Originally Posted by

**RZhang**
Hello all,

I have a question in deriving "time dilation" using the length contraction. Can anyone help me to find where the problem is?

Suppose the time is measured using a light traveling along a stick which is moving with a speed v with respect of the ground. The time interval in the reference frame on the stick is: t0 = L0/c, where L0 is the length of the stick measured in the reference frame of the stick, and c is the speed of the light.

Now, a person on the ground sees the stick with with length L, where L = v L0. Then the person on the ground sees the time interval for the light to travel along the stick is, t = L/c. Therefore, t = v t0. This is different from the Einstein's equation, t = t0/v. However, I couldn't find the logic problem in the above derivation. Anyone can explain it?

Thanks in advance!

John