Problem : To measure length of a scale Rest frame : The frame w.r.t. which scale is at rest Moving frame : The frame w.r.t. which the scale is moving with speed v along +ve x-axis In rest frame ,the positions of the two ends of the scale are (measured simultaneously ) x1 and x2. So length L = x2 -x1 and t1 =t2=t In moving frame, the positions of the two ends of the scale are (measured simultaneously ) x'1 and x'2. So length L' = x'2 -x'1 and t'1 =t'2=t Now, x'2 -x'1 = γ ( x2 -x1 - v(t2 - t1) ) ⇒ L' = γ L as t2 = t1 and x2 -x1 = γ ( x'2 -x'1 - v(t'2 - t'1) ) ⇒ L= γ L' as t'2 = t'1 What is wrong here? I am asking this as I often do this mistake. I think, What I am doing here is I am measuring (x2 ,x1),and (x'2 ,x'1) simultaneously. So, I am having four events. What I should do: I am supposed to have only two events for measuring the length and these two events should be such that these are simultaneous in the moving frame while non - simultaneous in the rest frame. Let's denote the two events as A and B. Now, the coordinates of A and B are in rest frame [(t2,x2 ),(t1,x1)] respectively and the coordinates of A and B are in moving frame [(t'2,x'2),(t'1,x'1)] respectively and t'1 =t'2 Now, x'2 -x'1 = γ ( x2 -x1 - v(t2 - t1) ) Now, expressing t2 and t1in prime coordinates using Lorentz transformation and doing further calculation gives L= γ L' and x2 -x1 = γ ( x'2 -x'1 - v(t'2 - t'1) ) ⇒ L= γ L' as t'2 = t'1 Is this correct?