Search for Lorentz invariance violation through tests of the gravitational inverse square law at short ranges

Abstract

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...

Experimental Design for Testing Local Lorentz Invariance Violations in Gravity

“…As the new experimental design is based on HUST-2011 experiment, we can estimate the error bar similarly. In HUST-2011 experiment [38], experimental error of the constant term (C 0 ) and harmonic terms (C m , S m ) at 2σ have achieved the level at 1.9 × 10 −16 Nm and 0.45 × 10 −16 Nm, respectively. The error of C 0 is dominant by the systematic error, while the errors of C m , S m are limited by the thermal noise, which is at the same level to the statistical errors in current experiment.…”

“…In fact, the infinite plate is not existent in true life, so the Lorentz violating force between two planes is not zero, and we find it is dominated by the edge effect. Based on the experimental data of testing the gravitational inverse square law (HUST-2011) with a pendulum, we have analyzed the LLI violation effect and constrained the violating coefficients at the level of 10 −8 m 2 [38]. Moreover, we perform a combined analysis and achieved the best level of LLI violation at 10 −9 m 2 [25].…”

Experimental Studies on the Lorentz Symmetry in Post-Newtonian Gravity with Pulsars

“…The LLI violation (LLIv) in gravitational interaction modifies the local Lorentzian transformation property of gravitation, and leads to various anomalous phenomena in gravitational experiments [2,3,[7][8][9][10][11], including lunar laser ranging [12,13], atom interferometry [14], pulsar timing [15][16][17][18][19], cosmic rays [20,21], very long baseline interferometry [22], and short-range experiments in laboratory [23][24][25][26]. In this short contribution, I will focus on the recent limits on LLIv obtained from precision pulsar timing experiments [7,[15][16][17][18][19]27,28] in the theoretical frameworks of parametrized post-Newtonian (PPN) gravity [2,29] and the pure gravity sector of the standard-model extension (SME) [1,6,7].…”

Enhanced sensitivity to Lorentz invariance violations in short-range gravity experiments

“…However, the plane-on-plane configuration is not optimal for testing LIV. The LIV force is suppressed for parallel plate geometry, and vanishes altogether in the limit where one plate has infinite area [9]. A more effective geometry for testing LIV is realized with the striped plates as shown in Fig.…”

“…However, these experiments use planar geometry, as they are designed primarily to search for Yukawa-type non-Newtonian gravity [12]. The LIV force between two parallel, coaxial plates is suppressed, and in fact vanishes in the limit that one plate has infinite area [9].…”