The Principle of General Covariance and the Principle of ...

lems simultaneously, precisely through a ctose asso&a.tion
principles under discussion.
of the two
But then we feel that the student may fail to appreciate the
import of general covariance per se, seeing i t perhaps as a mere consequence
of the equivalence pri nci ple .
Therefore, we make some conjectures based on the
assumption
of general covariance without equi va lence . Thi s serves to i i lustra te the
independence of the former concept from the latter one 5 .
In this spirit we discuss in Sec.2,
the
particle under the influence of a force, and in Sec.
quations of electromagnetism as well as a hypothetical
the gravitational field. We conclude remembering the
of this paper.
law of motion of a
3 we present the e-
set of equationsfor
pedagogical nature
2. THE MOTION OF A MASSIVE PARTICLE UNDER THE
INFLUENCE OF A FORCE
In a Lorentz system of reference (x')
with metric
the equation of motion of a
f luence of a 4-force FV is
particle of inertial mass 40, under the in-
where s is the particle's proper time (c-1) and
is its bvelocity. FP is the net externa1 force appl ied on the particle,