The explanation of how we get to the equation γ = 1 / √1-v²/c² is through a diagram where light bounces back and forth between two mirrors. While the light is bouncing back and forth, a clock is ticking.

**the moving clock travelling past you at speed v ticks more slowly than the observer’s wristwatch clock.**

- The motion of the light clock (travelling at the same speed as the light and mirrors) does not affect the speed of light.The speed of light is a constant.
- The horizontal distance moved due to speed v is x = vt.

c²t² = c²τ² = v²t²

We can arrange that to center the equation around τ.

τ² = t²(c² – v²) / c²

Where τ is the wristwatch time and t is the observed time. We can use the above equation to show that t = γτ where γ = 1 / √1-v²/c²:

- τ² = t²(c² – v²) / c²
- τ² = (t²c² – t²v²) / c²
- τ² = t²- t²v² / c²
- τ² = t²(1- v²/c²)
**τ = t √ (1- v²/c²)**- If t = γτ, the γ = 1 / √1-v²/c².
- As v = 0, γ =1. As v = c, γ = infinity

## Summary

- The speed of light is the constant in the universe. Time slows down as you approach the speed of light.
- We can use the equation
**τ = t √ (1- v²/c²)**to work out how time dilates. The wristwatch time measure the time of the moving object relative to wristwatch. The observed time is the time observed by a clock of the same speed as the moving object. - As v = 0, γ =1. As v = c, γ = infinity