Diachronic Representation of Space-Time Applied to Problems in Special Relativity and in Quantum Optics.

Abstract

Abstract A central observer at Greenwich builds in real time a diachronic representation of 4-D(t) space-time by assigning two distinct times to a given remote event, such as a meteorite impact on Mars: (1) diachronic time read on his Greenwich clock (GMT) at observation time, and (2) synchronic or local Einstein time as directly seen from Greenwich on the Mars clock. In a spherical coordinate system the Greenwich diachronic observer uses local Einstein time relative to diachronic time as a radial coordinate, leaving the role of the fourth coordinate to dia-chronic time. In a 4-D(t) conceptual framework the same diachronic time applies integrally to all directly observed local Einstein times, thus implying an infinite diachronic speed for incoming light. In the 4-D(t) conceptual framework the de-tection of a photon is considered to be an instantaneous transfer of energy and momentum across the time gap between emitter and receiver. The Lorentz trans-formation can be obtained by requiring that history updated now and here be the same for another observer flying by. Some results are (1) the conventional (syn-chronic) speed of light c is identified with the flow of time, (2) the twin paradox is resolved in a twin-symmetric fashion, and (3) a new solution for the Einstein–Podolsky–Rosen paradox maintains harmony between special relativity and quan-tum mechanics. The diachronic approach presents the pedagogical advantage of using a single diagram to display space-time relationships of events in two coor-dinate systems in relative motion.