In the special case of an inertial observer in special relativity, by convention the coordinate time at an event is the same as the proper time measured by a clock that is at the same location as the event, that is stationary relative to the observer and that has been synchronised to the observer's clock using the Einstein synchronisation convention.
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.
[1] 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;[2] and this condition allows for the physical possibility and likelihood that they will not be simultaneous from the standpoint of another reference frame.
[3] For non-inertial observers, and in general relativity, coordinate systems can be chosen more freely.
in which: is a sum of gravitational potentials due to the masses in the neighborhood, based on their distances ri from the clock.
Only for explanatory purposes it is possible to conceive a hypothetical observer and trajectory on which the proper time of the clock would coincide with coordinate time: such an observer and clock have to be conceived at rest with respect to the chosen reference frame (v = 0 in (2) above) but also (in an unattainably hypothetical situation) infinitely far away from its gravitational masses (also U = 0 in (2) above).
This notional clock, because it is outside all gravity wells, is not influenced by gravitational time dilation.
There are four purpose-designed coordinate time scales defined by the IAU for use in astronomy.
Barycentric Coordinate Time (TCB) is based on a reference frame comoving with the barycenter of the Solar System, and has been defined for use in calculating motion of bodies within the Solar System.
[6] Accordingly, for many practical astronomical purposes, a scaled modification of TCB has been defined, called for historical reasons Barycentric Dynamical Time (TDB), with a time unit that evaluates to SI seconds when observed from the Earth's surface, thus assuring that at least for several millennia TDB will remain within 2 milliseconds of Terrestrial Time (TT),[7][8] albeit that the time unit of TDB, if measured by the hypothetical observer described above, at rest in the reference frame and at infinite distance, would be very slightly slower than the SI second (by 1 part in 1/LB = 1 part in 108/1.550519768).
[9] Geocentric Coordinate Time (TCG) is based on a reference frame comoving with the geocenter (the center of the Earth), and is defined in principle for use for calculations concerning phenomena on or in the region of the Earth, such as planetary rotation and satellite motions.
To a much smaller extent than with TCB compared with TDB, but for a corresponding reason, the SI second of TCG when observed from the Earth's surface shows a slight acceleration on the SI seconds realized by Earth-surface-based clocks.
Accordingly, Terrestrial Time (TT) has also been defined as a scaled version of TCG, with the scaling such that on the defined geoid the unit rate is equal to the SI second, albeit that in terms of TCG the SI second of TT is a very little slower (this time by 1 part in 1/LG = 1 part in 1010/6.969290134).