Time delays in BATSE energy channels for 668 GRBs

In the theory of parametrized post-Newtonian (PPN), the difference between the PPN parameters {gamma} of different particles or the same type of particle with different energies, {Delta}{gamma}, represents the violation of WEP. Current constraints on {Delta}{gamma} are derived from the observed time delay between correlated particles of astronomical sources.

However, the observed time delay is contaminated by other effects, such as the time delays due to different particle emission times, the potential Lorentz invariance violation, and none-zero photon rest mass. Therefore, current constraints are only upper limits. Here, we propose a new method to test WEP based on the fact that the gravitational time delay is direction-dependent while others are not.