TianQin is a planned space-based gravitational wave (GW) observatory consisting of three Earth-orbiting satellites with an orbital radius of about $10^5 \, {\rm km}$. The satellites will form an equilateral triangle constellation the plane of which is nearly perpendicular to the ecliptic plane. TianQin aims to detect GWs between $10^{-4} \, {\rm Hz}$ and $1 \, {\rm Hz}$ that can be generated by a wide variety of important astrophysical and cosmological sources, including the inspiral of Galactic ultra-compact binaries, the inspiral of stellar-mass black hole binaries, extreme mass ratio inspirals, the merger of massive black hole binaries, and possibly the energetic processes in the very early universe and exotic sources such as cosmic strings. In order to start science operations around 2035, a roadmap called the 0123 plan is being used to bring the key technologies of TianQin to maturity, supported by the construction of a series of research facilities on the ground. Two major projects of the 0123 plan are being carried out. In this process, the team has created a new-generation $17 \, {\rm cm}$ single-body hollow corner-cube retro-reflector which was launched with the QueQiao satellite on 21 May 2018; a new laser-ranging station equipped with a $1.2 \, {\rm m}$ telescope has been constructed and the station has successfully ranged to all five retro-reflectors on the Moon; and the TianQin-1 experimental satellite was launched on 20 December 2019—the first-round result shows that the satellite has exceeded all of its mission requirements.

Short-range experiments testing the gravitational inverse-square law at the submillimeter scale offer uniquely sensitive probes of Lorentz invariance. A combined analysis of results from the short-range gravity experiments HUST-2015, HUST-2011, IU-2012, and IU-2002 permits the first independent measurements of the 14 nonrelativistic coefficients for Lorentz violation in the puregravity sector at the level of 10 −9 m 2 , improving by an order of magnitude the sensitivity to numerous types of Lorentz violation involving quadratic curvature derivatives and curvature couplings.

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A search for sidereal variations in the non-Newtonian force between two tungsten plates separated at millimeter ranges sets experimental limits on Lorentz invariance violation involving quadratic couplings of Riemann curvature. We show that the Lorentz invariance violation force between two finite flat plates is dominated by the edge effects, which includes a suppression effect leading to lower limits than previous rough estimates. From this search, we determine the current best constraints of the Lorentz invariance violating coefficients at a level of 10 −8 m 2 .PACS numbers: 04.25.Nx,04.80.Cc Local Lorentz invariance is at the foundation of both the Standard Model of particles physics and General Relativity (GR), however, the later theory is formulated as a classical theory, which demands some changes in its foundational structure to merge gravity with quantum mechanics. Even if local Lorentz invariance is exact in the underlying theory of quantum gravity, spontaneous breaking of this symmetry may occur, leading to tiny observable effects [1,2]. On the other hand, Lorentz violations could also be large but "hard-to-see", despite many experiments to date setting very tight bounds across many physical sectors [3]. This would occur if the Lorentz invariance violation is "countershaded" as pointed out in ref [4]. Thus in general, the investigation of local Lorentz invariance violations in the spacetime theory of gravity is a valuable tool to probe the foundations of GR [5,6] without preconceived notions of the numeric sensitivity.Recently, the studies of Lorentz invariance violation in the pure-gravity sector shows that general quadratic curvature coupling will lead to interesting new effects in short-range experiments that could have escaped detection in conventional studies to date [7]. Accordingly a crude estimation has been made on the possible constraints for these types of Lorentz invariance violation [7], predicted to be tested to the level of 10 −8 to 10 −10 m 2 using short-range experiments, such as the EotWash [8, 9], Wuhan [10,11], and Bloomington[12] experiments. However, for the latter two results, edge effects are not considered properly. In this work we obtain the best current constraint of the Lorentz invariance violation at level 10 −8 m 2 from a detailed reanalysis of prior data taken from the Wuhan experiment (HUST-2011).Effective field theory is a powerful and unique tool for investigating physics at attainable scales, and is suited for exploration of local Lorentz invariance in gravity. For centuries after Newton's Principia, our experimental understanding of gravity remains in some respects remark- * E-mail: junluo@sysu.edu.cn † E-mail: michael.tobar@uwa.edu.au ably limited. We are confident that Newton's law describes the dominant physics in long-range gravity and GR provides accurate relativistic corrections. However, in short-range gravity, it is presently unknown whether gravity obeys Newton's law, and many models attempting to unify gravity and the other fundamental forces in the same...

Precision measurements of the inverse-square law via experiments on short-range gravity provide sensitive tests of Lorentz symmetry. A combined analysis of data from experiments at the Huazhong University of Science and Technology and Indiana University sets simultaneous limits on all 22 coefficients for Lorentz violation correcting the Newton force law as the inverse sixth power of distance. Results are consistent with no effect at the level of 10 −12 m 4 .