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  • richardmitnick 3:05 pm on December 10, 2018 Permalink | Reply
    Tags: Loop Quantum Gravity, , Viewpoint: Black Hole Evolution Traced Out with Loop Quantum Gravity, White hole   

    From Physics: “Viewpoint: Black Hole Evolution Traced Out with Loop Quantum Gravity” 

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    From Physics

    December 10, 2018
    Carlo Rovelli
    Center of Theoretical Physics
    CNRS
    Aix-Marseille University
    Toulon University, Marseille, France

    Loop quantum gravity—a theory that extends general relativity by quantizing spacetime—predicts that black holes evolve into white holes.

    1
    Figure 1: Artist rendering of the black-to-white-hole transition. Using loop quantum gravity, Ashtekar, Olmedo, and Singh predict that black holes evolve into white holes. F. Vidotto/University of the Basque Country.

    Black holes are remarkable entities. On the one hand, they have now become familiar astrophysical objects that have been observed in large numbers and in many ways: we have evidence of stellar-mass holes dancing around with a companion star, of gigantic holes at the center of galaxies pulling in spiraling disks of matter, and of black hole pairs merging in a spray of gravitational waves. All of this is beautifully accounted for by Einstein’s century-old theory of general relativity. Yet, on the other hand, black holes remain highly mysterious. We see matter falling into them, but we are in the dark about what happens to this matter when it reaches the center of the hole.

    Abhay Ashtekar and Javier Olmedo at Pennsylvania State University in University Park and Parampreet Singh at Louisiana State University, Baton Rouge, have taken a step toward answering this question [1]. They have shown that loop quantum gravity—a candidate theory for providing a quantum-mechanical description of gravity—predicts that spacetime continues across the center of the hole into a new region that exists in the future and has the geometry of the interior of a white hole. A white hole is the time-reversed image of a black hole: in it, matter can only move outwards. The passage “across the center” into a future region is counterintuitive; it is possible thanks to the strong distortion of the spacetime geometry inside the hole that is allowed by general relativity. This result supports a hypothesis under investigation by numerous research groups: the future of all black holes may be to convert into a real white hole, from which the matter that has fallen inside can bounce out. However, existing theories have not been able to fully show a way for this bounce to happen. That loop quantum gravity manages to do it is an indication that this theory has ripened enough to tackle real-world situations.

    The reason why we are in the dark about aspects of black hole physics is that quantum phenomena dominate at the center and in the future of these objects. Classical general relativity predicts that a black hole lives forever and that its center is a “singularity” where space and time end. These predictions are not realistic because they disregard quantum effects. To tackle these effects we need a quantum theory of gravity. We don’t yet have consensus on such a theory, but we have candidates, some of which are now reaching the point of allowing actual calculations on the quantum behavior of black holes. Loop quantum gravity, which has a clean conceptual structure and a well-defined mathematical formulation based on representing the fabric of space as a spin network that evolves in time, is one such theory.

    During the last few years, a number of research groups have applied loop theory to explore the evolution of black holes. These efforts are building a compelling picture based on a black-to-white-hole transition scenario (Fig. 1), which can be summarized as follows [2]. At the center of the black hole, space and time do not end in a singularity, but continue across a short transition region where the Einstein equations are violated by quantum effects. From this region, space and time emerge with the structure of a white hole interior, a possibility suggested in the 1930s by physicist John Lighton Synge [3]. As the hole’s center evolves, its external surface, or “horizon,” slowly shrinks because of the emission of radiation—a phenomenon first described by Stephen Hawking. This shrinkage continues until the horizon reaches the Planck size (the characteristic scale of quantum gravity) or earlier [4, 5], at which point a quantum transition (“quantum tunneling”) happens at the horizon, turning it into the horizon of a white hole (Fig. 2). Thanks to the peculiar distorted relativistic geometry, the white hole interior born at the center joins the white horizon, completing the formation of the white hole.

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    Figure 2: Diagram representing the spacetime evolution of a black hole into a white hole via a quantum transition. The vertical axis represents time; the horizontal axis represents distance from the center. C. Rovelli/Aix-Marseille University; adapted by APS/Alan Stonebraker

    Loosely speaking, the full phenomenon is analogous to the bouncing of a ball. A ball falls to the ground, bounces, and then moves up. The upward motion after the bounce is the time-reversed version of the falling ball. Similarly, a black hole “bounces” and emerges as its time-reversed version—a white hole. Collapsing matter does not disappear at the center: it bounces up through the white hole. Energy and information that fell into the black hole emerge from the white hole. The configuration where the compression is maximal, which separates the black hole from the white hole, is called a “Planck star.” Because of the huge time distortion allowed by relativity, the time for the process to happen can be short (microseconds) when measured from inside the hole but long (billions of years) when measured from the outside. Black holes might be bouncing stars seen in extreme slow motion.

    This is a compelling picture because it removes the singularity at a black hole’s center and resolves the paradox of the apparent disappearance of energy and information into a black hole. Until now, this black-to-white-hole picture was not derived from an actual quantum theory of gravity; it was just conjectured—and implemented with ad hoc modifications to Einstein’s general relativity equations. Ashtekar, Olmedo, and Singh have shown that a crucial ingredient of this scenario, the transition at the center, follows from a genuine quantum gravity theory, namely, loop theory. The result was obtained through an approximation of the full loop-quantum-gravity equations [5]—similar to the one employed in previous work aimed at resolving the big bang singularity [6].

    It is important to note that the Ashtekar-Olmedo-Singh model addresses only the transition at the center of the hole. To complete the picture, we also need the calculation of the tunneling at the horizon [7]. Preliminary steps in this direction have been taken, but the problem is open. Its solution would lead to a complete understanding of the quantum physics of black holes.

    It is not implausible that empirical observations could support this scenario. Models suggest that several observed astrophysical phenomena could be related to the black-to-white-hole transition [8]. Among these are fast radio bursts (FRBs) and certain high-energy cosmic rays. Both could be produced by matter and photons that were trapped in black holes produced in the early Universe and liberated by the black-to-white-hole transition. For the moment, however, the astrophysical data are insufficient to determine whether the statistical properties of observed FRBs and cosmic rays confirm this hypothesis [8]. Another intriguing possibility is that small holes produced by the black-to-white-hole transition may be stable: in which case, these “remnants” could be a component of dark matter [9].

    We are only beginning to understand the quantum physics of black holes, but in this still speculative field, the Ashtekar-Olmedo-Singh result gives us a welcome fixed point: loop gravity predicts that the interior of a black hole continues into a white hole. The importance of any progress in this field goes beyond understanding black holes. The center of a black hole is where our current theory of spacetime, as given by Einstein’s general relativity, fails. Understanding the physics of this region would mean understanding quantum space and quantum time.

    This research is published in Physical Review Letters and Physical Review D.

    References

    A. Ashtekar, J. Olmedo, and P. Singh, “Quantum transfiguration of Kruskal black holes,” Phys. Rev. Lett. 121, 241301 (2018); “Quantum extension of the Kruskal spacetime,” Phys. Rev. D 98, 126003 (2018).
    E. Bianchi, M. Christodoulou, F. D’Ambrosio, H. M. Haggard, and C. Rovelli, “White holes as remnants: A surprising scenario for the end of a black hole,” Class. Quant. Grav. 35, 225003 (2018).
    J. L. Synge, “The gravitational field of a particle,” Proc. Roy. Irish Acad. A 53, 83 (1950).
    C. Rovelli and F. Vidotto, “Planck stars,” Int. J. Mod. Phys. D 23, 1442026 (2014).
    L. Modesto, “Black hole interior from loop quantum gravity,” Adv. High Energy Phys. 2008, 459290 (2008).
    I. Agullo and P. Singh, “Loop quantum cosmology: A brief review,” Loop Quantum Gravity, 100 Years of General Relativity Vol. 4, edited by A. Ashtekar and J. Pullin (World Scientific, Singapore, 2017)[Amazon][WorldCat].
    H. Haggard and C. Rovelli, “Black hole fireworks: Quantum-gravity effects outside the horizon spark black to white hole tunneling,” Phys. Rev. D 92, 104020 (2015).
    A. Barrau, B. Bolliet, F. Vidotto, and C. Weimer, “Phenomenology of bouncing black holes in quantum gravity: A closer look,” J. Cosmol. Astropart. Phys. 2016, 022 (2016); A. Barrau, K. Martineau, and F. Moulin, “Status report on the phenomenology of black holes in loop quantum gravity: Evaporation, tunneling to white holes, dark matter and gravitational waves,” Universe 4, 102 (2018).
    C. Rovelli and F. Vidotto, “Small black/white hole stability and dark matter,” Universe 4, 127 (2018).

    See the full article here .

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  • richardmitnick 9:51 am on August 14, 2018 Permalink | Reply
    Tags: , , Loop Quantum Gravity,   

    From Don Lincoln at: Fermi National Accelerator Lab: “Loop Quantum Gravity” Video 

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    From Fermi National Accelerator Lab , an enduring source of strength for the US contribution to scientific research world wide.

    FNAL’s Don Lincoln

    While there are many challenges facing modern particle physics, perhaps the ultimate one (and certainly among the most difficult) is to describe the nature of gravity in the quantum realm. Despite a century of effort, scientists have had only the most cursory of success. In this video, Fermilab’s Dr. Don Lincoln talks about the idea of quantum gravity and sketches out the need for this difficult advance.

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  • richardmitnick 4:07 pm on June 20, 2017 Permalink | Reply
    Tags: , Conjectures about gravity, Cosmic censorship conjecture, Loop Quantum Gravity, Naked singularity in a four-dimensional universe, , , , Singularities, , Then Stephen said ‘You want to bet?’, Weak gravity   

    From Quanta: “Where Gravity Is Weak and Naked Singularities Are Verboten’ 

    Quanta Magazine
    Quanta Magazine

    June 20, 2017
    Natalie Wolchover

    1
    Mike Zeng for Quanta Magazine

    Physicists have wondered for decades whether infinitely dense points known as singularities can ever exist outside black holes, which would expose the mysteries of quantum gravity for all to see. Singularities — snags in the otherwise smooth fabric of space and time where Albert Einstein’s classical gravity theory breaks down and the unknown quantum theory of gravity is needed — seem to always come cloaked in darkness, hiding from view behind the event horizons of black holes. The British physicist and mathematician Sir Roger Penrose conjectured in 1969 that visible or “naked” singularities are actually forbidden from forming in nature, in a kind of cosmic censorship. But why should quantum gravity censor itself?

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    Roger Penrose in Berkeley, California, in 1978, nine years after proposing the cosmic censorship conjecture. George M. Bergman, Berkeley. Source: Archives of the Mathematisches Forschungsinstitut Oberwolfach

    Now, new theoretical calculations provide a possible explanation for why naked singularities do not exist — in a particular model universe, at least. The findings indicate that a second, newer conjecture about gravity, if it is true, reinforces Penrose’s cosmic censorship conjecture by preventing naked singularities from forming in this model universe. Some experts say the mutually supportive relationship between the two conjectures increases the chances that both are correct. And while this would mean singularities do stay frustratingly hidden, it would also reveal an important feature of the quantum gravity theory that eludes us.

    “It’s pleasing that there’s a connection” between the two conjectures, said John Preskill of the California Institute of Technology, who in 1991 bet Stephen Hawking that the cosmic censorship conjecture would fail (though he actually thinks it’s probably true).

    The new work, reported in May in Physical Review Letters by Jorge Santos and his student Toby Crisford at the University of Cambridge and relying on a key insight by Cumrun Vafa of Harvard University, unexpectedly ties cosmic censorship to the 2006 weak gravity conjecture [JHEP], which asserts that gravity must always be the weakest force in any viable universe, as it is in ours. (Gravity is by far the weakest of the four fundamental forces; two electrons electrically repel each other 1 million trillion trillion trillion times more strongly than they gravitationally attract each other.) Santos and Crisford were able to simulate the formation of a naked singularity in a four-dimensional universe with a different space-time geometry than ours. But they found that if another force exists in that universe that affects particles more strongly than gravity, the singularity becomes cloaked in a black hole. In other words, where a perverse pinprick would otherwise form in the space-time fabric, naked for all the world to see, the relative weakness of gravity prevents it.

    Santos and Crisford are running simulations now to test whether cosmic censorship is saved at exactly the limit where gravity becomes the weakest force in the model universe, as initial calculations suggest. Such an alliance with the better-established cosmic censorship conjecture would reflect very well on the weak gravity conjecture. And if weak gravity is right, it points to a deep relationship between gravity and the other quantum forces, potentially lending support to string theory over a rival theory called loop quantum gravity. The “unification” of the forces happens naturally in string theory, where gravity is one vibrational mode of strings and forces like electromagnetism are other modes. But unification is less obvious in loop quantum gravity, where space-time is quantized in tiny volumetric packets that bear no direct connection to the other particles and forces. “If the weak gravity conjecture is right, loop quantum gravity is definitely wrong,” said Nima Arkani-Hamed, a professor at the Institute for Advanced Study who co-discovered the weak gravity conjecture.

    The new work “does tell us about quantum gravity,” said Gary Horowitz, a theoretical physicist at the University of California, Santa Barbara.

    The Naked Singularities

    In 1991, Preskill and Kip Thorne, both theoretical physicists at Caltech, visited Stephen Hawking at Cambridge. Hawking had spent decades exploring the possibilities packed into the Einstein equation, which defines how space-time bends in the presence of matter, giving rise to gravity. Like Penrose and everyone else, he had yet to find a mechanism by which a naked singularity could form in a universe like ours. Always, singularities lay at the centers of black holes — sinkholes in space-time that are so steep that no light can climb out. He told his visitors that he believed in cosmic censorship. Preskill and Thorne, both experts in quantum gravity and black holes (Thorne was one of three physicists who founded the black-hole-detecting LIGO experiment), said they felt it might be possible to detect naked singularities and quantum gravity effects. “There was a long pause,” Preskill recalled. “Then Stephen said, ‘You want to bet?’”

    The bet had to be settled on a technicality and renegotiated in 1997, after the first ambiguous exception cropped up. Matt Choptuik, a physicist at the University of British Columbia who uses numerical simulations to study Einstein’s theory, showed that a naked singularity can form in a four-dimensional universe like ours when you perfectly fine-tune its initial conditions. Nudge the initial data by any amount, and you lose it — a black hole forms around the singularity, censoring the scene. This exceptional case doesn’t disprove cosmic censorship as Penrose meant it, because it doesn’t suggest naked singularities might actually form. Nonetheless, Hawking conceded the original bet and paid his debt per the stipulations, “with clothing to cover the winner’s nakedness.” He embarrassed Preskill by making him wear a T-shirt featuring a nearly-naked lady while giving a talk to 1,000 people at Caltech. The clothing was supposed to be “embroidered with a suitable concessionary message,” but Hawking’s read like a challenge: “Nature Abhors a Naked Singularity.”

    The physicists posted a new bet online, with language to clarify that only non-exceptional counterexamples to cosmic censorship would count. And this time, they agreed, “The clothing is to be embroidered with a suitable, truly concessionary message.”

    The wager still stands 20 years later, but not without coming under threat. In 2010, the physicists Frans Pretorius and Luis Lehner discovered a mechanism [Physical Review Letters]for producing naked singularities in hypothetical universes with five or more dimensions. And in their May paper, Santos and Crisford reported a naked singularity in a classical universe with four space-time dimensions, like our own, but with a radically different geometry. This latest one is “in between the ‘technical’ counterexample of the 1990s and a true counterexample,” Horowitz said. Preskill agrees that it doesn’t settle the bet. But it does change the story.

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    Lucy Reading-Ikkanda/Quanta Magazine

    The Tin Can Universe

    The new discovery began to unfold in 2014, when Horowitz, Santos and Benson Way found that naked singularities could exist in a pretend 4-D universe called “anti-de Sitter” (AdS) space whose space-time geometry is shaped like a tin can. This universe has a boundary — the can’s side — which makes it a convenient testing ground for ideas about quantum gravity: Physicists can treat bendy space-time in the can’s interior like a hologram that projects off of the can’s surface, where there is no gravity. In universes like our own, which is closer to a “de Sitter” (dS) geometry, the only boundary is the infinite future, essentially the end of time. Timeless infinity doesn’t make a very good surface for projecting a hologram of a living, breathing universe.

    Despite their differences, the interiors of both AdS and dS universes obey Einstein’s classical gravity theory — everywhere outside singularities, that is. If cosmic censorship holds in one of the two arenas, some experts say you might expect it to hold up in both.

    Horowitz, Santos and Way were studying what happens when an electric field and a gravitational field coexist in an AdS universe. Their calculations suggested that cranking up the energy of the electric field on the surface of the tin can universe will cause space-time to curve more and more sharply around a corresponding point inside, eventually forming a naked singularity. In their recent paper, Santos and Crisford verified the earlier calculations with numerical simulations.

    But why would naked singularities exist in 5-D and in 4-D when you change the geometry, but never in a flat 4-D universe like ours? “It’s like, what the heck!” Santos said. “It’s so weird you should work on it, right? There has to be something here.”

    Weak Gravity to the Rescue

    In 2015, Horowitz mentioned the evidence for a naked singularity in 4-D AdS space to Cumrun Vafa, a Harvard string theorist and quantum gravity theorist who stopped by Horowitz’s office. Vafa had been working to rule out large swaths of the 10^500 different possible universes that string theory naively allows. He did this by identifying “swamplands”: failed universes that are too logically inconsistent to exist. By understanding patterns of land and swamp, he hoped to get an overall picture of quantum gravity.

    Working with Arkani-Hamed, Luboš Motl and Alberto Nicolis in 2006, Vafa proposed the weak gravity conjecture as a swamplands test. The researchers found that universes only seemed to make sense when particles were affected by gravity less than they were by at least one other force. Dial down the other forces of nature too much, and violations of causality and other problems arise. “Things were going wrong just when you started violating gravity as the weakest force,” Arkani-Hamed said. The weak-gravity requirement drowns huge regions of the quantum gravity landscape in swamplands.

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    Jorge Santos (left) and Toby Crisford of the University of Cambridge have found an unexpected link between two conjectures about gravity.
    Courtesy of Jorge Santos

    Weak gravity and cosmic censorship seem to describe different things, but in chatting with Horowitz that day in 2015, Vafa realized that they might be linked. Horowitz had explained Santos and Crisford’s simulated naked singularity: When the researchers cranked up the strength of the electric field on the boundary of their tin-can universe, they assumed that the interior was classical — perfectly smooth, with no particles quantum mechanically fluctuating in and out of existence. But Vafa reasoned that, if such particles existed, and if, in accordance with the weak gravity conjecture, they were more strongly coupled to the electric field than to gravity, then cranking up the electric field on the AdS boundary would cause sufficient numbers of particles to arise in the corresponding region in the interior to gravitationally collapse the region into a black hole, preventing the naked singularity.

    Subsequent calculations by Santos and Crisford supported Vafa’s hunch; the simulations they’re running now could verify that naked singularities become cloaked in black holes right at the point where gravity becomes the weakest force. “We don’t know exactly why, but it seems to be true,” Vafa said. “These two reinforce each other.”

    Quantum Gravity

    The full implications of the new work, and of the two conjectures, will take time to sink in. Cosmic censorship imposes an odd disconnect between quantum gravity at the centers of black holes and classical gravity throughout the rest of the universe. Weak gravity appears to bridge the gap, linking quantum gravity to the other quantum forces that govern particles in the universe, and possibly favoring a stringy approach over a loopy one. Preskill said, “I think it’s something you would put on your list of arguments or reasons for believing in unification of the forces.”

    However, Lee Smolin of the Perimeter Institute, one of the developers of loop quantum gravity, has pushed back, arguing that if weak gravity is true, there might be a loopy reason for it. And he contends that there is a path to unification [J.Phys.A] of the forces within his theory — a path that would need to be pursued all the more vigorously if the weak gravity conjecture holds.

    Given the apparent absence of naked singularities in our universe, physicists will take hints about quantum gravity wherever they can find them. They’re as lost now in the endless landscape of possible quantum gravity theories as they were in the 1990s, with no prospects for determining through experiments which underlying theory describes our world. “It is thus paramount to find generic properties that such quantum gravity theories must have in order to be viable,” Santos said, echoing the swamplands philosophy.

    Weak gravity might be one such property — a necessary condition for quantum gravity’s consistency that spills out and affects the world beyond black holes. These may be some of the only clues available to help researchers feel their way into the darkness.

    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 9:41 am on July 26, 2016 Permalink | Reply
    Tags: , , , Causal Dynamical Triangulation, Dimensional reduction, , Loop Quantum Gravity,   

    From Ethan Siegel: “Dimensional Reduction: The Key To Physics’ Greatest Mystery?” 

    From Ethan Siegel

    Jul 26, 2016
    Sabine Hossenfelder

    1
    A visualization of a 3-torus model of space, where lines or sheets in series could reproduce a larger-dimensional structure. Image credit: Bryan Brandenburg, under c.c.a.-s.a.-3.0.

    What if the Universe – and fundamentally, space itself – were like a pile of laundry?

    It doesn’t sound like a sober thought, but it’s got math behind it, so physicists think there might be something to it. Indeed the math has piled up lately. They call it “dimensional reduction,” the idea that space on short distances has fewer than three dimensions – and it might help physicists to quantize gravity.

    We’ve gotten used to space with additional dimensions, rolled up so small (or compactified) that we can’t observe them. But how do you get rid of dimensions instead? To understand how it works we first have clarify what we mean by “dimension.”

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    A 3-D object like a pipe will have a Hausdorff dimension of 1, as the lines only have one dimension to spread out as long as they’d like, which is also seen in the reduction to a line as you zoom out. Image credit: Alex Dunkel (Maky) of Wikipedia, based on Brian Greene’s The Elegant Universe, under a c.c.a.-s.a.-4.0 license.

    We normally think about dimensions of space by picturing a series of lines which spread from a point. How quickly the lines dilute with the distance from the point tells us the “Hausdorff dimension” of a space. The faster the lines diverge from each other with distance, the larger the Hausdorff dimension. If you speak through a pipe, for example, sound waves spread less and your voice carries farther. The pipe hence has a lower Hausdorff dimension than our normal 3-dimensional office cubicles. It’s the Hausdorff dimension that we colloquially refer to as just dimension.

    For dimensional reduction, however, it is not the Hausdorff dimension which is relevant, but instead the “spectral dimension,” which is a slightly different concept. We can calculate it by first getting rid of the “time” in “space-time” and making it into space (period). We then place a random walker at one point and measure the probability that it returns to the same point during its walk. The smaller the average return probability, the higher the probability the walker gets lost, and the higher the number of spectral dimensions.

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    Isotropic random walk on the euclidean lattice Z^3. This picture shows three different walks after 10 000 unit steps, all three starting from the origin. Image credit: Zweistein, under c.c.a.-s.a.-3.0.

    Normally, for a non-quantum space, both notions of dimension are identical. However, add quantum mechanics and the spectral dimension at short distances goes down from four to two. The return probability for short walks becomes larger than expected, and the walker is less likely to get lost – this is what physicists mean by “dimensional reduction.”

    The spectral dimension is not necessarily an integer; it can take on any value. This value starts at 4 when quantum effects can be neglected, and decreases when the walker’s sensitivity to quantum effects at shortest distances increases. Physicists therefore also like to say that the spectral dimension “runs,” meaning its value depends on the resolution at which space-time is probed.

    Dimensional reduction is an attractive idea because quantizing gravity is considerably easier in lower dimensions, where the infinities that plague traditional attempts to quantize gravity go away. A theory with a reduced number of dimensions at the shortest distances therefore has a much higher chance to remain consistent, and therefore to provide a meaningful theory for the quantum nature of space and time. Not so surprisingly, among physicists, dimensional reduction has received quite some attention lately.

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    Cross section of the quintic Calabi–Yau manifold. Unlike taking a cross section, dimensional reduction is about having reduced degrees of freedom when it comes to the probability of returning to your starting point in a finite number of steps. Public domain.

    This strange property of quantum-spaces was first found in Causal Dynamical Triangulation, an approach to quantum gravity that relies on approximating curved spaces by triangular patches. In this work, the researchers did a numerical simulation of a random walk in such a triangulized quantum-space, and found that the spectral dimension goes down from four to two. Or actually, to 1.80 ± 0.25, if you want to know precisely.

    Instead of doing numerical simulations, it is also possible to study the spectral dimension mathematically, which has since been done in various other approaches. For this, physicists exploit that the behavior of the random walk is governed by a differential equation – the diffusion equation (a.k.a., the heat equation) – which depends on the curvature of space. In quantum gravity, spatial curvature has quantum fluctuations, so instead it’s the average curvature value which enters the diffusion equation. From the diffusion equation, one then calculates the return probability for the random walk.

    Through this method, physicists have inferred the spectral dimension also in Asymptotically Safe Gravity, an approach to quantum gravity which relies on the resolution-dependence (the “running”) of quantum field theories. And they found the same drop as in Causal Dynamical Triangulations: from four to two spectral dimensions.

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    A representation of a spin network in Loop quantum gravity. Image credit: Markus Poessel (Mapos) of Wikimedia Commons, under c.c.a.-s.a.-3.0.

    Another indication that dimensional reduction might be important comes from Loop Quantum Gravity, where the scaling of the area operator with length changes at short distances. In this case, is somewhat questionable whether the notion of curvature makes sense at all on short distances. Ignoring this philosophical conundrum, one can construct the diffusion equation anyway, and one finds that the spectral dimension – surprise – drops from four to two.

    And finally, there is Horava-Lifshitz gravity, yet another modification of gravity which some believe helps with quantizing it. Here too, dimensional reduction, from four to two, has been found.

    It is difficult to visualize what is happening with the dimensionality of space if it goes down continuously, rather than in discrete steps as in the example with the laundry pile. Perhaps a good way to picture it, as Calcagni, Eichhorn and Saueressig suggest, is to think of the quantum fluctuations of space-time as hindering a particle’s random walk, thereby slowing it down. It wouldn’t have to be that way, though. Quantum fluctuations could have also kicked the particle around wildly, thereby increasing the spectral dimension rather than decreasing it. But that’s not what the math tells us.

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    Real gravitational effects occur in spacetime, not just space, and must propagate at the speed of light through space and time. Image credit: SLAC National Accelerator Laboratory.

    One shouldn’t take this picture too seriously though, because we’re talking about a random walk in space, not space-time, and so it’s not a real physical process. Turning time into space might seem strange, but it is a common mathematical simplification which is often used for calculations in quantum theory. Still, it makes it difficult to interpret what is happening physically.

    I find it intriguing that several different approaches to quantum gravity share a behavior like this. Maybe it is a general property of quantum space-time? But then, there are many different types of random walks, and while these different approaches to quantum gravity share a similar scaling behavior for the spectral dimension, they differ in the type of random walk that produces this scaling. So maybe the similarities are only superficial.

    And, of course, this idea has no observational evidence speaking for it. Maybe never will. But one day, I’m sure, all the math will click into place and everything will make perfect sense. Meanwhile, have another.

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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 4:31 pm on January 13, 2016 Permalink | Reply
    Tags: , Loop Quantum Gravity, ,   

    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 11:15 am on October 15, 2014 Permalink | Reply
    Tags: , , Loop Quantum Gravity, , , , ,   

    From NOVA: “Are White Holes Real?” 

    PBS NOVA

    NOVA

    Tue, 19 Aug 2014
    Maggie McKee

    Sailors have their krakens and their sea serpents. Physicists have white holes: cosmic creatures that straddle the line between tall tale and reality. Yet to be seen in the wild, white holes may be only mathematical monsters. But new research suggests that, if a speculative theory called loop quantum gravity is right, white holes could be real—and we might have already observed them.

    wh

    A white whole is, roughly speaking, the opposite of a black hole. “A black hole is a place where you can go in but you can never escape; a white hole is a place where you can leave but you can never go back,” says Caltech physicist Sean Carroll. “Otherwise, [both share] exactly the same mathematics, exactly the same geometry.” That boils down to a few essential features: a singularity, where mass is squeezed into a point of infinite density, and an event horizon, the invisible “point of no return” first described mathematically by the German physicist Karl Schwarzschild in 1916. For a black hole, the event horizon represents a one-way entrance; for a white hole, it’s exit-only.

    There is excellent evidence that black holes really exist, and astrophysicists have a robust understanding of what it takes to make one. To imagine how a white hole might form, though, we have to go out on a bit of an astronomical limb. One possibility involves a spinning black hole. According to [Albert] Einstein’s general theory of relativity, the rotation smears the singularity into a ring, making it possible in theory to travel through the swirling black hole without being crushed. General relativity’s equations suggest that someone falling into such a black hole could fall through a tunnel in space-time called a wormhole and emerge from a white hole that spits its contents into a different region of space or period of time.

    Though mathematical solutions to those equations exist for white holes, “they’re not realistic,” says Andrew Hamilton, an astrophysicist at the University of Colorado at Boulder. That is because they describe universes that contain only black holes, white holes and wormholes—no matter, radiation or energy. Indeed, previous research, including Hamilton’s, suggests that anything that falls into a spinning black hole will essentially plug up the wormhole, preventing the formation of a passage to a white hole.

    But there’s a light at the end of the wormhole, so to speak. General relativity, from which Hamilton draws his predictions, breaks down at a black hole’s singularity. “The energy density and the curvature become so large that classical gravity is not a good description of what’s happening there,” says Stephen Hsu, a physicist at Michigan State University in East Lansing. Perhaps a more complete model of gravity—one that works as well on the quantum scale as it does on large ones—would negate the instability and allow for white holes, he says.

    Indeed, a unified theory that merges gravity and quantum mechanics is one of the holy grails of contemporary physics. Applying one such theory, loop quantum gravity, to black holes, theorists Hal Haggard and Carlo Rovelli of Aix-Marseille University in France have shown that black holes could metamorphose into white holes via a quantum process. In July, they published their work online.

    Loop quantum gravity proposes that space-time is made up of fundamental building blocks shaped like loops. According to Haggard and Rovelli, the loops’ finite size prevents a dying star from collapsing all the way down into a point of infinite density, and the shrinking object rebounds into a white hole instead. This process may take just a few thousandths of a second, but thanks to the intense gravity involved, the effects of relativity make the transformation appear to take much, much longer to anyone watching from afar. That means that minuscule black holes born in the infant universe could “now be ready to pop off like firecrackers,” forming white holes, according to a report in Nature. Some of the explosions astronomers thought were supernovae may actually be the wails of newborn white holes.

    The black-to-white conversion could resolve a nettlesome conundrum known as the black hole information paradox. The notion that information can be destroyed is anathema in physics, and general relativity says that anything, including information, that falls into a black hole can never escape. These two statements are not at odds if black holes simply act as locked safes for any information they slurp up, but Stephen Hawking showed 40 years ago that black holes actually evaporate over time. That led to the disturbing possibility that the information contained within them could be lost too, triggering a debate that rages to this day.

    But if a black hole instead turns into a white hole, then “all the information is recovered,” says Haggard. “We are quite excited about this mechanism because it avoids so many of the thorny issues that surround this discussion.”

    The new work is preliminary, however, and it is far from clear whether loop quantum gravity is an accurate description of reality. The only glimpse we get of white holes might turn out to be those we model in labs and kitchen sinks. But Carroll says that’s okay. Just thinking about these possibly mythical cosmic creatures can improve physicists’ intuition, “even if the real world is messy and not like those exact situations,” he says. “That’s the way in which white holes are very useful.”

    See the full article here.

    NOVA is the highest rated science series on television and the most watched documentary series on public television. It is also one of television’s most acclaimed series, having won every major television award, most of them many times over.

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