Paul Gruner, Elementary geometric representation of the formulas of the special theory of relativity
“ Posing , we immediately find that the coordinates of a point satisfy the requirements of the theory of relativity: With this mode of representation which contains no imaginary quantity, it is easy and simple to graphically demonstrate the different results of the theory of relativity (length contraction, dilatation of clocks, change in mass, energy, volume, etc. ) . ”
Paul Gruner, Graphical representation of the four-dimensional space-time universe
“ To develop the phenomena of the theory of relativity, it is useful to measure time by the path traveled by light , being the speed of light equal to unity. Also it is best to choose a non-orthogonal system of coordinates as "subspace" ”
Paul Gruner, Translation:An elementary geometrical representation of the transformation formulas of the special… (1921)
“ With this easily constructed coordinate systems, length contraction and clock retardation can be seen without further ado. Fig. 1 In the "primed" system (Fig. 2) the world-lines parallel to the time axis provide the "world history" of the point resting in this system. always represents the length of a rod resting in it. Fig. 2 The observers resting in the "unprimed" system can only measure this length , by finding out the location and of the endpoints of at equal clock-indication (thus upon a line parallel to ) ; they find ”
