  The k-calculus was advanced by Hermann Bondi as a means of explaining special
relativity using only simple algebra (Bondi H.: Relativity and Common Sense,
London, Heinemann, 1964). As used by Bondi, k is Doppler shift. This paper
extends the k-calculus to include gravitational red shift and to develop
techniques for an introductory treatment of general relativity in which the
emphasis is on mathematical deduction from physical measurement procedure.
Using ideas of geometric optics, geodesic motion is understood from the
refraction of the wave function due curvature. The k-calculus gives a very
simple derivation of Schwarzschild, showing that the geometry is equivalent to
the existence of a fundamental minimum time, proportional to rest mass, between
the interactions of elementary particles. The Newtonian approximation is seen
from direct application of red shift to the wave function. Finally differential
geometry is introduced, showing that the k-calculus gives an equivalent
treatment of general relativity up to and including the general form of
Einstein's field equation.
