# Formula: Time Dilation Time    Proper time    Relative velocity

## Time

Unit
This is the time interval between two events that passes on the moving clock from the point of view of an observer at rest. Since the gamma factor $$\gamma$$ is greater than 1: $$\gamma ~=~ \frac{1}{ \sqrt{1 ~-~ \frac{v^2}{c^2}} } > 1$$ $$\Delta t'$$ is greater than $$\Delta t$$. Consequently, a stationary observer sees that more time $$\Delta t'$$ has elapsed on the moving clock than on his stationary clock, $$\Delta t$$.

If the moving clock moves with velocity $$v = 2 \cdot 10^8 \, \frac{\text m}{\text s}$$ relative to the stationary observer, the gamma factor is: $\gamma ~=~ \frac{1}{ \sqrt{1 ~-~ \frac{(2 \cdot 10^8 \, \frac{\text m}{\text s})^2}{(2 \cdot 10^8 \, \frac{\text m}{\text s})^2}} } ~=~ 1.7$ Now, if time $$\Delta t = 1 \, \text{s}$$ has passed on the clock of an observer at rest, more time has passed on the clock in motion: $\Delta t' ~=~ \gamma \, \Delta t ~=~ 1.7 \,\text{s}$

## Proper time

Unit
The proper time is the time interval between two events measured by a stationary observer on his stationary (unmoving) clock. Since $$\Delta t$$ is smaller than $$\Delta t'$$, less time passes on the clock at rest than on the clock moving relative to it.

## Relative velocity

Unit
This is the velocity of the moving clock, from the point of view of an observer at rest. The relative velocity $$v$$ is always smaller than the speed of light $$c$$.

The greater the velocity $$v$$ of the moving clock, the greater the amount of time $$\Delta t'$$ that passes on the moving clock, as seen by an observer at rest.

## Speed of light

Unit
Speed of light is a physical constant and indicates how fast light travels in empty space (vacuum). It has the following exact value in vacuum: $$c ~=~ 299 \, 792 \, 458 \, \frac{ \mathrm{m} }{ \mathrm{s} }$$

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