Abstract
In this paper the ‘‘free fall’’ motion of a test tetrad in a weak gravitational field is studied. This is done with the intention of exploring the geometry locally through geodesics and parallel transport. By use of the so-called ‘‘radial gauge’’ the action of the field on the test tetrad just in terms of the Riemann tensor is expressed. The average effect of small quantized fluctuations of the field can thus be computed using the Feynman–De Witt propagator. Since the dimension L of the test particle must be finite, only fluctuations of wavelength λ≥L have to be considered. The corresponding corrections to the geometry are proportional to lPlanck/L. Such dependence on L spoils, in fact, a genuine geometrical description.
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