## K11 STR and Minkowski Diagrams

Epstein diagrams are not used in any of the STR introductions known to me - except of course in the original [15] by Epstein himself. Most books use Minkowski diagrams when graphically displaying the situation of two inertial frames moving relative to each other. These Minkowski diagrams obviously have certain advantages, but I think Epstein diagrams are more suitable for a first and even a second exposure to the STR. Epstein diagrams are entirely indispensable if additionally one wishes to get a concrete feel for the GTR. That is the main reason I have written this book.

I will highlight here only the significant differences between the Minkowski diagrams and Epstein diagrams and leave the details to the numerous reference books which include an introduction to the use of Minkowski diagrams.

Here, red moves with v = 0.5 • c along black’s x-axis (note the helping green dashed line). The Minkowski diagram generally uses tan(φ) = v / c, where we have sin(φ) = v / c in the Epstein diagram. The event E takes place at point 2 and at time 1.5 for black. Red assigns event E approximately the coordinates x’ ≈ 1.45 and t' ≈ 0.58 (the dashed red lines are parallel to the red coordinate axes). The tick marks are shown on the light gray calibration hyperbolas y^{2} = 1 + x^{2} and x^{2} = 1 + y^{2} respectively. Light particles move in the inertial frame either perpendicular or parallel to the blue angle bisector. In Epstein diagrams, on the other hand, light particles move in each frame perpendicular to its time-axis.

Almost all introductions to the STR which are not limited to a qualitative description of the phenomena also present Minkowski diagrams. In our bibliography examples are [14], [19], [25] and [26]. But the most beautiful introduction to Minkowski-Diagrams is given by Sander Bais in [44] !

As an addendum to the second edition of his book [15] Epstein presents a method to convert simple Epstein-Diagrams into Minkowski-Diagrams and vice versa. Alfred Hepp and Martin Gubler have worked this out. In their online-paper they present color-drawings of this process and give a further hint to the spacetime-diagrams of the Loedel type, which combine some of the advantages of the diagrams of the Minkowski and Epstein type.