Claus Lämmerzahl

Bose-Einstein Condensation in Microgravity

Going Down the Tube Two pillars of modern physics are quantum mechanics and general relativity. So far, both have remained apart with no quantum mechanical description of gravity available. Van Zoest et al. (p. 1540; see the Perspective by Nussenzveig and Barata) present work with a macroscopic quantum mechanical system—a Bose-Einstein condensate (BEC) of rubidium atoms in which the cloud of atoms is cooled into a collective quantum state—in microgravity. By dropping the BEC down a 146-meter-long drop chamber and monitoring the expansion of the quantum gas under these microgravity conditions, the authors provide a proof-of-principle demonstration of a technique that can probe the boundary of quantum mechanics and general relativity and perhaps offer the opportunity to reconcile the two experimentally. Studies of atomic quantum states in free-fall conditions may provide ways to test predictions of general relativity. Albert Einstein’s insight that it is impossible to distinguish a local experiment in a “freely falling elevator” from one in free space led to the development of the theory of general relativity. The wave nature of matter manifests itself in a striking way in Bose-Einstein condensates, where millions of atoms lose their identity and can be described by a single macroscopic wave function. We combine these two topics and report the preparation and observation of a Bose-Einstein condensate during free fall in a 146-meter-tall evacuated drop tower. During the expansion over 1 second, the atoms form a giant coherent matter wave that is delocalized on a millimeter scale, which represents a promising source for matter-wave interferometry to test the universality of free fall with quantum matter.

Gyros, Clocks, Interferometers...: Testing Relativistic Gravity in Space

According to widespread expectations, we will shortly witness a new era in experimental gravitation. More accurate measurements of classical, weak field effects will soon be performed. Examples of these classical effects are the bending of light rays by the solar mass (or its modern counterparts, based on radio propagation effects), and the relativistic perturbations of the orbit of Mercury. In addition, we will shortly probe a new domain, where predicted but not yet measured effects (e.g. the Lense-Thirring effect, gravitational waves) will provide significant new tests of general relativity and its foundations. Particularly promising are the relativistic tests in space. Some of these experiments require the use of dedicated missions (e.g. GPB, STEP, LISA), while others are part of complex missions dedicated to astronomy or space exploration in general (e.g. Cassini, BepiColombo, GAIA). The aim of this book is to provide a detailed review of the subject of experimental gravitation in space. These are the proceedings of an international advanced school which took place in 1999 in Bad Honnef. A positive aspect of this book is that both experimental techniques and theoretical background are presented side by side. Particular emphasis is given to tests of the Lense-Thirring effect and the equivalence principle, and to applications of spaceborne atomic clocks. In such a rapidly developing field, it is almost inevitable that some experimental techniques are left out, and the editors quite rightly decided to focus on only some of the topics in the field of experimental gravitation. The book starts with an excellent review by Nordtvedt on solar system tests of general relativity. The second section is dedicated to the Lense-Thirring effect, offering a very good introduction for readers unfamiliar with gravitomagnetism. On the experimental side, this part is dominated by the review by Everitt et al on the status of GPB. Also well covered is the equivalence principle (EP). We mention Haugan and Lammerzahls review of the role of the EP in gravitational field theories. From the experimental side, Nordtvedt gives an update on the status of the LLR experiment, now able to test the validity of the EP to an accuracy of the order of 10-13, along with a confirmation of the de Sitter precession and an upper limit on the time variation of Newtons constant. In the future, experiments like STEP will be able to test the EP to an accuracy several orders of magnitude better than that currently available from LLR. Lockerbie et al give an updated review of the status of STEP, which gives a clear idea of the very challenging technical progress required in order to meet these expectations. I found the section on gravitational waves somewhat disappointing. It includes theoretical papers by Blanchet et al on the generation of gravitational radiation, and by Grishchuk on the cosmological background. However, the experimental part is very poorly covered, with a single presentation by Rudiger et al on the GEO600 ground-based laser interferometer (thus, not even a space experiment). Completely missing are contributions on space experiments based on laser interferometry (e.g. LISA) or on the Doppler technique (e.g. Cassini). The book would have certainly gained from the inclusion of a detailed discussion on the status and plans of such detectors. Finally, like other titles from Springer-Verlags series on Lecture Notes in Physics, this book is very well produced, although it would certainly have benefited from accurate editing before going to press. Several typos were found (the most evident case being the misspelling of Thirring in the title of Part II). Cited references are extensive and very useful, although, again, they could have been produced with a single and more accurate format throughout the book. In summary, I strongly recommend this book, in particular to professionals and graduate students interested in learning some theoretical aspects of modern experimental gravitation. Giacomo Giampieri

Solar system effects in Schwarzschild-de Sitter space-time

Abstract The Schwarzschild–de Sitter space–time describes the gravitational field of a spherically symmetric mass in a universe with cosmological constant Λ . Based on this space–time we calculate Solar system effects like gravitational redshift, light deflection, gravitational time delay, perihelion shift, geodetic or de Sitter precession, as well as the influence of Λ on a Doppler measurement, used to determine the velocity of the Pioneer 10 and 11 spacecraft. For Λ = Λ 0 ∼ 10 −52 m −2 the cosmological constant plays no role for all of these effects, while a value of Λ ∼ − 10 −37 m −2 , if hypothetically held responsible for the Pioneer anomaly, is not compatible with the perihelion shift.

Quantum Physics Exploring Gravity in the Outer Solar System: The SAGAS Project

We summarise the scientific and technological aspects of the Search for Anomalous Gravitation using Atomic Sensors (SAGAS) project, submitted to ESA in June 2007 in response to the Cosmic Vision 2015–2025 call for proposals. The proposed mission aims at flying highly sensitive atomic sensors (optical clock, cold atom accelerometer, optical link) on a Solar System escape trajectory in the 2020 to 2030 time-frame. SAGAS has numerous science objectives in fundamental physics and Solar System science, for example numerous tests of general relativity and the exploration of the Kuiper belt. The combination of highly sensitive atomic sensors and of the laser link well adapted for large distances will allow measurements with unprecedented accuracy and on scales never reached before. We present the proposed mission in some detail, with particular emphasis on the science goals and associated measurements and technologies.

The Search for quantum gravity signals

We give an overview of ongoing searches for effects motivated by the study of the quantum‐gravity problem. We describe in greater detail approaches which have not been covered in recent “Quantum Gravity Phenomenology” reviews. In particular, we outline a new framework for describing Lorentz invariance violation in the Maxwell sector. We also discuss the general strategy on the experimental side as well as on the theoretical side for a search for quantum gravity effects. The role of test theories, kinematical and dymamical, in this general context is emphasized. The present status of controlled laboratory experiments is described, and we also summarize some key results obtained on the basis of astrophysical observations.

High precision thermal modeling of complex systems with application to the flyby and Pioneer anomaly

Thermal modeling of complex systems faces the problems of an effective digitalization of the detailed geometry and properties of the system, calculation of the thermal flows and temperature maps, treatment of the thermal radiation including possible multiple reflections, inclusion of additional external influences, extraction of the radiation pressure from calculated surface data as well as computational effectiveness. In previous publications [1, 2] the solution to these problems have been outlined and a first application to the Pioneer spacecraft have been shown. Here we like to present the application of our thermal modeling to the Rosetta flyby anomaly as well as to the Pioneer anomaly. The analysis outlines that thermal recoil pressure is not the cause of the Rosetta flyby anomaly but likely resolves the anomalous acceleration observed for Pioneer 10.

Riemannian light cone from vanishing birefringence in premetric vacuum electrodynamics

We consider premetric electrodynamics with a local and linear constitutive law for the vacuum. Within this framework, we find quartic Fresnel wave surfaces for the propagation of light. If we require vanishing birefringence in vacuum, then a Riemannian light cone is implied. No proper Finslerian structure can occur. This is generalized to dynamical equations of any order.

Constraints on space-time torsion from Hughes-Drever experiments

The coupling of space–time torsion to the Dirac equation leads to effects on the energy levels of atoms which can be tested by Hughes–Drever type experiments. Reanalysis of these experiments carried out for testing the anisotropy of mass and anomalous spin couplings can lead to the till now tightest constraint on the axial torsion by K ≤ 1.5 · 10 m.Abstract The coupling of space-time torsion to the Dirac equation leads to effects on the energy levels of atoms which can be tested by Hughes-Drever type experiments. Reanalysis of these experiments carried out for testing the anisotropy of mass and anomalous spin couplings can lead to the till now tightest constraint on the axial torsion by K ≤ 1.5 × 10 −15 m −1 .

Geodesic equation in Schwarzschild-(anti-)de Sitter space-times: Analytical solutions and applications

The complete set of analytic solutions of the geodesic equation in a Schwarzschild-(anti-)de Sitter space-time is presented. The solutions are derived from the Jacobi inversion problem restricted to the set of zeros of the theta function, called the theta divisor. In its final form the solutions can be expressed in terms of derivatives of Kleinian sigma functions. The different types of the resulting orbits are characterized in terms of the conserved energy and angular momentum as well as the cosmological constant. Using the analytical solution, the question whether the cosmological constant could be a cause of the Pioneer anomaly is addressed. The periastron shift and its post-Schwarzschild limit is derived. The developed method can also be applied to the geodesic equation in higher dimensional Schwarzschild space-times.

The pseudodifferential operator square root of the Klein-Gordon equation

A nonlocal square root of the Klein–Gordon equation is proposed. This nonlocal equation is a special relativistic equation for a scalar field of first order in the time derivative. Its space derivative part is described by a pseudodifferential operator. The usual quantum mechanical formalism can be set up. The nonrelativistic limit and the classical limit in the form of plane wave solutions and the Ehrenfest theorem are correctly included. The nonlocality of the wave equation does not disturb the light cone structure, and the relativity principle of special relativity is fulfilled. Uniqueness and existence of solutions of the Cauchy problem for this equation can be proved. The second quantized version of this theory turns out to be macrocausal.