Using Observations of Distant Quasars to Constrain Quantum Gravity
  Aims. The small-scale nature of spacetime can be tested with observations of
distant quasars. We comment on a recent paper by Tamburini et al. (A&A, 533,
71) which claims that Hubble Space Telescope observations of the most distant
quasars place severe constraints on models of foamy spacetime.
  Methods. If space is foamy on the Planck scale, photons emitted from distant
objects will accumulate uncertainties in distance and propagation directions
thus affecting the expected angular size of a compact object as a function of
redshift. We discuss the geometry of foamy spacetime, and the appropriate
distance measure for calculating the expected angular broadening. We also
address the mechanics of carrying out such a test. We draw upon our previously
published work on this subject (Christiansen et al. 2011), which carried out
similar tests as Tamburini et al. and also went considerably beyond their work
in several respects.
  Results. When calculating the path taken by photons as they travel from a
distant source to Earth, one must use the comoving distance rather than the
luminosity distance. This then also becomes the appropriate distance to use
when calculating the angular broadening expected in a distant source. The use
of the wrong distance measure causes Tamburini et al. to overstate the
constraints that can be placed on models of spacetime foam. In addition, we
consider the impact of different ways of parametrizing and measuring the
effects of spacetime foam. Given the variation of the shape of the point-spread
function (PSF) on the chip, as well as observation-specific factors, it is
important to select carefully -- and document -- the comparison stars used as
well as the methods used to compute the Strehl ratio.
