The Einstein ’ s equivalence principle can be tested by using parameterized post-Newtonian parameters , of which the parameter \gamma has been constrained by comparing the arrival times of photons with different energies .
It has been constrained by a variety of astronomical transient events , such as gamma-ray bursts ( GRBs ) , fast radio bursts as well as pulses of pulsars , with the most stringent constraint of \Delta \gamma \lesssim 10 ^ { -15 } .
In this letter , we consider the arrival times of lights with different circular polarization .
For a linearly polarized light , it is the combination of two circularly polarized lights .
If the arrival time difference between the two circularly polarized lights is too large , their combination may lose the linear polarization .
We constrain the value of \Delta \gamma _ { p } < 1.6 \times 10 ^ { -27 } by the measurement of the polarization of GRB 110721A , which is the most stringent constraint ever achieved .