A variation on this constraint can be derived by considering birefringence when the difference is a function of . A realistic polarization measurement is an aggregate of the polarization of received photons in a narrow energy band. If there is significant power across the entire band, then a polarized signal must have the polarization direction at the top nearly the same as the direction at the bottom. If the birefringence effect is energy dependent, however, the polarization vectors across the band rotate differently with energy. This causes polarization “diffusion” as the photons propagate. Given enough time the spread in angle of the polarization vectors becomes comparable to and the initial linear polarization is lost. Measurement of linear polarization from distant sources therefore constrains the size of this effect and hence the Lorentz violating coefficients. We can easily estimate the constraint from this effect by looking at when the polarization at two different energies (representing the top and bottom of some experimental band) is orthogonal, i.e. . Using Equation (77) for the polarization gives
Three main results have been derived using this approach. Birefringence has been applied to the mSME in [178, 179]. Here, the ten independent components of the two coefficients and (see Section 5.3) that control birefringence are expressed in terms of a ten-dimensional vector . The actual bound, calculated from the observed polarization of sixteen astrophysical objects, is .19 A similar energy band was used to constrain in Equation (40) to be . Recently, the reported polarization of GRB021206  was used to constrain to , but since the polarization claim is uncertain [248, 274] such a figure cannot be treated as an actual constraint.
© Max Planck Society and the author(s)