Lack of observational evidence for quantum structure of space-time at Plank scales

It has been noted (Lieu & Hillmann, 2002) that the cumulative affect of Planck-scale phenomenology, or the structure of space-time at extremely small scales, can be lead to the loss of phase of radiation emitted at large distances from the observer. We elaborate on such an approach and demonstrate that such an effect would lead to an apparent blurring of distant point-sources. Evidence of the diffraction pattern from the HST observations of SN 1994D and the unresolved appearance of a Hubble Deep Field galaxy at z=5.34 lead us to put stringent limits on the effects of Planck-scale phenomenology.Comment: 12 pages, 3 figures, accepter for ApJ