A phenomenological description of space-time noise in quantum gravity

Abstract

Space-time ‘foam’ is a geometric picture of the smallest size scales in the Universe, which is characterized mainly by the presence of quantum uncertainties in the measurement of distances. All quantum-gravity theories should predict some kind of foam^1,2, but the description of the properties of this foam varies according to the theory, thereby providing a possible means of distinguishing between such theories. I previously showed³ that foam-induced distance fluctuations would introduce a new source of noise to the measurements of gravity-wave interferometers, but the theories are insufficiently developed⁴ to permit detailed predictions that would be of use to experimentalists. Here I propose a phenomenological approach that directly describes space-time foam, and which leads naturally to a picture of distance fluctuations that is independent of the details of the interferometer. The only unknown in the model is the length scale that sets the overall magnitude of the effect, but recent data⁵ already rule out the possibility that this length scale could be identified with the ‘string length’ (10^-34 m < L_s < 10^-33 m). Length scales even smaller than the ‘Planck length’ (L_P ≈ 10^-35 m) will soon be probed experimentally.