12. Michel A. Duguay, Diachronic Representation of Space‐Time Applied to Problems in Special Relativity and in Quantum Optics

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Volume 18: Pages 239-262, 2005

Diachronic Representation of SpaceTime Applied to Problems in Special Relativity and in Quantum Optics

Michel A. Duguay

Centre d'Optique, Photonique et Laser, Département de génie électrique et de génie informatique, Université Laval, Québec, Québec G1K 7P4 Canada

A central observer at Greenwich builds in real time a diachronic representation of 4D(t) spacetime 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 diachronic time. In a 4D(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 4D(t) conceptual framework the detection of a photon is considered to be an instantaneous transfer of energy and momentum across the time gap between emitter and receiver. The Lorentz transformation 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 (synchronie) speed of light c is identified with the flow of time, (2) the twin paradox is resolved in a twinsymmetric fashion, and (3) a new solution for the EinsteinPodolskyRosen paradox maintains harmony between special relativity and quantum mechanics. The diachronic approach presents the pedagogical advantage of using a single diagram to display spacetime relationships of events in two coordinate systems in relative motion.

Keywords: special relativity, quantum optics, EinsteinPodolskyRosen paradox

Received: April 21, 2005; Published online: December 15, 2008