tag:blogger.com,1999:blog-58266329603566940902019-06-21T03:33:24.949-05:00International Loop Quantum Gravity Seminar<a href="http://ilqgse.blogspot.com">En Español</a>
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The International Loop Quantum Gravity Seminar is held every two weeks via teleconference among the main research groups in loop quantum gravity. Slides are distributed in advance and audio posted after the seminar at the Seminar's website.
This blog presents summaries for the general public of the content of the seminars.</p>Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.comBlogger53125tag:blogger.com,1999:blog-5826632960356694090.post-15243619598679981002019-05-27T13:56:00.000-05:002019-05-27T13:56:36.138-05:00Experimental detection of the discreteness of timeTuesday, Apr 30th<br /><b></b><br /><b>Marios Christodoulou, University of Hong Kong</b><br /><b>Title: The possibility of experimental detection of the discreteness of time</b><br /><a href="http://relativity.phys.lsu.edu/ilqgs/christodoulou043019.pdf">PDF</a> of the talk (230K)<br /><a href="http://relativity.phys.lsu.edu/ilqgs/christodoulou043019.mp4">Audio+Slides</a> of the talk (21M) <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-AFw_EUGRdgg/WlZES_T69cI/AAAAAAAAJ1U/g9lUmOOYkv8YwQDJEoGWizGsyDWr39pPwCPcBGAYYCw/s1600/photo_bilbao.jpeg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="900" data-original-width="1600" height="180" src="https://2.bp.blogspot.com/-AFw_EUGRdgg/WlZES_T69cI/AAAAAAAAJ1U/g9lUmOOYkv8YwQDJEoGWizGsyDWr39pPwCPcBGAYYCw/s320/photo_bilbao.jpeg" width="320" /></a></div>By Jorge Pullin, LSU<br /><br />One of the most striking properties of quantum mechanics is that a system that classically can be in only two possible states, A and B, can, at the quantum level, also be in a "superposition" of A and B. If one measures what state it is in, one will get A with a certain probability and B with another. This led to the famous "<a href="https://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat">Schroedinger cat</a>" thought experiment in which the cat is in a state in which it is both alive and dead until one measures it. Such superpositions are not seen in everyday macroscopic life -like in the case of a cat- because interactions with the environment quickly determine the state of the system before we can measure it. They definitely exist and are needed to explain the microscopic world. With improvements in quantum technologies however, physicists are starting to construct systems of increasing size that can be in a quantum superposition. There is even talk of preparing not quite a Schroedinger cat, but a <a href="https://www.scientificamerican.com/article/schroedingers-bacterium-could-be-a-quantum-biology-milestone/">Schroedinger bacterium.</a><br /><br />An interesting situation to consider in these types of superpositions of states is what happens when one takes gravity into account. One could conceivably have a mass that is in a superposition of two states corresponding to the mass in different positions in space. What would be the resulting gravitational field? Would it correspond to the mass in one position or the other? We know we cannot couple classical and quantum theories consistently so to address this problem one needs to consider quantum states of the gravitational field.<br /><br />What this talk explored is that the "Schroedinger bacterium" types of experiments can potentially be sensitive to the structure of space-time at very short distances when one considers the quantum nature of gravity. They therefore offer an unexpected possibility of probing certain conjectured behaviors. For instance, if time were discrete, these types of experiments could see their results modified, even if the discreteness is at the "Planck level" (the basic unit of time at the Planck level is the Planck time, or 10<sup>-44</sup> seconds, for comparison the best atomic clocks can probe only up to 10<sup>-19</sup> seconds). This opens new possibilities for probing quantum gravitational effects with low energy experiments in the lab.Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-90259411060196405312019-03-20T13:11:00.000-05:002019-03-20T13:11:41.278-05:00Implications of a dynamical cosmological constantTuesday, Mar 19th<br /><b></b><br /><b>Lee Smolin, Perimeter Institute</b><br /><b>Title: Implications of a dynamical cosmological constant </b><br /><a href="http://relativity.phys.lsu.edu/ilqgs/smolin031919.pdf">PDF</a> of the talk (10M)<br /><a href="http://relativity.phys.lsu.edu/ilqgs/smolin031919.mp4">Audio+Slides</a> of the talk (28M)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-EVZTvOUz_OQ/XJE8u1zj7CI/AAAAAAAAK6s/38uBrSskm7cu3OyQi7btu_fvecn7g-l3wCLcBGAs/s1600/re.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="499" data-original-width="749" height="213" src="https://1.bp.blogspot.com/-EVZTvOUz_OQ/XJE8u1zj7CI/AAAAAAAAK6s/38uBrSskm7cu3OyQi7btu_fvecn7g-l3wCLcBGAs/s320/re.jpg" width="320" /></a></div>By Jorge Pullin, LSU<br /><br />Experimental cosmologists have determined that 95% of the content of the universe is not made up of ordinary matter. The vast majority of the universe consists of strange forms of matter known as dark matter and dark energy. Some people believe that in reality there is no such matter, but a modification of Einstein's general relativity is needed to explain the universe in large scales. That is, just ordinary matter with a new theory of gravity.<br /><br />The cosmological constant was a term Einstein added to his equations in 1917 in a futile attempt to make the universe static (at the time it was not known the universe expands). The extra terms it implies in the equations has a behavior similar to dark energy.<br /><br />Cosmologists have proposed several generalizations of Einstein's theory involving extra fields and constants in order to attempt to explain dark energy and dark matter. However, more complex theories tend to depend on extra parameters that need to be determined, limiting their predictive power. Essentially one can adjust parameters to fit any observed behavior. Also, there is a high degree of arbitrariness in how one can modify Einstein's theory.<br /><br />The aim of this talk is to introduce a basic principle for the creation of generalized theories that does not involve extra fields. To give more details we have to discuss some basic concepts. Most classical equations of motion, like those of general relativity, can be derived from what is known as an "action principle". The "action" is a function of the variables of the theory such that if one requires that it be a minimum (or a maximum), the equations of the theory follow. That is, the condition for minimization (or maximization) is that the equations of the theory hold. It turns out one can add to the action of a theory some terms such that the resulting equations of motion remain unchanged. Such terms (usually multiplied times a constant) are called "topological terms". The proposal of this talk is to add to the action such terms but allow the constant that multiplies them (called "cosmological constant" in the talk, generalizing the idea of Einstein) to change with time and even possibly space. So if the term were constant we would just recover the usual Einstein theory, but when it is not, one gets a new theory.<br /><br />Three such theories are proposed in the talk, with various properties discussed. In particular, the geometry they imply is more general than that of Einstein's theory, in addition to a metric to describe space-time another quantity called torsion appears. This is still early days for these theories and various properties are being worked out. In particular, cosmological models have been studied. It appears that the one of the considered "cosmological constants" appears to be clumped around ordinary matter. This is just like dark matter behaves, it tends to clump around galaxies, modifying the orbits of outer stars (this is how dark matter was detected, the stars did not move as they were supposed to given the mass of the galaxy). More complex concepts, like black holes, are yet to be worked out in the new theories as well as several other properties, but some initial glimmers of interesting possibilities are emerging.Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-83142397531022322472019-03-19T10:04:00.000-05:002019-03-19T10:04:27.274-05:00Towards loop quantum gravity effective dynamicsTuesday, Feb. 19th<br /><b></b><br /><b>Andrea Dapor, LSU</b><br /><b>Title: Toward LQG effective dynamics </b><br /><a href="http://relativity.phys.lsu.edu/ilqgs/dapor021919.pdf">PDF</a> of the talk (250K)<br /><a href="http://relativity.phys.lsu.edu/ilqgs/dapor021919.mp4">Audio+Slides</a> of the talk (57M)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-RKmUVS22QPA/XI_qSpAQUlI/AAAAAAAAK6U/TBPg-J-E26Aq8UyhrV2V7RVQWKnGSp9YACLcBGAs/s1600/daporandrea.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="398" data-original-width="300" height="320" src="https://2.bp.blogspot.com/-RKmUVS22QPA/XI_qSpAQUlI/AAAAAAAAK6U/TBPg-J-E26Aq8UyhrV2V7RVQWKnGSp9YACLcBGAs/s320/daporandrea.jpg" width="241" /></a></div>By Jorge Pullin, LSU<br /><br />The dynamics of loop quantum gravity is quite complex. This is understandable, as it should reproduce in the classical limit the dynamics of general relativity which in itself is quite complex. This has led investigators to concentrate on situations with a lot of symmetry, in order to achieve simplifications. One of those simplifications is loop quantum cosmology, which studies homogeneous and isotropic spacetimes, i.e. spacetimes that are the same at all points and in all directions. This might seem like too drastic a simplification, but the dynamics of our universe at large scales is well approximated by it.<br /><br />Imposing a symmetry in the quantum theory is not easy. One has to choose a subset of quantum states that are symmetric and study the action of quantum operators on them. All these operations take place in the full theory and therefore can potentially be as complex as dealing with it in generality. This led people to seek a further approximation: impose the symmetry in the classical theory and only then quantize. The problem is that when one imposes the symmetry at a classical level, general relativity simplifies too much and a lot of the techniques of loop quantum gravity are not applicable anymore. Nevertheless people proceeded by using techniques analogous to those of loop quantum gravity. The resulting construction is known as loop quantum cosmology and has been studied for over a decade.<br /><br />This talk dealt with the first approach, namely choose a set ofsuitably symmetric states in the quantum theory and study the action of the quantum operators on them. Remarkably some portions of loop quantum cosmology can be retrieved from this approach, but not quite. Some of the quantum operators differ. The talk studied the resulting quantum cosmologies. The picture that emerges is rather different from traditional loop quantum cosmology. There one has that the Big Bang, the singularity that arises at the origin of the universe when all matter is concentrated at a point, is replaced by a Big Bounce in which there is high -but finite- density of matter. If one studies the evolution back in time one can go past the Bounce and one emerges into a previous universe that eventually becomes big and classical like the one we live in. So the picture that emerges is that our universe originated in a large classical universe like ours that contracted, increased in density, became highly quantum, bounced at a finite density, and started to expand eventually becoming classical again. The modified dynamics of the approach followed in the talk leads to a different picture. Our universe starts in a large but highly quantum universe that is highly symmetric (it is known as De Sitter spacetime), it eventually bounces and starts expanding until it becomes the classical universe we live in. The talk also explored the implications for the singularity inside black holes and showed that the modified dynamics leads to a transition in which the black hole explodes into a "white hole" where everything that went into the black hole comes out. This behavior had been suggested by other approaches, but the details differ. The whole approach relies on a conjecture about how the chosen symmetric states in the full theory behave. Proving the conjecture is a future challenge awaiting.Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-26483900796178703092019-02-07T14:06:00.000-06:002019-02-07T14:06:03.510-06:00Modified loop quantum cosmologyTuesday, Feb. 5th<br /><b></b><br /><b>Parampreet Singh, LSU</b><br /><b>Title: Modified loop quantum cosmologies </b><br /><a href="http://relativity.phys.lsu.edu/ilqgs/singh020519.pdf">PDF</a> of the talk (2M)<br /><a href="http://relativity.phys.lsu.edu/ilqgs/singh020519.mp4">Audio+Slides</a>of the talk (52M)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-HrE61RQ7CPw/XFxcOuWTUkI/AAAAAAAAK3k/bjKJYE8taegRxdcDktl4pJDWwrdUjNxegCLcBGAs/s1600/param.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="401" data-original-width="248" height="320" src="https://2.bp.blogspot.com/-HrE61RQ7CPw/XFxcOuWTUkI/AAAAAAAAK3k/bjKJYE8taegRxdcDktl4pJDWwrdUjNxegCLcBGAs/s320/param.jpg" width="197" /></a></div>By Jorge Pullin, LSU<br /><br />Due to the complexity of the Einstein equations candidates for theories of quantum gravity are fairly complex. In fact, we still do not have good control of the quantum Einstein equations in loop quantum gravity. One possibility to make progress is to consider situations with high symmetry, where most degrees of freedom are frozen and one analyzes only a few. Unfortunately, freezing degrees of freedom in the quantum theory is fairly complex.<br /><br />An alternative approach is to freeze the degrees of freedom at a classical level and then quantize the resulting theory. This technique is known as "minisuperspace" approach. It is not guaranteed that results obtained in this approach will mimic those of the full theory in a symmetric situation but at least it gives an idea of what is possible to expect.<br /><br />One of the most studied minisuperspaces is that of homogeneous cosmologies, where all degrees of freedom are frozen with the exception of the size of the universe. In loop quantum gravity this approach is known as loop quantum cosmology.<br /><br />When one quantizes theories, even as simple as the ones one considers in homogeneous minisuperspaces, there are quantization ambiguities. In a <a href="https://ilqgs.blogspot.com/2018/01/cosmological-dynamics-from-full-loop.html">recent talk</a>, an alternative quantization of loop quantum cosmology to the traditional one exploiting one of those ambiguities was presented.<br /><br />This talk presented a thorough analysis of the alternative quantization, partly using the so-called "effective" approach in which one writes down classical equations of motion that are supposed to capture the modifications that the quantum theory introduces in the behavior of the universe. The stability of the solutions was discussed with and without cosmological constant and the behavior of inflation in various types of models was presented. The elimination of the big bang singularity was analyzed in various scenarios that lead to different types of singularity. The emerging picture is of a universe that starts in a deep quantum state and then "bounces" into a large classical universe like the one we live in.Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-50445414446660202102019-02-07T10:06:00.000-06:002019-02-07T10:06:35.379-06:002+1 D loop quantum gravity on the edgeTuesday, Jan. 22nd<br /><b></b><br /><b>Barak Shoshany, Perimeter Institute</b><br /><b>Title: 2+1D loop quantum gravity on the edge </b><br /><a href="http://relativity.phys.lsu.edu/ilqgs/shoshany012219.pdf">PDF</a> of the talk (9M)<br /><a href="http://relativity.phys.lsu.edu/ilqgs/shoshany012219.mp4">Audio+Slides</a>of the talk (32M)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-XSmqJCYMj3A/XFdGmWTsmyI/AAAAAAAAK3M/OZOY-fiQ-ecKG8rSFmG4CY5gA4CJJHoBgCLcBGAs/s1600/shoshany.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="965" data-original-width="965" height="200" src="https://1.bp.blogspot.com/-XSmqJCYMj3A/XFdGmWTsmyI/AAAAAAAAK3M/OZOY-fiQ-ecKG8rSFmG4CY5gA4CJJHoBgCLcBGAs/s200/shoshany.jpg" width="200" /></a></div>By Jorge Pullin, LSU<br /><br />A technique for studying quantum field theories that has been very successfully applied to the Yang-Mills theories of particle physics is discretization. In it, one replaces the differential equations for the theory for equations in finite differences. Among other things, this makes them amenable to treat them using computers.<br /><br />A problem that arises when trying to apply these techniques in gravity is that the discretization tends to clash with the symmetries of the theory. In theories of gravity of geometric type, like general relativity, points in space-time can be smoothly moved around, a symmetry known as diffeomorphisms. The rigid nature of discretization breaks that symmetry.<br /><br />This talk addresses this problem through a technique known as coarse graining. In it, one breaks physical systems into subsystems and characterizes the latter through observable quantities that are invariant under the symmetries of the theory. This leads to observables associated with the edges of the region, hence the title of the talk. The coarse graining allows to introduce discretizations compatible with the symmetries of general relativity. This is shown in detail in this talk for the 2+1 dimensional case.<br /><br />One of the features found is that when piecing together the domains of the coarse graining, the edge degrees of freedom cancel out and one is left only with corner degrees of freedom that can be thought as "particle excitations". The space of quantum states is that of ordinary loop quantum gravity (spin networks) with the addition of the particle excitations. The work shows that spin networks can be obtained by classically discretizing general relativity. This opens possibilities for studying the classical limit and the dynamics. Work is in progress to generalize the results to 3+1 dimensions.Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-5865682429806747472018-12-06T15:02:00.000-06:002018-12-06T15:02:19.575-06:00Quantum theory of charged isolated horizonsTuesday, Dec. 4th<br /><b></b><br /><b>Konstantin Eder, Hanno Sahlmann, FAU Erlangen</b><br /><b>Title: Quantum theory of charged isolated horizons </b><br /><a href="http://relativity.phys.lsu.edu/ilqgs/sahlmann120418.pdf">PDF</a> of the talk (600K) <br /><a href="http://relativity.phys.lsu.edu/ilqgs/sahlmann120418.mp4">Audio+Slides</a> of the talk (32M)<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-Euv06nHfuQk/XAl824vuDWI/AAAAAAAAKsg/tKDvj3Egjn0i6lGQga21M8aVM_HxeAX4QCEwYBhgL/s1600/Screen%2BShot%2B2018-12-06%2Bat%2B1.47.22%2BPM.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="551" data-original-width="906" height="194" src="https://2.bp.blogspot.com/-Euv06nHfuQk/XAl824vuDWI/AAAAAAAAKsg/tKDvj3Egjn0i6lGQga21M8aVM_HxeAX4QCEwYBhgL/s320/Screen%2BShot%2B2018-12-06%2Bat%2B1.47.22%2BPM.png" width="320" /></a></div>By Jorge Pullin, LSU<br /><br />Thermodynamics is the branch of physics that deals with systems about which we have incomplete information. A prototypical thermodynamics system is a gas: we will never be able to follow the motion of all the molecules of a gas, there are too many. One describes such systems using macro variables. Some are well known like the volume, the pressure or the temperature. A less well known macro variable is the entropy, which is a measure of our ignorance about the system. When physical systems interact the total entropy always increases. <br />It came as a surprise when Bekenstein proposed that black holes had a thermodynamic description. Since the area of the horizon of a black hole is proportional to its mass and everything that falls into the black hole cannot get out, it means that when something interacts with a black hole its mass always grows. And since we cannot know what is in the interior of a black hole, the area of the horizon is a measure of that ignorance. So Bekenstein suggested that the entropy of a black hole was proportional to its area. The thermodynamic picture got completed when in 1975 Hawking showed that if one took into account quantum effects, black holes radiated as a black body with a given temperature.<br /><br />Loop quantum gravity provides a detailed explanation of the entropy of a black hole. In loop quantum gravity finite surfaces can in principle have zero area. They get endowed with "quanta of area" when they are pierced by the loops that characterize the quantum states. A surface can be endowed with a certain value of the area by many different loop quantum gravity states. So just giving the area we have a certain ignorance of the quantum state that gave rise to it. A detailed counting of that ignorance is therefore a notion of entropy and it has been shown that it is proportional to the area.<br /><br />This talks extends these results to the case in which black holes are in the presence of quantum fields, more specifically Yang-Mills fields, which are the theories that describe particle physics. It shows that the entropy is still proportional to the area, but that higher order corrections may depend on the charges of the Yang-Mills fields. This provides a nice consistency test that shows that the entropy is still mainly proportional to the area even if one is in a non-vacuum situation with the presence of fields.Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-47294637861861792462018-11-28T13:07:00.000-06:002018-11-28T13:07:13.054-06:00A holographic description for boundary gravitons in 4DTuesday, Nov 20<br /><b></b><br /><b>Bianca Dittrich, Perimeter Institute</b><br /><b>Title: A holographic description for boundary gravitons in 4D </b><br /><a href="http://relativity.phys.lsu.edu/ilqgs/dittrich112018.pdf">PDF</a> of the talk (5M)<br /><a href="http://relativity.phys.lsu.edu/ilqgs/dittrich112018.mp4">Audio+Slides</a>< of the talk (38M)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-gLaOmRIiFhw/W_1csR1DJaI/AAAAAAAAKrU/1C7Jysik-N09AvfNA3chJzlw78NvvGD8gCLcBGAs/s1600/bianca-dittrich_c-2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1022" data-original-width="848" height="320" src="https://1.bp.blogspot.com/-gLaOmRIiFhw/W_1csR1DJaI/AAAAAAAAKrU/1C7Jysik-N09AvfNA3chJzlw78NvvGD8gCLcBGAs/s320/bianca-dittrich_c-2.jpg" width="265" /></a></div>By Jorge Pullin, LSU<br /><br />Holography has become a central concept in gravity. It is the idea that the description of gravity in a region of spacetime can be mapped to the description of a quantum field theory on the boundary of the spacetime. It originated in string theory as part of the "Maldacena conjecture" but it proved to be a more fundamental concept that does not require string theory for its formulation.<br /><br />In this talk, holography was first reviewed in the context of three dimensional spacetimes, where the theory of gravity is much simpler than in four space-time dimensions, as spacetimes are locally flat in 3D. In particular, the example of the torus was discussed in detail. It was presented how to use Regge calculus (an approximation to general relativity using a triangulation in terms of simplices) to construct the boundary theory.<br /><br />The talk then moved to four dimensional spacetimes starting with the simpler example of the flat sector of gravity where one only considers flat spacetimes. Again, the boundary theory was constructed using Regge calculus and the example of the three torus was discussed. It concluded with some future directions for the full theory, discussion of the symmetry group of the theory at infinity and possible implications for black hole entropy.Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-5007566882644738202018-10-24T15:55:00.000-05:002018-10-24T15:55:13.564-05:00A unified geometric framework for boundary charges and dressingsTuesday, Oct 23rd<br /><b></b><br /><b>Aldo Riello, Perimeter Institute</b><br /><b>Title: A unified geometric framework for boundary charges and dressings </b><br /><a href="http://relativity.phys.lsu.edu/ilqgs/riello102318.pdf">PDF</a> of the talk (2M)<br /><a href="http://relativity.phys.lsu.edu/ilqgs/riello102318.mp4">Audio+Slides</a> of the talk (41M)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-lxfxgDZGCn4/W8-jL-7ojQI/AAAAAAAAKks/cfBSXc1yM1s4rodTHB8cqhkbX2VtJmzCACLcBGAs/s1600/download.jpeg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="228" data-original-width="221" src="https://3.bp.blogspot.com/-lxfxgDZGCn4/W8-jL-7ojQI/AAAAAAAAKks/cfBSXc1yM1s4rodTHB8cqhkbX2VtJmzCACLcBGAs/s1600/download.jpeg" /></a></div>By Jorge Pullin, LSU (with some help from Aldo)<br /><br />The electromagnetic force and all the subatomic interactions are described by a class of theories known as “gauge theories”. Even gravitation, in its modern formulation due to Einstein, is a gauge theory of sorts, although a more complicated one. The mathematical formulation of these theories is characterized by peculiar redundancies, as if the simplest way to describe the system is through a plethora of different descriptions rather than through a single “true” one. This is most often seen as a mathematical quirk rather than as a hint of some deep property of nature. This talk explores the latter possibility and build on the idea that the rationale for gauge theories must be found not so much in some property of a single system taken in isolation, but rather in the way systems can come together and talk to each other. The first hint of this can be found in the fact that the natural objects populating a gauge theory (“observables”) are intrinsically nonlocal and therefore can’t be easily localized in a given region, without carefully keeping track of what happens at its boundaries. The simplest example of this phenomenon can be found in the electron, that can never be separated from its electric field, which in turn can be detected even at a distance from the electron. This talk presents a novel mathematical framework that by embracing the relational perspective unifies many seemingly unrelated aspects of gauge theories and might – in its future developments – clarifies the analogous but harder conceptual issues one finds on their way to quantum gravity. Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-60971910922419502972018-10-18T10:56:00.000-05:002018-10-18T10:56:48.837-05:00Quantum extension of black holes<span style="background-color: white;">Tuesday, Oct 9th</span><br /><b></b><br /><b>Javier Olmedo, LSU</b><br /><b>Title: Quantum Extension of Kruskal Black Holes </b><span style="background-color: white;"></span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/olmedo100918.pdf">PDF</a><span style="background-color: white;"> of the talk (500k)</span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/olmedo100918.mp4">Audio+Slides</a><span style="background-color: white;"> of the talk (17M)</span><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-iPgzXNslsow/W8etchztSDI/AAAAAAAAKh4/yaYKE1tPO-gZjVFmHd6UZCGwdkxzkM5PQCEwYBhgL/s1600/Javier_Olmedo.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="512" data-original-width="512" height="320" src="https://3.bp.blogspot.com/-iPgzXNslsow/W8etchztSDI/AAAAAAAAKh4/yaYKE1tPO-gZjVFmHd6UZCGwdkxzkM5PQCEwYBhgL/s320/Javier_Olmedo.jpg" width="320" /></a></div>By Jorge Pullin, LSU<br /><br />In the interior of black holes the coordinates t and r swap roles. As one falls "towards the center" one is actually moving forward in time. This makes the interior of a black hole look like a contracting cosmology of a particular type, known as Kantowski-Sachs cosmology. This has allowed the use of loop quantum cosmology techniques to treat the interior of black holes. There have been several discussions of this, but they have some shortcomings. To begin with, they only cover the interior of the black hole. Moreover, some of the proposals have physical quantities with undesirable dependences on fiducial elements introduced in order to quantize or on the mass of the space-time.<br /><br />This talk discusses overcoming these problems. To begin with, it is shown that the quantum treatment eliminates the singularity inside black holes and replaces with a region of large curvature. The value of the maximum curvature is universal and independent on the mass of the space-time. Moreover, it gives the same mass for the black hole to the past and to the future (unlike other treatments). In addition, the quantum theory is extended to the exterior region of the black hole. In the future it is expected to extend these ideas to other type of black hole space-times, like those with charge, spin and cosmological constant. Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-56805748417513321212018-10-08T17:56:00.000-05:002018-10-08T17:56:22.415-05:00Computing volumes in spin foams<div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-dw1SIhOMUWo/W6pDiHFdlgI/AAAAAAAAKhA/Z37bzx_T-s03d0p1lw7Tj5ASYc6hBOuKQCLcBGAs/s1600/bahr.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="240" data-original-width="173" src="https://2.bp.blogspot.com/-dw1SIhOMUWo/W6pDiHFdlgI/AAAAAAAAKhA/Z37bzx_T-s03d0p1lw7Tj5ASYc6hBOuKQCLcBGAs/s1600/bahr.jpg" /></a></div><span style="background-color: white;">Tuesday, Sep 25th</span><br /><b></b><br /><b>Benjamin Bahr, DESY</b><br /><b>Title: 4-volume in spin foam models from knotted boundary graphs </b><span style="background-color: white;"></span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/bahr092518.pdf">PDF</a><span style="background-color: white;"> of the talk (3M)</span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/bahr092518.mp4">Audio+Slides</a><span style="background-color: white;"> of the talk (15M)</span><br /><br />by Jorge Pullin, LSU<br /><br />There is an approach to quantum mechanics known as the path integral approach. In it, one considers all possible classical trajectories, not only the ones satisfying the equations of motion and assigns probabilities to each of them using a formula. The probabilities are summed and that gives the quantum probability to go from an initial state to a final state. In loop quantum gravity the initial and final states are given by spin networks, which are graphs with intersections and "colors" (a number) assigned to each edge. The trajectories connecting initial and final states therefore resemble a "foam" and are given the names of spin foams.<br /><br />In this talk it was shown how to compute volumes of polytopes (regions of space-time bounded by flat sides, a generalization to higher dimensions of polyhedra of 3d) in spin foam quantum gravity. The calculation has nice connections with knot theory, the branch of math that studies how curves entangle with each other.<br /><br />One of the central elements of spin foams is the formula that assigns the probabilities, known as a "vertex". The construction in this talk gives ideas for extending the current candidates for vertices, including the possibility of adding a cosmological constant and suggests possible connections with Chern-Simons theories (a special type of field theories) and also with quantum groups.Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-51043436815786659042018-05-01T11:54:00.000-05:002018-05-01T11:54:44.931-05:00Cosmological perturbations in terms of observables and physical clocksTuesday, Apr 17th<br /><b></b><br /><b>Kristina Giesel, FAU Erlangen-Nürnberg</b><br /><b>Title: Gauge invariant observables for cosmological perturbations </b><br /><a href="http://relativity.phys.lsu.edu/ilqgs/giesel041718.pdf">PDF</a> of the talk (8M)<br /><a href="http://relativity.phys.lsu.edu/ilqgs/giesel041718.mp4">Audio+Slides</a> of the talk (15M)<br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-Zv8zh7SNvqI/Wtzfgidil0I/AAAAAAAAKLw/Hweh9nuAoZwwxM1yNfaSG2QF3mCY2l71wCEwYBhgL/s1600/giesel-a016249e0816edcd70c9ee3a55b0ccb85ee20ac838fb1980b6a652d657de1840.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="220" data-original-width="220" src="https://3.bp.blogspot.com/-Zv8zh7SNvqI/Wtzfgidil0I/AAAAAAAAKLw/Hweh9nuAoZwwxM1yNfaSG2QF3mCY2l71wCEwYBhgL/s1600/giesel-a016249e0816edcd70c9ee3a55b0ccb85ee20ac838fb1980b6a652d657de1840.jpg" /></a></div>By Jorge Pullin, LSU<br /><br />When one sets up to quantize general relativity something unusual happens. When one constructs a key quantity for describing the evolution called the Hamiltonian, it turns out it vanishes. What the framework is telling us is that since in general relativity one can choose arbitrary coordinates, the coordinate t that one normally associated with time is arbitrary. That means that the evolution described in terms of it is arbitrary.<br /><br /><br /><br />Of course this does not mean that the evolution predicted by general relativity is arbitrary. It is just that one is choosing to describe it in terms of a coordinate that is arbitrary. So how can one get to the invariant part of the evolution? Basically one needs to construct a clock out of physical quantities. Then one asks how other variables evolve in terms of the variable of the clock. The relational information between such variables is coordinate independent and therefore characterizes the evolution in an invariant way.<br /><br />Cosmological perturbation theory is an approximation in which one assumes that the universe at large scales is homogeneous and isotropic plus small perturbations. One can then expand the Einstein equations keeping only the lower order terms in the small perturbations. That makes the equations much more manageable. Up to now most studies of cosmological perturbations were done in coordinate dependent fashion, in particular the evolution was described in terms of a coordinate t. This talk discusses how to formulate cosmological perturbation theory in terms of physical clocks and physically observable quantities. Several choices of clocks are discussed.Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-26217553631515450372018-04-22T11:58:00.003-05:002018-05-01T12:22:43.117-05:00Quantum gravity inside and outside black holesTuesday, Apr 3rd<br /><b></b><br /><b>Hal Haggard, Bard College</b><br /><b>Title: Quantum Gravity Inside and Outside Black Holes </b><br /><a href="http://relativity.phys.lsu.edu/ilqgs/haggard040318.pdf">PDF</a> of the talk (5M)<br /><a href="http://relativity.phys.lsu.edu/ilqgs/haggard040318.mp4">Audio+Slides</a> of the talk (19M)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-jBxhPI0_-Kg/Wty9LR7Ha_I/AAAAAAAAKLg/x2jkKO65hyAaZNnicC70uhPJKZUlGaQgwCLcBGAs/s1600/Hal-Haggard.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="415" data-original-width="285" height="320" src="https://1.bp.blogspot.com/-jBxhPI0_-Kg/Wty9LR7Ha_I/AAAAAAAAKLg/x2jkKO65hyAaZNnicC70uhPJKZUlGaQgwCLcBGAs/s320/Hal-Haggard.jpg" width="218" /></a></div>By Jorge Pullin, Louisiana State University<br /><br />The talk consisted of two distinct parts. The second part discussed black holes exploding into white holes. We have <a href="http://ilqgs.blogspot.com.uy/2018/01/black-holes-exploding-into-white-hole.html">covered the topic in this blog before</a>, and the new results were a bit technical for a new update, mainly a better handle on the time the process takes, so we will not discuss them here.<br /><br />The first part concerned itself with how the interior of a black hole would look like in a quantum theory. Black holes are regions of space-time from which nothing can escape and are bounded by a spherical surface called the horizon. Anything that ventures beyond the horizon can never escape the black hole. Black holes develop when stars exhaust their nuclear fuel and start to contract under the attraction of gravity. Eventually gravity becomes too intense for anything to escape and a horizon forms.<br /><br />The interior of the horizon however, is drastically different if a black hole has rotation or not. If the black hole does not rotate, anything that falls into the black hole is crushed in a central singularity where, presumably, all the mass of the initial star concentrated. If the black hole has rotation however, the structure is more complicated and infalling matter can avoid hitting the singularity and move into further regions of space-time inside the black hole.<br /><br />This raises the question: what happens with all this in a quantum theory of gravity. Presumably a state representing a non-rotating black hole will consist of a superposition of black holes with rotation, peaked around zero rotation, but with contributions from black holes with small amounts of rotation. How does the interior of a non-rotating quantum black hole look when it is formed through a superposition of rotating black holes? This is an interesting question since the interior of rotating black holes are so different from their non-rotating relatives.<br /><br />The talk concludes that the resulting interior actually does resemble that of a non-rotating black hole. The key observation is that one cannot trust the classical theory all the way to the singularity and that leads to the superposition having large curvatures where one would have expected the singularity of the non-rotating black hole to be.Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-19318046612949908252018-03-25T14:36:00.002-05:002018-03-25T14:36:24.723-05:00Cosmological non Gaussianity from loop quantum cosmologyTuesday, Mar 6th<br /><b></b><br /><b>Ivan Agullo, LSU</b><br /><b>Title: Non-Gaussianity from LQC </b><br /><a href="http://relativity.phys.lsu.edu/ilqgs/agullo030618.pdf">PDF</a> of the talk (22M)<br /><a href="http://relativity.phys.lsu.edu/ilqgs/agullo030618.mp4">Audio+Slides</a> [.mp4 19MB]<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-0FXS3_LYtNs/WraJQDu_lCI/AAAAAAAAKFE/ajDrx0OXn2EXJ9ZZ_bPKim_Aj1h4ZfE7wCLcBGAs/s1600/agullo.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="266" data-original-width="200" src="https://2.bp.blogspot.com/-0FXS3_LYtNs/WraJQDu_lCI/AAAAAAAAKFE/ajDrx0OXn2EXJ9ZZ_bPKim_Aj1h4ZfE7wCLcBGAs/s1600/agullo.jpg" /></a></div>By Jorge Pullin, LSU<br /><br />The standard picture of cosmology is that the universe started in the "big bang" and then underwent a period of rapid expansion, called inflation. During those initial moments, densities are very high and matter is fused into a primordial "soup" that is opaque, light cannot travel through it. As the universe expands and cools, eventually electrons and protons form atoms and the universe becomes transparent to light. The afterglow of that initial phase can then travel freely through the universe and eventually reaches us. Due to the expansion of the universe that light "cools" (its frequency is lowered). In the 1960's to Bell Telephone Co. engineers were working on a microwave antenna and discovered a noise they could not get rid of. That noise was the afterglow of the Big Bang, that by then had cooled off into microwaves. That afterglow has been measured with increasing precision using satellites. It is remarkably homogeneous, if one looks into two different directions of the universe, the difference in temperature (frequency) of the microwave radiation is equal to one part in 100,000. The diagram below has those temperature differences magnified 100,000 times to make them visible, different colors correspond to different temperatures. The whole celestial sphere is mapped into the oval.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-D1zCK6PoI8w/WraKjOYU7TI/AAAAAAAAKFQ/twrfTfIl_dwIbZfyxnSswEpCdP-hDNaOwCLcBGAs/s1600/Ilc_9yr_moll4096%2B%25281%2529.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="165" data-original-width="330" height="160" src="https://1.bp.blogspot.com/-D1zCK6PoI8w/WraKjOYU7TI/AAAAAAAAKFQ/twrfTfIl_dwIbZfyxnSswEpCdP-hDNaOwCLcBGAs/s320/Ilc_9yr_moll4096%2B%25281%2529.png" width="320" /></a></div>At first, it appears that the distribution of temperature is sort of random. But it is not, it has a lot of structure. To characterize the structure, one picks a direction and then moves away from it a certain angle and draws a circle of all directions forming the same angle with the original direction one picked. One then averages the temperature along the circle. Then one averages the result for all possible initial choices of direction. If the distribution were truly random, if one plotted the average computed as a function of the angle, one would get a constant, no angle would be preferred over others. But what one gets is shown in the following diagram,<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-YJ9rhuKLmw8/WraLUs3eHxI/AAAAAAAAKFY/OiwA8405xHYWGEBu5w9UchKB7fzreRyfwCLcBGAs/s1600/450px-PowerSpectrumExt.svg.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="368" data-original-width="450" height="261" src="https://2.bp.blogspot.com/-YJ9rhuKLmw8/WraLUs3eHxI/AAAAAAAAKFY/OiwA8405xHYWGEBu5w9UchKB7fzreRyfwCLcBGAs/s320/450px-PowerSpectrumExt.svg.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">In the vertical are the averages, in the horizontal, the angles. The dots are experimental measurements. The continuous curve is what one gets if one evolves a quantum field through the inflationary period, starting from the most "quiescent" quantum state possible at the beginning, called "the vacuum state". The incredibly good agreement between theory and experiment is a great triumph of the inflationary model. The quantity plotted above is technically known as the "two point correlation". Loop quantum cosmology slightly changes the predictions of standard inflation, mostly for very large angles. There, the experimental measurements have a lot of uncertainty and are not able to tell us if loop quantum cosmology or traditional inflation give a better result. Perhaps in a few years better measurements will allow us to distinguish between them. If loop quantum cosmology is favored it would be a tremendously important experimental confirmation. But we are not there yet.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">One can generalize the construction we made with two directions and an angle between them to three directions and three angles between them, and so on for higher number of directions. These would be known technically as the three point correlation, four point correlation, etc. If the distribution of temperatures were given by a probabilistic distribution known as a Gaussian, all the higher order correlations are determined by the two point correlation, there is no additional information in them. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">In this talk a study of the three point correlations for loop quantum cosmology was presented. It was shown that non-Gaussianities appear. That is, the three point correlation is not entirely determined by the two point one. Satellites are able to measure non-Gaussianities. In the talk it was shown that depending on the values chosen for the quantum fields at the beginning of the universe, the non-Gaussianities predicted by loop quantum gravity can be made compatible with experiment. This is not strictly speaking an experimental confirmation since one had a parameter one could adjust. But the good news is that the values needed to fit the data appear very natural. Again, future measurement should place tighter bounds on all this.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Image credits: Cosmic microwave background <a href="https://en.wikipedia.org/wiki/Cosmic_microwave_background">Wikipedia page.</a></div><br />Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-58037684182797996382018-03-25T14:05:00.000-05:002018-03-25T14:05:02.435-05:00Quantum spacetimes on a quantum computerTuesday, Mar 20th<br /><b></b><br /><b>Keren Li, Tsinghua University</b><br /><b>Title: Quantum spacetime on a quantum simulator </b><br /><a href="http://relativity.phys.lsu.edu/ilqgs/li032018.pdf">PDF</a> of the talk (3M)<br /><a href="http://relativity.phys.lsu.edu/ilqgs/li032018.mp4">Audio+Slides</a> [.mp4 11MB]<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-K8tq55jyXPo/WrfwN4Zf_hI/AAAAAAAAKGo/YxWw-JxzE4QEIIK_WTohjdYPuw5UgC8ygCLcBGAs/s1600/keren.jpeg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1067" data-original-width="1600" height="213" src="https://1.bp.blogspot.com/-K8tq55jyXPo/WrfwN4Zf_hI/AAAAAAAAKGo/YxWw-JxzE4QEIIK_WTohjdYPuw5UgC8ygCLcBGAs/s320/keren.jpeg" width="320" /></a></div>By Jorge Pullin, LSU<br /><br /><br />In loop quantum gravity the quantum states are labeled by objects known as "spin networks". These are graphs in space with intersections. If one evolves a spin network in time one gets a "spin foam". If one had a static situation, the various spatial slices of a spin foam would be the same, as shown in the figure,<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-uyda9VyR7As/WraQsC4D77I/AAAAAAAAKFo/kJAZ-Z9z_FIv8v9K7SibyDCut6mgUVW1gCLcBGAs/s1600/Screen%2BShot%2B2018-03-24%2Bat%2B12.53.08%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="289" data-original-width="300" src="https://4.bp.blogspot.com/-uyda9VyR7As/WraQsC4D77I/AAAAAAAAKFo/kJAZ-Z9z_FIv8v9K7SibyDCut6mgUVW1gCLcBGAs/s1600/Screen%2BShot%2B2018-03-24%2Bat%2B12.53.08%2BPM.png" /></a></div>If one were in a dynamical situation, new vertices are created,<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Rv5KxBUwXQ0/WraQ2Yj8NQI/AAAAAAAAKFs/DCgoduAsHbkLLF_xzMy8zmuCklmPdS1pwCLcBGAs/s1600/Screen%2BShot%2B2018-03-24%2Bat%2B12.54.18%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="280" data-original-width="301" src="https://1.bp.blogspot.com/-Rv5KxBUwXQ0/WraQ2Yj8NQI/AAAAAAAAKFs/DCgoduAsHbkLLF_xzMy8zmuCklmPdS1pwCLcBGAs/s1600/Screen%2BShot%2B2018-03-24%2Bat%2B12.54.18%2BPM.png" /></a></div>To compute the probability of transitioning from a spin network to another is what calculations in spin foams are about. The details of these computations resemble computations people do in quantum mechanics of systems with spins. This allows to make a parallel between these computations and the ones that are involved in setting up a quantum computer, specifically the qubits that are constructed using nuclear magnetic resonance systems (NMR). In this talk it was described how the evolution of a very simple spin foam known as the tetrahedron can be simulated on an NMR quantum computer of four qubits and how the experimental measurements reproduce very well theoretical calculations of spin foam models.<br /><br />Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-32369955036710580762018-02-06T15:20:00.000-06:002018-02-06T15:20:37.115-06:00Using symmetries to determine the dynamics<span style="background-color: white;">Tuesday, Feb 6th</span><br /><b></b><br /><b>Ilya Vilensky, Florida Atlantic University</b><br /><b>Title: The unique form of dynamics in LQC </b><span style="background-color: white;"></span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/vilensky020618.pdf">PDF</a><span style="background-color: white;"> of the talk (0.5M)</span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/vilensky020618.mp4">Audio+Slides</a><span style="background-color: white;"> [.mp4 11MB]</span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-70KfZBUF37I/WnoZHLTZzTI/AAAAAAAAJ8c/L_-wVJaUi-kibyRLIrmpYFs3_GzrjNk5QCLcBGAs/s1600/photo18.jpeg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1217" height="320" src="https://4.bp.blogspot.com/-70KfZBUF37I/WnoZHLTZzTI/AAAAAAAAJ8c/L_-wVJaUi-kibyRLIrmpYFs3_GzrjNk5QCLcBGAs/s320/photo18.jpeg" width="243" /></a></div><span style="background-color: white;"><br /></span><br /><br /><br />By Jorge Pullin, LSU<br /><br />Loop quantum cosmology is the application of ideas of loop quantum gravity to the context of cosmology, where one freezes most degrees of freedom and studies just a few large scale ones, like the volume of the universe or its anisotropy. Loop quantum cosmology is not "derived" from loop quantum gravity, in the sense of choosing in the full theory quantum states that are very symmetric with only a few degrees of freedom and study their evolution. That is at the moment, too complicated. In loop quantum cosmology one first freezes the degrees of freedom one wishes to ignore and then proceeds to quantize the remaining ones. It is not clear that this coincides with "quantizing and then freezing". It is therefore important to run cross checks to make sure that at least within the approximation considered, things are consistent.<br /><br />In spite of the enormous simplification one obtains when one first freezes most degrees of freedom and then quantizes, there are still quite a few ambiguities in the quantization process. This talk showed in the example of anisotropic universes, how imposing the residual symmetries and left after freezing most degrees of freedom, and demanding that the correct classical limit follow, allows to cut down on the number of ambiguities present. This increases the confidence in results previously obtained in loop quantum cosmology, some of which may have observable implications for the anisotropies of the cosmic microwave background radiation.Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-60086072692864652422018-01-29T12:38:00.000-06:002018-01-29T12:38:10.410-06:00New dynamics for quantum gravity<span style="background-color: white;">Tuesday, Jan 23rd</span><br /><b></b><br /><b>Cong Zhang, Univ. Warsaw/Beijing</b><br /><b>Title: Some analytical results about the Hamiltonian operator in LQG </b><span style="background-color: white;"></span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/zhang012318.pdf">PDF</a><span style="background-color: white;"> of the talk (1.7M)</span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/zhang012318.mp4">Audio+Slides</a><span style="background-color: white;"> [.mp4 10MB]</span><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-MmshFvtLeKY/Wm9jhb20VAI/AAAAAAAAJ4s/RBKHF_PFqhE8Kju5ViViZMs2ylnLvisggCLcBGAs/s1600/image1.jpeg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://1.bp.blogspot.com/-MmshFvtLeKY/Wm9jhb20VAI/AAAAAAAAJ4s/RBKHF_PFqhE8Kju5ViViZMs2ylnLvisggCLcBGAs/s320/image1.jpeg" width="240" /></a></div><br /><br />by Jorge Pullin, LSU<br /><br />One of the central elements when building quantum theories using the approach known as "canonical" is to define a quantity known as the Hamiltonian. This quantity is responsible for the time evolution of the system under study. In general relativity, when one tries to construct such quantity one notices it vanishes. This is because in general relativity one can choose any arbitrary time variable and therefore there is not a uniquely selected evolution. One needs to make a choice. One such choice is to use matter to play the role of a clock. That leads to one having a non-vanishing Hamiltonian. In this work a detailed construction for the quantum operator associated with such Hamiltonian in loop quantum gravity was presented. The implementation presented differs from others done in the past. Among the attractive elements is that it can be shown in certain circumstances that the operator has the desirable mathematical property known as "self-adjointness". This property ensures that physical quantities in the theory are represented by real (as opposed to complex) numbers.<br /><br />A discussion was also presented of how the operator acts on certain states that behave semi-classically known as "coherent states", in particular in the context of cosmological models. It was observed that it leads to an expanding universe.Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-35550724827347434762018-01-15T16:00:00.000-06:002018-01-15T16:00:03.668-06:00Construction of Feynman diagrams for group field theory<span style="background-color: white;">Tuesday, Dec 5th</span><br /><b></b><br /><b>Marco Finocchiaro, Albert Einstein Institute</b><br /><b>Title: Recursive graphical construction of GFT Feynman diagrams </b><span style="background-color: white;"></span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/finocchiaro120517.pdf">PDF</a><span style="background-color: white;"> of the talk (1M)</span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/finocchiaro120517.mp4">Audio+Slides</a><span style="background-color: white;"> [.mp4 24MB]</span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-eEwO3ce1Hh4/Wl0gt3tfLsI/AAAAAAAAJ2M/ot7suhY8Tz0DmoJWyqNWHy4gtuYYdLm0wCLcBGAs/s1600/Screen%2BShot%2B2018-01-15%2Bat%2B3.44.01%2BPM.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1309" data-original-width="1111" height="320" src="https://1.bp.blogspot.com/-eEwO3ce1Hh4/Wl0gt3tfLsI/AAAAAAAAJ2M/ot7suhY8Tz0DmoJWyqNWHy4gtuYYdLm0wCLcBGAs/s320/Screen%2BShot%2B2018-01-15%2Bat%2B3.44.01%2BPM.png" width="271" /></a></div><span style="background-color: white;"><br /></span><span style="background-color: white;">By Jorge Pullin, LSU.</span><br />A common technique for computing probability amplitudes in quantum field theory consists in expanding such objects as power series in term of the coupling constant of the theory. Each term in the expansion, usually involving complicated expressions, can be represented in a pictorial way by using diagrams. This graphical technique (known as "Feynman diagrams method") allows to write down and organize the terms in the perturbative series in a much easier way. <br /><br />Group field theories (GFTs) are ordinary quantum field theories on group manifolds. Their Feynman amplitudes (i.e. amplitudes associated to Feynman graphs) correspond by construction to Quantum Gravity Spinfoam amplitudes. There exists an analogue situation in 1+1 dimensional theories known as matrix models, which are quantum field theories whose Feynman diagrams are related to the path integrals for gravity in 1+1 dimensions. From this point of view group field theories can be seen as a four dimensional generalization of matrix models. <br /><br />The seminar, articulated in three parts, dealt with several aspects concerning the construction of GFT's Feynman diagrams and the evaluation of the corresponding amplitudes. In the first part a general introduction to group field theory was provided, stressing the importance of studying the divergences appearing in the amplitudes' computations. Indeed they can be used as tools to constraint and test the type of theories that can be built. In the second part the main methods to extract the amplitudes' divergences were briefly reviewed. Moreover a new GFT/Spinfoam model for Euclidean quantum gravity was presented. The last part was devoted to the seminar's main topic, namely the generation of Feynman graphs in group field theory. Beyond the leading order in the power series expansion this is often a difficult task. It was shown how to construct GFT's Feynman diagrams using recursive graphical relations that are suitable for implementations in computers. Future works will deal with making the computations parallelizable.<br /><br />Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-36060725028730805982018-01-15T15:41:00.000-06:002018-01-15T15:41:19.039-06:00Entanglement in loop quantum gravity<span style="background-color: white;">Tuesday, Nov 7th</span><br /><b></b><br /><b>Eugenio Bianchi, PennState</b><br /><b>Title: Entanglement in loop quantum gravity </b><span style="background-color: white;"></span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/bianchi110717.pdf">PDF</a><span style="background-color: white;"> of the talk (9M)</span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/bianchi110717.mp4">Audio+Slides</a><span style="background-color: white;"> [.mp4 19MB]</span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-oUgukYNpXts/WlZAg-ngaVI/AAAAAAAAJ08/oGG5Y9hOZi0LbZaQuHci8MzgwuZShMT2gCLcBGAs/s1600/Eugenio_Bianchi3.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="661" data-original-width="992" height="213" src="https://4.bp.blogspot.com/-oUgukYNpXts/WlZAg-ngaVI/AAAAAAAAJ08/oGG5Y9hOZi0LbZaQuHci8MzgwuZShMT2gCLcBGAs/s320/Eugenio_Bianchi3.jpg" width="320" /></a></div><span style="background-color: white;"><br /></span><span style="background-color: white;"><br /></span><span style="background-color: white;">By Jorge Pullin, LSU</span><br /><span style="background-color: white;"><br /></span><span style="background-color: white;">Entanglement is one of the most fascinating new concepts introduced in quantum mechanics. When quantum systems interact, the resulting systems properties cannot be described by considering the properties of the individual systems. One needs to consider global properties of the set of systems as a whole. Not only one cannot reconstruct the properties of the whole from the properties of the constituent parts. It turns out that the properties of the constituent parts cannot be determined if one does not know the properties of the whole. Entanglement entropy is a quantity that measures "how much entanglement" there is in a set of quantum systems. This seminar dealt with the application of this concept to the quantum states of loop quantum gravity. Here one tries to understand how different regions of space become entangled with each other in a quantum geometry and how the entanglement entropy measures such entanglement. </span><br /><span style="background-color: white;"><br /></span><span style="background-color: white;">This is not a mere theoretical development. Quantum theory plays an important role in cosmology. We now know that the fluctuations we see in the cosmic microwave background radiation are the product of the evolution of the vacuum state of the inflaton field during inflation. If one assumes that before inflation the field was in a vacuum state and evolves it, the state develops non-trivial correlations that are precisely the ones observed in the cosmic background radiation fluctuations. </span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-efnKnkBtits/WlZDmryLgII/AAAAAAAAJ1I/FSJQR82LRX8osEqeksads3CcmgdLk99BwCLcBGAs/s1600/Ilc_9yr_moll4096.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="256" data-original-width="512" height="160" src="https://4.bp.blogspot.com/-efnKnkBtits/WlZDmryLgII/AAAAAAAAJ1I/FSJQR82LRX8osEqeksads3CcmgdLk99BwCLcBGAs/s320/Ilc_9yr_moll4096.png" width="320" /></a></div><div style="text-align: center;"><span style="background-color: white;">The cosmic microwave background fluctuations. Credit: NASA/WMAP team.</span></div><span style="background-color: white;"><br /></span><span style="background-color: white;"><br /></span><span style="background-color: white;">The vacuum state of a quantum field is a highly entangled state. Therefore the correlations one observes in the cosmic microwave background are directly related to entanglement. This seminar raises the mesmerizing possibility that the particular type of entanglement that occurs in the states of loop quantum gravity could leave an observable imprint in the cosmic microwave background radiation. This occurs through their evolution from the big bounce that loop quantum cosmology replaces the big bang with up to the beginning of inflation influencing the type of vacuum the inflaton starts in. </span>Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-78772014554800120332018-01-10T11:59:00.000-06:002018-01-10T11:59:37.207-06:00Black holes exploding into white hole fireworks<span style="background-color: white;">Tuesday, Oct 24th</span><br /><b></b><br /><b>Marios Christodoulou, Aix Marseille U/SUSTec Shenzen</b><br /><b>Title: Geometry transition in covariant LQG: black to white </b><span style="background-color: white;"></span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/christodoulou102417.pdf">PDF</a><span style="background-color: white;"> of the talk (3M)</span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/christodoulou102417.mp4">Audio+Slides</a><span style="background-color: white;"> [.mp4 11MB]</span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-AFw_EUGRdgg/WlZES_T69cI/AAAAAAAAJ1Q/rypcATz_iDkrBjJtmXURu-DMRM0x068kwCLcBGAs/s1600/photo_bilbao.jpeg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="900" data-original-width="1600" height="180" src="https://4.bp.blogspot.com/-AFw_EUGRdgg/WlZES_T69cI/AAAAAAAAJ1Q/rypcATz_iDkrBjJtmXURu-DMRM0x068kwCLcBGAs/s320/photo_bilbao.jpeg" width="320" /></a></div><span style="background-color: white;"><br /></span><span style="background-color: white;"><br /></span><span style="background-color: white;">By Jorge Pullin, LSU</span><br /><span style="background-color: white;"><br /></span><span style="background-color: white;">Black holes are regions of space-time where gravity is so intense that nothing, including light, can escape, hence they are black. They are expected to form as stars exhaust their nuclear fuel and start to contract due to gravitational attraction. Eventually they become so dense that a black hole forms. According to classical general relativity, the star matter continues to contract inside the black hole until the density diverges. That is what is known as a "singularity". Obviously nothing can diverge in nature so it is believed that the singularities are an indication that one has pushed general relativity beyond its domain of validity. One expects that at high densities quantum effects should arise and a theory of quantum gravity is needed. There has been some progress in spherically symmetric loop quantum gravity that indicates that the singularity is replaced by a highly quantum region that eventually leads to another classical region of space-time beyond it. </span><br /><span style="background-color: white;"><br /></span><span style="background-color: white;">At the same time Hawking showed in the 70's that if one puts quantum fields to live on the classical background of a black hole, radiation is emitted as if the black hole behaved as a black body with a temperature inversely proportional to the black hole's mass. There is no contradiction with the black hole radiating because the radiation is produced by the quantum field outside the black hole. If the black hole radiates, then it should lose energy. Hawking's calculation cannot study this, because it assumes the quantum field lives in a fixed black hole background. It is expected that more precise calculations including the back-reaction of the field on the background should make the black hole shrink as it emits radiation. As the temperature increases as the black hole loses mass (it is inversely proportional to the mass) the black hole heats up and radiates more. Eventually it should evaporate completely. No detailed analysis of such evaporation is available at present. Such evaporation raises many questions, in particular what happened to the singularity inside the black hole (or the highly quantum region that apparently replaces it). What happened to all the information of the matter that formed the black hole? Is it lost?</span><br /><span style="background-color: white;"><br /></span><span style="background-color: white;">The work described in this seminar posits that the highly quantum region inside the black hole transitions into the future into a "white hole" (the time reverse of a black hole). A great explosion in which all the information that entered the black hole exits. This scenario is known as "fireworks". An important question is: does the explosion happen fast enough for it to make the loss of information through Hawking radiation irrelevant? In this seminar spin foams are used to try to address the question. The calculation at hand is to compute the probability of transition from a black hole to a white hole. There are many assumptions needed to make such calculation, so the results are at the moment tentative. However, the main conclusion seems to be that the explosion takes as long as the process of Hawking evaporation to take place. This may rule out the "fireworks" as candidates for fast radio bursts that have been observed by astronomers, but may keep in play other astrophysical predictions associated with them.</span>Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-43354621585021449542018-01-10T10:00:00.000-06:002018-01-10T10:00:09.443-06:00Cosmological dynamics from full loop quantum gravity<span style="background-color: white;">Tuesday, Sept 26th</span><br /><b>Andrea Dapor and Klaus Liegener, FAU Erlangen</b><br /><b>Title: Cosmological Effective Hamiltonian from full Loop Quantum Gravity </b><span style="background-color: white;"></span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/dapor092617.pdf">PDF</a><span style="background-color: white;"> of the talk (2.2M)</span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/dapor092617.mp4">Audio+Slides</a><span style="background-color: white;"> [.mp4 13MB]</span><br /><span style="background-color: white;"><br /></span><br /><span style="background-color: white;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-If-X3veskOQ/WlEeHv4kgNI/AAAAAAAAJ0M/ahG0IPCBoiQ9GynX-Jko_zoBR21z0TQNQCLcBGAs/s1600/Screen%2BShot%2B2018-01-06%2Bat%2B1.05.47%2BPM.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="393" data-original-width="754" height="166" src="https://3.bp.blogspot.com/-If-X3veskOQ/WlEeHv4kgNI/AAAAAAAAJ0M/ahG0IPCBoiQ9GynX-Jko_zoBR21z0TQNQCLcBGAs/s320/Screen%2BShot%2B2018-01-06%2Bat%2B1.05.47%2BPM.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;"><span style="background-color: white;">By Jorge Pullin, LSU</span></div><div class="separator" style="clear: both; text-align: left;"><span style="background-color: white;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="background-color: white;">Due to the complexity of theories like general relativity, a common line of attack to understand the theory is to consider situations with high symmetry. In them, one freezes almost all degrees of freedom but a few and studies them. Examples are the studies of homogeneous cosmologies, where the only degrees of freedom left are the volume of the universe and perhaps variables characterizing its anisotropy. In some cases people choose to freeze most of the degrees of freedom and then quantize the remaining ones. This is called "minisuperspace" quantization. In the case of cosmologies that means that one is left with just a handful of degrees of freedom, turning a field theory with infinitely many degrees of freedom like general relativity into a "mechanical system" in the sense of having only a finite number of degrees of freedom. The resulting quantization is therefore much simplified and a lot of progress can be made. The field of study of these quantizations is known as "loop quantum cosmology". The hope is that the resulting theories resemble what happens when one follows the evolution of a highly symmetric state in the full theory. This is, however, not guaranteed. There are known examples where "reducing then quantizing" does not yield the same result as "quantizing then reducing".</span></div><div class="separator" style="clear: both; text-align: left;"><span style="background-color: white;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="background-color: white;">The seminar dealt with an attempt to "quantize then reduce" loop quantum gravity and see if the results of loop quantum cosmology follow for such an approach. This requires choosing quantum states in the full theory whose probabilities are "peaked" around homogeneous geometries and that evolve maintaining the homogeneity. States that are peaked around certain classical solutions and follow their evolution in quantum theory are known as "coherent states". In this talk such states for loop quantum gravity based on cubic lattices were constructed and their evolution was studied. It was noted that the resulting evolution does not coincide with the one usually chosen in loop quantum cosmology. When one quantizes theories there are ambiguities in how one proceeds and choices need to be made in how one write certain classical equations as quantum operators. It turns out that one of the choices usually made in loop quantum cosmology does not match with what one gets in the "quantize then reduce" approach. This suggests novel dynamics to study in the context of loop quantum cosmology that may affect the emerging picture of how our universe's Big Bang got replaced by a Big Bounce. In the traditional loop quantum cosmology approach the bounce is preceded by a large classical universe like ours. In the new dynamics suggested in this talk the bounce is preceded by a large but very quantum universe with a large Planck-scale cosmological constant. In the distant past our universe asymptotes to a very symmetrical universe known as De Sitter space. Further studies need to be done to check the consistency of the approach. </span></div><div class="separator" style="clear: both; text-align: left;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><span style="background-color: white;"><br /></span>Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-45919510721758186682018-01-10T09:36:00.000-06:002018-01-10T09:36:18.617-06:00Intrinsic time geometrodynamics<span style="background-color: white;">Tuesday, Sept 12th</span><br /><b>Eyo Eyo Ita, University of South Africa</b><br /><b><b>Title: Intrinsic time quantum geometrodynamics: emergence of General Relativity and cosmic time</b> </b><span style="background-color: white;"></span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/ita091217.pdf">PDF</a><span style="background-color: white;"> of the talk (1.5M)</span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/ita091217.mp4">Audio+Slides</a><span style="background-color: white;"> [.mp4 8MB]</span><br /><span style="background-color: white;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-zALrAFrbQBI/WlEXQWIz1NI/AAAAAAAAJz0/5mH66gzHhqcZFHH84UtZYhrH0-EWK6nfgCLcBGAs/s1600/Eyo3small.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="154" data-original-width="150" src="https://2.bp.blogspot.com/-zALrAFrbQBI/WlEXQWIz1NI/AAAAAAAAJz0/5mH66gzHhqcZFHH84UtZYhrH0-EWK6nfgCLcBGAs/s1600/Eyo3small.jpg" /></a></div>By Jorge Pullin, LSU<br /><br />Usual Newtonian mechanics describes the motions of systems with respect to an absolute time variable usually called t. Already special relativity introduces the idea that time is not absolute and that it ticks at different rates for different observers. General relativity goes beyond that: one can pick any variable to play the role of time. The result of that is that if one tries to understand the dynamics of the theory as an "evolution in time" one runs into difficulties. This is important because many of our ideas of how to quantize theories are implemented dynamically. One needs what is known as a "Hamiltonian formulation" of the theory in order to implement what is known as "canonical quantization". In the Hamiltonian formulation there is a quantity known as the Hamiltonian that is responsible for time evolution. If one attempts to construct a Hamiltonian formulation for general relativity one discovers that the Hamiltonian vanishes. This reflects the fact that if one is allowed to pick any time variable one essentially can get any evolution one wants. This was the source of quite a bit of confusion and explains why a suitable Hamiltonian formulation took almost 50 years to emerge, being general relativity from 1915 and the Hamiltonian formulation only finally understood in the early 60's. Today we know that if one wants to have a defined Hamiltonian and evolution one needs to choose a time variable. The intrinsic geometrodynamics essentially chooses the volume of space as time variable. This seminar discussed the details and its implications for quantization in particular in the so-called "path integral quantization". Among the results a natural vacuum for the theory is found that involves the well known mathematical invariant related to the Chern-Simons form, suggesting perhaps that general relativity could be turned into a renormalizable quantum field theory.Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-33541736008860561832018-01-06T16:08:00.002-06:002018-01-06T16:08:33.360-06:00Gravitational path integral and group theory<b>Pietro Dona, Penn State</b><br /><b>Title: SU(2) graph invariants, Regge actions and polytopes </b><span style="background-color: white;"></span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/dona101017.pdf">PDF</a><span style="background-color: white;"> of the talk (10M)</span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/dona101017.mp4">Audio+Slides</a><span style="background-color: white;"> [.mp4 16MB]</span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-MwOcrfuqvmY/WlE1cUcYUlI/AAAAAAAAJ0c/HQVDpntkEHUuVN0yGlRGZgmYyyhYuHddQCLcBGAs/s1600/Screen%2BShot%2B2018-01-06%2Bat%2B2.45.16%2BPM.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="416" data-original-width="183" height="320" src="https://1.bp.blogspot.com/-MwOcrfuqvmY/WlE1cUcYUlI/AAAAAAAAJ0c/HQVDpntkEHUuVN0yGlRGZgmYyyhYuHddQCLcBGAs/s320/Screen%2BShot%2B2018-01-06%2Bat%2B2.45.16%2BPM.png" width="140" /></a></div><span style="background-color: white;"><br /></span><span style="background-color: white;">By Jorge Pullin, LSU</span><br /><br /><span style="background-color: white;"><br /></span><span style="background-color: white;">In the loop quantum gravity approach to quantum gravity the quantum states are given by spin networks, graphs with intersections and "colors" associated with each link. The colors are a shorthand to characterize that each link in the graph is associated with a mathematical quantity known as an element of a group. A group is a type of mathematical set with a composition law that is associative, has a neutral element and has an opposite element. For instance, real numbers form a group under addition. Matrices of numbers also form groups under multiplication. When links of a spin network meet at an intersection, the respective group elements associated with them get multiplied into a mathematical entity known as "intertwiner". Such intertwiners are constructed with what are known as invariant tensors in the group. </span><br /><span style="background-color: white;"><br /></span><span style="background-color: white;">One of the approaches to quantizations of field theories is the path integral approach. In it, one assigns probabilities to each physical trajectory and sums over all possible trajectories. When applied in the context of loop quantum gravity one gets trajectories in time of spin networks, which give rise to what are known as "spin foams". The probability of a given trajectory is quantified in terms of a number related to how the spin networks branch out into the future known as a "vertex". There are several proposals for such vertices to represent the dynamics of general relativity, at present it is not clear which one of the proposed ones represents nature more accurately. One of the most studied ones is the EPRL (Engle-Pereira-Rovelli-Livine) vertex. Other vertices that have simpler nature have also been proposed. This seminar deals with the evaluation of these vertices. This requires calculations in group theory. These calculations may have broader applicability than in just quantum gravity as these types of mathematical entities appear in many physical domains. Numerical calculations of the vertices have been carried out and asymptotic analyses performed for some of the more simplified vertices. The objective is to later extend the results to the EPRL vertex.</span>Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-46665885834707400542017-08-20T12:45:00.000-05:002017-08-20T12:45:15.988-05:00Simplicial group field theory<span style="background-color: white;">Tuesday, May 2nd</span><br /><b>Marco Finocchiaro, Albert Einstein Institute</b><br /><b>Title: Simplicial Group Field Theory models for Euclidean quantum gravity: recent developments </b><span style="background-color: white;"></span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/finocchiaro050217.pdf">PDF</a><span style="background-color: white;"> of the talk (2M)</span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/finocchiaro050217.mp4">Audio+Slides</a><span style="background-color: white;"> [.mp4 15MB]</span><br /><span style="background-color: white;"><br /></span><span style="background-color: white;">by Jorge Pullin, Louisiana State University</span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-40_svw_O03Y/WZnGxtv8vnI/AAAAAAAAJkE/0HpAT5Q4QeYoGlYbVKNwTIAkCbEdvOFTACLcBGAs/s1600/PictureI.jpeg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1358" height="320" src="https://2.bp.blogspot.com/-40_svw_O03Y/WZnGxtv8vnI/AAAAAAAAJkE/0HpAT5Q4QeYoGlYbVKNwTIAkCbEdvOFTACLcBGAs/s320/PictureI.jpeg" width="271" /></a></div><span style="background-color: white;"><br /></span>The approach to quantum gravity known as “spin foams” is based on the quantization technique known as the path integral. In this technique probabilities are assigned for a given slice of space to transition to a future slice in a space-time. Since in loop quantum gravity spatial slices are associated to spin networks, as these evolve in time transitioning to slices of the future one gets the “spin foams”. Group field theory is a technique in which an ordinary (but non-local) quantum field theory is constructed in such a way that its Feynman diagrams yield the probabilities of the spin foam approach. There is an analogue en 1+1 dimensions known as “matrix models” that were widely studied in the 1990’s. Group field theories can be viewed as their generalization to four dimensions.<br /><br /> Formulating spin foams in terms of group field theories has several advantages. Results do not depend on the triangulations picked, as one expects it should be but is not obvious in terms of spin foams. One can import techniques from field theories, in particular to introduce notions of renormalizability and a continuum limit.<br /><br /> In this talk a particular group field theory model is presented and discussed in some detail. In particular a numerical analysis of the resulting probabilities was made. And results were compared to a popular model of spin foams, the EPRL model. Certain insights on the possible choices in the construction of the model and how it could influence the ultraviolet behavior and possible singularities present were discussed. Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-43263310373110407692017-08-08T15:43:00.000-05:002017-08-08T15:43:21.067-05:00Loop quantum gravity with homogeneously curved vacuum<span style="background-color: white;">Tuesday, Apr 18th</span><br /><b>Bianca Dittrich, Perimeter Institute</b><br /><b>Title: (3+1) LQG with homogeneously curved vacuum </b><span style="background-color: white;"></span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/dittrich041817.pdf">PDF</a><span style="background-color: white;"> of the talk (8M)</span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/dittrich041817.mp4">Audio+Slides</a><span style="background-color: white;"> [.mp4 17MB]</span><br /><span style="background-color: white;"><br /></span><span style="background-color: white;">by Jorge Pullin, Louisiana State</span><br /><span style="background-color: white;"><br /></span><span style="background-color: white;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-gIUvp3AW7Ws/UnK032ccxEI/AAAAAAAAEUA/OYMCf2I87xM/s1600/bianca.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-gIUvp3AW7Ws/UnK032ccxEI/AAAAAAAAEUA/OYMCf2I87xM/s1600/bianca.jpg" /></a></div><span style="background-color: white;"><br /></span>The way geometries are studied mathematically one starts with a set of points that has a notion of proximity. One can say when points are close to each other. This is not the same as being able to measure distances in the set. That requires the introduction of an additional mathematical structure, a metric. The sets of points with notion of proximity are known as “manifolds”. General relativity is formulated on a manifold and is a theory about a metric to be imposed on that manifold. Ordinary quantum field theories, like quantum electrodynamics, require the introduction of a metric before they can be formulated, so they are of different nature than general relativity. Theories that do not require a metric in order to be formulated are known as “background independent”. Interestingly, although general relativity is a theory about a metric, it can be formulated without any prior metric. There exist quantum field theories that can be formulated without a metric. They are known as topological field theories and they typically, contrary to ordinary field theories, have only a finite number of degrees of freedom. This means that they are much easier to treat and to quantize. <br /><br />An example of a topological field theory is general relativity in three space-time dimensions. In one dimension less than four, the Einstein equations just say that the metric is flat, except at a finite number of points. So space-time is flat everywhere with curvature concentrated at just a few points. An example of a space that is flat everywhere except at a point is a cone. The only place that is curved is the tip. One has to remember that the notion of curvature we are talking here is one that can be measured from inside the space-time (typically by going around a circle and seeing if a vector carried around returns parallel to itself). If you do that in a cone on any circle that does not thread the tip, the vector comes back parallel to itself. So space-times in three dimensional general relativity are said to have “conical singularities” at the points where the curvature is non-zero. As other topological field theories, general relativity in three space-time dimensions has a finite number of degrees of freedom. This explains why Witten was able to complete its quantization in the mid 1980’s whereas the quantization of four dimensional general relativity is still a big outstanding problem today. <br /><br /><br />In this talk a generalization of three dimensional general relativity to four dimensions was presented. The resulting theory in four space-time dimensions has curvature concentrated at edges (strings) –as opposed to points as we had in the three dimensional case- and elsewhere the metric is flat. This makes them much easier to quantize than general relativity. Among the results was the construction of four dimensional quantum geometries similar to those in a previous model by Crane and Yetter. Also a role for quantum groups, that had been conjectured to arise when one considers a cosmological constant was found providing more evidence to this assertion. The space of quantum states (Hilbert space) was rigorously constructed and leads to insights about how the continuum limit of the theory could emerge. The hope is that one could build on these theories to construct new representations for loop quantum gravity in four space-time dimensions and hopefully to implement on them the (quantum) dynamics of general relativity. <br /><br /><br />Also a notion of duality emerges. In this context, duality means a certain relationship between the metric and the curvature of the space-time at a classical level. Here it can be implemented at a quantum level and quantum space of states associated with the metric (areas) and curvatures can be introduced and are dual to each other. Similar spaces had been proposed for general relativity, but here there is much more mathematical control over them, so this provides a controlled arena to test ideas that are being put forward in the context of loop quantum gravity in four space-time dimensions. <br /><br />Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0tag:blogger.com,1999:blog-5826632960356694090.post-67588452880396895032017-04-28T12:51:00.000-05:002017-04-28T12:51:22.954-05:00Transition times through the black hole bounce<span style="background-color: white;">Tuesday, Apr 4th</span><br /><b>Parampreet Singh, LSU</b><br /><b>Title: Transition times through the black hole bounce </b><span style="background-color: white;"></span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/singh040417.pdf">PDF</a><span style="background-color: white;"> of the talk (2M)</span><br /><a href="http://relativity.phys.lsu.edu/ilqgs/singh040417.mp4">Audio+Slides</a><span style="background-color: white;"> [.mp4 18MB]</span><br /><span style="background-color: white;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-RoMaXdHqZYQ/WQNwkMR7ROI/AAAAAAAAJWs/BE_i6AfsUxw9vhWUqe0Rs3HIGQQmr5G0gCLcB/s1600/param2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-RoMaXdHqZYQ/WQNwkMR7ROI/AAAAAAAAJWs/BE_i6AfsUxw9vhWUqe0Rs3HIGQQmr5G0gCLcB/s320/param2.jpg" width="304" /></a></div><span style="background-color: white;">by Gaurav Khanna, University of Massachu</span><span style="background-color: white;">setts Dartmouth</span><br /><span style="background-color: white;"><br /></span><span style="background-color: white;"><br /></span> Loop quantum cosmology (LQC) is an application of loop quantum gravity theory in the context of spacetimes with a high degree of symmetry (e.g. homogeneity, isotropy). One of the main successes of LQC is the resolution of "singularities" that generically appear in the classical theory. An example of this is the "big bang" singularity that causes a complete breakdown of general relativity (GR) in the very early universe. Models studied within the framework of LQC replace this "big bang" with a "big bounce" and do not suffer a singular breakdown like in the classical theory. <br /><br /><br />It is, therefore, natural to consider applying similar techniques to study black holes; after all, these solutions of GR are also plagued with a central singularity. In addition, it is plausible that a LQC model may shed some light on long-standing issues in black hole physics, i.e., information loss, Hawking evaporation, firewalls, etc. <br /><br /><br />Now, if one restricts the model only to the Schwarzschild black hole interior region, the spacetime can actually be considered as a homogeneous, anisotropic cosmology (the Kantowski-Sachs spacetime). This allows techniques of LQC to be readily applied to the black hole case. In fact, a good deal of study has been performed in this direction by Ashtekar, Bojowald, Modesto and many others for over a decade. While these models are able to resolve the central black hole singularity and include important improvements over previous versions, they still have a number of issues. <br /><br /><br />Recently, Singh and Corichi (2016), proposed a new LQC model for the black hole interior that attempts to address these issues. In this talk, Singh describes some of the resulting phenomenology that emerges from that improved model.<br /><br />The main emphasis of this talk is on the following questions:<br /> <br /><br />(1) Is the "bounce" in the context of a black hole LQC model, i.e., transition from a black hole to a white hole, symmetric? Isotropic and homogeneous models in LQC have generally exhibited symmetric bounces. But, that is not expected to hold in the context of more general models.<br />(2) Does quantum gravity play a role only once during the bounce process?<br />(3) What quantitative statements can be made about the time-scales of this process; and what are the full implications of those details?<br /> (4) Do all black holes, independent of size, exhibit very similar characteristics? <br /><br /><br />Based on detailed numerical calculations that Singh reviews in his presentation, he uncovers the following features from this model: <br /><br /><br />(1) The bounce is indeed not symmetric; for example, the sizes of the parent black hole and the offspring white hole are widely different. Other details on this asymmetry appear below.<br />(2) Two distinct quantum regimes appear in this model, with very different associated time-scales.<br />(3) In terms of the proper time of an observer, the time spent in the quantum white hole geometry is much larger than in the quantum black hole. And, in particular, the time for the observer to reach the white hole horizon is exceedingly large. This also implies that the formation of the white hole interior geometry happens a lot quicker than the formation of its horizon.<br />(4) The relation of the bounce time with the black hole mass, does depend on whether the black hole is large or small. <br /><br /><br />On the potential implications of such details on some of the important open questions in black hole physics, Singh speculates: <br /><br /><br />(1) For large black holes, the time to develop a white hole (horizon) is much larger than the Hawking evaporation time. This may suggest that for an external observer, a black hole would disappear long before the white hole appears!<br />(2) For small black holes, the time to form a white hole is smaller than Hawking time, i.e., small black holes explode before they can evaporate! <br /><br /><br />These could have some interesting implications for the various proposed black hole evaporation paradigms. Given the concreteness of the results Singh presents, they are also likely to be relevant to the many previous phenomenological studies on black hole to white hole transitions including Planck stars. <br /><br /><br />The two main limitations of Singh's results are: (1) the current model ignores the black hole exterior entirely; and (2) the conclusions rely on effective dynamics, and not the full quantum evolution. These may be addressed in future work. <br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />Jorge Pullinhttp://www.blogger.com/profile/07465581283254332265noreply@blogger.com0