Eur. Phys. J. C (2013) 73: 2337
https://doi.org/10.1140/epjc/s10052-013-2337-6

Regular Article - Theoretical Physics

Constraints on spacetime anisotropy and Lorentz violation from the GRAAL experiment

¹ Institute of High Energy Physics, Chinese Academy of Sciences, 100049, Beijing, China
² Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, 100049, Beijing, China

^* e-mail: wangsai@ihep.ac.cn
^** e-mail: saiwangihep@gmail.com

Received: 17 December 2012
Revised: 30 January 2013
Published online: 28 February 2013

Abstract

The GRAAL experiment could constrain the variations of the speed of light. The anisotropy of the speed of light may imply that the spacetime is anisotropic. Finsler geometry is a reasonable candidate to deal with the spacetime anisotropy. In this paper, the Lorentz invariance violation (LIV) of the photon sector is investigated in the locally Minkowski spacetime. The locally Minkowski spacetime is a class of flat Finsler spacetime and refers a metric with the anisotropic departure from the Minkowski one. The LIV matrices used to fit the experimental data are represented in terms of these metric deviations. The GRAAL experiment constrains the spacetime anisotropy to be less than 10⁻¹⁴. In addition, we find that the simplest Finslerian photon sector could be viewed as a geometric representation of the photon sector in the minimal standard model extension (SME).