Proper Time

d\tau = \frac{dt}{\gamma} = dt\sqrt{1 - \frac{v^2}{c^2}}

Proper time is the time measured by a clock moving with the object. It is always shorter than coordinate time measured by a stationary observer.

Variables

d\tau

Proper time interval

Coordinate time interval

\gamma

Lorentz factor

unitless

Velocity

m/s

Speed of light

m/s

The proper time is an invariant quantity in special relativity.

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