timeproper

Timeproper is a term used in some discussions to denote the invariant time experienced along the worldline of a physical system, closely related to proper time. It is not a standard term in physics, but appears in educational texts and online glossaries as an alternative naming for proper time, emphasizing the perspective of the clock or observer along the path.

In physics, timeproper refers to the elapsed time measured by a clock carried by an object as it moves through spacetime. In special relativity, for an object with coordinate time t and velocity v relative to an inertial frame, the timeproper elapsed between events along the object's path is Δτ = ∫ sqrt(1 − v^2(t)/c^2) dt. In general relativity, along a worldline xμ(λ), timeproper is given by Δτ = ∫ sqrt(gμν dxμ/dλ dxν/dλ) dλ, where gμν is the spacetime metric. The timeproper (like proper time) is invariant under coordinate transformations and represents the actual time a clock would register along that path.

In usage, timeproper is meant to stress the clock-based duration experienced by the system as opposed to external coordinate time, and it plays a central role in discussions of time dilation and the twin paradox. Because it is not universally standardized, some authors prefer the conventional term “proper time,” using timeproper mainly in pedagogical or clarifying contexts.

See also: proper time, worldline, spacetime interval, time dilation.