Preprint typeset using LATEX style emulateapj v. 5/2/11 NEW CONSTRAINTS ON QUANTUM GRAVITY FROM X-RAY AND GAMMA-RAY OBSERVATIONS

One aspect of the quantum nature of spacetime is its “foaminess ” at very small scales. We reassess previous proposals to use astronomical observations of distant quasars and AGN to test models of spacetime foam. We show explicitly how wavefront distortions on small scales cause the image intensity to decay to the point where distant objects become undetectable when the path-length fluctuations become comparable to the wavelength of the radiation. We use X-ray observations from Chandra to constrain on the parameter α in the expression for cosmic phase shifts to be & 0.58, which rules out the random walk model (with α = 1/2). Here α is defined by the expression for the path-length fluctuations, δ`, of a source at distance `, wherein δ ` ' `1−α`αP, with `P being the Planck length. Much firmer constraints can be set utilizing detections of quasars at GeV energies with Fermi, and at TeV energies with ground-based Cherenkov telescopes: α & 0.67 and α & 0.72, respectively. These limits on α seem to rule out predictions of α = 2/3 for the holographic model. We also discuss the less certain possibility that spacetime foam may directly blur images by deflecting photon trajectories. We show that these are not essential to constraining models of space-time foam. However, we demonstrate that X-ray microlensing studies of quadruply lensed quasars indicate that any blurring in the X-ray band must be at levels smaller than a micro-arcsecond, even when accumulated over cosmological distances