# Why does the thought experiment of a photon bouncing of a mirror imply anything for other objects?

Okay, so I am reading a book, "The Elegant Universe" by Brian Greene, which talks about motion and its effect on time.

Greene makes the point that time changes with motion by saying that if you have two mirrors and bounce a photon off of them it will have bounced off them very very often during a second. But, if you have the mirrors moving you must shoot the photon at an angle so it will be able to hit the mirrors and not miss and fly off. Since you are shooting diagonally it takes the photon more time to hit each mirror. So it's basically saying that time changes the closer you come to light speed.

Why? Why does this hold true for all matter? How does bouncing a photon around prove anything?

• what the photon and the mirrors do, don't have any effect on other objects not connected with the mirrors. Besides, if you want to assess if there is any effect e.g. on other activities that happen in the house, then you should judge the movement of the photon and the mirrors in the frame of coordinates of the house. – Sofia Feb 22 '15 at 17:16

We bounce a photon around to create a clock. It is postulated that the speed of light is the same in all frames. In the rest frame, the time it takes for light to make a round trip is $$\Delta t=\frac{2L}{c}$$ In the moving frame we have a (relative) velocity $u$. Using a little geometry, we find that $$c\Delta t'=2\sqrt{(\tfrac{1}{2}u\Delta t')^2+L^2}$$ You can easily solve this to obtain $$\Delta t'=\gamma\Delta t,\quad \gamma=(1-u^2/c^2)^{-1/2}$$ which is the basic equation for time dilation.