A Metric Determined by Photon Exchange

Abstract

The k-calculus was advanced by Hermann Bondi as a means of explaining special relativity using only simple algebra [1]. Bondi's argument was placed in the context of classical electrodynamics. In this paper it is placed in context of particle theoretic QED. The central derivations are reviewed, using proofs only slightly more elegant than those in Bondi's books. As used by Bondi, k is Doppler red shift. The relativistic measurement of position is placed in the context of an information theoretic interpretation of quantum mechanics as a theory of measurement results. The law of geodesic motion is seen as consequent on the refraction of the wave function due curvature, as in geometric optics. The k-calculus is extended to include gravitational red shift and to account for gravity by observing that, after allowing a small inherent delay in the reflection of a photon, the metric defined by the radar method obeys Einstein's field equation. A very simple derivation of Schwarzschild is given using the k-calculus and avoiding differential geometry and calculation of Christoffel symbols. The Newtonian approximation is seen from a direct application of red shift to the wave function.