Two different works in mathematical physics are presented: A construction of conformal infinity in null and spatial directions is constructed for the Rainbow-flat space-time corresponding to doubly special relativity. From this construction a definition of asymptotic DSRness is put forward which is com- patible with the correspondence principle of Rainbow gravity. Furthermore a result equating asymptotically flat space-times with asymptotically DSR spacetimes is presented. An overview of microlocality in braided ribbon networks is presented. Follow- ing this, a series of definitions are presented to explore the concept of microlocality and the topology of ribbon networks. Isolated substructure of ribbon networks are introduced, and a theorem is proven that allows them to be relocated. This is fol- lowed by a demonstration of microlocal translations. Additionally, an investigation into macrolocality and the implications of invariants in braided ribbon networks are presented.

In this thesis we first apply the 1+3 covariant description of general relativity to analyze n-fluid Friedmann-Lemaitre (FL) cosmologies; that is, homogeneous and isotropic cosmologies whose matter-energy content consists of n non-interacting fluids. We are motivated to study FL models of this type as observations suggest the physical universe is closely described by a FL model with a matter content consisting of radiation, dust and a cosmological constant. Secondly, we use the 1+3 covariant description to analyse scalar, vector and tensor perturbations of FL cosmologies containing a perfect fluid and a cosmological constant. In particular, we provide a thorough discussion of the behaviour of perturbations in the physically interesting cases of a dust or radiation background.

Two different works in mathematical physics are presented: A construction of conformal infinity in null and spatial directions is constructed for the Rainbow-flat space-time corresponding to doubly special relativity. From this construction a definition of asymptotic DSRness is put forward which is com- patible with the correspondence principle of Rainbow gravity. Furthermore a result equating asymptotically flat space-times with asymptotically DSR spacetimes is presented. An overview of microlocality in braided ribbon networks is presented. Follow- ing this, a series of definitions are presented to explore the concept of microlocality and the topology of ribbon networks. Isolated substructure of ribbon networks are introduced, and a theorem is proven that allows them to be relocated. This is fol- lowed by a demonstration of microlocal translations. Additionally, an investigation into macrolocality and the implications of invariants in braided ribbon networks are presented.

<p>The present thesis deals with electromagnetic effectscreated by the motion or inhomogeneity of a dielectricmedium.In the first paper the quantum R\"ontgen effect isdiscussed. Here a rotating Bose-Einstein condensate -- oranother kind of quantum fluid -- is placed in a chargedcapacitor. The medium's rotation creates a magnetic field.Quantum media can only rotate in form of vortices, which leadsto a magnetic field corresponding to the field of a magneticmonopole. In the remaining part of the thesis the geometricalrepresentation of electromagnetic fields in moving andinhomogeneous media is discussed. It is shown that aninhomogeneously moving dielectric, e.g., a vortex, defines aspace-time metric and light rays follow null-geodesics definedby this metric. This means that light propagation in a movingmedium is analogous to light propagation in a gravitationalfield. The possibility of creating laboratory models ofastronomical objects, e.g., black holes is discussed. Theapplicability of the newly developed media with extremely lowgroup velocity for the actual creation of such an experiment isconsidered. Furthermore, a model for the case of the slowlymoving medium is discussed. Here the light propagation isanalogous to the motion of a charged particle propagatingthrough a magnetic field. The velocity of the flow correspondsto the vector potential. Consequently, light propagation in avortex corresponds to the Aharonov-Bohm effect. Finally, acomplete geometrical description of light in an inhomogeneousdielectric at rest is presented. It is shown that lighttrajectories are geodesics of a three-dimensional metricdefined by the medium. Here even the propagation of the fieldsis discussed in the language of differential geometry and it isshown that the field vectors are parallel transported along therays. These considerations can be generalized to thefour-dimensional case where the field-strength tensor isparallel transported along the ray. This emphasizes thefar-reaching analogy between light in moving media and light ingravitational fields.</p>

Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (p. 425-428).

No description available.

This dissertation identified and addressed four of the unresolved issues pertaining to the proposition that nonabsolute/ relativistic (N/R) thinking is one of the possible unifying commonalities underlying the selected models of postformal reasoning, namely Problem Finding, Dialectical Reasoning, Relativistic Operations and Reflective Judgment. A total of 254 participants aged 10 to 48 and attending Grade 5 to doctoral studies were involved. Each participant was administered eight tests in pencil-and-paper format to measure eight different constructs of thinking. Different specific hypotheses were evaluated through different statistical approaches. The four identified issues were addressed as follows: Firstly, nonabsolute/ relativistic thinking was reconceptualized and operationally defined as a multidimensional and multilevel construct. Two dimensions were proposed: the basic form and the epistemic view. Within the basic form dimension, two levels were proposed: the formal and the postformal forms. Secondly, a battery of three tests was specifically designed by Arlin and the author to measure the different dimensions and levels of nonabsolute/ relativistic thinking. Thirdly, strong empirical evidence was obtained supporting the general hypothesis that nonabsolute/ relativistic thinking is a possible unifying commonality underlying the four selected postformal models. Within the construct of nonabsolute/ relativistic thinking, two dimensions, the basic form and the epistemic view, can be differentiated as hypothesized. Fourthly, empirical evidence was also obtained supporting the general hypothesis that nonabsolute/ relativistic thinking is an instance of both formal and postformal reasoning. Specifically within the basic form dimension, two qualitatively different forms, the formal and the postformal, can be differentiated as hypothesized. Findings also suggested that the development of a nonabsolute epistemic view might play a crucial role in the development of the postformal form. Therefore, the emergence of the postformal form can be explained by a paradigm shift from an absolute to a nonabsolute epistemic view. Performances in the tests of the postformal form and of the epistemic view in combination were found to be good predictors of performances in the selected postformal tests. Significant implications of the findings are that nonabsolute/ relativistic thinking represents a form of metamorphosis from closed-system to open-system thinking and it might serve as a potential springboard in the development of higher order thinking.

The continuous, kinematical Hilbert space of loop quantum gravity is built upon a family of spaces $\mathcal{H}_\Gamma$, each associated to a different \textit{graph} $\Gamma$, i.e. a network of interconnected one-dimensional links $\l$, embedded within a spatial geometry. The kinematics of loop quantum gravity are well-established, but difficult problems remain for the dynamics. There are two steps in getting to the quantum theory from the classical one: first, the embedded graphs are used to define a smearing of the continuous gravitational fields to obtain a holonomy $h_\l$ and flux $\X_\l$ for each link of the graph, giving a phase space $P_\Gamma$; second, this phase space is quantized to yield a finite dimensional Hilbert space $\mathcal{H}_\Gamma$. The intermediate classical theory in terms of $P_\Gamma$ phase spaces remains largely unexplored, and here we endeavour to develop it. If we can find such a theory that is consistent with general relativity, then we will have a theory of gravity based upon finite-dimensional phase spaces that is nicely set up for quantization \`a la loop quantum gravity. To begin, we first review the basic elements of the quantum theory before introducing the classical phase space structure. Within this framework we show that there is a one-to-one correspondence between the data on a graph and an equivalence class of continuous geometries. We find that a particular member of each class, the spinning geometry, makes a promising candidate as a gauge choice to represent the $(h_\l, \X_\l)$ data in the continuous theory, helping us to formulate a dynamics for the discrete theory. Considering all of the possible graphs, it is important to know how we can evolve from one phase space into another, and how the dynamics in $P_\Gamma$ relates to the continuous evolution. There is a geometrical description of phase spaces where dynamics appears as a class of subspaces within a symplectic manifold. We use this picture to formulate a dynamics between $P_\Gamma$ phase spaces, and demonstrate this process on a simple model that mimics the case of full gravity. Following this, we study a system of point particles in three-dimensional gravity which provides an illuminating demonstration of what we hope to accomplish for full gravity. We develop the classical theory of point particles and show that it can be described by an evolving triangulation where discrete bistellar flips can occur. From here we define the loop gravity theory and show that it agrees with the continuous theory, having two-to-two moves on the graph which mirror the bistellar flips in the triangulation. The results are promising for finding a dynamics for four-dimensional loop gravity, and if the full theory is developed further, we expect it will lead to a breakthrough in the quantum dynamics.

A (3+1)-evolutionary method in the framework of Regge Calculus, known as "Parallelisable Implicit Evolutionary Scheme", is analysed and revised so that it accounts for causality. Furthermore, the ambiguities associated with the notion of time in this evolutionary scheme are addressed and a solution to resolving such ambiguities is presented. The revised algorithm is then numerically tested and shown to produce the desirable results and indeed to resolve a problem previously faced upon implementing this scheme. An important issue that has been overlooked in "Parallelisable Implicit Evolutionary Scheme" was the restrictions on the choice of edge lengths used to build the space-time lattice as it evolves in time. It is essential to know what inequalities must hold between the edges of a 4-dimensional simplex, used to construct a space-time, so that the geometry inside the simplex is Minkowskian. The only known inequality on the Minkowski plane is the "Reverse Triangle Inequality" which holds between the edges of a triangle constructed only from space-like edges. However, a triangle, on the Minkowski plane, can be built from a combination of time-like, space-like or null edges. Part of this thesis is concerned with deriving a number of inequalities that must hold between the edges of mixed triangles. Finally, the Raychaudhuri equation is considered from the point of view of Regge Calculus. The Raychaudhuri equation plays an important role in many areas of relativistic Physics and Astrophysics, most importantly in the proof of singularity theorems. An analogue to the Raychaudhuri equation in the framework of Regge Calculus is derived. Both (2+1)-dimensional and (3+1)-dimensional cases are considered and analogues for average expansion and shear scalar are found.

Brown and York's gravitational microcanonical density of states is extended to general spacetime dimension and shown to be dependent upon features of the 4 dimensional gravitational action for its interpretation. Black hole entropy is calculated from the density of states path integral in general spacetime dimension, and the interpretation is shown to be likewise dependent upon the dimension of spacetime. The entropy of de Sitter and Rindler horizons are calculated using the black hole density of states and the notion of local horizon entropy density is shown to be supported. The applicability of the microcanonical ensemble to black hole mechanics is discussed at a fundamental level focussing on the absence of angular velocity as an external parameter in the gravitational Hamiltonian. The rotational ensemble and a new ensemble - the angular momentum ensemble - are introduced following Jaynes' information theory approach to statistical mechanics and proposed as more compelling candidates to calculate black hole entropy as a function of state. A program to calculate the density of states path integral non-perturbatively using causal dynamical triangulations is initiated. Regge calculus expressions for extrinsic curvature are extended to the case of Lorentzian hypersurfaces and used to derive Regge calculus expressions for quasilocal energy-momentum. The Regge version of the black hole density of states action is derived and specialised to the 3d and 4d spacetime constructions of causal dynamical triangulations. Finally, the recent suggestion that entropy is observer dependent is shown to be incompatible with the Tolman law for the equilibrium temperature in a gravitational field.