proper time

Proper time is time measured when the clock is at rest relative to the observer. The distinction between proper time and the measured time is necessary because of the effects of time dilation, which is outlined in Einstein's theory of special relativity. To be more precise, proper time is the time measured between two events which happen in the same location. Suppose there is another frame of reference, which is moving in velocity v, so the events are occurring in different places according to it, then the relation between the time measured between the two events in the resting frame and the moving frame is

\tau = (\Delta t_{proper}) = (\Delta t_{relative}) \cdot \sqrt{1-v^2/c^2}

Since

\sqrt{1-v^2/c^2} \le 1

, it is seen that

(\Delta t_{proper}) \le (\Delta t_{relative})

. In other words, the proper time is the shortest time difference that could be measured between two events. From this property comes the law of interval invariance in special relativity. The interval, defined as

\tau ^2 = {(\Delta t)}^2  - {(\Delta x)}^2

is invariant size and stays the same in all inertial frames of reference. If t is plotted against x, the interval forms a hyperbola which intersect the t axis at

( 0 , \tau )

. Noting that led to the development of Minkowski space and four-vectors, which described the effects disscused above (and also the Lorentz transformation) as mathematical vector operations on an hyperbolic geometry four-dimensional vector space. In Minkowski space, the invariant interval is the norm of the "event" four-vector.

Proper Time

See also