The Lack of Observational Evidence for the Quantum Structure of Spacetime at Planck Scales

It has been noted (Lieu & Hillmann) that the cumulative effect of Planck-scale phenomenology, or the structure of spacetime at extremely small scales, can be lead to the loss of the 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 Hubble Space Telescope 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