1 Length Measurement of a Moving Rod by a Single Observer: Length Contraction, Length Expansion and no Distortion. Bernhard Rothenstein and Marius Costache brothenstein@gmail.com Abstract. We extend the results presented by Weinstein [1] concerning the measurement of the length of a moving rod by a single observer, without making assumptions concerning the distance between the moving rod and the observer who measures its length. 1. Introduction Weinstein [1] considers a rod of proper length L 0 at rest in the inertial reference frame I’. It is parallel to the x’ axis, positioned apart from it at a distance h (Figure 1). An observer 0 (0,0) R′ located at the origin O’ and at rest relative to I’ measures its proper length L 0 . Let 2’ be the leading edge of rod characterized by the space coordinates ( 2 2 2 2 2 2 ( cos , sin ) x r y r θ θ ′ ′ ′ ′ ′ ′ = = and 1’ its trailing end characterized by its space coordinates ( 1 1 1 1 1 1 cos , sin x r y r θ θ ′ ′ ′ ′ ′ ′ = = ), using Cartesian and polar coordinates as well as shown in Figure 1. Observer 0 R′ located at the origin O’ of I’ detects the light signals form both ends at a single time t’=0. The events associated with the non-simultaneous emissions of the light signals from the two ends of the rod are ( ) 1 1 1 1 1 cos ; sin ; / r r r c θ θ ′ ′ ′ ′ ′ and ( ) 2 2 2 2 2 cos ; sin ; / r r r c θ θ ′ ′ ′ ′ ′ . The receptions of the two signals, at O’, are characterized by zero space and time coordinates. Consider the same experiment from the inertial reference frame I in standard configuration with I’. The corresponding axes of the two frames are parallel to each other, I’ moves with constant velocity V relative to I in the positive direction of the permanently overlapped x,x’ axes and at the origin of time the origins O and O’ are located at the same point in space. What we compare are the length L of the rod measured in I and its proper length L 0 measured in I’. The results presented by Weinstein [1] are the result of some assumptions concerning how big or how small is the length of the position vector 1 r ′ . The purpose of our paper is to present results free of such assumptions.