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Fast radio bursts (FRBs) are short duration ($\sim$millisecond) radiotransients with cosmological origin. The simple sharp features of the FRBsignal have been utilized to probe two fundamental laws of physics, namey,testing Einstein's weak equivalence principle and constraining the rest mass ofthe photon. Recently, \cite{hessels18} found that after correcting fordispersive delay, some of the bursts in FRB 121102 have complex time-frequencystructures that include sub-pulses with a time-frequency downward driftingproperty. Using the delay time between sub-pulses in FRB 121102, here we showthat the parameterized post-Newtonian parameter $\gamma$ is the same forphotons with different energies to the level of$\left|\gamma_1-\gamma_2\right|<2.5\times 10^{-16}$, which is 1000 times betterthan previous constraints from FRBs using similar methods. We also obtain astringent constraint on the photon mass, $m_{\gamma} < 5.1\times10^{-48}$ g,which is 10 times smaller than previous best limits on the photon mass derivedthrough the velocity dispersion method.

Limits on the Weak Equivalence Principle and Photon Mass with FRB 121102 Sub-pulses