Scientific Series

We will give a short overview of non-perturbative quantum gravity models and discuss some key common problems for these models. In particular we will analyze what background independence requires from a theory of quantum gravity.

We investigate a simple theory where Baryon number (B) and Lepton number (L) are local gauge symmetries. In this theory B and L are on the same footing and the anomalies are cancelled by adding a single new fermionic generation. There is an interesting realization of the seesaw mechanism for neutrino masses. Furthermore there is a natural suppression of flavour violation in the quark and leptonic sectors since the gauge symmetries and particle content forbid tree level flavor changing neutral currents involving the quarks or charged leptons. Also one finds that the stability of a dark matter candidate is an automatic consequence of the gauge symmetry. Some constraints and signals at the Large Hadron Collider are briefly discussed.

Topological phases in spin systems are exciting frontiers of research with intimate connections to quantum coding theory. However, there is a disconnection between quantum codes and the idea of topology, in the absence of geometry and physical realizability. Here, we introduce a toy model, in which quantum codes are constrained to not only have a local geometric description, but also have translation and scale symmetries. These additional physical constraints enable us to assign topologically invariant properties to geometric shapes of logical operators of the code. Topological phases of the model are analyzed by geometrically classifying logical operators. The classification scheme also has topologically universal properties which are invariant under local unitary transformations and local perturbations, and may explain how global symmetries of a system Hamiltonian give rise to topological phases in correlated spin systems.

I will present recent numerical results obtained in collaboration with Frans Pretorius that describe head-on collisions of two solitons coupled to the general relativistic gravitational field and boosted to ultra relativistic energies. The calculations show, for the first time, that at sufficiently high energies such a collision leads to black hole formation, consistent with hoop conjecture arguments. This implies that the non-linear gravitational interaction between the kinetic energy of the solitons results in gravitational collapse, and the arguments for black hole formation in super-Planck scale particle collisions are robust. I will also speculate on the nature of the threshold of black hole formation in the model.

The Wheeler delayed choice experiment, Elitzur-Vaidman interaction-free measurement, and Hosten-Kwiat counterfactual computation will be discussed to answer Bohr's forbidden question: "Where is a quantum particle while it is inside a Mach-Zehnder Interferometer?". I will argue that the naive application of Wheeler's approach fails to explain a weak trace left by the particle and that the two-state vector description is required.

Two of the most exciting observables in the cosmic microwave background (CMB) radiation, which could deeply impact our picture of the early universe, are non-Gaussianity and tensor modes. A potential detection of tensor modes can be explained in terms of a model of large field inflation. Theoretical considerations suggest that a symmetry should be invoked in order to protect the flatness of the inflaton potential and hence an axion enjoying a shift symmetry is a natural candidate. As main example, I will present a model of inflation in string theory based on axion monodromy. Non-perturbative effects typically correct the axion potential leading to small sinusoidal modulations on top of an otherwise flat slow roll potential. It can be shown analytically that a resonance between the oscillations of the background and the oscillations of the curvature fluctuations is responsible for the production of an observably large non-Gaussian signal. An explicit expression for the shape of this resonant non-Gaussianity will be presented. There is essentially no overlap between this shape and the local, equilateral, and orthogonal shapes, and in fact resonant non-Gaussianity is not captured by the simplest version of the effective field theory of inflation. Hopefully the analytic expression for resonant non-Gaussianity will be useful to further observationally constrain this class of models.

Galaxy mergers, which are a natural consequence of hierarchical assembly of galaxies, are expected to produce binary black holes, which subsequently merge. The detection and analysis of gravitational waves from these sources is the major aim of the next generation gravitational wave detector: LISA, the Laser Interferometric Space Antenna. These gravitational waves encode a tremendous amount of information, but to make the connection with astrophysics and cosmology, it is necessary to identify the galaxies hosting these mergers via the associated electromagnetic counterpart to these mergers. I will describe these mergers events and discuss the various regimes where potential electromagnetic counterparts can be found. I will also describe some recent work, which holds much promise for the prompt identification of these mergers -- an electromagnetic precursor from tidal forcing.

In causal set quantum gravity, spacetime is assumed to have a fundamental atomicity or discreteness, and is replaced by a locally finite poset, the causal set. After giving a brief review of causal sets, I will discuss two distinct approaches to constructing a quantum dynamics for causal sets. In the first approach one borrows heavily from the continuum to construct a partition function for causal sets. This is illustrated in a 2-d model of causal sets, in which typicality replaces quantum probabilities. The second approach is intrinsic, and uses the quantum measure formulation in which dynamics is described in the language of measure theory and observables are measurable sets in an event algebra. Using the example of complex percolation dynamics I will show that naive attempts to carry out this process for the quantum measure may not work. I will end by discussing possible ways to address this question.

Quantum Bayesianism is a point of view on quantum foundations that says that there is no such thing as a “measurement problem” because there is no such THING as a quantum state: Quantum states are not things---instead information. But the view doesn’t stop there; it starts there! Taking the idea seriously over the last 15 years has been the direct motivation for a number of theorems and objects in quantum information theory: from the no-broadcasting theorem, to the quantum de Finetti theorem, and even some quantum cryptographic alphabets. I will review some of this, and then move on to the holy grail of present efforts: Finding an efficient representation of quantum states in terms of a singular probability function. Doing so leads to the hard technical problem of demonstrating the existence of a certain very symmetric sets of quantum states, and holds out the hope of understanding the amount of “quantum stuff” in a physical system in terms of a single parameter. (I.e., there is the THING that the quantum state is not).

In the Scholium in Newton's Principia which contains the discussions about absolute space, time, and the bucket experiment, Newton also posed a problem that Julian Barbour has denoted the "Scholium problem". Newton writes there "But how are we to obtain the true motions from their causes, effects, and apparent differences, and the converse, shall be explained more at large in the following treatise. For to this end it was that I composed it". This problem was clearly considered very important by Newton who claims he wrote the Principia dedicated to this problem. Interestingly Newton never returned to the problem. In this talk we are going to give a mathematical precise formulation of the Scholium problem. A subpart of the Scholium problem consists of determining how accurate the observers clock is. We are going to start from that end and see that the problem of defining duration is inseparately intertwined with the full scholium problem.

We report on a new class of fast-roll inflationary models. In a part of its parameter space, inflationary perturbations exhibit quite unusual phenomena such as scalar and tensor modes freezing out at widely different times, as well as scalar modes reentering the horizon during inflation. One specific point in parameter space is characterized by extraordinary behavior of the scalar perturbations. Freeze-out of scalar perturbations as well as particle production at horizon crossing are absent. Also the behavior of the perturbations around this quasi-de Sitter background is dual to a quantum field theory in flat space-time. Finally, the form of the primordial power spectrum is determined by the interaction between different modes of scalar perturbations.