From continuum mechanics to general relativity

Using ideas from continuum mechanics we construct a theory of gravity. We show that this theory is equivalent to Einstein's theory of general relativity; it is also a much faster way of reaching general relativity than the conventional route. Our approach is simple and natural: we form a very general model and then apply two physical assumptions supported by experimental evidence. This easily reduces our construction to a model equivalent to general relativity. Finally, we suggest a simple way of modifying our theory to investigate non-standard space-time symmetries.Comment: 7 pages, this essay received a honorable mention in the 2014 essay competition of the Gravity Research Foundatio

Rotational elasticity

We consider an infinite 3-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis which gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory we choose the coframe and a density. We write down the general dynamic variational functional for our rotational theory of elasticity, assuming our material to be physically linear but the kinematic model geometrically nonlinear. Allowing geometric nonlinearity is natural when dealing with rotations because rotations in dimension 3 are inherently nonlinear (rotations about different axes do not commute) and because there is no reason to exclude from our study large rotations such as full turns. The main result of the paper is an explicit construction of a class of time-dependent solutions which we call plane wave solutions; these are travelling waves of rotations. The existence of such explicit closed form solutions is a nontrivial fact given that our system of Euler-Lagrange equations is highly nonlinear. In the last section we consider a special case of our rotational theory of elasticity which in the stationary setting (harmonic time dependence and arbitrary dependence on spatial coordinates) turns out to be equivalent to a pair of massless Dirac equations

Just enough inflation: power spectrum modifications at large scales

We show that models of `just enough' inflation, where the slow-roll evolution lasted only $50-60$ e-foldings, feature modifications of the CMB power spectrum at large angular scales. We perform a systematic and model-independent analysis of any possible non-slow-roll background evolution prior to the final stage of slow-roll inflation. We find a high degree of universality since most common backgrounds like fast-roll evolution, matter or radiation-dominance give rise to a power loss at large angular scales and a peak together with an oscillatory behaviour at scales around the value of the Hubble parameter at the beginning of slow-roll inflation. Depending on the value of the equation of state parameter, different pre-inflationary epochs lead instead to an enhancement of power at low-$\ell$, and so seem disfavoured by recent observational hints for a lack of CMB power at $\ell\lesssim 40$. We also comment on the importance of initial conditions and the possibility to have multiple pre-inflationary stages.Comment: 31 pages, 13 figure

Procedures and toolsused in the investigationof New Zealand's historical earthquakes

New Zealand’s tectonic setting, astride an obliquely convergent tectonic boundary, means that it has experienced many large earthquakes in its 200-year written historical records. The task of identifying and studying the largest early instrumental and pre-instrumental earthquakes, as well as identifying the smaller events, is being actively pursued in order to reduce gaps in knowledge and to ensure as complete and comprehensive a catalogue as is possible. The task of quantifying historical earthquake locations and magnitudes is made difficult by several factors. These include the range of possible earthquake focal depths, and the sparse, temporally- and spatially-variable historical population distribution which affects the availability of felt intensity information, and hence, the completeness levels of the catalogue. This paper overviews the procedures and tools used in the analysis, parameterisation, and recording of historical New Zealand earthquakes, with examples from recently studied historical events. In particular, the 1855 M 8+ Wairarapa earthquake is discussed, as well as its importance for the eminent 19th century British geologist, Sir Charles Lyell, and for future global understanding of the connection between large earthquakes and sudden uplift, tilting and faulting on a regional scale

Quantum Estimation of Parameters of Classical Spacetimes

We describe a quantum limit to measurement of classical spacetimes. Specifically, we formulate a quantum Cramer-Rao lower bound for estimating the single parameter in any one-parameter family of spacetime metrics. We employ the locally covariant formulation of quantum field theory in curved spacetime, which allows for a manifestly background-independent derivation. The result is an uncertainty relation that applies to all globally hyperbolic spacetimes. Among other examples, we apply our method to detection of gravitational waves using the electromagnetic field as a probe, as in laser-interferometric gravitational-wave detectors. Other applications are discussed, from terrestrial gravimetry to cosmology.Comment: 23 pages. This article supersedes arXiv:1108.522

Nature of band-gap states in V-doped TiO2 revealed by resonant photoemission

Band-gap states in V-doped TiO2 have been studied by photoemission spectroscopy over a range of photon energies encompassing the Ti 3p and V 3p core thresholds. The states show resonant enhancement at photon energies significantly higher than found for Ti 3d states introduced into TiO2 by oxygen deficiency or alkalimetal adsorbates. This demonstrates that the gap states relate to electrons trapped on dopant V cations rather than host Ti cations

Estimating the metric in curved spacetime with quantum fields

The geometry of space‐time is determined by physical measurements made with clocks and rulers. In so far as these are physical systems, the ultimate accuracy achievable is determined by quantum mechanics. In this paper we use methods from quantum parameter estimation theory to obtain uncertainty principles constraining how well we can estimate the components of a metric tensor using quantum field states propagating in curved space‐time, which is treated entirely classically

Quantum Communication with an Accelerated Partner

An unsolved problem in relativistic quantum information research is how to model efficient, directional quantum communication between localised parties in a fully quantum field theoretical framework. We propose a tractable approach to this problem based on solving the Heisenberg evolution of localized field observables. We illustrate our approach by analysing, and obtaining approximate analytical solutions to, the problem of communicating coherent states between an inertial sender, Alice and an accelerated receiver, Rob. We use these results to determine the efficiency with which continuous variable quantum key distribution could be carried out over such a communication channel.Comment: Additional explanatory text and typo in Eq.17 correcte