# Time dilation

Time dilation is a physics concept related to relativity. In Albert Einstein's theories of relativity, there are two types of time dilation:

1. In special relativity, clocks that are moving run slower, according to a stationary observer's clock. For example, if Person A moves faster than Person B, Person A will experience time at a slower rate, and a clock he is carrying will tick slower than the clock person B is carrying.
2. In general relativity, clocks that are near to a strong gravitational field (such as a planet) run slower.

## Time dilation due to relative velocity

The formula for determining time dilation in special relativity is:

$\Delta t' = \frac{\Delta t}{\sqrt{1-v^2/c^2}} \,$

where

$\Delta t \,$ is the time interval for an observer (e.g. ticks on his clock) – this is known as the proper time,
$\Delta t' \,$ is the time interval for the person moving with velocity v with respect to the observer,
$v \,$ is the relative velocity between the observer and the moving clock,
$c \,$ is the speed of light.

It could also be written as:

$\Delta t' = \gamma \Delta t \,$

where

$\gamma = \frac{1}{\sqrt{1-v^2/c^2}} \,$ is the Lorentz factor.

A simple summary is that more time is measured on the clock at rest than the moving clock; therefore, the moving clock is "running slow".

When both clocks are not moving, relative to each other, the two times measured are the same. This can be proven mathematically by

$\Delta t' = \frac{\Delta t}{\sqrt{1-0/c^2}} = {\Delta t} \,$

For example: In a spaceship moving at 99% of the speed of light, a year passes. How much time will pass on earth?

$v=0.99c \,$
$\Delta t=1\,$ year
$\Delta t'=? \,$

Substituting into :$\Delta t' = \frac{\Delta t}{\sqrt{1-v^2/c^2}} \,$

$\Delta t'=\frac{1}{\sqrt{1-(.99c)^{2}/c^{2}}}=\frac{1}{\sqrt{1-\frac{(.99)^{2}(c)^{2}}{c^{2}}}}=\frac{1}{\sqrt{1-(.99)^{2}}}=\frac{1}{\sqrt{1-0.9801}}=\frac{1}{\sqrt{0.0199}}=7.08881205$years

So approximately 7.09 years will pass on earth, for each year in the spaceship.

In ordinary life today, where people move at speeds much less than the speed of light, the speeds are not great enough to produce any detectable time dilation effects. Such vanishingly small effects can be safely ignored. It is only when an object approaches speeds on the order of 30,000 km/s (10% the speed of light) that time dilation becomes important.

However, there are practical uses of time dilation. One example is with regard to keeping the clocks on GPS satellites accurate. Without accounting for time dilation, GPS would be useless.