Is the physics within the Solar system really understood?

A collection is made of presently unexplained phenomena within our Solar system and in the universe. These phenomena are (i) the Pioneer anomaly, (ii) the flyby anomaly, (iii) the increase of the Astronomical Unit, (iv) the quadrupole and octupole anomaly, and (v) Dark Energy and (vi) Dark Matter. A new data analysis of the complete set of Pioneer data is announced in order to search for systematic effects or to confirm the unexplained acceleration. We also review the mysterious flyby anomaly where the velocities of spacecraft after Earth swing--bys are larger than expected. We emphasize the scientific aspects of this anomaly and propose systematic and continuous observations and studies at the occasion of future flybys. Further anomalies within the Solar system are the increase of the Astronomical Unit and the quadrupole and octupole anomaly. We briefly mention Dark Matter and Dark Energy since in some cases a relation between them and the Solar system anomalies have been speculated.Comment: 22 pages, 3 figures, submitted for the proceedings of the 359th WE-Heraeus Seminar on "Lasers, Clocks, and Drag-Free: Technologies for Future Exploration in Space and Tests of Gravity

Summary of session C1: experimental gravitation

The fact that gravity is a metric theory follows from the Einstein equivalence principle. This principle consists of (i) the universality of free fall, (ii) the universality of the gravitational redshift and (iii) the local validity of Lorentz invariance. Many experiments searching for deviations from standard general relativity test the various aspects of the Einstein equivalence principle. Here we report on experiments covering the whole Einstein equivalence principle. Until now all experiments have been in agreement with the Einstein equivalence principle. As a consequence, gravity has to be described by a metric theory. Any metric theory of gravity leads to effects such as perihelion shift, deflection of light, gravitational redshift, gravitational time delay, Lense–Thirring effect, Schiff effect, etc. A particular theory of that sort is Einstein's general relativity. For weak gravitational fields which are asymptotically flat any deviation from Einstein's general relativity can be parametrized by a few constants, the PPN parameters. Many astrophysical observations and space experiments are devoted to a better measurement of the effects and, thus, of the PPN parameters. It is clear that gravity is best tested for intermediate ranges, that is, for distances between 1 m and several astronomical units. It is highly interesting to push forward our domain of experience and to strengthen the experimental foundation of gravity also beyond these scales. This point is underlined by the fact that many quantum gravity and unification-inspired theories suggest deviation from the standard laws of gravity at very small or very large scales. In this session summary we briefly outline the status and report on the talks presented in session C1 about experimental gravitation

Analytic solutions of the geodesic equation in axially symmetric space-times

The complete sets of analytic solutions of the geodesic equation in Taub--NUT--(anti-)de Sitter, Kerr--(anti-)de Sitter and also in general Plebanski--Demianski space--times without acceleration are presented. The solutions are given in terms of the Kleinian sigma functions.Comment: 4 pages, 4 figures, accepted for publication in EP

Lorentz invariance violation and charge (non--)conservation: A general theoretical frame for extensions of the Maxwell equations

All quantum gravity approaches lead to small modifications in the standard laws of physics which lead to violations of Lorentz invariance. One particular example is the extended standard model (SME). Here, a general phenomenological approach for extensions of the Maxwell equations is presented which turns out to be more general than the SME and which covers charge non--conservation (CNC), too. The new Lorentz invariance violating terms cannot be probed by optical experiments but need, instead, the exploration of the electromagnetic field created by a point charge or a magnetic dipole. Some scalar--tensor theories and higher dimensional brane theories predict CNC in four dimensions and some models violating Special Relativity have been shown to be connected with CNC and its relation to the Einstein Equivalence Principle has been discussed. Due to this upcoming interest, the experimental status of electric charge conservation is reviewed. Up to now there seem to exist no unique tests of charge conservation. CNC is related to the precession of polarization, to a modification of the $1/r$--Coulomb potential, and to a time-dependence of the fine structure constant. This gives the opportunity to describe a dedicated search for CNC.Comment: To appear in Physical Review

Quantum nondemolition measurements of a particle in electric and gravitational fields

In this work we obtain a nondemolition variable for the case in which a charged particle moves in the electric and gravitational fields of a spherical body. Afterwards we consider the continuous monitoring of this nondemolition parameter, and calculate along the ideas of the so called restricted path integral formalism, the corresponding propagator. Using these results the probabilities associated with the possible measurement outputs are evaluated. The limit of our results, as the resolution of the measuring device goes to zero, is analyzed, and the dependence of the corresponding propagator upon the strength of the electric and gravitational fields are commented. The role that mass plays in the corresponding results, and its possible connection with the equivalence principle at quantum level, are studied.Comment: Accepted in International Journal of Modern Physics D, 14 page

Ideal-Modified Bosonic Gas Trapped in an Arbitrary Three Dimensional Power-Law Potential

We analyze the effects caused by an anomalous single-particle dispersion relation suggested in several quantum-gravity models, upon the thermodynamics of a Bose-Einstein condensate trapped in a generic 3-dimensional power-law potential. We prove that the shift in the condensation temperature, caused by a deformed dispersion relation, described as a non-trivial function of the number of particles and the shape associated to the corresponding trap, could provide bounds for the parameters associated to such deformation. Additionally, we calculate the fluctuations in the number of particles as a criterium of thermodynamic stability for these systems. We show that the apparent instability caused by the anomalous fluctuations in the thermodynamic limit can be suppressed considering the lowest energy associated to the system in question.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1202.380

Space--time fluctuations and the spreading of wavepackets

Using a density matrix description in space we study the evolution of wavepackets in a fluctuating space-time background. We assume that space-time fluctuations manifest as classical fluctuations of the metric. From the non-relativistic limit of a non-minimally coupled Klein-Gordon equation we derive a Schr\"odinger equation with an additive gaussian random potential. This is transformed into an effective master equation for the density matrix. The solutions of this master equation allow to study the dynamics of wavepackets in a fluctuating space-time, depending on the fluctuation scenario. We show how different scenarios alter the diffusion properties of wavepackets.Comment: 11 page

Quantum Tests of the Foundations of General Relativity

The role of the equivalence principle in the context of non-relativistic quantum mechanics and matter wave interferometry, especially atom beam interferometry, will be discussed. A generalised form of the weak equivalence principle which is capable of covering quantum phenomena too, will be proposed. It is shown that this generalised equivalence principle is valid for matter wave interferometry and for the dynamics of expectation values. In addition, the use of this equivalence principle makes it possible to determine the structure of the interaction of quantum systems with gravitational and inertial fields. It is also shown that the path of the mean value of the position operator in the case of gravitational interaction does fulfill this generalised equivalence principle.Comment: Classical and Quantum Gravity 15, 13 (1998