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  • richardmitnick 5:44 pm on April 17, 2019 Permalink | Reply
    Tags: Albert Einstein's theory of general relativity, , Einstein’s Unfinished Revolution: The Search for What Lies Beyond the Quantum, , , ,   

    From Scientific American: “Cosmologist Lee Smolin says that at certain key points, the scientific worldview is based on fallacious reasoning” 

    Scientific American

    From Scientific American

    April 17, 2019
    Jim Daley

    Lee Smolin, author of six books about the philosophical issues raised by contemporary physics, says every time he writes a new one, the experience completely changes the direction his own research is taking. In his latest book, Einstein’s Unfinished Revolution: The Search for What Lies Beyond the Quantum, Smolin, a cosmologist and quantum theorist at the Perimeter Institute for Theoretical Physics in Ontario, tackles what he sees as the limitations in quantum theory.

    1
    Credit: Perimeter Institute

    “I want to say the scientific worldview is based on fallacious reasoning at certain key points,” Smolin says. In Einstein’s Unfinished Revolution, he argues one of those key points was the assumption that quantum physics is a complete theory. This incompleteness, Smolin argues, is the reason quantum physics has not been able to solve certain questions about the universe.

    “Most of what we do [in science] is take the laws that have been discovered by experiments to apply to parts of the universe, and just assume that they can be scaled up to apply to the whole universe,” Smolin says. “I’m going to be suggesting that’s wrong.”

    Join Smolin at the Perimeter Institute as he discusses his book and takes the audience on a journey through the basics of quantum physics and the experiments and scientists who have changed our understanding of the universe. The discussion, “Einstein’s Unfinished Revolution,” is part of Perimeter’s public lecture series and will take place on Wednesday, April 17, at 7 P.M. Eastern time. Online viewers can participate in the discussion by tweeting to @Perimeter using the #piLIVE hashtag.

    See the full article here .


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

     
  • richardmitnick 10:08 am on April 10, 2019 Permalink | Reply
    Tags: Albert Einstein's theory of general relativity, Although the telescopes are not physically connected they are able to synchronize their recorded data with atomic clocks — hydrogen masers — which precisely time their observations., , , , BlackHoleCam, , Data were flown to highly specialised supercomputers — known as correlators — at the Max Planck Institute for Radio Astronomy and MIT Haystack Observatory to be combined., , , , Sagittarius A* the supermassive black hole at the center of our galaxy, VLBI-very-long-baseline interferometry   

    From European Southern Observatory: “Astronomers Capture First Image of a Black Hole” 

    ESO 50 Large

    From European Southern Observatory

    10 April 2019

    Heino Falcke
    Chair of the EHT Science Council, Radboud University
    The Netherlands
    Tel: +31 24 3652020
    Email: h.falcke@astro.ru.nl

    Luciano Rezzolla
    EHT Board Member, Goethe Universität
    Germany
    Tel: +49 69 79847871
    Email: rezzolla@itp.uni-frankfurt.de

    Eduardo Ros
    EHT Board Secretary, Max-Planck-Institut für Radioastronomie
    Germany
    Tel: +49 22 8525125
    Email: ros@mpifr.de

    Calum Turner
    ESO Public Information Officer
    Garching bei München, Germany
    Tel: +49 89 3200 6655
    Email: pio@eso.org

    ESO, ALMA, and APEX contribute to paradigm-shifting observations of the gargantuan black hole at the heart of the galaxy Messier 87.

    1
    The Event Horizon Telescope (EHT) — a planet-scale array of eight ground-based radio telescopes forged through international collaboration — was designed to capture images of a black hole. Today, in coordinated press conferences across the globe, EHT researchers reveal that they have succeeded, unveiling the first direct visual evidence of a supermassive black hole and its shadow.

    This breakthrough was announced today in a series of six papers published in a special issue of The Astrophysical Journal Letters. The image reveals the black hole at the centre of Messier 87 [1], a massive galaxy in the nearby Virgo galaxy cluster. This black hole resides 55 million light-years from Earth and has a mass 6.5 billion times that of the Sun [2].

    The EHT links telescopes around the globe to form an unprecedented Earth-sized virtual telescope [3]. The EHT offers scientists a new way to study the most extreme objects in the Universe predicted by Einstein’s general relativity during the centenary year of the historic experiment that first confirmed the theory [4].

    “We have taken the first picture of a black hole,” said EHT project director Sheperd S. Doeleman of the Center for Astrophysics | Harvard & Smithsonian. “This is an extraordinary scientific feat accomplished by a team of more than 200 researchers.”

    Black holes are extraordinary cosmic objects with enormous masses but extremely compact sizes. The presence of these objects affects their environment in extreme ways, warping spacetime and superheating any surrounding material.

    “If immersed in a bright region, like a disc of glowing gas, we expect a black hole to create a dark region similar to a shadow — something predicted by Einstein’s general relativity that we’ve never seen before,” explained chair of the EHT Science Council Heino Falcke of Radboud University, the Netherlands. “This shadow, caused by the gravitational bending and capture of light by the event horizon, reveals a lot about the nature of these fascinating objects and has allowed us to measure the enormous mass of Messier 87’s black hole.”

    Multiple calibration and imaging methods have revealed a ring-like structure with a dark central region — the black hole’s shadow — that persisted over multiple independent EHT observations.

    “Once we were sure we had imaged the shadow, we could compare our observations to extensive computer models that include the physics of warped space, superheated matter and strong magnetic fields. Many of the features of the observed image match our theoretical understanding surprisingly well,” remarks Paul T.P. Ho, EHT Board member and Director of the East Asian Observatory [5]. “This makes us confident about the interpretation of our observations, including our estimation of the black hole’s mass.”

    “The confrontation of theory with observations is always a dramatic moment for a theorist. It was a relief and a source of pride to realise that the observations matched our predictions so well,” elaborated EHT Board member Luciano Rezzolla of Goethe Universität, Germany.

    Creating the EHT was a formidable challenge which required upgrading and connecting a worldwide network of eight pre-existing telescopes deployed at a variety of challenging high-altitude sites. These locations included volcanoes in Hawai`i and Mexico, mountains in Arizona and the Spanish Sierra Nevada, the Chilean Atacama Desert, and Antarctica.

    The EHT observations use a technique called very-long-baseline interferometry (VLBI) which synchronises telescope facilities around the world and exploits the rotation of our planet to form one huge, Earth-size telescope observing at a wavelength of 1.3mm. VLBI allows the EHT to achieve an angular resolution of 20 micro-arcseconds — enough to read a newspaper in New York from a café in Paris [6].

    The telescopes contributing to this result were ALMA, APEX, the IRAM 30-meter telescope, the James Clerk Maxwell Telescope, the Large Millimeter Telescope Alfonso Serrano, the Submillimeter Array, the Submillimeter Telescope, and the South Pole Telescope [7]. Petabytes of raw data from the telescopes were combined by highly specialised supercomputers hosted by the Max Planck Institute for Radio Astronomy and MIT Haystack Observatory.

    Max Planck Institute for Radio Astronomy Bonn Germany

    MIT Haystack Observatory, Westford, Massachusetts, USA, Altitude 131 m (430 ft)

    ESO/NRAO/NAOJ ALMA Array in Chile in the Atacama at Chajnantor plateau, at 5,000 metres

    ESO/MPIfR APEX high on the Chajnantor plateau in Chile’s Atacama region, at an altitude of over 4,800 m (15,700 ft)

    IRAM 30m Radio telescope, on Pico Veleta in the Spanish Sierra Nevada,, Altitude 2,850 m (9,350 ft)

    East Asia Observatory James Clerk Maxwell telescope, Mauna Kea, Hawaii, USA,4,207 m (13,802 ft) above sea level

    The University of Massachusetts Amherst and Mexico’s Instituto Nacional de Astrofísica, Óptica y Electrónica
    Large Millimeter Telescope Alfonso Serrano, Mexico, at an altitude of 4850 meters on top of the Sierra Negra

    CfA Submillimeter Array Mauna Kea, Hawaii, USA, Altitude 4,080 m (13,390 ft)

    U Arizona Submillimeter Telescope located on Mt. Graham near Safford, Arizona, USA, Altitude 3,191 m (10,469 ft)

    South Pole Telescope SPTPOL. The SPT collaboration is made up of over a dozen (mostly North American) institutions, including the University of Chicago, the University of California, Berkeley, Case Western Reserve University, Harvard/Smithsonian Astrophysical Observatory, the University of Colorado Boulder, McGill University, The University of Illinois at Urbana-Champaign, University of California, Davis, Ludwig Maximilian University of Munich, Argonne National Laboratory, and the National Institute for Standards and Technology. It is funded by the National Science Foundation. Altitude 2.8 km (9,200 ft)

    European facilities and funding played a crucial role in this worldwide effort, with the participation of advanced European telescopes and the support from the European Research Council — particularly a €14 million grant for the BlackHoleCam project [8]. Support from ESO, IRAM and the Max Planck Society was also key. “This result builds on decades of European expertise in millimetre astronomy”, commented Karl Schuster, Director of IRAM and member of the EHT Board.

    The construction of the EHT and the observations announced today represent the culmination of decades of observational, technical, and theoretical work. This example of global teamwork required close collaboration by researchers from around the world. Thirteen partner institutions worked together to create the EHT, using both pre-existing infrastructure and support from a variety of agencies. Key funding was provided by the US National Science Foundation (NSF), the EU’s European Research Council (ERC), and funding agencies in East Asia.

    “ESO is delighted to have significantly contributed to this result through its European leadership and pivotal role in two of the EHT’s component telescopes, located in Chile — ALMA and APEX,” commented ESO Director General Xavier Barcons. “ALMA is the most sensitive facility in the EHT, and its 66 high-precision antennas were critical in making the EHT a success.”

    “We have achieved something presumed to be impossible just a generation ago,” concluded Doeleman. “Breakthroughs in technology, connections between the world’s best radio observatories, and innovative algorithms all came together to open an entirely new window on black holes and the event horizon.”
    Notes

    [1] The shadow of a black hole is the closest we can come to an image of the black hole itself, a completely dark object from which light cannot escape. The black hole’s boundary — the event horizon from which the EHT takes its name — is around 2.5 times smaller than the shadow it casts and measures just under 40 billion km across.

    [2] Supermassive black holes are relatively tiny astronomical objects — which has made them impossible to directly observe until now. As the size of a black hole’s event horizon is proportional to its mass, the more massive a black hole, the larger the shadow. Thanks to its enormous mass and relative proximity, M87’s black hole was predicted to be one of the largest viewable from Earth — making it a perfect target for the EHT.

    [3] Although the telescopes are not physically connected, they are able to synchronize their recorded data with atomic clocks — hydrogen masers — which precisely time their observations. These observations were collected at a wavelength of 1.3 mm during a 2017 global campaign. Each telescope of the EHT produced enormous amounts of data – roughly 350 terabytes per day – which was stored on high-performance helium-filled hard drives. These data were flown to highly specialised supercomputers — known as correlators — at the Max Planck Institute for Radio Astronomy and MIT Haystack Observatory to be combined. They were then painstakingly converted into an image using novel computational tools developed by the collaboration.

    [4] 100 years ago, two expeditions set out for Principe Island off the coast of Africa and Sobral in Brazil to observe the 1919 solar eclipse, with the goal of testing general relativity by seeing if starlight would be bent around the limb of the sun, as predicted by Einstein. In an echo of those observations, the EHT has sent team members to some of the world’s highest and most isolated radio facilities to once again test our understanding of gravity.

    [5] The East Asian Observatory (EAO) partner on the EHT project represents the participation of many regions in Asia, including China, Japan, Korea, Taiwan, Vietnam, Thailand, Malaysia, India and Indonesia.

    [6] Future EHT observations will see substantially increased sensitivity with the participation of the IRAM NOEMA Observatory, the Greenland Telescope and the Kitt Peak Telescope.

    [7] ALMA is a partnership of the European Southern Observatory (ESO; Europe, representing its member states), the U.S. National Science Foundation (NSF), and the National Institutes of Natural Sciences(NINS) of Japan, together with the National Research Council (Canada), the Ministry of Science and Technology (MOST; Taiwan), Academia Sinica Institute of Astronomy and Astrophysics (ASIAA; Taiwan), and Korea Astronomy and Space Science Institute (KASI; Republic of Korea), in cooperation with the Republic of Chile. APEX is operated by ESO, the 30-meter telescope is operated by IRAM (the IRAM Partner Organizations are MPG (Germany), CNRS (France) and IGN (Spain)), the James Clerk Maxwell Telescope is operated by the EAO, the Large Millimeter Telescope Alfonso Serrano is operated by INAOE and UMass, the Submillimeter Array is operated by SAO and ASIAA and the Submillimeter Telescope is operated by the Arizona Radio Observatory (ARO). The South Pole Telescope is operated by the University of Chicago with specialized EHT instrumentation provided by the University of Arizona.

    [8] BlackHoleCam is an EU-funded project to image, measure and understand astrophysical black holes. The main goal of BlackHoleCam and the Event Horizon Telescope (EHT) is to make the first ever images of the billion solar masses black hole in the nearby galaxy Messier 87 and of its smaller cousin, Sagittarius A*, the supermassive black hole at the centre of our Milky Way. This allows the determination of the deformation of spacetime caused by a black hole with extreme precision.

    More information

    This research was presented in a series of six papers published today in a special issue of The Astrophysical Journal Letters.

    The EHT collaboration involves more than 200 researchers from Africa, Asia, Europe, North and South America. The international collaboration is working to capture the most detailed black hole images ever by creating a virtual Earth-sized telescope. Supported by considerable international investment, the EHT links existing telescopes using novel systems — creating a fundamentally new instrument with the highest angular resolving power that has yet been achieved.

    The EHT consortium consists of 13 stakeholder institutes; the Academia Sinica Institute of Astronomy and Astrophysics, the University of Arizona, the University of Chicago, the East Asian Observatory, Goethe-Universitaet Frankfurt, Institut de Radioastronomie Millimétrique, Large Millimeter Telescope, Max Planck Institute for Radio Astronomy, MIT Haystack Observatory, National Astronomical Observatory of Japan, Perimeter Institute for Theoretical Physics, Radboud University and the Smithsonian Astrophysical Observatory.

    Links

    ESO EHT web page
    EHT Website & Press Release
    ESOBlog on the EHT Project

    Papers:

    Paper I: The Shadow of the Supermassive Black Hole
    Paper II: Array and Instrumentation
    Paper III: Data processing and Calibration
    Paper IV: Imaging the Central Supermassive Black Hole
    Paper V: Physical Origin of the Asymmetric Ring
    Paper VI: The Shadow and Mass of the Central Black Hole

    See the full article here .


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    ESO is the foremost intergovernmental astronomy organisation in Europe and the world’s most productive ground-based astronomical observatory by far. It is supported by 16 countries: Austria, Belgium, Brazil, the Czech Republic, Denmark, France, Finland, Germany, Italy, the Netherlands, Poland, Portugal, Spain, Sweden, Switzerland and the United Kingdom, along with the host state of Chile. ESO carries out an ambitious programme focused on the design, construction and operation of powerful ground-based observing facilities enabling astronomers to make important scientific discoveries. ESO also plays a leading role in promoting and organising cooperation in astronomical research. ESO operates three unique world-class observing sites in Chile: La Silla, Paranal and Chajnantor. At Paranal, ESO operates the Very Large Telescope, the world’s most advanced visible-light astronomical observatory and two survey telescopes. VISTA works in the infrared and is the world’s largest survey telescope and the VLT Survey Telescope is the largest telescope designed to exclusively survey the skies in visible light. ESO is a major partner in ALMA, the largest astronomical project in existence. And on Cerro Armazones, close to Paranal, ESO is building the 39-metre EEuropean Extremely Large Telescope, the E-ELT, which will become “the world’s biggest eye on the sky”.

     
  • richardmitnick 9:16 am on August 20, 2018 Permalink | Reply
    Tags: Albert Einstein's theory of general relativity, ARC Center of Excellence, , , , , , , ,   

    From ARC Centres of Excellence via Science Alert: “We May Soon Know How a Crucial Einstein Principle Works in The Quantum Realm” 

    arc-centers-of-excellence-bloc

    From ARC Centres of Excellence

    via

    Science Alert

    1
    (NiPlot/iStock)

    20 AUG 2018
    MICHELLE STARR

    The puzzle of how Einstein’s equivalence principle plays out in the quantum realm has vexed physicists for decades. Now two researchers may have finally figured out the key that will allow us to solve this mystery.

    Einstein’s physical theories have held up under pretty much every classical physics test thrown at them. But when you get down to the very smallest scales – the quantum realm – things start behaving a little bit oddly.

    The thing is, it’s not really clear how Einstein’s theory of general relativity and quantum mechanics work together. The laws that govern the two realms are incompatible with each other, and attempts to resolve these differences have come up short.

    But the equivalence principle – one of the cornerstones of modern physics – is an important part of general relativity. And if it can be resolved within the quantum realm, that may give us a toehold into resolving general relativity and quantum mechanics.

    The equivalence principle, in simple terms, means that gravity accelerates all objects equally, as can be observed in the famous feather and hammer experiment conducted by Apollo 15 Commander David Scott on the Moon.

    It also means that gravitational mass and inertial mass are equivalent; to put it simply, if you were in a sealed chamber, like an elevator, you would be unable to tell if the force outside the chamber was gravity or acceleration equivalent to gravity. The effect is the same.

    “Einstein’s equivalence principle contends that the total inertial and gravitational mass of any objects are equivalent, meaning all bodies fall in the same way when subject to gravity,” explained physicist Magdalena Zych of the ARC Centre of Excellence for Engineered Quantum Systems in Australia.

    “Physicists have been debating whether the principle applies to quantum particles, so to translate it to the quantum world we needed to find out how quantum particles interact with gravity.

    “We realised that to do this we had to look at the mass.”

    According to relativity, mass is held together by energy. But in quantum mechanics, that gets a bit complicated. A quantum particle can have two different energy states, with different numerical values, known as a superposition.

    And because it has a superposition of energy states, it also has a superposition of inertial masses.

    This means – theoretically, at least – that it should also have a superposition of gravitational masses. But the superposition of quantum particles isn’t accounted for by the equivalence principle.

    “We realised that we had to look how particles in such quantum states of the mass behave in order to understand how a quantum particle sees gravity in general,” Zych said.

    “Our research found that for quantum particles in quantum superpositions of different masses, the principle implies additional restrictions that are not present for classical particles – this hadn’t been discovered before.”

    This discovery allowed the team to re-formulate the equivalence principle to account for the superposition of values in a quantum particle.

    The new formulation hasn’t yet been applied experimentally; but, the researchers said, opens a door to experiments that could test the newly discovered restrictions.

    And it offers a new framework for testing the equivalence principle in the quantum realm – we can hardly wait.

    The team’s research has been published in the journal Nature Physics.

    See the full article here .

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    The objectives for the ARC Centres of Excellence are to:

    undertake highly innovative and potentially transformational research that aims to achieve international standing in the fields of research envisaged and leads to a significant advancement of capabilities and knowledge
    link existing Australian research strengths and build critical mass with new capacity for interdisciplinary, collaborative approaches to address the most challenging and significant research problems
    develope relationships and build new networks with major national and international centres and research programs to help strengthen research, achieve global competitiveness and gain recognition for Australian research
    build Australia’s human capacity in a range of research areas by attracting and retaining, from within Australia and abroad, researchers of high international standing as well as the most promising research students
    provide high-quality postgraduate and postdoctoral training environments for the next generation of researchers
    offer Australian researchers opportunities to work on large-scale problems over long periods of time
    establish Centres that have an impact on the wider community through interaction with higher education institutes, governments, industry and the private and non-profit sector.

     
  • richardmitnick 7:44 pm on April 24, 2018 Permalink | Reply
    Tags: Albert Einstein's theory of general relativity, “Newton was the first physicist” says Sylvester James Gates a physicist at Brown University, , Peter Woit - “When you go far enough back you really can’t tell who’s a physicist and who’s a mathematician”, , Riemannian geometry, , The relationship between physics and mathematics goes back to the beginning of both subjects   

    From Symmetry: “The coevolution of physics and math” 

    Symmetry Mag
    Symmetry

    04/24/18
    Evelyn Lamb

    1
    Artwork by Sandbox Studio, Chicago

    Breakthroughs in physics sometimes require an assist from the field of mathematics—and vice versa.

    In 1912, Albert Einstein, then a 33-year-old theoretical physicist at the Eidgenössische Technische Hochschule in Zürich, was in the midst of developing an extension to his theory of special relativity.

    With special relativity, he had codified the relationship between the dimensions of space and time. Now, seven years later, he was trying to incorporate into his theory the effects of gravity. This feat—a revolution in physics that would supplant Isaac Newton’s law of universal gravitation and result in Einstein’s theory of general relativity—would require some new ideas.

    Fortunately, Einstein’s friend and collaborator Marcel Grossmann swooped in like a waiter bearing an exotic, appetizing delight (at least in a mathematician’s overactive imagination): Riemannian geometry.

    This mathematical framework, developed in the mid-19th century by German mathematician Bernhard Riemann, was something of a revolution itself. It represented a shift in mathematical thinking from viewing mathematical shapes as subsets of the three-dimensional space they lived in to thinking about their properties intrinsically. For example, a sphere can be described as the set of points in 3-dimensional space that lie exactly 1 unit away from a central point. But it can also be described as a 2-dimensional object that has particular curvature properties at every single point. This alternative definition isn’t terribly important for understanding the sphere itself but ends up being very useful with more complicated manifolds or higher-dimensional spaces.

    By Einstein’s time, the theory was still new enough that it hadn’t completely permeated through mathematics, but it happened to be exactly what Einstein needed. Riemannian geometry gave him the foundation he needed to formulate the precise equations of general relativity. Einstein and Grossmann were able to publish their work later that year.

    “It’s hard to imagine how he would have come up with relativity without help from mathematicians,” says Peter Woit, a theoretical physicist in the Mathematics Department at Columbia University.

    The story of general relativity could go to mathematicians’ heads. Here mathematics seems to be a benevolent patron, blessing the benighted world of physics with just the right equations at the right time.

    But of course the interplay between mathematics and physics is much more complicated than that. They weren’t even separate disciplines for most of recorded history. Ancient Greek, Egyptian and Babylonian mathematics took as an assumption the fact that we live in a world in which distance, time and gravity behave in a certain way.

    “Newton was the first physicist,” says Sylvester James Gates, a physicist at Brown University. “In order to reach the pinnacle, he had to invent a new piece of mathematics; it’s called calculus.”

    Calculus made some classical geometry problems easier to solve, but its foremost purpose to Newton was to give him a way to analyze the motion and change he observed in physics. In that story, mathematics is perhaps more of a butler, hired to help keep the affairs in order, than a savior.

    Even after physics and mathematics began their separate evolutionary paths, the disciplines were closely linked. “When you go far enough back, you really can’t tell who’s a physicist and who’s a mathematician,” Woit says. (As a mathematician, I was a bit scandalized the first time I saw Emmy Noether’s name attached to physics! I knew her primarily through abstract algebra.)

    Throughout the history of the two fields, mathematics and physics have each contributed important ideas to the other. Mathematician Hermann Weyl’s work on mathematical objects called Lie groups provided an important basis for understanding symmetry in quantum mechanics. In his 1930 book The Principles of Quantum Mechanics, theoretical physicist Paul Dirac introduced the Dirac delta function to help describe the concept in particle physics of a pointlike particle—anything so small that it would be modeled by a point in an idealized situation. A picture of the Dirac delta function looks like a horizontal line lying along the bottom of the x axis of a graph, at x=0, except at the place where it intersects with the y axis, where it explodes into a line pointing up to infinity. Dirac declared that the integral of this function, the measure of the area underneath it, was equal to 1. Strictly speaking, no such function exists, but Dirac’s use of the Dirac delta eventually spurred mathematician Laurent Schwartz to develop the theory of distributions in a mathematically rigorous way. Today distributions are extraordinarily useful in the mathematical fields of ordinary and partial differential equations.

    Though modern researchers focus their work more and more tightly, the line between physics and mathematics is still a blurry one. A physicist has won the Fields Medal, one of the most prestigious accolades in mathematics. And a mathematician, Maxim Kontsevich, has won the new Breakthrough Prizes in both mathematics and physics. One can attend seminar talks about quantum field theory, black holes, and string theory in both math and physics departments. Since 2011, the annual String Math conference has brought mathematicians and physicists together to work on the intersection of their fields in string theory and quantum field theory.

    String theory is perhaps the best recent example of the interplay between mathematics and physics, for reasons that eventually bring us back to Einstein and the question of gravity.

    String theory is a theoretical framework in which those pointlike particles Dirac was describing become one-dimensional objects called strings. Part of the theoretical model for those strings corresponds to gravitons, theoretical particles that carry the force of gravity.

    Most humans will tell you that we perceive the universe as having three spatial dimensions and one dimension of time. But string theory naturally lives in 10 dimensions. In 1984, as the number of physicists working on string theory ballooned, a group of researchers including Edward Witten, the physicist who was later awarded a Fields Medal, discovered that the extra six dimensions of string theory needed to be part of a space known as a Calabi-Yau manifold.

    When mathematicians joined the fray to try to figure out what structures these manifolds could have, physicists were hoping for just a few candidates. Instead, they found boatloads of Calabi-Yaus. Mathematicians still have not finished classifying them. They haven’t even determined whether their classification has a finite number of pieces.

    As mathematicians and physicists studied these spaces, they discovered an interesting duality between Calabi-Yau manifolds. Two manifolds that seem completely different can end up describing the same physics. This idea, called mirror symmetry, has blossomed in mathematics, leading to entire new research avenues. The framework of string theory has almost become a playground for mathematicians, yielding countless new avenues of exploration.

    Mina Aganagic, a theoretical physicist at the University of California, Berkeley, believes string theory and related topics will continue to provide these connections between physics and math.

    “In some sense, we’ve explored a very small part of string theory and a very small number of its predictions,” she says. Mathematicians and their focus on detailed rigorous proofs bring one point of view to the field, and physicists, with their tendency to prioritize intuitive understanding, bring another. “That’s what makes the relationship so satisfying.”

    The relationship between physics and mathematics goes back to the beginning of both subjects; as the fields have advanced, this relationship has gotten more and more tangled, a complicated tapestry. There is seemingly no end to the places where a well-placed set of tools for making calculations could help physicists, or where a probing question from physics could inspire mathematicians to create entirely new mathematical objects or theories.

    See the full article here .

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    Symmetry is a joint Fermilab/SLAC publication.


     
  • richardmitnick 8:22 pm on March 18, 2018 Permalink | Reply
    Tags: Albert Einstein's theory of general relativity, , Mathematics vs Physics, , , , Shake a Black Hole, , The black hole stability conjecture   

    From Quanta: “To Test Einstein’s Equations, Poke a Black Hole” 

    Quanta Magazine
    Quanta Magazine

    mathematical physics
    https://sciencesprings.wordpress.com/2018/03/17/from-ethan-siegel-where-is-the-line-between-mathematics-and-physics/

    March 8, 2018
    Kevin Hartnett

    1
    Fantastic animation. Olena Shmahalo/Quanta Magazine

    In November 1915, in a lecture before the Prussian Academy of Sciences, Albert Einstein described an idea that upended humanity’s view of the universe. Rather than accepting the geometry of space and time as fixed, Einstein explained that we actually inhabit a four-dimensional reality called space-time whose form fluctuates in response to matter and energy.

    Einstein elaborated this dramatic insight in several equations, referred to as his “field equations,” that form the core of his theory of general relativity. That theory has been vindicated by every experimental test thrown at it in the century since.

    Yet even as Einstein’s theory seems to describe the world we observe, the mathematics underpinning it remain largely mysterious. Mathematicians have been able to prove very little about the equations themselves. We know they work, but we can’t say exactly why. Even Einstein had to fall back on approximations, rather than exact solutions, to see the universe through the lens he’d created.

    Over the last year, however, mathematicians have brought the mathematics of general relativity into sharper focus. Two groups have come up with proofs related to an important problem in general relativity called the black hole stability conjecture. Their work proves that Einstein’s equations match a physical intuition for how space-time should behave: If you jolt it, it shakes like Jell-O, then settles down into a stable form like the one it began with.

    “If these solutions were unstable, that would imply they’re not physical. They’d be a mathematical ghost that exists mathematically and has no significance from a physical point of view,” said Sergiu Klainerman, a mathematician at Princeton University and co-author, with Jérémie Szeftel, of one of the two new results [https://arxiv.org/abs/1711.07597].

    To complete the proofs, the mathematicians had to resolve a central difficulty with Einstein’s equations. To describe how the shape of space-time evolves, you need a coordinate system — like lines of latitude and longitude — that tells you which points are where. And in space-time, as on Earth, it’s hard to find a coordinate system that works everywhere.

    Shake a Black Hole

    General relativity famously describes space-time as something like a rubber sheet. Absent any matter, the sheet is flat. But start dropping balls onto it — stars and planets — and the sheet deforms. The balls roll toward one another. And as the objects move around, the shape of the rubber sheet changes in response.

    Einstein’s field equations describe the evolution of the shape of space-time. You give the equations information about curvature and energy at each point, and the equations tell you the shape of space-time in the future. In this way, Einstein’s equations are like equations that model any physical phenomenon: This is where the ball is at time zero, this is where it is five seconds later.

    “They’re a mathematically precise quantitative version of the statement that space-time curves in the presence of matter,” said Peter Hintz, a Clay research fellow at the University of California, Berkeley, and co-author, with András Vasy, of the other recent result [https://arxiv.org/abs/1606.04014].

    In 1916, almost immediately after Einstein released his theory of general relativity, the German physicist Karl Schwarzschild found an exact solution to the equations that describes what we now know as a black hole (the term wouldn’t be invented for another five decades). Later, physicists found exact solutions that describe a rotating black hole and one with an electrical charge.

    These remain the only exact solutions that describe a black hole. If you add even a second black hole, the interplay of forces becomes too complicated for present-day mathematical techniques to handle in all but the most special situations.

    Yet you can still ask important questions about this limited group of solutions. One such question developed out of work in 1952 by the French mathematician Yvonne Choquet-Bruhat. It asks, in effect: What happens when you shake a black hole?

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    Lucy Reading-Ikkanda/Quanta Magazine

    This problem is now known as the black hole stability conjecture. The conjecture predicts that solutions to Einstein’s equations will be “stable under perturbation.” Informally, this means that if you wiggle a black hole, space-time will shake at first, before eventually settling down into a form that looks a lot like the form you started with. “Roughly, stability means if I take special solutions and perturb them a little bit, change data a little bit, then the resulting dynamics will be very close to the original solution,” Klainerman said.

    So-called “stability” results are an important test of any physical theory. To understand why, it’s useful to consider an example that’s more familiar than a black hole.

    Imagine a pond. Now imagine that you perturb the pond by tossing in a stone. The pond will slosh around for a bit and then become still again. Mathematically, the solutions to whatever equations you use to describe the pond (in this case, the Navier-Stokes equations) should describe that basic physical picture. If the initial and long-term solutions don’t match, you might question the validity of your equations.

    “This equation might have whatever properties, it might be perfectly fine mathematically, but if it goes against what you expect physically, it can’t be the right equation,” Vasy said.

    For mathematicians working on Einstein’s equations, stability proofs have been even harder to find than solutions to the equations themselves. Consider the case of flat, empty Minkowski space — the simplest of all space-time configurations. This solution to Einstein’s equations was found in 1908 in the context of Einstein’s earlier theory of special relativity. Yet it wasn’t until 1993 that mathematicians managed to prove that if you wiggle flat, empty space-time, you eventually get back flat, empty space-time. That result, by Klainerman and Demetrios Christodoulou, is a celebrated work in the field.

    One of the main difficulties with stability proofs has to do with keeping track of what is going on in four-dimensional space-time as the solution evolves. You need a coordinate system that allows you to measure distances and identify points in space-time, just as lines of latitude and longitude allow us to define locations on Earth. But it’s not easy to find a coordinate system that works at every point in space-time and then continues to work as the shape of space-time evolves.

    “We don’t know of a one-size-fits-all way to do this,” Hintz wrote in an email. “After all, the universe does not hand you a preferred coordinate system.”

    The Measurement Problem

    The first thing to recognize about coordinate systems is that they’re a human invention. The second is that not every coordinate system works to identify every point in a space.

    Take lines of latitude and longitude: They’re arbitrary. Cartographers could have anointed any number of imaginary lines to be 0 degrees longitude.

    2

    And while latitude and longitude work to identify just about every location on Earth, they stop making sense at the North and South poles. If you knew nothing about Earth itself, and only had access to latitude and longitude readings, you might wrongly conclude there’s something topologically strange going on at those points.

    This possibility — of drawing wrong conclusions about the properties of physical space because the coordinate system used to describe it is inadequate — is at the heart of why it’s hard to prove the stability of space-time.

    “It could be the case that stability is true, but you’re using coordinates that are not stable and thus you miss the fact that stability is true,” said Mihalis Dafermos, a mathematician at the University of Cambridge and a leading figure in the study of Einstein’s equations.

    In the context of the black hole stability conjecture, whatever coordinate system you’re using has to evolve as the shape of space-time evolves — like a snugly fitting glove adjusting as the hand it encloses changes shape. The fit between the coordinate system and space-time has to be good at the start and remain good throughout. If it doesn’t, there are two things that can happen that would defeat efforts to prove stability.

    First, your coordinate system might change shape in a way that makes it break down at certain points, just as latitude and longitude fail at the poles. Such points are called “coordinate singularities” (to distinguish them from physical singularities, like an actual black hole). They are undefined points in your coordinate system that make it impossible to follow an evolving solution all the way through.

    Second, a poorly fitting coordinate system might disguise the underlying physical phenomena it’s meant to measure. To prove that solutions to Einstein’s equations settle down into a stable state after being perturbed, mathematicians must keep careful track of the ripples in space-time that are set in motion by the perturbation. To see why, it’s worth considering the pond again. A rock thrown into a pond generates waves. The long-term stability of the pond results from the fact that those waves decay over time — they grow smaller and smaller until there’s no sign they were ever there.

    The situation is similar for space-time. A perturbation will set off a cascade of gravitational waves, and proving stability requires proving that those gravitational waves decay. And proving decay requires a coordinate system — referred to as a “gauge” — that allows you to measure the size of the waves. The right gauge allows mathematicians to see the waves flatten and eventually disappear altogether.

    “The decay has to be measured relative to something, and it’s here where the gauge issue shows up,” Klainerman said. “If I’m not in the right gauge, even though in principle I have stability, I can’t prove it because the gauge will just not allow me to see that decay. If I don’t have decay rates of waves, I can’t prove stability.”

    The trouble is, while the coordinate system is crucial, it’s not obvious which one to choose. “You have a lot of freedom about what this gauge condition can be,” Hintz said. “Most of these choices are going to be bad.”

    Partway There

    A full proof of the black hole stability conjecture requires proving that all known black hole solutions to Einstein’s equations (with the spin of the black hole below a certain threshold) are stable after being perturbed. These known solutions include the Schwarzschild solution, which describes space-time with a nonrotating black hole, and the Kerr family of solutions, which describe configurations of space-time empty of everything save a single rotating black hole (where the properties of that rotating black hole — its mass and angular momentum — vary within the family of solutions).

    Both of the new results make partial progress toward a proof of the full conjecture.

    Hintz and Vasy, in a paper posted to the scientific preprint site arxiv.org in 2016 [see above 1606.04014], proved that slowly rotating black holes are stable. But their work did not cover black holes rotating above a certain threshold.

    Their proof also makes some assumptions about the nature of space-time. The original conjecture is in Minkowski space, which is not just flat and empty but also fixed in size. Hintz and Vasy’s proof takes place in what’s called de Sitter space, where space-time is accelerating outward, just like in the actual universe. This change of setting makes the problem simpler from a technical point of view, which is easy enough to appreciate at a conceptual level: If you drop a rock into an expanding pond, the expansion is going to stretch the waves and cause them to decay faster than they would have if the pond were not expanding.

    “You’re looking at a universe undergoing an accelerated expansion,” Hintz said. “This makes the problem a little easier as it appears to dilute the gravitational waves.”

    Klainerman and Szeftel’s work has a slightly different flavor. Their proof, the first part of which was posted online last November [see above 1711.07597], takes place in Schwarzschild space-time — closer to the original, more difficult setting for the problem. They prove the stability of a nonrotating black hole, but they do not address solutions in which the black hole is spinning. Moreover, they only prove the stability of black hole solutions for a narrow class of perturbations — where the gravitational waves generated by those perturbations are symmetric in a certain way.

    Both results involve new techniques for finding the right coordinate system for the problem. Hintz and Vasy start with an approximate solution to the equations, based on an approximate coordinate system, and gradually increase the precision of their answer until they arrive at exact solutions and well-behaved coordinates. Klainerman and Szeftel take a more geometric approach to the challenge.

    The two teams are now trying to build on their respective methods to find a proof of the full conjecture. Some expert observers think the day might not be far off.

    “I really think things are now at the stage that the remaining difficulties are just technical,” Dafermos said. “Somehow one doesn’t need new ideas to solve this problem.” He emphasized that a final proof could come from any one of the large number of mathematicians currently working on the problem.

    For 100 years Einstein’s equations have served as a reliable experimental guide to the universe. Now mathematicians may be getting closer to demonstrating exactly why they work so well.

    See the full article here .

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

     
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