Proper time

Proper time is the time elapsed along a particular path through spacetime, measured by a clock following that path. Its value is invariant under changes of coordinates.

Spacetime interval: A coordinate-invariant measure of separation between events in spacetime. Proper time is obtained from the spacetime interval along a timelike path.
Special relativity: A theory of space, time, and motion in inertial frames, based on invariant light speed. Proper time first appears as an invariant measure of elapsed time in this theory.
Twin paradox: A special-relativistic scenario in which twins following different paths reunite at different ages. The age difference is the difference in proper time accumulated along their world lines.
Coordinate system: A scheme assigning numerical coordinates to points in a space or spacetime. Coordinates describe a path, but changing them does not change its proper time.
World line: A path through spacetime representing an object's history. A clock's proper time accumulates along its world line.
General relativity: A theory of gravitation in which matter and energy shape spacetime geometry. Its curved spacetime metric extends proper-time calculations to gravity.
Gravitational time dilation: The difference in clock rates associated with different gravitational potentials or spacetime locations. Proper time quantifies the readings of clocks at distinct positions in a gravitational field.
Coordinate transformation: A change in the numerical coordinates used to represent points or events. It alters coordinate-time descriptions while leaving proper time invariant.
Metric tensor: A mathematical object that defines distances, angles, and causal structure on a manifold. The spacetime metric determines the interval from which proper time is calculated.
Coordinate time: A time coordinate assigned to events within a chosen coordinate system. Unlike proper time, coordinate time depends on the spacetime coordinates chosen.

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