Quantum reference frames

Tuesday, March 7th
Flaminia Giacomini, ETH Zurich

Quantum reference frames
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By Jorge Pullin, LSU

It is generally accepted that the energies at which full quantum gravity effects will be relevant are so high that there is no chance of generating them in the laboratory. Full quantum gravity is only expected to be relevant in extreme environments like deep inside black holes or near the origin of the universe.

Nevertheless, there is interest is studying situations in which both quantum effects and gravity are important. Experiments can currently probe gravitational effects of masses as small as 90 milligrams, or quantum superpositions at scales of half a meter. These types of situations, though short of fully quantum gravitational in essence, can offer experimental guidance in a field that is notoriously short of it.

The talk focused on the issue of quantum reference frames. Reference frames are commonly used in physics and are treated as idealizations. In reality, any reference frame is a physical system and is subject to the laws of quantum mechanics like any other. Taking that into account leads to modifications in the form of the laws of physics from the one they take in idealized frames. In particular several important quantum properties like the "entanglement" that physical systems exhibit is a frame dependent phenomenon. Also the equivalence principle, the statement that all masses fall at the same acceleration in gravity, can be extended to be valid in quantum reference frames and in situations such as a massive object in a spatial quantum superposition.

The summary is that we do not currently know which experiments will prove definitively that gravity has quantum features, and probing regimes involving quantum mechanics and gravity can offer guidance on how to quantize gravity.

 Tuesday, November 8th

Mehdi Assanioussi, University of Warsaw

Matter in LQG
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by Jorge Pullin, LSU

Traditional quantum field theories are formulated using a mathematical framework called the Fock representation. In such mathematical framework physical elements like the notion of particles like photons and their properties have a well-defined mathematical counterpart. This framework is also used in quantum field theory in curved space-time, an approximation to full quantum gravity in which one treats gravity classically as a curved space-time and studies quantum fields that live on it. Quantum field theory in curved space-time has been extensively developed since the 1960’s and has led to major predictions like Hawking radiation or particle production in the early universe. If loop quantum gravity is to provide a good description of nature, one expects a connection of its framework with that of quantum field theory in curved space-time should emerge.

To this aim, Varadarajan, in the early years of this century, developed the r-Fock representation for quantum fields on flat and curved space-times. This representation has elements in common both with the loop representation used in loop quantum gravity and the Fock representation. At first it was only developed for Abelian quantum fields (like photons) and this was viewed as a limitation of the framework. Later, Ashtekar and Lewandowski presented a generalization to non-Abelian fields (like gluons), but it had some technical difficulties. The speaker, together with Lewandowski, has recently developed an alternative version of the r-Fock representation that bypasses the technical difficulties. The talk discussed this approach and outlined possibilities for it. Open questions include how to formulate the dynamics of loop quantum gravity in this representation and if it could help recover the continuum picture of classical space-time from the inherently discrete picture that loop quantum gravity yields at the quantum level.

The search for tabletop quantum gravity signatures

 Tuesday, Apr 5th

Marios Christodoulou, University of Vienna

The search for `table-top' quantum gravity signatures
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By Jorge Pullin, LSU

We know that the strong, weak and electromagnetic interactions require of quantum mechanics for their correct descriptions. This is in part because those three forces are important at the microscopic level and we know that at that level classical mechanics fails. Gravity is a bit different. At the microscopic level, its effects are negligible. For instance, the electric repulsion of two electrons (they have the same charge) is 10⁴⁴ (that is one followed by 44 zeros) times larger than their gravitational attraction. Gravity is important in the macroscopic world, where quantum effects are washed out due to the large presence of degrees of freedom. Do we need to quantize gravity, then? Conceptual reasons suggest it, we do not really know how to consistently couple classical and quantum theories.

Recently, advances in quantum technologies have allowed to study gravitational interactions among objects of ever shrinking sizes. This opens the possibility of revealing quantum phenomena. In particular a phenomenon called entanglement in which the properties of the two masses become intertwined. But do they include quantum aspects of gravity? The issue is hotly debated. The experiments involve tiny levitated masses that are at microscopic distances from each other. Usually dynamics becomes clearer when masses are far away from each other, since one can introduce notions like waves, photons and gravitons, that are more difficult to characterize close to their sources. This has led to several claims and counterclaims in the literature. The talk gave an overview of the issues and papers involved and suggested that experiments in the relatively near future could help clarify the situation and perhaps offer a conclusive probe of the quantum nature of gravity.

Clock dependence and unitarity in quantum cosmology

Tuesday, Mar 22nd
Lucía Menéndez-Pidal, Nottingham University

Clock dependence and unitarity in quantum cosmology
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By Jorge Pullin, LSU

In ordinary physics, time (and space) are given once and for all. They are "background" quantities that do not evolve. In theories of gravity like general relativity, where one describes gravitational effects not as the result of a force but as a deformation of space-time, things are different. To begin with, unless one considers a concrete gravitational configuration (a concrete space-time), time (and space) simply do not exist. Even after considering a given space-time, to interpret it as "an evolution" of space (and matter) as "a function of time", requires some care, especially when one is considering the quantum version of things. The most obvious procedure is to consider some variable of the problem, like the value of a matter field, and use it to "keep time". Some such choices can obviously be very bad. For instance, if one chooses the position of a rock that does not move as one's "time", the resulting "evolution" of what one is trying to study will not be something easily recognizable. Even if one makes "judicious" choices, it is not at all clear that the resulting evolutions can be considered physically equivalent. Difficulties are further compounded by details of how the Einstein equations operate.

This talk considered these questions in the simplified setting of homogeneous cosmologies, where spatial dependence is very simple, allowing to make calculations explicit and controlled. Even in this simplified setting, the talk showed there are several subtleties. One of the central properties of ordinary quantum systems, called unitarity, that essentially implies that information is not destroyed, is not automatically guaranteed. In loop quantum gravity applied to cosmology (loop quantum cosmology) the Big Bang singularity usually is eliminated and evolution is regular where in classical general relativity infinities appear. The talk showed that this feature is not guaranteed and depends on the choice of time made.

Polymerized black hole constraints from Hawking radiation

Tuesday February 8th 2022
Jeremy Auffinger, Univ. Lyon

Polymerized black hole constraints from Hawking radiation
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By Jorge Pullin, LSU

Black holes come in different kinds. The ones people are most familiar with are those that result when a star, with a mass a few times that of the Sun, collapses. Their mass is therefore a multiple of the mass of the Sun and are called "stellar sized" black holes. There are much larger black holes, with a mass a million to a billion times the mass of the Sun. These black holes are at the center of galaxies and presumably they formed by absorbing surrounding stars and other black holes. They are called supermassive black holes. A third class of black holes, which has not been observed directly yet, would consist of much smaller black holes. They are produced in the early universe from fluctuations in the density of matter. 

The way stars rotate around when they are in galaxies suggests that the latter contain more matter than what is visible. This is the origin of the conjectured "dark matter" present in them. There are various proposals for what could constitute dark matter, ranging from elementary particles of various kinds to primordial black holes. 

In the 1970's Hawking showed theoretically that black holes emit radiation much like a heated piece of metal does, with a characteristic temperature. The latter is inversely proportional to the black hole mass. For stellar-sized black holes, the temperature is very small, a millionth of a degree. As a result, the Hawking radiation from such black holes is unobservable in practice. Primordial black holes, as they are much smaller, would have a much higher temperature and therefore more Hawking radiation. This radiation has not been observed (yet) so it can be used to constrain the presence of these types of black holes. If one takes them as a candidate for dark matter, it helps put constraints on the resulting dark matter models.

Loop quantum gravity has been applied over the last decade to spherically symmetric situations, including black holes. Various different models have emerged, differing in the assumptions and provide a picture that differs in some details. But the main feature is they eliminate the infinities that appear in classical general relativity inside black holes and are known as the singularity. This was a long expected result of any successful approach to quantum gravity, as infinities do not exist in reality.

This talk analyzed the modifications to the calculations of Hawking radiation from primordial black holes, and consequently in dark matter models that involve them, if one considers the black holes that stem from loop quantum gravity. If the radiation from these black holes is ever observed it could therefore provide valuable experimental information about loop quantum gravity.

Imprints of black hole area quantization in gravitational waves

Tuesday, Jan 25th Adrián del Río, PennState

Imprints of black hole area quantization in gravitational waves
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By Jorge Pullin, LSU

One of the distinct places where quantum mechanics has an imprint on our everyday life is in atomic spectra. The theory says that atoms can only absorb and emit certain discrete quantities of energy (quanta) when they interact, for instance, with an electromagnetic field. Since the energy of photons is directly related with their frequency, this means that atoms emit light at specific frequencies. An example of this is easily seen by sprinkling table salt on an open flame. It will turn yellow, the color associated with the typical quanta of sodium. 

Quantum gravity theories predict that the mass (and therefore the area) of black holes is quantized. This means that when black holes interact with gravitational waves, the frequencies involved will be quantized. The situation is analogous to  that of atoms and electromagnetic radiation. This talk shows that this quantization can leave imprints in the types of gravitational waves that are currently being detected by interferometric gravitational wave observatories like LIGO or VIRGO. These waves come from collisions of black holes. The collisions perturb the holes and the latter "ring down" emitting gravitational waves, much like a bell rings down emitting sound waves (in fact, for Solar sized black holes the frequencies are similar, of the order of kiloHertz). This ring down would have imprints from the quantization of the area that appear as "echos", repetitive patterns in the waves emitted. 

The quantization of areas has long been expected in theories of quantum gravity. Usually people assumed that the quantization would be given by some integer multiple of the "fundamental" area given by the Planck length squared. The Planck length is the fundamental length one can construct using the gravitational constant G, the speed of light c and Planck's constant of the quantum theory known as "hbar". This talk showed that if areas are quantized in this way, then there are potentially observable consequences in gravitational waves detected from black hole collisions. Loop quantum gravity, on the other hand, has a more sophisticated prediction about the quantization of areas. In it, the quanta are not equally spaced, but quickly "bunch up" as one considers larger areas. This implies that for large black holes like the one LIGO can observe, the effects of the quantization are incredibly small. In a sense this can be viewed a positive aspect of the theory, since no deviations from the predictions of the classical theory have been actually observed in gravitational wave detections.

Quantization of the volume of the simplest grain of space

Tuesday, October 19th

Hal Haggard, Bard College

Quantization of the Volume of the Simplest Grain of Space
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By Jorge Pullin, LSU

There exists a concept in mathematics called "asymptotic resurgence" in which an infinite sum of terms exhibits a surprising behavior. The terms that appear late in the summation around one physically relevant point are exactly the same as the terms that appear early in the sum around another physically relevant point. The result is a rich connection between the physics at the two different extremes and has applications in many areas of physics, for instance in the calculations of intensities of rainbows.

This talk applies these ideas to the calculation of the volume in loop quantum gravity. The volume of a region of space is discrete in that theory and has a complicated expression depending on the details of the quantum state one is considering. The expressions are known but are difficult to interpret. Previous studies have dealt with them primarily through numerical methods. In this talk an approximate expression is derived that can be much more easily interpreted and studied. It applies it to the simplest "grain" of space, a tetrahedron. A neat illustration of the power of the insights that can be learned from having an easier to interpret expression is the following movie following tetrahedra of different shape but equal volume:

To quote the concluding slide: "Quantization of geometry provides a remarkable laboratory for understanding resurgent perturbative/non-perturbative relations and, due to the richness of its underlying quantum structure, may even require extensions of this formalism."