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.

Thursday, February 7, 2019

Modified loop quantum cosmology

Tuesday, Feb. 5th

Parampreet Singh, LSU
Title: Modified loop quantum cosmologies 
PDF of the talk (2M)
Audio+Slidesof the talk (52M)
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 
PDF of the talk (9M)
Audio+Slidesof the talk (32M)
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.