Editing Proper time (section)

{{short description|Elapsed time between two events as measured by a clock that passes through both events}}
In [[theory of relativity|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 [[event (relativity)|event]]s on a world line is the change in proper time, which is independent of coordinates, and is a [[Lorentz scalar]].<ref>{{harvnb|Zwiebach|2004|p=25}}</ref> The interval is the quantity of interest, since proper time itself is fixed only up to an arbitrary additive constant, namely the setting of the clock at some event along the world line.

The proper time interval between two events depends not only on the events, but also the world line connecting them, and hence on the motion of the clock between the events. It is expressed as an integral over the world line (analogous to [[arc length]] in [[Euclidean space]]). An accelerated clock will measure a smaller elapsed time between two events than that measured by a non-accelerated ([[inertial]]) clock between the same two events. The [[twin paradox]] is an example of this effect.<ref>{{cite book |title=Foundations of Modern Cosmology |edition=illustrated |first1=John F. |last1=Hawley |first2=J Katherine A. |last2=Holcomb |publisher=Oxford University Press |year=2005 |isbn=978-0-19-853096-1 |page=204 |url=https://books.google.com/books?id=s5MUDAAAQBAJ}} [https://books.google.com/books?id=s5MUDAAAQBAJ&pg=PA204 Extract of page 204]</ref>

[[Image:Proper and coordinate time.png|thumb|The dark blue vertical line represents an inertial observer measuring a coordinate time interval ''t'' between events ''E''<sub>1</sub> and ''E''<sub>2</sub>. The red curve represents a clock measuring its proper time interval ''τ'' between the same two events.]]

By convention, proper time is usually represented by the Greek letter ''τ'' ([[tau]]) to distinguish it from [[coordinate time]] represented by ''t''. Coordinate time is the time between two events as measured by an observer using that observer's own method of assigning a time to an event. In the special case of an inertial observer in [[special relativity]], the time is measured using the observer's clock and the observer's definition of simultaneity.

The concept of proper time was introduced by [[Hermann Minkowski]] in 1908,<ref>{{harvnb|Minkowski|1908|pp=53–111}}</ref> and is an important feature of [[Minkowski diagram]]s.