Spacetime Chronology and Radar Coordinates
摘要
Chapter 19 offers a summary of the different methods that astronomers have devised in order to measure the “distances” of observed objects by devices located on the Earth. It discusses how “parallax” methods (based on the geometry of Euclidean \(\mathbb {R}^{3}\) ) were related to the apparent magnitude and absolute magnitude of stellar objects via a logarithmic “photometric scale” assuming that visible light was emitted from point objects isotropically in space with an intensity that reduced inversely as the square of the Newtonian distance from the source. Modern astrometry makes no such assumptions but rather defines a ladder of cosmic distance scales based on the astrophysics of “standard candles” and “gravitational lensing” within the Einstein-Maxwell paradigm. The chapter concludes by introducing a particular spacetime chart for a general Einsteinian spacetime that can, in principle, be used to assign an instantaneous coordinate distance to a “nearby” spacetime event that can, in principle, reflect received light signals instantaneously in any spatial direction. This so-called radar methodology has been used for testing the clock hypothesis using spacecraft in our Solar System. However, it is argued that such chronological methods for analysing the properties of extra-galactic objects in a dynamic Universe demand a more sophisticated analysis (see Sect. 36.2 ) that exploits wave-particle duality.