Almost product manifolds as the low energy geometry of Dirichlet branes

Any candidate theory of quantum gravity must address the breakdown of the classical smooth manifold picture of space-time at distances comparable to the Planck length. String theory, in contrast, is formulated on conventional space-time. However, we show that in the low energy limit, the dynamics of generally curved Dirichlet p-branes possess an extended local isometry group, which can be absorbed into the brane geometry as an almost product structure. The induced kinematics encode two invariant scales, namely a minimal length and a maximal speed, without breaking general covariance. Quantum gravity effects on D-branes at low energy are then seen to manifest themselves by the kinematical effects of a maximal acceleration. Experimental and theoretical implications of such new kinematics are easily derived. We comment on consequences for brane world phenomenology.Comment: 12 pages, invited article in European Physical Journal C, reprinted in Proceedings of the International School on Subnuclear Physics 2003 Erice (World Scientific

How quantizable matter gravitates: a practitioner's guide

We present the practical step-by-step procedure for constructing canonical gravitational dynamics and kinematics directly from any previously specified quantizable classical matter dynamics, and then illustrate the application of this recipe by way of two completely worked case studies. Following the same procedure, any phenomenological proposal for fundamental matter dynamics must be supplemented with a suitable gravity theory providing the coefficients and kinematical interpretation of the matter equations, before any of the two theories can be meaningfully compared to experimental data.Comment: 45 pages, no figure

Echo Delay and Overlap with Emitted Orientation Sounds and Doppler-shift Compensation in the Bat, Rhinolophus ferrumequinum

The compensation of Doppler-shifts by the bat, Rhinolophusferrumequinum, functions only when certain temporal relations between the echo and the emitted orientation sound are given. Three echo configurations were used: a) Original orientation sounds were electronically Doppler-shifted and played back either cut at the beginning (variable delay) or at the end (variable duration) of the echo. b) Artificial constant frequency echoes with variable delay or duration were clamped to the frequency of the emitted orientation sound at different Doppler-shifts. c) The echoes were only partially Doppler-shifted and the Doppler-shifted component began after variable delays or had variable durations. With increasing delay or decreasing duration of the Doppler-shifted echo the compensation amplitude for a sinusoidally modulated + 3 kHz Dopplershift (modulation rate 0.08 Hz) decreases for all stimulus configurations (Figs. 1, 2, 3). The range of the Doppler-shift compensation system is therefore limited by the delay due to acoustic travel time to about 4 m distance between bat and target. In this range the overlap duration of the echo with the emitted orientation sound is always sufficiently long, when compared with data on the orientation pulse length during target approach from Schnitzler (1968) (Fig. 5)

Inelastic collisions in an exactly solvable two-mode Bose-Einstein Condensate

Inelastic collisions occur in Bose-Einstein condensates, in some cases, producing particle loss in the system. Nevertheless, these processes have not been studied in the case when particles do not escape the trap. We show that such inelastic processes are relevant in quantum properties of the system such as the evolution of the relative population, the self trapping effect and the probability distribution of particles. Moreover, including inelastic terms in the model of the two-mode condensate allows for an exact analytical solution. Using this solution, we show that collisions favor the generation of entanglement between the modes of the condensate as long as the collision rate does not exceed the natural frequency of the system

Geometry of physical dispersion relations

To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements to have predictive matter field dynamics and an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible.Comment: revised version, new section on applications added, 46 pages, 9 figure

Sectional Curvature Bounds in Gravity: Regularisation of the Schwarzschild Singularity

A general geometrical scheme is presented for the construction of novel classical gravity theories whose solutions obey two-sided bounds on the sectional curvatures along certain subvarieties of the Grassmannian of two-planes. The motivation to study sectional curvature bounds comes from their equivalence to bounds on the acceleration between nearby geodesics. A universal minimal length scale is a necessary ingredient of the construction, and an application of the kinematical framework to static, spherically symmetric spacetimes shows drastic differences to the Schwarzschild solution of general relativity by the exclusion of spacelike singularities.Comment: 20 pages, 1 figure, REVTeX4, updated reference

Brans-Dicke geometry

We reveal the non-metric geometry underlying omega-->0 Brans-Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking constrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.Comment: 8 pages, v2 with additional comment and reference