 
Summary: grqc/980105115Jan1998
Microscopic Fields and Macroscopic Averages
in Einstein's Unified Field Theory*
S. Antoci
Dip. di Fisica "A. Volta", Via Bassi 6, 27100 Pavia, Italia
ABSTRACT. The problem of the relation between microscopic and macroscopic reality in the
generally covariant theories is first considered, and it is argued that a sensible definition of the
macroscopic averages imposes a restriction of the allowed transformations of coordinates to suit
ably defined macroscopic transformations. Spacetime averages of the geometric objects of a gen
erally covariant theory are then defined, and the reconstruction of some features of macroscopic
reality from hypothetic microscopic structures through such averages is attempted in the case
of the geometric objects of Einstein's unified field theory. It is shown with particular examples
how a fluctuating microscopic structure of the metric field can rule the constitutive relation for
macroscopic electromagnetism both in vacuo and in nondispersive material media. Moreover, if
both the metric and the skew field aik
that represents the electric displacement and the magnetic
field are assumed to possess a wavy microscopic behaviour, nonvanishing average generalized force
densities < Tm
k;m > are found to occur in the continuum, that originate from a resonance process,
in which at least three waves need to be involved. The previously required limitation of covari
