We consider the standard problem of observational astronomy, i.e. the observations of light emission from a distant region of spacetime in general relativity. The goal is to describe the changes between the measurements of the light performed by a sample of observers slightly displaced with respect to each other and moving with different 4-velocities and 4-accelerations. In our approach, all results of observations can be expressed as functions of the kinematic variables, describing the motions of the observers and the emitting bodies with respect to their local inertial frames, and four linear bilocal geodesic operators, describing the influence of the spacetime geometry on light propagation. The operators are functionals of the curvature tensor along the line of sight. The results are based on the assumption that the regions of emissions and observations are sufficiently small so that the spacetime curvature effects are negligible within each of them, although they are significant for the light propagation between them. The new formulation provides a uniform approach to optical phenomena in curved spacetimes and, as an application, we discuss the problem of a fully relativistic definition of the parallax and position drifts (or proper motions). We then use the results to construct combinations of observables which are completely insensitive to the motion of both the observer and the emitter. These combinations by construction probe the spacetime geometry between the observation and emission regions and in our formalism we may express them as functionals of the Riemann tensor along the line of sight. For short distances one of these combinations depends only on the matter content along the line of sight. This opens up the possibility to measure the matter content of a spacetime in a tomographylike manner irrespective of the motions of the emitter and the observer.Even if A enters the differential equation linearly, the general solution contains a nonlinear dependence.

No abstract

No abstract

We present a method to compute exact expressions for optical observables for static spherically symmetric spacetimes in the framework of the bilocal geodesic operator formalism. The expressions are obtained by solving the linear geodesic deviation equations for null geodesics, using the spacetime symmetries and the associated conserved quantities. We solve the equations in two different ways: by varying the geodesics with respect to their initial data and by directly integrating the equation for the geodesic deviation. The results are very general and can be applied to a variety of spacetime models and configurations of the emitter and the observer. We illustrate some of the aspects with an example of Schwarzschild spacetime, focusing on the behaviour of the angular diameter distance, the parallax distance, and the distance slip between the observer and the emitter outside the photon sphere.

Electron correlation time dependent density functional theory (TD-DFT) was used to investigate various self-assembled photoactive quantum entangled supramolecular systems. The prebiotic kernel contains provitamin D and sensitizer (1,4-bis(N,N-dimethylamino)naphthalene) attached covalently to a oxo-guanine nucleotide and the precursor of fatty acid (pFA) molecules. As a result the associated electron correlation interactions compress the overall system resulting in an even smaller gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) electron energy levels and photoexcited electron tunnelling occurs from the sensitizer to the pFA, or from provitamin D to the same pFA molecule. Analysis of TD-DFT method calculated absorption spectrum and images of electron transfer trajectories in the different excited states allow to separate quantum photosynthetic transitions and quantum entangled states which show that provitamin D enhance the photosynthetic process in the near UV region and converts into vitamin D. Two variable, quantum entangled AND logic gate was discovered in these photosynthetic prebiotic kernel systems containing provitamin D, which consist of two input photoactive sensitizer derivatives containing two different variable inputs and one output. Quantum mechanical investigations of supramolecular systems containing light emitting molecule 3,6-di(9-carbazolyl)-9-(2-ethylhexyl)carbazole (TCz) allowed to create five variable logical identity function device and quantum entangled two variable OR different light emitting logic photon-electron-photon converter, i.e., quantum logic device. These quantum logical devices might be applied for the construction of molecular processors of quantum optical computers or can be regulators of natural and artificial cells.