Generalizing Optical Geometry

We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz and Lasota 1997, Class. Quantum Grav. 14 (1997) A23). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson, Class. Quantum Grav. 23 (2006) 1) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity.Comment: 19 pages, 1 figure. A more general analysis is presented than in the former version. See also the companion papers arXiv:0708.2493, arXiv:0708.2533 and arXiv:0708.253

Foreword

While several studies have explored how short-term ecological responses to disturbance vary among ecosystems, experimental studies of how contrasting ecosystems recover from disturbance in the longer term are few. We performed a simple long-term experiment on each of 30 contrasting forested islands in northern Sweden that vary in size; as size decreases, time since fire increases, soil fertility and ecosystem productivity declines, and plant species diversity increases. We predicted that resilience of understory plant community properties would be greatest on the larger, more productive islands, and that this would be paralleled by greater resilience of soil biotic and abiotic properties. For each island, we applied three disturbance treatments of increasing intensity to the forest understory once in 1998, i.e., light trimming, heavy trimming, and burning; a fourth treatment was an undisturbed control. We measured recovery of the understory vascular plant community annually over the following 14 years, and at that time also assessed recovery of mosses and several belowground variables. Consistent with our predictions, vascular plant whole-community variables (total cover, species richness, diversity [Shannon's HI, and community composition) recovered significantly more slowly on the smaller (least fertile) than the larger islands, but this difference was not substantial, and only noticeable in the most severely disturbed treatment. When an index of resilience was used, we were unable to detect effects of island size on the recovery of any property. We found that mosses and one shrub species (Empetrum hermaphroditum) recovered particularly slowly, and the higher abundance of this shrub on small islands was sufficient to explain any slower recovery of whole-ecosystem variables on those islands. Further, several belowground variables had not fully recovered from the most intense disturbance after 14 yr, and counter to our predictions, the degree of their recovery was never influenced by island size. While several studies have shown large variation among plant communities in their short-term response (notably resistance) to environmental perturbations, our results reveal that when perturbations are applied equally to highly contrasting ecosystems, differences in resilience among them in the longer term can be relatively minor, regardless of the severity of disturbance

The inverse conjunction fallacy

If people believe that some property is true of all members of a class such as sofas, then they should also believe that the same property is true of all members of a conjunctively defined subset of that class such as uncomfortable handmade sofas. A series of experiments demonstrated a failure to observe this constraint, leading to what is termed the inverse conjunction fallacy. Not only did people often express a belief in the more general statement but not in the more specific, but also when they accepted both beliefs, they were inclined to give greater confidence to the more general. It is argued that this effect underlies a number of other demonstrations of fallacious reasoning, particularly in category-based induction. Alternative accounts of the phenomenon are evaluated, and it is concluded that the effect is best interpreted in terms of intensional reasoning [Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review, 90, 293–315.]

The Body Politics of Data

The PhD project The Body Politics of Data is an artistic, practice-based study exploring how feminist methodologies can create new ways to conceptualise digital embodiment within the field of art and technology. As a field of practice highly influenced by scientific and technical methodologies, the discursive and artistic tools for examining data as a social concern are limited. The research draws on performance art from the 60s, cyberfeminist practice, Object Oriented Feminism and intersectional perspectives on data to conceive of new models of practice that can account for the body political operations of extractive big data technologies and Artificial Intelligence. The research is created through a body of individual and collective experimental artistic projects featured in the solo exhibition The Body Politics of Data at London Gallery West (2020). It includes work on maternity data and predictive products in relation to reproductive health in the UK, created in collaboration with Loes Bogers (2016-2017), workshops on “bodily bureaucracies” with Autonomous Tech Fetish (2013-2016) and Accumulative Care, a feminist model of care for labouring in the age of extractive digital technologies. This research offers an embodied feminist methodology for artistic practice to become investigative of how processes of digitalisation have adverse individual and collective effects in order to identify and resist the forms of personal and collective risk emerging with data driven technologies

Inertial forces and the foundations of optical geometry

Assuming a general timelike congruence of worldlines as a reference frame, we derive a covariant general formalism of inertial forces in General Relativity. Inspired by the works of Abramowicz et. al. (see e.g. Abramowicz and Lasota, Class. Quantum Grav. 14 (1997) A23), we also study conformal rescalings of spacetime and investigate how these affect the inertial force formalism. While many ways of describing spatial curvature of a trajectory has been discussed in papers prior to this, one particular prescription (which differs from the standard projected curvature when the reference is shearing) appears novel. For the particular case of a hypersurface-forming congruence, using a suitable rescaling of spacetime, we show that a geodesic photon is always following a line that is spatially straight with respect to the new curvature measure. This fact is intimately connected to Fermat's principle, and allows for a certain generalization of the optical geometry as will be further pursued in a companion paper (Jonsson and Westman, Class. Quantum Grav. 23 (2006) 61). For the particular case when the shear-tensor vanishes, we present the inertial force equation in three-dimensional form (using the bold face vector notation), and note how similar it is to its Newtonian counterpart. From the spatial curvature measures that we introduce, we derive corresponding covariant differentiations of a vector defined along a spacetime trajectory. This allows us to connect the formalism of this paper to that of Jantzen et. al. (see e.g. Bini et. al., Int. J. Mod. Phys. D 6 (1997) 143).Comment: 42 pages, 7 figure

An intuitive approach to inertial forces and the centrifugal force paradox in general relativity

As the velocity of a rocket in a circular orbit near a black hole increases, the outwardly directed rocket thrust must increase to keep the rocket in its orbit. This feature might appear paradoxical from a Newtonian viewpoint, but we show that it follows naturally from the equivalence principle together with special relativity and a few general features of black holes. We also derive a general relativistic formalism of inertial forces for reference frames with acceleration and rotation. The resulting equation relates the real experienced forces to the time derivative of the speed and the spatial curvature of the particle trajectory relative to the reference frame. We show that an observer who follows the path taken by a free (geodesic) photon will experience a force perpendicular to the direction of motion that is independent of the observers velocity. We apply our approach to resolve the submarine paradox, which regards whether a submerged submarine in a balanced state of rest will sink or float when given a horizontal velocity if we take relativistic effects into account. We extend earlier treatments of this topic to include spherical oceans and show that for the case of the Earth the submarine floats upward if we take the curvature of the ocean into account.Comment: 14 pages, 21 figure

Boundary Conditions for Singular Perturbations of Self-Adjoint Operators

Let A:D(A)\subseteq\H\to\H be an injective self-adjoint operator and let \tau:D(A)\to\X, X a Banach space, be a surjective linear map such that \|\tau\phi\|_\X\le c \|A\phi\|_\H. Supposing that \text{\rm Range} (\tau')\cap\H' =\{0\}, we define a family $A^\tau_\Theta$ of self-adjoint operators which are extensions of the symmetric operator $A_{|\{\tau=0\}.}$. Any $\phi$ in the operator domain $D(A^\tau_\Theta)$ is characterized by a sort of boundary conditions on its univocally defined regular component \phireg, which belongs to the completion of D(A) w.r.t. the norm \|A\phi\|_\H. These boundary conditions are written in terms of the map $\tau$, playing the role of a trace (restriction) operator, as \tau\phireg=\Theta Q_\phi, the extension parameter $\Theta$ being a self-adjoint operator from X' to X. The self-adjoint extension is then simply defined by A^\tau_\Theta\phi:=A \phireg. The case in which $A\phi=T*\phi$ is a convolution operator on LD, T a distribution with compact support, is studied in detail.Comment: Revised version. To appear in Operator Theory: Advances and Applications, vol. 13