The Phase Coherence of Light from Extragalactic Sources: Direct Evidence against FirstOrder PlanckScale Fluctuations in Time and Space
Abstract
We present a method of directly testing whether time continues to have its usual meaning on scales of <=t_{P}=(ℏG/c^{5})^{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 σ_{t}/t=a_{0}(t_{P}/t)^{α}, where a_{0} and α are positive constants ~1 likewise, distances are subject to an ultimate uncertainty cσ_{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 ω and k, 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 firstorder (α=1) quantum gravity fluctuations with an amplitude a_{0}>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}.
 Publication:

The Astrophysical Journal
 Pub Date:
 March 2003
 DOI:
 10.1086/374350
 arXiv:
 arXiv:astroph/0301184
 Bibcode:
 2003ApJ...585L..77L
 Keywords:

 Cosmology: Distance Scale;
 Cosmology: Early Universe;
 Gravitation;
 Radiation Mechanisms: General;
 Techniques: Interferometric;
 Time;
 Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 Title change. One reference added. Final version accepted by ApJL