We present a method of directly testing whether time continues to have its usual meaning on scales of ≤ s, the Planck time. According to quantum gravity, the time t of an event cannot 5 1/2 Ϫ44 t p (បG/c ) ≈ 5.4 # 10 P be determined more accurately than a standard deviation of the form , where and a are positive a j /t p a (t /t) a t 0 P 0 constants ∼1; likewise, distances are subject to an ultimate uncertainty , where c is the speed of light. As a cj t 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 q and , each having a different phase k velocity . For the entire accessible range of the electromagnetic spectrum this effect is extremely small, but q/k it 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 Hubble Space Telescope detection of Airy rings from the active galaxy PKS 1413ϩ135, located at a distance of 1.2 Gpc, excludes all first-order ( ) quantum gravity fluctuations with an amplitude . The same result may be used to deduce that a p 1 a 1 0.003 0 the speed of light in vacuo is exact to a few parts in 10 32 .