$E = \gamma m c^{2}$

where $\gamma$ is the Lorentz factor. Then the period of P is given by

$\begin{align} \hat{\tau} \, = \frac{h}{E } = \frac{ h }{ \gamma m c^{2} } \end{align}$

If P is isolated and described within an ideal frame of reference, then the elapsed time between some ordered pair of events is related to the period as

$\Delta t = ( \, f-i\, ) \, \hat{\tau}$

where $i$ and $f$ are initial and final event indices. So in terms of the mass

$\begin{align} \Delta t = \frac{ h \, (\, f-i \, ) }{ \gamma m c^{2} } \end{align}$

If P is a clock, this is the elapsed time that it would indicate between events. For comparison, set $\gamma = 1$ to define

$\begin{align} \Delta t ^{\ast} \equiv \frac{ h \, (\, f-i \, ) }{ m c^{2} } \end{align}$

This is the elapsed time that would be recorded if P was at rest. These two quantities are related as

$\begin{align} \Delta t = \frac{ \Delta t ^{\ast} }{ \gamma } \end{align}$

Since the Lorentz factor for a particle in motion is always greater than one, a moving particle always experiences less elapsed time than a stationary particle. This effect is called **time dilation**.

Related WikiMechanics articles.