Good evening, As an effort for trying to understand Lorentz transformations, I'm trying to use them to derive the "length contraction" result. Consider two reference frames, O (non-primed) and O' (primed), moving with respect to each other with a velocity v. Consider them to be under http://en.wikipedia.org/wiki/Lorent...rmation_for_frames_in_standard_configuration". Choosing the non-primed reference frame, the Lorentz transformations for position (x-axis) and time (t-axis) will be: x = γ(x' + vt') t = γ(t' + vx'/c²) The inverse transformations will be: x' = γ(x - vt) t' = γ(t - vx/c²) Where γ is the Lorentz factor and c is the speed of light in vacuum. Now, I will try to derive the length contraction result. Suppose I have a thin rod moving along with the primed reference frame. One end of the object is at x'1 x'2. Then, the length of the object in the primed reference frame is L' = x'2 - x'1. To find the corresponding coordinates of the ends of the rod in the non-primed frame (x1 and x2), I will use the inverse transformation for position: x1 = γ(x'1 + vt') x2 = γ(x'2 + vt') The length of the rod as measured by the non-primed frame will be: x2 - x1 = γ(x'2 + vt') - γ(x'1 + vt') x2 - x1 = γ(x'2 - x'1) L = γL' This is wrong. I should have obtained L' = γL, because the non-primed frame sees the rod shorter than the primed frame does. In other words, the length measured by the non-primed frame should be shorter than the proper length. What am I thinking wrong? Thank you in advance.