This thesis presents a brief review of gravitation and cosmology, and then gives an overview of the theory of cosmological perturbations; subsequently some applications are discussed, such as large-scale structure formation. Cosmological perturbations are here presented both in the Newtonian paradigm and in two di¤erent relativistic approaches. The relativistic approaches are (i) the metric approach, where small variations of the metric tensor are considered, and (ii) the covariant approach, which focusses on small variations of the curvature. Dealing with these two approaches also involves addressing the gauge problem –how to map an idealized world model into a more accurate world model.

Time-dependent molecular properties are important for the experimental characterization of molecular materials. We show how these properties can be calculated, for optical and x-ray frequencies, using novel quantum chemical methods. For xray absorption there are important relativistic effects appearing, due to the high velocity electrons near the atomic nuclei. These effects are treated rigorously within the four-component static exchange approximation. We also show how electron correlation can be taken into account in the calculation of x-ray absorption spectra, in time-dependent density functional theory based on the complex polarization propagator approach. The methods developed have been applied to systems of experimental interest|molecules in the gas phase and adsorbed on metal surfaces. The effects of molecular vibrations have been take into account both within and beyond the harmonic approximation.

In general relativity, the nature of mass is non-local. However, an appropriate def-inition of mass at a quasi-local level could give a more detailed characterization ofthe gravitational field around massive bodies. Several attempts have been made tofind such a definition. One of the candidates is the Hawking mass. This thesispresents a method for calculating the spin coefficients used in the expression for theHawking mass, and gives a closed-form expression for the Hawking mass of ellipsoidal2-surfaces in Minkowski spacetime. Furthermore, the Hawking mass is shown to havethe correct limits, both in Minkowski and Schwarzschild, along particular foliationsof leaves approaching a metric 2-sphere. Numerical results for Schwarzschild are alsopresented.

This thesis considers entanglement, an important resource for quantum information processing tasks, while taking into account the theory of relativity. Not only is this a more complete description of quantum information, but it is necessary to fully understand quantum information processing tasks done by systems in arbitrary motion. It is shown that accelerated measurements on the vacuum of a free Dirac spinor field results in an entangled state for an inertial observer. The physical mechanism at work is the Davies-Unruh effect. The entanglement produced increases as a function of the acceleration, reaching maximal entanglement in the asymptotic limit of infinite acceleration. The dynamics of entanglement between two Unruh-DeWitt detectors, one stationary and the other undergoing non-uniform acceleration, was studied numerically. In the ultraweak coupling limit, the entanglement decreases as a function of time for the parameters considered and decreases faster than if the moving detector had had a uniform acceleration.

A written report of a paper titled Holographic dual of collimated radiation by Veronika E. Hubeny where a new and easier method is proposed to estimate the “radiation due to an accelerated quark in a strongly coupled medium”. The method is able to reproduce the results from an earlier paper without the need of solving the linearized Einstein equations but by way of calculating geodesics in AdS using the AdS/CFT correspondence and the gravitational dual of the quark being a string. A quick introduction to synchrotron radiation and general relativity is given after which the AdS/CFT correspondence is introduced along with the results and method of V. Hubeny. / A bachelor thesis in theoretical physics.

This thesis considers entanglement, an important resource for quantum information processing tasks, while taking into account the theory of relativity. Not only is this a more complete description of quantum information, but it is necessary to fully understand quantum information processing tasks done by systems in arbitrary motion. It is shown that accelerated measurements on the vacuum of a free Dirac spinor field results in an entangled state for an inertial observer. The physical mechanism at work is the Davies-Unruh effect. The entanglement produced increases as a function of the acceleration, reaching maximal entanglement in the asymptotic limit of infinite acceleration. The dynamics of entanglement between two Unruh-DeWitt detectors, one stationary and the other undergoing non-uniform acceleration, was studied numerically. In the ultraweak coupling limit, the entanglement decreases as a function of time for the parameters considered and decreases faster than if the moving detector had had a uniform acceleration.

Axiomatic quantum field theory is one approach to the project of merging the special theory of relativity with that of ordinary quantum mechanics. The project begins with the postulation of a set of axioms. Axioms should be motivated by reasonable physical principles in a way that illustrates how a given axiom is true. Motivations are often grounded in the principles of the parent theories: ordinary quantum mechanics or the theory of special relativity. Amongst the set of axioms first proposed by Haag and Kastler in 1963 is the axiom of microcausality. Microcausality requires the observables of regions at space-like separation to commute. This thesis seeks to answer the question ‘What principles from the special theory of relativity or ordinary quantum mechanics motivate, or justify, accepting microcausality as an axiom?’ The first chapter will provide the necessary background to investigate this question and the second chapter will undertake that investigation. In conclusion, microcausality cannot be well-motivated by individual principles rooted in the special theory of relativity or ordinary quantum mechanics.

The linguistic relativity hypothesis (LRH), otherwise known as the Sapir-Whorf Hypothesis (SWH), has been passionately debated over the last 60 years. It has undergone a renewed upsurge in scientific, anthropological and social interest. Several attempts have been made to prove or disprove the moderate version of the theory without producing conclusive results. This study analyses the history of the LRH and attempts to clarify its uses and limitations pertaining to ESL discourse in Swedish upper-secondary schools. Pedagogical implications of the study indicate that, if the LRH is correct, there could be a colossal, logistical impact on the national testing of semantic information in English studies which would have to be addressed in order to effectively and fairly assess every student based on their individual, cognitive skills and culturally influenced knowledge of language.

<p>We consider complete asymptotically flat Riemannian manifolds that are the graphs of smooth functions over $\mathbb R^n$. By recognizing the scalar curvature of such manifolds as a divergence, we express the ADM mass as an integral of the product of the scalar curvature and a nonnegative potential function, thus proving the Riemannian positive mass theorem in this case. If the graph has convex horizons, we also prove the Riemannian Penrose inequality by giving a lower bound to the boundary integrals using the Aleksandrov-Fenchel inequality. We also prove the ZAS inequality for graphs in Minkowski space. Furthermore, we define a new quasi-local mass functional and show that it satisfies certain desirable properties.</p> / Dissertation

Turkish speakers differentiate the blue region of color spectrum into mavi (blue) and lacivert (dark blue) / whereas non-Turkish speakers in this study had only one color term in the blue region. The present study aimed to explore the predictions of the Linguistic Relativity Hypothesis. Operationally, Categorical Perception (CP) effects were used. In Experiment 1, Turkish speakers performed a naming task to determine an average category boundary between mavi and lacivert. In Experiment 2, both Turkish and non-Turkish speakers&rsquo / color-difference detection thresholds were estimated on the average boundary as well as within the mavi and lacivert categories. The thresholds were also estimated in the green region, in which both groups had only one color term. 2-TAFC method, which eliminates the effects of memory or labeling and isolates the perceptual processes, was used to estimate the thresholds. Turkish speakers, and not non-Turkish speakers, were predicted to show CP effects only in the blue region: thresholds should be lower on the boundary than within-category. The result revealed that Turkish speakers&rsquo / color-difference detection thresholds were lower than those of non-Turkish speakers both in the blue and the green regions. The difference in the green region does not rule out the LRH. It is possible that this difference resulted from the limitations of the study. Finally, in Experiment 3, Turkish speakers&rsquo / thresholds were also estimated on their individual boundaries. The patterns of the thresholds revealed by Experiment 3 were similar to the pattern of the thresholds in Experiment 2.