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 ≤tP = (ℏG/c5)1/2 ≈ 5.4 × 10-44 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 σt/t = a0(tP/t)α, where a0 and α are positive constants ~1; likewise, distances are subject to an ultimate uncertainty cσt, 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 ω and , each having a different phase velocity ω/k. For the entire accessible range of the electromagnetic spectrum this effect is extremely small, but 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 1413+135, located at a distance of 1.2 Gpc, excludes all first-order (α = 1) quantum gravity fluctuations with an amplitude a0 > 0.003. The same result may be used to deduce that the speed of light in vacuo is exact to a few parts in 1032.