 
Summary: grqc/990609423Jun1999
A FOURDIMENSIONAL HOOKE'S LAW CAN
ENCOMPASS LINEAR ELASTICITY AND INERTIA
S. ANTOCI AND L. MIHICH
Abstract. The question is examined, whether the formally straight
forward extension of Hooke's timehonoured stressstrain relation to the
four dimensions of special and of general relativity can make physical
sense. The fourdimensional Hooke's law is found able to account for
the inertia of matter; in the flat space, slow motion approximation the
field equations for the "displacement" fourvector field i
can encom
pass both linear elasticity and inertia. In this limit one just recovers the
equations of motion of the classical theory of elasticity.
1. Introduction
After having fostered the birth of the fourdimensional approach to special
relativity [1], macroscopic electromagnetism has found its natural expression
in the four dimensional language of general relativity, both in vacuo [2] and
in matter [3], [4]. Its field quantities and its field equations have achieved
a canonical form, that can be summarized as follows [5]: the unconnected
spacetime manifold suffices for writing Maxwell's equation in the naturally
