Session 19. Neutrinos, Gravitational Waves and Strong-field Gravity III
Poster, Sunday-Wednesday, March 23, 2003, Duration of Meeting

## [19.03] Where is the Planck time?

R. Lieu, H. Hillman (Physics Dept., Univ. Alabama at Huntsville)

It is widely believed that the Universe was created in a violent (kT ~h/tP \approx 1029 eV) explosion lasting tP \approx 5.4 \times 10-44 s, where tP = (\hbar G/c5)\frac{1}{2}, the Planck time, is an interval during which even time is a fuzzy concept. We present a method of directly testing whether time has its usual (i.e. classical) meaning on scales of \leq tP. If indeed time and space cannot be known more precisely than tP and c tP, the same must apply to the period and wavelength of light, so that even the most monochromatic plane wave must in reality be a superposition of waves with independently varying \omega and 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 Planck scale space-time fluctuations. This result may be used to deduce that the speed of light in vacuo is exact to a few parts in 1032.