In the light clock experiment of the time dilation theory, why does the light travel in triangles for the light clock in motion when the outside observer is viewing it. I'm not able to understand why does the light travel a longer distance for the light clock in motion as compared to the stationery light clock. The distance between the mirrors in both the light clock is the same. The only difference is that one is in motion and the other is not. If the distance between the mirrors in both the light clocks is the same, then why does light have to travel in triangles for the light clock in motion when the outside observer is viewing it. Why can't it travel straight as it does in the stationery light clock. Please explain. I'm unable to understand the concept of time dilation.
1 Answers
Just like in Newtonian mechanics, the components of motion are independent.
Let's move away from special relativity and work with a nonrelativistic example. Imagine Alice is on a train moving past Bob. Alice throws a ball straight up in the air and catches it. She sees the ball follow a straight line path straight up then straight down. The displacement of the ball in her reference frame is $(x,y)=(0,v_0t-\frac{1}{2}gt^2)$. Bob sees the train moving with speed $v_t$ and everything else moving with the train. So he observers the ball follow a parabolic path $(x,y)=(v_tt,v_0t-\frac{1}{2}gt^2)$. Bob doesn't see Alice catch the ball at $x=0$, he sees her catch it at $x=\frac{2v_0v_t}{g}$.
Now, going back to the path of light bouncing between mirrors. Just like with the ball, the light is moving straight up and down in the frame of the mirrors, but the mirrors themselves are moving, adding their sideways motion to the light. This imparts a sideways velocity to the light. In Newtonian physics, this would combine with the vertical velocity, $c$ of the light to create a total speed $\sqrt{c^2+v^2}$. Instead, in special relativity, the speed of light is fixed at $c$, making the vertical component of the velocity $\sqrt{c^2-v^2}$. It is because of this decreased vertical component of the speed of light that time dilation occurs.
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