Time Dilation
 Kain Kebat, Iban people. Sarawak, Upper Rajah River, early 20th century, 39 x 79 cm. The unusually small size and simple rusa and tangkong motifs suggest this was a girl's bidang. From the Teo Family collection, Kuching. Photograph by D Dunlop.
This article expresses ideas from theory of special relativity. Let P be a material particle, and consider that it may be a clock in motion. Describe P using $E$ its mechanical energy and $m$ the rest mass which are related as

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

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.

 Next step: cause and effect.

Related WikiMechanics articles.

page revision: 152, last edited: 12 Aug 2017 10:16