  The relation between microscopic and macroscopic entities in the generally
covariant theories is considered, and it is argued that a sensible definition
of the macroscopic averages requires a restriction of the allowed
transformations of coordinates. Spacetime averages of the geometric objects of
Einstein's unified field theory are then defined, and the reconstruction of
some features of macroscopic reality from hypothetic microscopic structures is
attempted. It is shown how a fluctuating microscopic behaviour of the metric
field can rule the constitutive relation for electromagnetism both in vacuo and
in nondispersive material media. Moreover, if both the metric and the skew
tensor density that represents the electric displacement and the magnetic field
are assumed to possess a wavy microscopic structure, nonvanishing generalized
force densities can appear in the continuum. They originate from a resonance
process, in which at least three waves need to be involved. This process only
occurs if the wavevectors fulfil the three-wave resonance condition, so
ubiquitous in quantum physics. The wavy behaviour of the metric is essential
for the occurrence of this resonance phenomenon.
