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The theoretical calculations of the dynamic E2-M1 polarizability at the magic wavelength of the Sr optical clock are inconsistent with experimental results. We investigate role of negative-energy states in the E2 and M1 polarizabilities. Our result for E2-M1 polarizability difference $-$7.74(3.92)$\times$10$^{-5}$ a.u. is dominated by the contribution from negative-energy states to M1 polarizability and has the same sign as and consistent with all the experimental values. In addition, we apply the present calculations to various other optical clocks, further confirming the importance of negative-energy states to the M1 polarizability., Comment: 7 pages, 3 figures, arXiv admin note: this is an extended version of arXiv:2301.06740

This article summarizes the talks in the session GW2 of the Sixteenth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation, and Relativistic Field Theories, 5-10 July, 2021, on Mid-frequency (0.1-10 Hz) gravitational waves: Sources and detection methods with a review on strain power spectral density amplitude of various mid-frequency gravitational wave projects/concepts and with extended summaries on the progress of ZAIGA project and on the conceptual study of AMIGO., Comment: 16 pages, 3 figures, 1 table

This article is a foreword for the special issue on Gravitational Wave Detection and Fundamental Physics in Space for International Journal of Physics D. In the foreword, we review briefly the history of the development of mission concepts and projects for the gravitational wave detection in space together with fundamental physics missions. We summarize briefly the gravitational-wave detection-in-space science goals and the current progress in the experimental & technological developments presented in the articles of this special issue, and list the articles with publication information and arXiv numbers., 5 pages. arXiv admin note: text overlap with arXiv:1610.01148

We use both mass and internal energy specified rubidium atoms to jointly test the weak equivalence principle (WEP). We improve the four-wave double-diffraction Raman transition method (FWDR) we proposed before to select atoms with certain mass and angular momentum state, and perform dual-species atom interferometer. By combining $^{87}$Rb and $^{85}$Rb atoms with different angular momenta, we compare the differential gravitational acceleration of them, and determine the value of E\"{o}tv\"{o}s parameter, $\eta$, which measures the strength of the violation of WEP. For one case ($^{87}$Rb$|\emph{F}=1\rangle$ - $^{85}$Rb$|\emph{F}=2\rangle$),the statistical uncertainty of $\eta$ is $1.8 \times 10^{-10}$ at integration time of 8960 s. With various systematic errors correction, the final value is $\eta=(-4.4 \pm 6.7) \times 10^{-10}$. Comparing with the previous WEP test experiments using atoms, this work gives a new upper limit of WEP violation for $^{87}$Rb and $^{85}$Rb atom pairs., Comment: 5 pages, 3 figures

We indicate the progress of experimental gravity, present an outlook in this field, and summarise the Observational/Experimental Parallel Session together with a related plenary talk on gravitational waves of the 2nd LeCosPA Symposium., Comment: 1 figure, Second LeCosPa Simposium, December 2015, Taipei Taiwan

In the last two decades we have seen important mutual stimulations between the community working on electrodynamics of continuous media and the community working on spacetime structure. This is highlighted by the publication of two important monographs from two communities: Foundations of Classical Electrodynamics by F. W. Hehl and Yu. N. Obukhov (Birkh\"auser, Boston 2003) and Differential Forms in Electromagnetics by I. V. Lindell (IEEE Press-Wiley, Piscataway, NJ 2004; see also a new book "Multiforms, Dyadics, and Electromagnetic Media" by the same author in 2015). Starting around 1960, magnetoelectric effects and magnetoelectric media have been a focus of study. Somewhat later, the constitutive tensor density framework was used to construct spacetime structure theoretically and empirically. Earlier, in putting Maxwell equations into a form compatible with general relativity, Einstein noticed that the Maxwell equations can be formulated in a form independent of the metric gravitational potential in 1916; only the constitutive tensor density depends on the metric. This was followed by further stimulating and clarifying works of Weyl in 1918, Murnaghan in 1921, Kottler in 1922 and Cartan in 1923. Year 2016 is the centennial of the start of this historical development. International Journal of Modern Physics D of World Scientific is celebrating the occasion by publishing this special issue on Spacetime Structure and Electrodynamics. We have invited researchers to submit original research articles that would contribute to a better understanding of the phenomena inherent to spacetime structure and electrodynamic media., Comment: 5 pages with links to arXiv

Recently, there has been an interest in inflation and modified gravity with a Weyl term added to the general-relativistic action (N. Derulle, M. Sasaki, Y. Sendouda and A. Youssef, JCAP, 3, 040 (2011)). In this paper we study empirical constraint on this modified gravity from solar-system experiments/observations. We first derive linearized equation of motion in the weak field limit and solve it for isolated system in the slow motion limit. We then use it to derive the light propagation equations, and obtain the relativistic Shapiro time delay and the light deflection in one-body central problem. Applying these results to the solar-system measurements, we obtain constraints on the Weyl term parameter {\gamma}_W; the most stringent constraint, which comes from the Cassini relativistic time delay experiment, is for {\gamma}_W to be less than 0.0015 AU^2, or |{\gamma}_W|^(1/2) less than 0.039 AU (19 s). Analysis of precision laboratory gravity experiments put further limit on the Weyl term parameter {\gamma}_W to below the laboratory scale., Comment: 13 pages

In this talk, we review the empirical status for modern gravitational theories with emphases on (i) Equivalence Principles; (ii) Lense-Thirring effects and the implications of Gravity Probe B experiment; (iii) Solar-System Tests of Cosmological Models., Comment: 7 pages, 1 table, plenary talk presented at ICGAC10 (Xth International Conference on Gravitation, Astrophysics and Cosmology), Quy-Nhon, Vietnam, December 17-22, 2011

The ultra-precise Gravity Probe B experiment measured the frame-dragging effect and geodetic precession on four quartz gyros. We use this result to test WEP II (Weak Equivalence Principle II) which includes rotation in the universal free-fall motion. The free-fall E\"otv\"os parameter eta for rotating body is < = 10**(-11) with four-order improvement over previous results. The anomalous torque per unit angular momentum parameter lambda is constrained to (-0.05 +- 3.67) \times 10**(-15) s-1, (0.24 +- 0.98) \times 10**(-15) s-1, and (0 +- 3.6) \times 10**(-13) s-1 respectively in the directions of geodetic effect, frame-dragging effect and angular momentum axis; the dimensionless frequency-dependence parameter {\kappa} is constrained to (1.75 +- 4.96) \times 10**(-17), (1.80 +- 1.34) \times 10**(-17), and (0 +- 3) \times 10**(-14) respectively., Comment: 9 pages, 2 figures, 3 tables

ASTROD is a relativity mission concept encompassing multi-purposes. One of its main purposes is to detect gravitational waves sensitive to low-frequency band similar to LISA, but shifted to lower frequencies. In this aspect, ASTROD would complement LISA in probing the Universe and study strong-field black hole physics. Since ASTROD will be after LISA, in the Cosmic Vision time-frame 2015-2025, a ten-fold improvement over LISA accelerometer noise goal would be possible, allowing us to test relativistic gravity to 1 ppb and improve the gravitational-wave sensitivity. In this paper, we address to this possible improvement, especially in the frequency range below 0.1 mHz. We look into possible thermal noise improvement, magnetic noise improvement, spurious discharging noise improvement and local gravitational noise improvement. We discuss various possibilities of lower-frequency gravitational-wave responses and their significance to potential astrophysical sources., Comment: 21 pages, 2 figures. Accepted for publication in General Relativity and Gravitation

ASTROD I is planned as a single spacecraft mission. It will use interferometric and pulse ranging techniques between the spacecraft and ground stations, to make high precision measurements of the parameters that describe the solar system, and to test relativistic gravity with improved accuracy. At the heart of the spacecraft is a test mass, which the spacecraft will follow using a drag-free control system. The mission critically depends on maintaining the geodesic motion of the test mass. Charging of the test mass due to cosmic rays and solar particles will disturb its geodesic motion. We have modelled the charging process using the GEANT4 toolkit and a simplified, geometrical model and estimate that the ASTROD I test mass will charge positively, at a rate of 24 +/-7 e+/s, due to cosmic ray protons and alpha particles (3He and 4He) at solar minimum. We have used the results of this simulation to estimate the magnitude of disturbances associated with test mass charging, for the worst-case scenario, taking into account uncertainties in the model and potential charging contributions from minor cosmic-ray components., Comment: 17 pages, 11 figures, submitted to General Relativity and Gravitation

As ASTROD I travels through space, its test mass will accrue charge due to galactic cosmic-rays and solar energetic particles incident on the spacecraft. This test mass charge will result in Coulomb forces between the test mass and the surrounding electrodes. In earlier work using the GEANT4 toolkit, we predicted a net charging rate of nearly 9.0 +e/s from cosmic-ray protons between 0.1 and 1000 GeV at solar maximum, and rising to 26.5 +e/s at solar minimum. Here we use GEANT4 to simulate the charging process due to solar energetic particle events and to estimate the magnitude of acceleration noise due to this charging. The predicted charging rates range from 2840 to 64300 +e/s, at peak intensity, for the 4 largest SEP events in September and October 1989. For the 2 larger events, the acceleration disturbances due to charging exceeds the ASTROD I acceleration noise budget requirement. Continuous discharge should be considered for suppressing this charging noise. The acceleration noise during the 2 small events is well below the design target, although during these events, the net charging rate will be dominated by these solar fluxes., Comment: 10 pages,8 figures, COSPAR2006 H0.1-1, submitted

ASTROD-GW (ASTROD [Astrodynamical Space Test of Relativity using Optical Devices] optimized for Gravitational Wave detection) is a gravitational-wave mission with the aim of detecting gravitational waves from massive black holes, extreme mass ratio inspirals (EMRIs) and galactic compact binaries, together with testing relativistic gravity and probing dark energy and cosmology. Mission orbits of the 3 spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun-Earth Lagrange points L3, L4 and L5. The 3 spacecrafts range interferometrically with one another with arm length about 260 million kilometers. For 260 times longer arm length, the detection sensitivity of ASTROD-GW is 260 fold better than that of eLISA/NGO in the lower frequency region by assuming the same acceleration noise. Therefore, ASTROD-GW will be a better cosmological probe. In previous papers, we have worked out the time delay interferometry (TDI) for the ecliptic formation. To resolve the reflection ambiguity about the ecliptic plane in source position determination, we have changed the basic formation into slightly inclined formation with half-year precession-period. In this paper, we optimize a set of 10-year inclined ASTROD-GW mission orbits numerically using ephemeris framework starting at June 21, 2035, including cases of inclination angle is 0{\deg} (no inclination), 0.5{\deg}, 1.0{\deg}, 1.5{\deg}, 2.0{\deg}, 2.5{\deg} and 3.0{\deg}. We simulate the time delays of the first and second generation TDI configurations for the different inclinations, and compare/analyse the numerical results to attain the requisite sensitivity of ASTROD-GW by suppressing laser frequency noise below the secondary noises. To explicate our calculation process for different inclination cases, we take the 1.0{\deg} as example to show the orbit optimization and TDI simulation., Comment: 25 pages, 7 figures and 5 tables. arXiv admin note: text overlap with arXiv:1205.5175

We introduce a linearized bi-metric theory of gravity with two metrics. The metric g_{ab} describes null hypersurfaces of the gravitational field while light moves on null hypersurfaces of the optical metric \bar{g}_{ab}. Bi-metrism naturally arises in vector-tensor theories with matter being non-minimally coupled to gravity via long-range vector field. We derive explicit Lorentz-invariant solution for a light ray propagating in space-time of the bi-metric theory and disentangle relativistic effects associated with the two metrics. This anlysis can be valuable for future spaceborne laser missions ASTROD and LATOR dedicated to map various relativistic gravity parameters in the solar system to unparalleled degree of accuracy., Comment: 6 pages, figure and text improved. To appear in: Proceedings of the 359th WE-Heraeus Seminar on "Lasers, Clocks, and Drag-Free: Technologies for Future Exploration in Space and Tests of Gravity"}, ZARM, Bremen, Germany, May 30-June 1, 2005