What is proper time in special relativity?

In special relativity, what is proper time? Besides giving the correct definition, can you also give an example to explain it better. Thanks|||The time interval recorded by a clock attached to the observed body is called the ' Proper time '


Or


It is a time interval measured by a clock which at rest relative to the observer.





Ex:- Suppose you are sitting in a stationary train. A terrorist on the plot form fires two shots. You measure the time interval between the two shots by your watch. You are measuring the proper time.


The same time interval, if it is measured by your friend sitting in a different train which is chugging off with a velocity V relative to the terrorist, will be different. It is called non-proper time interval. (The watches must be exactly similar in all respects)


The clock (watch) moving with a velocity V slows down by a factor √(1 - V^2 / C^2 ) or the time interval increases by the same factor.


The difference in the two measurements becomes observable only when V is comparable to C (velocity of light)





For more details search the net for "Proper Time"





I hope it helps.|||In essence the proper time is the on-board or local - at the event - time.





'... In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. It depends not only on the events but also on the motion of the clock between the events. An accelerated clock will measure a proper time between two events that is shorter than the coordinate time measured by a non-accelerated (inertial) clock between the same events. The twin paradox is an example of this effect.








In terms of four-dimensional spacetime, proper time is analogous to arc length in three-dimensional (Euclidean) space. By convention, proper time is usually represented by the Greek letter τ (tau) to distinguish it from coordinate time represented by t or T.





By contrast, coordinate time is the time between two events as measured by a distant 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. A Euclidean geometrical analogy is that coordinate time is like distance measured with a straight vertical ruler, whereas proper time is like distance measured with a tape measure. If the tape measure is taut and vertical it measures the same as the ruler, but if the tape measure is not taut, or taut but not vertical, it will not measure the same as the ruler.





The concept of proper time was introduced by Hermann Minkowski in 1908. ...( 1 )'





example: - time dilation for relativistic velocity of travel 'v' with on-board elapsed proper-time τ and earth based clock coordinate time t.





t(Earth) = τ(traveller)


..............._________


...............√(1 - (v/c)²)