Coordinate Time - Coordinate Time, Proper Time, and Clock Synchronization

Coordinate Time, Proper Time, and Clock Synchronization

Fuller explanation of the concept of coordinate time arises from its relationships with proper time and with clock synchronization. Synchronization, along with the related concept of simultaneity, has to receive careful definition in the framework of general relativity theory, because many of the assumptions inherent in classical mechanics and classical accounts of space and time had to be removed. Specific clock synchronization procedures were defined by Einstein and give rise to a limited concept of simultaneity.

Two events are called simultaneous in a chosen reference frame if and only if the chosen coordinate time has the same value for both of them; and this condition allows for the physical possibility and likelihood that they will not be simultaneous from the standpoint of another reference frame.

But the coordinate time is not a time that could be measured by a clock located at the place that nominally defines the reference frame, e.g. a clock located at the solar system barycenter would not measure the coordinate time of the barycentric reference frame, and a clock located at the geocenter would not measure the coordinate time of a geocentric reference frame.