Strict Limit on $CPT$ Violation from Polarization of $\gamma$-Ray Bursts

We report the strictest observational verification of $CPT$ invariance in the photon sector, as a result of $\gamma$-ray polarization measurement of distant gamma-ray bursts (GRBs), which are the brightest stellar-sized explosions in the Universe. We detected $\gamma$-ray polarization of three GRBs with high significance levels, and the source distances may be constrained by a well-known luminosity indicator for GRBs. For the Lorentz- and $CPT$-violating dispersion relation $E_{\pm }^2=p^2\pm 2\xi p^3/M_{Pl}$, where $\pm$ denotes different circular polarization states of the photon, the parameter $\xi$ is constrained as $|\xi |<O({10}^{-15})$. Barring precise cancellation between quantum gravity effects and dark energy effects, the stringent limit on the $CPT$-violating effect leads to the expectation that quantum gravity presumably respects the $CPT$ invariance.