  It has been suggested that space-time might undergo fluctuations because of
its intrinsic quantum nature. These fluctuations would pose a fundamental limit
to the ability of measuring distances with arbitrary precision, beyond any
limitations due to standard quantum mechanics. Laser interferometers have
recently been proposed as being suited for a search for the existence of
space-time fluctuations. Here we present results of a search for space-time
fluctuations of very low fluctuation frequencies, in the range from 1 microHz
to 0.5 Hz. Rigid optical interferometers made out of sapphire and operated at
cryogenic temperature were used. We find an upper limit of 1.10^-24 Hz^-1 for
the normalized distance noise spectral density at 6 microHz, and of 1.10^-28
Hz^-1 above 5 mHz, and establish an experimental limit for the parameter of a
recently proposed random-walk hypothesis.
