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A fuller explanation of the concept of coordinate time arises from its relations 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.
is the coordinate time between the events for an observer at an arbitrarily large distance from the massive object (this assumes the far-away observer is using Schwarzschild coordinates, a coordinate system where a clock at infinite distance from the massive sphere would tick at one second per second of coordinate time, while closer clocks ...
The blue numbers indicate the coordinate time T in the inertial frame of the stay-at-home-twin, the red numbers the proper time τ of the rocket-twin, and "a" is the proper acceleration. The thin red lines represent lines of simultaneity in terms of the different momentary inertial frames of the rocket-twin.
In relativity, proper time (from Latin, meaning own time) along a timelike world line is defined as the time as measured by a clock following that line. The proper time interval between two events on a world line is the change in proper time, which is independent of coordinates, and is a Lorentz scalar. [1]
Multiple independent timeframes, in which time passes at different rates, have long been a feature of stories. [15] Fantasy writers such as J. R. R. Tolkien and C. S. Lewis have made use of these and other multiple time dimensions, such as those proposed by Dunne, in some of their most well-known stories. [15]
The coordinate system would collapse, in concordance with the fact that due to time dilation, time would effectively stop passing for them. These considerations show that the speed of light as a limit is a consequence of the properties of spacetime, and not of the properties of objects such as technologically imperfect space ships.
The modern understanding of time is based on Einstein's theory of relativity, in which rates of time run differently depending on relative motion, and space and time are merged into spacetime, where we live on a world line rather than a timeline. In this view time is a coordinate.
TT differs from Geocentric Coordinate Time (TCG) by a constant rate. Formally it is defined by the equation = +, where TT and TCG are linear counts of SI seconds in Terrestrial Time and Geocentric Coordinate Time respectively, is the constant difference in the rates of the two time scales, and is a constant to resolve the epochs (see below).