Information on my research for laymen
1904.04845: Resolving Spacetime Singularities within Quantum Gravity
L. Bosma, B. Knorr and F. Saueressig
A recurring theme in the discussion of quantum gravity is the existence of so-called spacetime singularities in Einstein's theory of General Relativity. These are regions of spacetime where our mathematical description of the physics involved breaks down. Among others Stephen Hawking proved mathematically that one usually cannot avoid forming singularities in General Relativity. A consistent theory of quantum gravity is believed to resolve this issue.
An aspect of the problem of spacetime singularities can already be seen in Newtonian gravity. The gravitational potential is inversely proportional to the distance, and thus the gravitational force between two bodies very close to each other is extremely strong. Very short distances are also the regime where quantum gravity is expected to give rise to deviations from General Relativity.
In a quantum field theory setup, we model forces by an exchange of messenger particles, for example the graviton for gravity or the photon (light) for the electromagnetic force. The nature of how these particles move through spacetime then has direct implications of how the corresponding force between objects behaves. As an example, for very large distances both photons and gravitons behave in a similar way: namely in such a way to give rise to an inverse square law for the force.
Our work tries to investigate the fate of the singularity in the Newtonian potential in a particular approach to quantum gravity. For this, we resolved how gravitons behave at very short length scales. We found that their behaviour at tiny scales roughly the size of a Planck length deviates from the classical behaviour predicted by General Relativity, and precisely in such a way that the gravitational potential between two test bodies stays finite at any distance. In particular this means that there is a finite binding energy in any gravitationally coupled system. This constitutes another step in the direction of singularity resolution in quantum gravity.
1810.07971: Lorentz symmetry is relevant
B. Knorr
Symmetries form a central part in our formulation of physical theories of nature. In daily life, this mainly concerns the geometrical shape of objects. For example, we often approximate celestial bodies as perfect balls even though clearly the Earth is not a perfect ball (as anyone not living in the Netherlands will immediately agree). Nevertheless, with this approximation we can describe the planetary motion rather accurately.
Theories in theoretical physics often have more abstract symmetries, in the sense of "what would happen if I would change this and that". This includes such trivial things as charge conjugation (all particles receive the opposite charge), but also more complicated symmetries which mix different fields in a very particular way.
One of the most fundamental symmetries in modern physics is Lorentz symmetry, the symmetry of spacetime transformations of special relativity (SR). In SR, there is no absolute time, every event happens relative to other events. This can be formulated as a symmetry under coordinate transformations - the same physics is described if I move while I observe the thing that I want to observe.
There are some ideas that this symmetry is not an exact symmetry of nature, even though it is spectacularly well tested - a typical deviation from this symmetry cannot be more than one part in a billion to one part in a million billion, depending on the precise nature of the violation. Nevertheless, such a symmetry breaking potentially resolves some of the open problems in theoretical physics, first and foremost the quantisation of gravity. To make this consistent with the experimental bounds, the violation can only be sizable at the tinies length scales, way smaller than an atom.
In the article I investigated the dependence of Lorentz symmetry violations on the length scale. The key result is that if there is some amount of Lorentz symmetry breaking at some very small scale, say some subatomic length scale, then necessarily the breaking is larger at larger length scales, say a meter. However, the magnitude by how much it is larger is almost negligible, and to a good approximation they are of the same size. This implies that the current experimental bounds also carry over to much smaller length scales than tested. This hence puts severe bounds on any theory of quantum gravity involving Lorentz symmetry breaking.
1804.03846: Towards reconstructing the quantum effective action of gravity
B. Knorr and F. Saueressig
Our world as we perceive it is continuous: we can move our hand by any tiny amount to the left or right with ease. This is to contrast with for example wearing a belt. There, we can choose between different holes to close it around our belly, and if we had too much cake, we might need a little bit more cake so that the next-wider hole fits our new figure.
In physics, we often have to approximate or simplify systems to be able to describe them. If we want to describe the motion of a ball flying through the air, one possibility is to first describe only a very small time interval, where we can approximate forces acting on the ball as constant. If we do this repeatedly, we can glue together these intervals and describe the full motion of the ball approximately. The general expectation then is that if we make these intervals smaller and smaller, our approximation gets better and better.
Causal Dynamical Triangulations (CDT) is an approach to describe the quantum properties of spacetime. In this approach, spacetime itself is approximated with the help of "spacetime atoms", which are glued together to form spacetime.
Unfortunately, CDT calculations require a lot of computer power if we want to study larger spacetimes. It is thus in general very hard to relate the results obtained in these simulations to a continuum description of quantum spacetime. In this work, we make a first step to close this gap.
For this, we study how quantum fluctuations of different "chunks" of volumes are related to each other. Imagine a donut (with chocolate cover, if you want). Quantum fluctuations would then mean that at different positions of this donut, it grows or shrinks by tiny amounts, without changing its total weight. Then you can ask how likely it is that the donut grwos at where you hold it while shrinking at the opposite site. This is essentially what we studied, just that our donuts are made out of "spacetime dough".
We described these calculations in a continuum language and compared to CDT results by our colleagues. What we found is amazing: it seems that quantum spacetime is not that much more complicated than classical spacetime. There is only one type of interactions that we had to add to General Relativity, with a very interesting interpretation - it could serve as an explanation for dark energy!
1710.07055: Infinite order quantum-gravitational correlations
B. Knorr
In physics we typically have very complicated problems which we don't know how to solve. Often, we however know the solution to a related, simpler problem. One key success strategy is thus to deform the original problem (by e.g. introducing a parameter) and solve the deformed problem with an approximation method, finally getting rid of the deformation. If we did everything right, we solved the original problem.
In quantum field theory, we often use this strategy. There, we can solve non-interacting theories and then try to solve the interacting theory by handling it as a small perturbation of the free theory. This is what we call perturbation theory.
Despite some problems, perturbation theory works remarkably well for most theories that we know. Nevertheless, certain effects are truly "non-perturbative", which means that they are inaccessible by these means. The quantisation of gravity is by some believed to belong to this class. An example from the Standard Model of Particle Physics is confinement, saying that we do not observe single quarks or gluons, but only their bound states like protons or neutrons. To study these phenomena, non-perturbative methods are necessary.
Even in these non-perturbative methods, we sometimes rely on some kind of deformations. In particular, one can study a problem non-perturbatively with respect to one quantity (say, a coupling constant), but perturbatively in another (e.g. the strength of quantum fluctuations of some field). One then has to assess whether these kinds of approximations capture the important physics.
In the Asymptotic Safety approach to quantum gravity, we use such a dual approach: we take into account the non-perturbative dependence on coupling constants (such as Newton's constant), but rely on an expansion of quantum fluctuations of the metric. To be truly non-perturbative, we would have to include the full dependence on these fluctuations. The paper paths the way to this. I explain how this dependence can be included systematically in a quantum gravity calculation, and present a proof of concept that it also works in practice.