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6.9 Phase coherence of light

An interesting and less well known method of constraining non-systematic Lorentz violation is looking at Airy rings (interference fringes) from distant astrophysical objects. In order for an interference pattern from an astrophysical source to be observed, the photons reaching the detector must be in phase across the detector surface. However, if the dispersion relation is fluctuating, then the phase velocity vf = w/k is also changing. If the fluctuations are uncorrelated, then initially in-phase collections of photons will lose phase coherence as they propagate. Uncorrelated fluctuations are reasonable, since for most of their propagation time, photons that strike across a telescope mirror are separated by macroscopic distances. Observation of Airy rings implies that photons are in phase and hence limits the fluctuations in the dispersion relation [204Jump To The Next Citation Point245233Jump To The Next Citation Point]. The aggregate phase fluctuation is given by [233]
n- 2 3-n Df = 2pf (n)LPl-D-----, (109) c
where LPl is the Planck length, D is the distance to the source, and c is the wavelength of the observed light. This technique was originally applied by [204], but the magnitude of the aggregate phase shift was overestimated. PKS1413+135, a galaxy at a distance of 1.2 Gpc, shows Airy rings at a wavelength of 1.6 mm. Demanding that the overall phase shift is less than 2p yields O(1) constraints for n = 5/2 and constraints of order 109 for n = 8/3. Hence this type of constraint is only able to minimally constrain Lorentz violating non-systematic models. In principle the frequency of light used for the measurement can be increased, however, in which case this type of constraint will improve. However, Coule [92] has argued that other effects mask the loss of phase coherence from quantum gravity, making even this approach uncertain.


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