theory is frequently summed up by its basic tenet: that the fundamental units of matter are not particles. They are one-dimensional, vibrating strings of energy.

    The theory’s purpose is to bridge a mathematic conflict between quantum mechanics and [Albert] Einstein’s theory of general relativity. Inside a black hole, for example, quantum mechanics dictates that gravity is impossible. Any attempt to adjust one theory to fit the other causes the whole delicate system to collapse. Instead of trying to do this, string theory creates a new mathematical framework in which both theories are natural results. Out of this framework emerges an astonishingly elegant way to unify the forces of nature, along with a correct qualitative description of all known elementary particles.

    As a system of mathematics, string theory makes a tremendous number of predictions. Testable predictions? None so far.

    Strings are thought to be the smallest objects in the universe, and computing their effects on the relatively enormous scales of particle physics experiments is no easy task. String theorists predict that new particles exist, but they cannot compute their masses.

    To exacerbate the problem, string theory can describe a variety of universes that differ by numbers of forces, particles or dimensions. Predictions at accessible energies depend on these unknown or very difficult details. No experiment can definitively prove a theory that offers so many alternative versions of reality.
    Putting string theory to the test

    But scientists are working out ways that experiments could at least begin to test parts of string theory. One prediction that string theory makes is the existence of particles with a unique property: a spin of greater than two.

    Spin is a property of fundamental particles. Particles that don’t spin decay in symmetric patterns. Particles that do spin decay in asymmetric patterns, and the greater the spin, the more complex those patterns get. Highly complex decay patterns from collisions between these particles would have left signature impressions on the universe as it expanded and cooled.

    Scientists could find the patterns of particles with greater than spin 2 in subtle variations in the distribution of galaxies or in the cosmic microwave background, according to Maldacena and Arkani-Hamed. Observational cosmologists would have to measure the primordial fluctuations over a wide range of length scales to be able to see these small deviations.

    The IAS theorists calculated what those measurements would theoretically be if these massive, high-spin particles existed. Such a particle would be much more massive than anything scientists could find at the LHC.

    A challenging proposition

    Cosmologists are already studying patterns in the cosmic microwave background. Experiments such as Planck, BICEP and POLAR BEAR are searching for polarization, which would be evidence that a nonrandom force acted on it.

    BICEP 2
    BICEP 2 interior
    BICEP

    POLARBEAR McGill Telescope
    PolarBear

    If they rewind the effects of time and mathematically undo all other forces that have interacted with this energy, they hope that what pattern remains will match the predicted twists imbued by inflation.

    The patterns proposed by Maldacena and Arkani-Hamed are much subtler and much more susceptible to interference. So any expectation of experimentally finding such signals is still a long way off.

    But this research could point us toward someday finding such signatures and illuminating our understanding of particles that have perhaps left their mark on the entire universe.
    The value of strings

    Whether or not anyone can prove that the world is made of strings, people have proven that the mathematics of string theory can be applied to other fields.

    In 2009, researchers discovered that string theory math could be applied to conventional problems in condensed matter physics. Since then researchers have been applying string theory to study superconductors.

    Fellow IAS theorist Edward Witten, who received the Fields Medal in 1990 for his mathematical contributions to quantum field theory and Supersymmetry, says Maldacena and Arkani-Hamed’s presentation was among the most innovative work he saw at the Strings ‘15 conference.

    Witten and others believe that such successes in other fields indicate that string theory actually underlies all other theories at some deeper level.

    “Physics—like history—does not precisely repeat itself,” Witten says. However, with similar structures appearing at different scales of lengths and energies, “it does rhyme.”

    See the full article here.

    Please help promote STEM in your local schools.

    STEM Icon

    Stem Education Coalition

    Symmetry is a joint Fermilab/SLAC publication.


     
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