Case for two-dimensional time

摘要

This paper brings in additional arguments in favor of two-dimensional time in the context of the diachronic approach to physical reality. The arguments are based on symmetry and convention considerations. Consider a distant event, for example, a meteorite impact on Mars now observedby us through a telescope in Greenwich, for example, or thanks to television signals sent by a Martian robot. Seen from Earth the Martian robot's clock displays what can be called synchronic local Einstein time, that clock having been synchronized by electromagnetic means according to Einstein'smethod. In the diachronic approach, this distant event is characterized by the offset between local Einstein time and the central terrestrial observer's own clock display in Greenwich. The latter display is taken to be the event's diachronic time and to constitute the fourth dimension of space-timein diachronic special relativity. The other temporal coordinate is the offset of local Einstein time with respect to central time, i.e., Greenwich time in the chosen example. In the diachronic approach, this offset serves as the radial coordinate in a spherical coordinate system centered onthe terrestrial observer. This time offset radial coordinate is currently used in astronomy, its values being typically expressed in light-years and interpreted as spatial distance. In the diachronic approach, the radial time offset is interpreted as a temporal distance. The two conceptualdistances are separated by 45° on a Minkowski space-time diagram. The two angles defining the telescope's orientation are the other two dimensions. At the now-here point (in Greenwich in the example), the two-dimensional time coordinate system allows one to speak of symmetry inthe up-dated historical content available to the central observer and to a second observer flying by. On their respective past light cones, the same events are displayed, and their diachronic time ordering is preserved, unlike in the conventional approach to special relativity. The preservationof photon detection time ordering is relevant to the explanation of some experiments with quantum entangled states. Implicit in the diachronic choice of coordinates is that a photon detection event is interpreted as an instantaneous transfer of energy and momentum from emitter to receiver.An important consequence of the diachronic approach is that the universe daily observed by astronomers is now regarded as part of our present physical reality from our terrestrial point of view. Moving the central observer into an orbit around a star like Sirius does not change the diachronicnature of the universe, so that this can also be taken by convention as another symmetry feature of the universe.