# Proper Time

In relativity, proper time is the elapsed time between two events as measured by a clock that passes through both events. The proper time depends not only on the events but also on the motion of the clock between the events. 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.

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.

The concept of proper time was introduced by Hermann Minkowski in 1908, and is a feature of Minkowski diagrams.

### Other articles related to "proper time, time":

Proper Time - Examples in General Relativity - Example 4: The Schwarzschild Solution — Time On The Earth
... The Schwarzschild solution has an incremental proper time equation of where t is time as calibrated with a clock distant from and at inertial rest with respect to the Earth, r is a radial ... To demonstrate the use of the proper time relationship, several sub-examples involving the Earth will be used here ... In this case, the Schwarzschild solution proper time equation becomes ...
Synchronous Frame
... the positions of bodies in space while the time coordinate x0 can be measured by clocks with any possible adjustment ... The problem thus arises how one can determine the real distances and time intervals by the values of x0, x1, x2, x3 ... First one must determine the true time (proper time), written by the symbol τ, with a coordinate x0 ...
Gravitational Time Dilation - Important Things To Stress
... According to General Relativity, gravitational time dilation is copresent with the existence of an accelerated reference frame ... observer's perspective corresponds to the local proper time ... Every infinitesimal region of space time may have its own proper time that corresponds to the gravitational time dilation there, where electromagnetic radiation and matter may be equally affected, since they are made ...
Special Relativity (alternative Formulations) - Euclidean Relativity
... The roles of time t and proper time have switched so that proper time takes the role of the coordinate for the 4th spatial dimension ... A universal velocity for all objects in 4D space-time appears from the regular time derivative ... In Wick rotation, time is replaced by, which also leads to a positive definite metric but it maintains proper time as the Lorentz invariant value whereas in Euclidean relativity becomes a coordinate ...
Physical Theories Modified By General Relativity - Classical Mechanics and Special Relativity - Inertia
... is given by the second derivative of position r with respect to time t ... motion is described mathematically as where xa is the position coordinate and τ is proper time ... (In Newtonian mechanics, τ ≡ t, the coordinate time) ...

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