### Relativistic Time Dilation

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 v/c = Red clock's frame of reference Green clock's frame of reference
In this simulation, two identical light clocks are shown, one green and the other red. The grid spacing is exactly 1 meter. The clocks run by bouncing a photon back and forth, vertically, between two mirrors. The time it takes the photon to go from top to bottom is one "tick". The two clocks have a relative horizontal velocity, that you can vary, which is a substantial fraction of the speed of light. You may view the animation from the reference frame of either clock. Which clock runs slower, due to time dilation?

### Hints

1. Vary the relative speed and see how the "ticking" of the clock(s) changes.
2. Then, view the animation from the other reference frame. What happens? Why?
3. In which reference frame do you measure the "proper time period", Dt0 , of the ticking green clock?
4. In that frame, what do you measure as the time period of the both green and red clocks?
5. In which reference frame do you measure the "proper time period", Dt0 , of the ticking red clock?
6. In that frame, what do you measure as the time period of the both green and red clocks?
7. What is the relativistic formula for the time interval that is dilated?
8. What other change do you note in the moving clock?

### Reference

See Serway and Beichner, Physics For Scientists and Engineers 5th Edition, Section 39.4

Illustration written by Steve Mellema