Experimental Design for Testing Local Lorentz Invariance Violations in Gravity

Ya-Fen Chen,Yu-Jie Tan,Cheng-Gang Shao

doi:10.3390/sym9100219

Abstract

Local Lorentz invariance is an important component of General Relativity. Testing for Local Lorentz invariance can not only probe the foundation stone of General Relativity but also help to explore the unified theory for General Relativity and quantum mechanics. In this paper, we search the Local Lorentz invariance violation associated with operators of mass dimension d = 6 in the pure-gravity sector with short-range gravitational experiments. To enlarge the Local Lorentz invariance violation signal effectively, we design a new experiment in which the constraints of all fourteen violation coefficients may be improved by about one order of magnitude.

Highlights

Local Lorentz Invariance (LLI), as a built-in element of General Relativity (GR), denotes that the physical results are kept invariant when rotations and boosts are performed on a physical system
Investigating the Lorentz violation is a worthy tool to test GR [7,8,9,10,11,12,13,14], and it may help us to explore the unified theory for GR and quantum mechanics
We focus on searching for LLI violation in pure-gravity sector for d = 6, which has been widely tested by short-range gravitational experiments, since the short-range experiments are better than other experiments to probe higher dimension coefficients with r-dependence

Summary

Introduction

Local Lorentz Invariance (LLI), as a built-in element of General Relativity (GR) (for recent overviews for its centenary see, for example, [1,2]), denotes that the physical results are kept invariant when rotations and boosts are performed on a physical system. For LLI violation in the pure-gravity part, the experimental classification falls into three parts: experiments on ground [21], solar system [22], and astrophysical measurements [23,24], in which the different limits for different mass dimensions of LLI violation effects are given. We focus on searching for LLI violation in pure-gravity sector for d = 6, which has been widely tested by short-range gravitational experiments, since the short-range experiments are better than other experiments to probe higher dimension coefficients with r-dependence. It is followed by a simple discussion on it.

LLI Violation

LLI Violation in Pendulum Experiments

Experimental Design

Discussion and Expected Result

Conclusions