Quantum gravity without vacuum dispersion

A generic prediction of quantum gravity is the vacuum dispersion of light, and hence that a photon's speed depends on its energy. We present further numerical evidence for a scale dependent speed of light in the causal dynamical triangulation (CDT) approach to quantum gravity. We show that the observed scale dependent speed of light in CDT can be accounted for by a scale dependent transformation of geodesic distance, whose specific functional form implies a discrete equidistant area spectrum. We make two non-trivial tests of the proposed scale transformation: a comparison with the leading order quantum correction to the gravitational potential and a comparison with the generalised uncertainty principle. In both cases, we obtain the same functional form. However, contrary to the widespread prediction of vacuum dispersion in quantum gravity, numerous experiments have now definitively ruled out linear vacuum dispersion beyond Planckian energy scales, and have now even constrained quadratic dispersion. Motivated by these experimental constraints we seek to reconcile quantum gravity with the absence of vacuum dispersion. We point out that given a scale dependent geodesic distance, a scale dependent time interval becomes essential to maintaining an invariant speed of light. We show how a particular scale dependent time interval allows a photon's speed to remain independent of its energy.Comment: Version published in International Journal of Modern Physics D. 13 pages, 3 figure

Hypothesis on the Nature of Time

We present numerical evidence that fictitious diffusing particles in the causal dynamical triangulation (CDT) approach to quantum gravity exceed the speed of light on small distance scales. We argue this superluminal behaviour is responsible for the appearance of dimensional reduction in the spectral dimension. By axiomatically enforcing a scale invariant speed of light we show that time must dilate as a function of relative scale, just as it does as a function of relative velocity. By calculating the Hausdorff dimension of CDT diffusion paths we present a seemingly equivalent dual description in terms of a scale dependent Wick rotation of the metric. Such a modification to the nature of time may also have relevance for other approaches to quantum gravity.Comment: 15 pages, 4 figures. Conforms with version to be published in PRD. Clarifications and references adde

Exploring Euclidean Dynamical Triangulations with a Non-trivial Measure Term

We investigate a nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) with a non-trivial measure term in the path integral. We are motivated to revisit this older formulation of dynamical triangulations by hints from renormalization group approaches that gravity may be asymptotically safe and by the emergence of a semiclassical phase in causal dynamical triangulations (CDT). We study the phase diagram of this model and identify the two phases that are well known from previous work: the branched polymer phase and the collapsed phase. We verify that the order of the phase transition dividing the branched polymer phase from the collapsed phase is almost certainly first-order. The nontrivial measure term enlarges the phase diagram, allowing us to explore a region of the phase diagram that has been dubbed the crinkled region. Although the collapsed and branched polymer phases have been studied extensively in the literature, the crinkled region has not received the same scrutiny. We find that the crinkled region is likely a part of the collapsed phase with particularly large finite-size effects. Intriguingly, the behavior of the spectral dimension in the crinkled region at small volumes is similar to that of CDT, as first reported in arXiv:1104.5505, but for sufficiently large volumes the crinkled region does not appear to have 4-dimensional semiclassical features. Thus, we find that the crinkled region of the EDT formulation does not share the good features of the extended phase of CDT, as we first suggested in arXiv:1104.5505. This agrees with the recent results of arXiv:1307.2270, in which the authors used a somewhat different discretization of EDT from the one presented here.Comment: 36 pages, 27 figures. Typos corrected, improved analysis of phase transition, and clarifications added. Conclusions unchanged. Conforms with version published in JHE

Evidence for Asymptotic Safety from Lattice Quantum Gravity

We calculate the spectral dimension for nonperturbative quantum gravity defined via Euclidean dynamical triangulations. We find that it runs from a value of ~3/2 at short distance to ~4 at large distance scales, similar to results from causal dynamical triangulations. We argue that the short distance value of 3/2 for the spectral dimension may resolve the tension between asymptotic safety and the holographic principle.Comment: 4 pages, 2 figures. Minor typos corrected, clarifications and reference added. Conforms with version published in PR

Evidence for Asymptotic Safety from Dimensional Reduction in Causal Dynamical Triangulations

We calculate the spectral dimension for a nonperturbative lattice approach to quantum gravity, known as causal dynamical triangulations (CDT), showing that the dimension of spacetime smoothly decreases from approximately 4 on large distance scales to approximately 3/2 on small distance scales. This novel result may provide a possible resolution to a long-standing argument against the asymptotic safety scenario. A method for determining the relative lattice spacing within the physical phase of the CDT parameter space is also outlined, which might prove useful when studying renormalization group flow in models of lattice quantum gravity.Comment: 21 pages, 8 figures, 4 tables. Typos corrected, 3 tables added. Conclusions unchanged. Conforms with version published in JHE

Is Asymptotically Weyl-Invariant Gravity Viable?

We explore the cosmological viability of a theory of gravity defined by the Lagrangian $f(\mathcal{R})=\mathcal{R}^{n\left(\mathcal{R}\right)}$ in the Palatini formalism, where $n\left(\mathcal{R}\right)$ is a dimensionless function of the Palatini scalar curvature $\mathcal{R}$ that interpolates between general relativity when $n\left(\mathcal{R}\right)=1$ and a locally scale-invariant and superficially renormalizable theory when $n\left(\mathcal{R}\right)=2$. We refer to this model as asymptotically Weyl-invariant gravity (AWIG). We analyse perhaps the simplest possible implementation of AWIG. A phase space analysis yields three fixed points with effective equation of states corresponding to de Sitter, radiation and matter-dominated phases. An analysis of the deceleration parameter suggests our model is consistent with an early and late period of accelerated cosmic expansion, with an intermediate period of decelerated expansion. We show that the model contains no obvious curvature singularities. Therefore, AWIG appears to be cosmologically viable, at least for the simple implementation explored.Comment: 13 pages, 6 figures, 3 tables. Replaced incorrect derivation in section 2 of previous version. Major changes to results and conclusions. Minor changes to metho

Searching for a continuum limit in causal dynamical triangulation quantum gravity

We search for a continuum limit in the causal dynamical triangulation (CDT) approach to quantum gravity by determining the change in lattice spacing using two independent methods. The two methods yield similar results that may indicate how to tune the relevant couplings in the theory in order to take a continuum limit.Comment: 19 pages, 8 figures. Title change and journal reference adde

Reactor R&D: Synthesis and Optimization of Metallic Nitride Fullerenes and the Introduction of Two New Classes of Endohedral Metallofullerenes, Metallic Nitride Azafullerenes and Oxo-metallic Fullerenes

Metallic nitride fullerenes (MNFs) were discovered in 1999. This class of endohedral fullerenes show promise in a new diverse range of useful applications. Since then, focus has shifted to the selective synthesis of these molecules with yields that would accommodate adequate sample distribution. Using the electric arc method, the traditional yield of these molecules has been very low (i.e. \u3c 5 mg), and only a small percentage of the fullerene products (i.e. \u3c 5%). This dissertation introduces the novel CAPTEAR (Chemically Adjusting Plasma Temperature, Energy, And Reactivity) method that allows the targeted synthesis of MNFs in high purity and yield. This method utilizes a nontraditional oxidizing method for fullerene synthesis that has not only provided optimization of MNFs, but also resulted in the discovery of two new classes of fullerenes: metallic nitride azafullerenes (MNAFs) and oxo-metallic fullerenes (OMFs). Evidence suggests that the nitrogen of the MNAF cage provides stability for the trimetallic nitride clusters, while the OMFs are the first fullerenes to encapsulate oxygen and incorporate a seven atom cluster inside a Cgo cage. Other efforts to increase yields resulted from scaling up production of fullerenes by using larger quantities of starting materials. These larger quantities required energy (electrical current) beyond the capacity of the traditional electric arc generator. Therefore, a new electric arc generator was designed and fabricated to accommodate these demands. This scale-up process resulted in yield increases by an average of 400%. However, to reduce the waste of scaling up as well as costs, our lab developed a recycling method for the expensive metal oxide starting materials. This method has greatly improved cost effectiveness and waste reduction