The phase coherence of light from extragalactic sources - direct evidence against first order Planck scale fluctuations in time and space

We present a method of directly testing whether time continues to have its usual meaning on scales of <= t_P = sqrt(hbar G/c^5) ~ 5.4E-44 s, the Planck time. According to quantum gravity, the time t of an event cannot be determined more accurately than a standard deviation of the form sigma_t/t = a_o (t_P/t)^a, where a_o and a are positive constants ~1; likewise distances are subject to an ultimate uncertainty c \sigma_t, where c is the speed of light. As a consequence, the period and wavelength of light cannot be specified precisely; rather, they are independently subject to the same intrinsic limitations in our knowledge of time and space, so that even the most monochromatic plane wave must in reality be a superposition of waves with varying omega and {\bf k}, each having a different phase velcocity omega/k. For the entire accessible range of the electromagnetic spectrum this effect is extremely small, but can cumulatively lead to a complete loss of phase information if the emitted radiation propagated a sufficiently large distance. Since, at optical frequencies, the phase coherence of light from a distant point source is a necessary condition for the presence of diffraction patterns when the source is viewed through a telescope, such observations offer by far the most sensitive and uncontroversial test. We show that the HST detection of Airy rings from the active galaxy PKS1413+135, located at a distance of 1.2 Gpc, secures the exclusion of all first order (a=1) quantum gravity fluctuations with an amplitude a_o > 0.003. The same result may be used to deduce that the speed of light in vacuo is exact to a few parts in 10^32.