Stringent limits on the existence of Planck time from stellar interferometry

Abstract

We present a method of directly testing whether time is `grainy' on scales of <= t_P = (hbar G/c^5)^0.5 ~ 5.4E-44 s, the Planck time. If the phenomenon exists, the energy and momentum of a photon (quantities which are independently measured) will be subject to ultimate uncertainties of the form dE/E ~ dp/p ~ (E/E_P)^a, where E=h/t_P and a~1, because surpassing these will lead to `super-clocks' and `super-rulers'. A well-known consequence is random perturbation of the photon dispersion equation by a correction term which to lowest order modifies the equation to the form p^2 = E^2[1 +/- a_o(E/E_P)^a], where a_o ~ 1 and c=1. As a result, the two wave velocities will fluctuate by different amounts, so that after propagating a sufficiently large distance the phase of the radiation will no longer be well-defined. Now, at optical frequencies, the technique of stellar interferometry readily ascertains whether light from an astronomical object retains is phase information upon arrival. Currently the furthest star from which interference fringes were seen, S Ser, is at ~ 1 kpc, implying that all models with a <= 13/15 are to be rejected. The decisive step, of course, is to test the presence or not of the first order term E/E_P itself (i.e. a=1); for this one must await the imminent observations of extra-galactic sources at > 1 Mpc by the Very Large Telescope Interferometer (the VLTI). Based upon the S Ser result, nonetheless, it is already possible to conclude that there is no first order departure from exactness in time over intervals ~ 4.2E-40 s (~10^4 times longer than the Planck time).