Tuesday, October 15, 2019

Effective dynamics from full loop quantum gravity

Tuesday, Oct 8

Muxin Han, Florida Atlantic University
Title: Effective dynamics from full loop quantum gravity
PDF of the talk (1M)
Audio+Slides of the talk (272M)
SRT (Subtitles) of the talk (98K)
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
PDFof the talk (2M)
Audio+Slidesof the talk (38M)
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.

Wednesday, October 9, 2019

Quantum geometry from higher gauge theory

Tuesday, Sep 10th

Bianca Dittrich, Perimeter Institute
Title: Quantum geometry from higher gauge theory
PDF of the talk (6M)
Audio+Slides of the talk (180M)
SRT (Subtitles) of the talk (63K)

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
PDF of the talk (89K)
Audio+Slides of the talk (200M)
SRT (Subtitles) of the talk (89K)
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.

Monday, May 27, 2019

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
PDF of the talk (230K)
Audio+Slides of the talk (21M)

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.

Wednesday, March 20, 2019

Implications of a dynamical cosmological constant

Tuesday, Mar 19th

Lee Smolin, Perimeter Institute
Title: Implications of a dynamical cosmological constant 
PDF of the talk (10M)
Audio+Slides of the talk (28M)
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.

Tuesday, March 19, 2019

Towards loop quantum gravity effective dynamics

Tuesday, Feb. 19th

Andrea Dapor, LSU
Title: Toward LQG effective dynamics 
PDF of the talk (250K)
Audio+Slides of the talk (57M)
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.