**Time dilation**

The fact that the speed of light is the same
in all reference frames has the consequence that moving clocks run slow. This means that
if two events occur at the same place, such as the ticks of a clock, a moving observer
will measure the time between the events to be longer. The relation between a time
measured by a stationary observer * t_{0}* to the time

The gamma factor appears often in
relativity. It is always greater than unity, but very close to it for
small velocities. (If the velocity were greater than
* c*, gamma would be undefined; but that never
happens, as we will see shortly.)

This result can be shown to result from the two fundamental
postulates by considering a *light clock*. This imaginary clock would work by
ticking every time a light pulse reflected back to the lower mirror as shown below.

The time between ticks and tocks for the stationary clock is:

One can now view the same clock as it moves past with
velocity * v*.

The time between ticks and tocks is again given by the
distance traveled by the red pulse divided by * c*.

Solving the above equation for * t*
in terms of

Thus the moving observer sees a longer time by the
factor **g** defined
above.

**We derived the time dilation effect using a very simple clock; but
the result applies equally to all clocks, including complex ones such as decaying
radioactive particles or even biological systems. It is therefore better to think
of the effect as an unexpected truth about space and time, rather than as a property
of the clock. In any case, the effect is NOT caused by forces operating on the
clock---since as you know, NO force is required to keep an object moving at constant
velocity.**