Time Dilation
Time dilation is a physics concept about changes in the passage of time, as related to relativity. Special relativity states that time can pass at different rates in different reference frames. The time depends on the velocity of one reference frame relative to another. In one reference frame, two events (for example, two ticks of a clock) will occur at the same position. In this reference frame, the time between the events is called one-position time or proper time, and is labeled Δt0. In another reference frame, an observer will see the two events happen in different positions. In the observer's reference frame, the time between events is called two-position time or observer time, and is labeled Δt. The observer time is always larger than the proper time. This effect is called time dilation. Both Δt0 and Δt are measured in seconds (s).
\[observed \: time=\frac{proper\: time}{\sqrt{1-\left ( \frac{velocity}{speed\: of\: light} \right )^{2}}} \]
\[\Delta t=\frac{\Delta t_{0}}{\sqrt{1-\left ( \frac{v}{c} \right )^{2}}} \]
Δt = the observer time, or two-position time (s)
Δt0 = the proper time, or one-position time (s)
v = velocity (m/s)
c = speed of light (3.0 x 108 m/s)
let Δt = y, Δt0=x
