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.

Tuesday, February 6, 2018

Using symmetries to determine the dynamics

Tuesday, Feb 6th

Ilya Vilensky, Florida Atlantic University
Title: The unique form of dynamics in LQC 
PDF of the talk (0.5M)
Audio+Slides [.mp4 11MB]

By Jorge Pullin, LSU

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.

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.

Monday, January 29, 2018

New dynamics for quantum gravity

Tuesday, Jan 23rd

Cong Zhang, Univ. Warsaw/Beijing
Title: Some analytical results about the Hamiltonian operator in LQG 
PDF of the talk (1.7M)
Audio+Slides [.mp4 10MB]

by Jorge Pullin, LSU

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.

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.

Monday, January 15, 2018

Construction of Feynman diagrams for group field theory

Tuesday, Dec 5th

Marco Finocchiaro, Albert Einstein Institute
Title: Recursive graphical construction of GFT Feynman diagrams 
PDF of the talk (1M)
Audio+Slides [.mp4 24MB]

By Jorge Pullin, LSU.
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.

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.

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.