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If the weak equivalence principle (WEP) is broken, the measured values of theparametrized post-Newtonian parameter $\gamma$ from photons with left- andright-handed circular polarizations should differ slightly, leading to thearrival-time difference of these two circular components. Thus, thepolarization vector of a linearly polarized light may rotate during thepropagation. The rotation angle of the polarization vector depends on both thephoton energy and the distance of the source. It is believed that if therotation angle differs by more than $\pi/2$ over an energy range, then the netpolarization of the signal would be significantly suppressed and could not beas high as the observed level. Thus, the detection of highly polarized photonsimplies that the relative rotation angle ($\Delta\Theta$) should not be toolarge. In this paper, we give a detailed calculation on the evolution ofgamma-ray burst (GRB) polarization arising from a possible violation of theWEP, and we find that more than $60\%$ of the initial polarization degree canbe conserved even if $\Delta\Theta$ is larger than $\pi/2$. In addition, totightly constrain the WEP violation, GRBs with harder spectra and polarizationobservations in a wider energy range seem to be favored. Applying our formulasto the measurements of linear polarization from GRB 110721A and GRB 061122, weobtain strict limits on the differences of the $\gamma$ values as low as$\Delta\gamma<1.3\times10^{-33}$ and $\Delta\gamma<0.8\times10^{-33}$. Theseprovide the most stringent limits to date on a deviation from the WEP,improving at least 6 orders of magnitude over previous bounds.

Precision Test of the Weak Equivalence Principle from Gamma-Ray Burst Polarization