Nonperturbative sum over topologies in 2D Lorentzian quantum gravity

The recent progress in the Causal Dynamical Triangulations (CDT) approach to quantum gravity indicates that gravitation is nonperturbatively renormalizable. We review some of the latest results in 1+1 and 3+1 dimensions with special emphasis on the 1+1 model. In particular we discuss a nonperturbative implementation of the sum over topologies in the gravitational path integral in 1+1 dimensions. The dynamics of this model shows that the presence of infinitesimal wormholes leads to a decrease in the effective cosmological constant. Similar ideas have been considered in the past by Coleman and others in the formal setting of 4D Euclidean path integrals. A remarkable property of the model is that in the continuum limit we obtain a finite space-time density of microscopic wormholes without assuming fundamental discreteness. This shows that one can in principle make sense out of a gravitational path integral including a sum over topologies, provided one imposes suitable kinematical restrictions on the state-space that preserve large scale causality.Comment: 10 pages, 4 figures. Talk given by S. Zohren at the Albert Einstein Century International Conference (Paris, July 18-22 2005

Sum over topologies and double-scaling limit in 2D Lorentzian quantum gravity

We construct a combined non-perturbative path integral over geometries and topologies for two-dimensional Lorentzian quantum gravity. The Lorentzian structure is used in an essential way to exclude geometries with unacceptably large causality violations. The remaining sum can be performed analytically and possesses a unique and well-defined double-scaling limit, a property which has eluded similar models of Euclidean quantum gravity in the past.Comment: 9 pages, 3 Postscript figures; added comments on strip versus bulk partition functio

New aspects of two-dimensional quantum gravity

Causal dynamical triangulations (CDT) can be used as a regularization of quantum gravity. In two dimensions the theory can be solved anlytically, even before the cut-off is removed and one can study in detail how to take the continuum limit. We show how the CDT theory is related to Euclidean 2d quantum gravity (Liouville quantum gravity), how it can be generalized and how this generalized CDT model has a string field theory representation as well as a matrix model representationof a new kind, and finally how it examplifies the possibility that time in quantum gravity might be the stochastic time related to the branching of space into baby universes.Comment: Lectures presented at the 49th Cracow School of Theoretical Physics, "Non-Perturbative Gravity and Quantum Chromodynamics", Zakopane May 31-June 10, 2009. To appear in Acta Physica Polonica B 40 (2009) 1001-103

Proper time is stochastic time in 2d quantum gravity

We show that proper time, when defined in the quantum theory of 2d gravity, becomes identical to the stochastic time associated with the stochastic quantization of space. This observation was first made by Kawai and collaborators in the context of 2d Euclidean quantum gravity, but the relation is even simpler and more transparent in he context of 2d gravity formulated in the framework of CDT (causal dynamical triangulations).Comment: 30 pages, Talk presented at the meeting "Foundations of Space and Time", Cape Town, 10-14 August 2009. To appear in the proceedings, CU

Topology change in causal quantum gravity

The role of topology change in a fundamental theory of quantum gravity is still a matter of debate. However, when regarding string theory as two-dimensional quantum gravity, topological fluctuations are essential. Here we present a third quantization of two-dimensional surfaces based on the method of causal dynamical triangulation (CDT). Formally, our construction is similar to the c = 0 non-critical string field theory developed by Ishibashi, Kawai and others, but physically it is quite distinct. Unlike in non-critical string theory the topology change of spatial slices is well controlled and regulated by Newton's constant.Comment: 4 pages, proceedings of the workshop JGRG 17 (Nagoya, Japan, December 2007

A Causal Alternative for c=0 Strings

We review a recently discovered continuum limit for the one-matrix model which describes "causal" two-dimensional quantum gravity. The behaviour of the quantum geometry in this limit is different from the quantum geometry of Euclidean two-dimensional quantum gravity defined by taking the "standard" continuum limit of the one-matrix model. Geodesic distance and time scale with canonical dimensions in this new limit, contrary to the situation in Euclidean two-dimensional quantum gravity. Remarkably, whenever we compare, the known results of (generalized) causal dynamical triangulations are reproduced exactly by the one-matrix model. We complement previous results by giving a geometrical interpretation of the new model in terms of a generalization of the loop equation of Euclidean dynamical triangulations. In addition, we discuss the time evolution of the quantum geometry.Comment: 10 pages, 4 figures, Presented at "The 48th Cracow School of Theoretical Physics: Aspects of Duality", June 13-22, 2008, Zakopane, Polan

Postcolonial Migration and Citizenship in the Netherlands

Can formerly colonized subjects and their descendants be full and equal citizens of the former metropoles – and if so, what would that look like? In this blogpost, we explore these politics of belonging in European postcolonial polities by looking at different conceptualizations of the relationship between the Dutch state and Surinamese-Dutch citizens and immigrants. In particular, we look at Dutch state discourses on the “civic integration” of Surinamese in the 2010s, and Surinamese-Dutch organisations’ discourses on family migration rights in the 1970s and 1980s. While Dutch government discourses tend to represent Surinamese-Dutch as too different to belong to the Dutch Nation, Surinamese-Dutch organisations claimed postcolonial citizenship as different and equal

A tight Tsirelson inequality for infinitely many outcomes

We present a novel tight bound on the quantum violations of the CGLMP inequality in the case of infinitely many outcomes. Like in the case of Tsirelson's inequality the proof of our new inequality does not require any assumptions on the dimension of the Hilbert space or kinds of operators involved. However, it is seen that the maximal violation is obtained by the conjectured best measurements and a pure, but not maximally entangled, state. We give an approximate state which, in the limit where the number of outcomes tends to infinity, goes to the optimal state for this setting. This state might be potentially relevant for experimental verifications of Bell inequalities through multi-dimenisonal entangled photon pairs.Comment: 5 pages, 2 figures; improved presentation, change in title, as published

Magnetomotive drive and detection of clamped-clamped mechanical resonators in water

We demonstrate magnetomotive drive and detection of doubly clamped string resonators in water. A compact 1.9 T permanent magnet is used to detect the fundamental and higher flexural modes of $\mathrm{200 \mu m}$ long resonators. Good agreement is found between the magnetomotive measurements and optical measurements performed on the same resonator. The magnetomotive detection scheme can be used to simultaneously drive and detect multiple sensors or scanning probes in viscous fluids without alignment of detector beams.Comment: 4 pages, 3 figure

Designing Liquid Rocket Engine Injectors for Performance, Stability, and Cost

NASA is developing the Space Launch System (SLS) for crewed exploration missions beyond low Earth orbit. Marshall Space Flight Center (MSFC) is designing rocket engines for the SLS Advanced Booster (AB) concepts being developed to replace the Shuttle-derived solid rocket boosters. One AB concept uses large, Rocket-Propellant (RP)-fueled engines that pose significant design challenges. The injectors for these engines require high performance and stable operation while still meeting aggressive cost reduction goals for access to space. Historically, combustion stability problems have been a critical issue for such injector designs. Traditional, empirical injector design tools and methodologies, however, lack the ability to reliably predict complex injector dynamics that often lead to combustion stability. Reliance on these tools alone would likely result in an unaffordable test-fail-fix cycle for injector development. Recently at MSFC, a massively parallel computational fluid dynamics (CFD) program was successfully applied in the SLS AB injector design process. High-fidelity reacting flow simulations were conducted for both single-element and seven-element representations of the full-scale injector. Data from the CFD simulations was then used to significantly augment and improve the empirical design tools, resulting in a high-performance, stable injector design