Einstein ’ s weak equivalence principle ( WEP ) states that any freely falling , uncharged test particle follows the same identical trajectory independent of its internal structure and composition .
Since the polarization of a photon is considered to be part of its internal structure , we propose that polarized photons from astrophysical transients , such as gamma-ray bursts ( GRBs ) and fast radio bursts ( FRBs ) , can be used to constrain the accuracy of the WEP through the Shapiro time delay effect .
Assuming that the arrival time delays of photons with different polarizations are mainly attributed to the gravitational potential of the Laniakea supercluster of galaxies , we show that a strict upper limit on the differences of the parametrized post-Newtonian parameter \gamma value for the polarized optical emission of GRB 120308A is \Delta \gamma < 1.2 \times 10 ^ { -10 } , for the polarized gamma-ray emission of GRB 100826A is \Delta \gamma < 1.2 \times 10 ^ { -10 } , and for the polarized radio emission of FRB 150807 is \Delta \gamma < 2.2 \times 10 ^ { -16 } .
These are the first direct verifications of the WEP for multiband photons with different polarizations .
In particular , the result from FRB 150807 provides the most stringent limit to date on a deviation from the WEP , improving by one order of magnitude the previous best result based on Crab pulsar photons with different energies .