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Violations of both the weak equivalence principle (WEP) and Lorentzinvariance can produce vacuum birefringence, which leads to an energy-dependentrotation of the polarization vector of linearly polarized emission from a givenastrophysical source. However, the search for the birefringent effect has beenhindered by our ignorance concerning the intrinsic polarization angle indifferent energy bands. Considering the contributions to the observed linearpolarization angle from both the intrinsic polarization angle and the rotationangles induced by violations of the WEP and Lorentz invariance, and assumingthe intrinsic polarization angle is an unknown constant, we simultaneouslyobtain robust bounds on possible deviations from the WEP and Lorentzinvariance, by directly fitting the multiwavelength polarimetric data of theoptical afterglows of gamma-ray burst (GRB) 020813 and GRB 021004. Here we showthat at the $3\sigma$ confidence level, the difference of the parameterizedpost-Newtonian parameter $\gamma$ values characterizing the departure from theWEP is constrained to be$\Delta\gamma=\left(-4.5^{+10.0}_{-16.0}\right)\times10^{-24}$ and thebirefringent parameter $\eta$ quantifying the broken degree of Lorentzinvariance is limited to be$\eta=\left(6.5^{+15.0}_{-14.0}\right)\times10^{-7}$. These are the firstsimultaneous verifications of the WEP and Lorentz invariance in the photonsector. More stringent limits can be expected as the analysis presented here isapplied to future multiwavelength polarization observations in the promptgamma-ray emission of GRB

Testing the Weak Equivalence Principle and Lorentz Invariance with Multiwavelength Polarization Observations of GRB Optical Afterglows