Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole

Tuesday, Dec 3rd.
Fabio Mele and Johannes Muench, University of Regensburg

Title: Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole
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By Jorge Pullin, LSU

When one crosses the horizon into a black hole the role of time and radius get interchanged. One is inevitably dragged into "the future" along the r direction towards the singularity at r=-0. The metric of the space-time, which outside the black hole depends on r, inside depends on t, it becomes time dependent as if it were a cosmological space-time. This in fact can be made into a mathematically precise correspondence. The space-time in the interior of a black hole is equivalent to a type of cosmology known as Kantowksi-Sachs. This led people to study it using loop quantum cosmology tools. In particular one finds that the singularity inside black holes gets replaced by a "bounce" into another region in space-time just like the Big Bang is replaced by a bounce in loop quantum cosmology.

This talk focused on some technical issues of these types of studies. In particular, when one studies physically observable quantities, mathematically one finds there are two of them, but only one has a physical interpretation, it is the mass of the black hole. Through a change of variables the authors were able to identify physically two observable quantities. They correspond to the mass of the black hole and the mass of the "white hole" that emerges once one bounces through the singularity. The new variables have several other advantages, in particular they simplify the dynamics quite a bit and it actually becomes exactly solvable.

Quasilocal holography in quantum gravity in 3 dimensions

Tuesday, Nov 5

Aldo Riello, Perimeter Institute

Title: Quasilocal holography in Quantum Gravity in 3 Dimensions
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By Jorge Pullin

Holography in the context of gravitational physics refers to describing a region of space-time through a theory on its boundary. The idea arises in several scenarios, in particular in string theory in the so called AdS/CFT correspondence.

In this talk the concept of holography was first studied in three dimensions. General relativity simplifies considerably in three dimensions since the Einstein equations in empty space imply that space-times are all flat. This allows to make considerable progress and in fact there exists a quantum theory of gravity in three dimensions, it is known as the Regge-Ponzano model. In the talk the relation of this model with degrees of freedom on the boundary of space-time were discussed. Both the case with and without a cosmological constant were considered. Many parallels with other results in the literature were found. The relation of the dynamics in the interior with that on the boundary and its corresponding states was outlined. Connections with other boundary treatments that were discussed in International Loop Seminars recently by Dittrich and Bonzom and by Wieland were also presented.

Quasi local energy from loop quantum gravity boundary modes

Tuesday, Oct 22

Wolfgang Wieland, Perimeter Institute
Title: Quasi-local energy from LQG boundary modes
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By Jorge Pullin

In physical theories situations can be broken up into subsystems that one can follow individually characterized by a finite number of variables.

However, for nonlinear theories like general relativity one does not necessarily know how to do that. This is related to several problems in the theory like the averaging problem in cosmology. In the latter one typically concentrates on a small number of degrees of freedom of the universe, like its scale, and writes equations for them, pretending the universe is homogeneous, it does not change from one point to the next. This is a coarse approximation, but several important results can be derived from it. The matter content of the universe is not homogeneous and therefore to treat it one typically considers an average. But the average of non-linear functions of some variables is not the same as evaluating those quantities with the average values of the variables. This is known as the averaging problem in cosmology.

In this talk it was proposed to build degrees of freedom for subsystems in general relativity by constructing the degrees of freedom of the whole system starting from those of subsystems. The construction was discussed first in the context of classical general relativity. In the last part of the talk a connection with loop quantum gravity was presented. When one considers subregions of space time in loop quantum gravity the loops pierce the boundaries of the subregions and constitute field theories of "punctures" on them. These naturally embody the degrees of freedom of the subregion. A connection with a particular formulation of loop quantum gravity known as the spinor formulation was also suggested.

Effective dynamics from full loop quantum gravity

Tuesday, Oct 8

Muxin Han, Florida Atlantic University
Title: Effective dynamics from full loop quantum gravity
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By Jorge Pullin, LSU


A hot topic of research is how to derive the equations of loop quantum cosmology from loop quantum gravity. Initial investigations started by freezing most degrees of freedom and keeping the ones relevant for cosmology and proceeding to quantize them using loop quantum gravity inspired techniques. In recent years the focus has moved towards trying to derive things directly from full loop quantum gravity. In this talk a proposal along these lines is put forward. The idea is to use the path integral approach to quantization. This is an approach in which the quantum theory is built by considering all possible paths of the dynamics of the system and assigning probabilities to them. The idea is to perform the path integral using a set of states known as coherent states and study the resulting equations of motion. The technique is applied to several proposals for the evolution operator (Hamiltonian) of the theory that have been put out in the literature. The technique is suitable for numerical evolution opening a contact with numerical relativity. It may be applicable in other situations of interest like cosmological perturbations and binary black holes.

New Loop Quantum Cosmology modifications from Symplectic Structures

Tuesday, May 14th

Klaus Liegener, LSU
Title: New Loop Quantum Cosmology modifications from Symplectic Structures
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By Jorge Pullin, LSU

Loop quantum gravity is based on a new set of variables for describing general relativity that were introduced by Abhay Ashtekar. These variables have a certain amount of redundancy, known as a gauge symmetry.

Loop quantum cosmology is an approximation to loop quantum gravity that attempts to model cosmologies by following only a very limited number of degrees of freedom. A current topic of great interest is to understand how and if this approximation captures behaviors of the full theory. This talk concentrated on the role the redundancies in the variables Ashtekar introduced play in the construction of loop quantum cosmologies. It proposes to use certain variables that better behave under the presence of these redundancies and draws implications for the dynamics of the resulting theory. In particular it implies, as is common in loop quantum cosmology, that the Big Bang at the beginning of the universe is replaced by a "bounce" from a previous universe. However, the dynamics of the current model implies the bounce is asymmetrical, the universe before and after it do not look the same. This had been encountered in some previous proposals for loop quantum cosmologies, but not in all of them.

Quantum geometry from higher gauge theory

Tuesday, Sep 10th

Bianca Dittrich, Perimeter Institute
Title: Quantum geometry from higher gauge theory
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By Jorge Pullin, LSU


Physical theories are usually formulated in terms of sets of redundant variables. A simple example would be to consider the position of a pendulum indicated by its x and y coordinates. One knows that x and y are not arbitrary, they are constrained by the length of the pendulum and the position it is hanged from. More complicated field theories, like electromagnetism or Yang-Mills theories are also formulated in terms of redundant gauge variables and there are constraints between them. When one quantizes theories, the constraints have to be promoted to quantum relations between operators, and this is typically problematic.

This talk advocates for an approach to quantum gravity in which one increases the level of redundancy by introducing extra variables with extra constraints. The resulting theories are equivalent to the original ones as classical theories, but their quantization can be more favorable. The idea is not entirely new, it has been carried out more or less implicitly in quantizations of gravity in three dimensions (or two spatial and one time dimension). In three dimensions the Einstein equations imply all space-times are flat, so the resulting theories are relatively simple to handle. The talk proposes following a similar route for gravity in three spatial and one time dimensions, as we think the real universe has. There are numerous technical issues that need to be overcome to complete this approach and this talk addresses some of them. Among them, implementing the new constraints implied by the new formulation. However, the constraints of the traditional formulation of gravity, that have proven to be very problematic, appear geometrically very transparent in the current approach.

Some comments on canonical gauge theories with boundaries

Tuesday, Sep 24th

Alejandro Corichi, UNAM Morelia
Title: Some comments on cannonical gauge theories with boundaries
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By Jorge Pullin, LSU


When field theories are usually formulated, it is assumed that the portion of space they live in is infinite. There are no boundaries to space, or more precisely, they are placed at infinity. Many physical situations, however, concern situations  with a bounded finite domain. The formulation of field theories requires modifications when boundaries are introduced. The equations of field theories are typically derived through a procedure from a function called the action. Extra terms have to be added to the action if one has a situation with finite boundaries.

Ordinary field theories like electromagnetism have infinitely many degrees of freedom. This means its variables are fields that are functions of space and one can view the value at each point in space as a different degree of freedom. In that sense they are generalizations of usual mechanical systems, which have a finite number of degrees of freedom. Topological field theories are models that, although they have variables that are fields that are functions of space, its equations imply that one only has a finite number of degrees of freedom. This implies many simplifications, and they have proved useful as models in which to test quantization techniques, avoiding the many complexities introduced by having an infinite number of degrees of freedom. Both ordinary and topological field theories are typically described in terms of redundant variables. That means that a several mathematical configurations correspond to a physical configuration. This implies there are symmetries in the theory, this is what is usually called "gauge" symmetries. This talk addressed the issue of topological field theories with boundaries and also ordinary field theories coupled to topological theories. A procedure to treat them was given and shown to work in a pair of examples. Some of the techniques would be of interest to explore fields in the vicinity of black holes, where the horizon (the surface beyond which nothing can return) acts as a natural boundary for fields living in the vicinity of the black hole.

Experimental detection of the discreteness of time

Tuesday, Apr 30th

Marios Christodoulou, University of Hong Kong
Title: The possibility of experimental detection of the discreteness of time
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By Jorge Pullin, LSU

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 "Schroedinger cat" 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 Schroedinger bacterium.

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.

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^-44 seconds, for comparison the best atomic clocks can probe only up to 10^-19 seconds). This opens new possibilities for probing quantum gravitational effects with low energy experiments in the lab.

Implications of a dynamical cosmological constant

Tuesday, Mar 19th

Lee Smolin, Perimeter Institute
Title: Implications of a dynamical cosmological constant 
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By Jorge Pullin, LSU

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.

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.

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.

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.

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.

Towards loop quantum gravity effective dynamics

Tuesday, Feb. 19th

Andrea Dapor, LSU
Title: Toward LQG effective dynamics 
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By Jorge Pullin, LSU

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.

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.

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.

Modified loop quantum cosmology

Tuesday, Feb. 5th

Parampreet Singh, LSU
Title: Modified loop quantum cosmologies 
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By Jorge Pullin, LSU

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.

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.

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.

When one quantizes theories, even as simple as the ones one considers in homogeneous minisuperspaces, there are quantization ambiguities. In a recent talk, an alternative quantization of loop quantum cosmology to the traditional one exploiting one of those ambiguities was presented.

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.

2+1 D loop quantum gravity on the edge

Tuesday, Jan. 22nd

Barak Shoshany, Perimeter Institute
Title: 2+1D loop quantum gravity on the edge 
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By Jorge Pullin, LSU

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.

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.

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.

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.