About length contraction Moving bodies are short

How can we measure the length of a moving body?

If (x 1 ;t) and (x 2 ;t) are the space-time coordinates of such events, then the length of the body is given by = |x 2 – x 1 | =  x What’s the relationship with the length of the body according to a reference frame in which the body is at rest (this length being called “proper length”).

A simple answer can be found by applying Lorentz’s transformation to the coordinates of the two events. From:x’ =  (x – V  t)we get:  x’ =  (  x – V  t). As  t = 0 and  x =, we finally get: where a contraction along the direction of motion is found, being  > 1.

Another way to get this result

What’s the relationship with the body’s length according to a reference frame in which the body is at rest?

 t’ is related to  t 0 by the time dilation law  t’ =  t 0 So, again, we get: