Wednesday, October 24, 2018

A unified geometric framework for boundary charges and dressings

Tuesday, Oct 23rd

Aldo Riello, Perimeter Institute
Title: A unified geometric framework for boundary charges and dressings 
PDF of the talk (2M)
Audio+Slides of the talk (41M)
By Jorge Pullin, LSU (with some help from Aldo)

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.

Thursday, October 18, 2018

Quantum extension of black holes

Tuesday, Oct 9th

Javier Olmedo, LSU
Title: Quantum Extension of Kruskal Black Holes 
PDF of the talk (500k)
Audio+Slides of the talk (17M)

By Jorge Pullin, LSU

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.

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.

Monday, October 8, 2018

Computing volumes in spin foams

Tuesday, Sep 25th

Benjamin Bahr, DESY
Title: 4-volume in spin foam models from knotted boundary graphs 
PDF of the talk (3M)
Audio+Slides of the talk (15M)

by Jorge Pullin, LSU

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.

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.

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.

Tuesday, May 1, 2018

Cosmological perturbations in terms of observables and physical clocks

Tuesday, Apr 17th

Kristina Giesel, FAU Erlangen-Nürnberg
Title: Gauge invariant observables for cosmological perturbations 
PDF of the talk (8M)
Audio+Slides of the talk (15M)

By Jorge Pullin, LSU

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.

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.

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.

Sunday, April 22, 2018

Quantum gravity inside and outside black holes

Tuesday, Apr 3rd

Hal Haggard, Bard College
Title: Quantum Gravity Inside and Outside Black Holes 
PDF of the talk (5M)
Audio+Slides of the talk (19M)
By Jorge Pullin, Louisiana State University

The talk consisted of two distinct parts. The second part discussed black holes exploding into white holes. We have covered the topic in this blog before, 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.

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.

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.

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.

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.

Sunday, March 25, 2018

Cosmological non Gaussianity from loop quantum cosmology

Tuesday, Mar 6th

Ivan Agullo, LSU
Title: Non-Gaussianity from LQC 
PDF of the talk (22M)
Audio+Slides [.mp4 19MB]
By Jorge Pullin,  LSU

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.
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,
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.

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. 

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.

Image credits: Cosmic microwave background Wikipedia page.

Quantum spacetimes on a quantum computer

Tuesday, Mar 20th

Keren Li, Tsinghua University
Title: Quantum spacetime on a quantum simulator 
PDF of the talk (3M)
Audio+Slides [.mp4 11MB]

By Jorge Pullin, LSU

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,
If one were in a dynamical situation, new vertices are created,
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.