## C6 Our Sample Problem as Epstein Diagram

We want to present the sample problem, which we solved at the end of

**B6**as an Epstein diagram. To keep everything as simple and clear as possible we will draw two diagrams: One from the point of view of black with a pipe at rest and the other from ‘the red’ point of view of the particle, which sees the pipe racing by.

First to the angle between the two time-axes: The sine value of v/c = 0.8 need not be converted into an angle. We need only count the little squares on our graph paper and select 20 squares for the circle radius, e.g.: 16/20 = 8/10 provides the correct angle (note the green auxiliary lines).

While the particle moves in space-time from O to B, the pipe ages according to the same segment, that is, OA = CD. The clocks at the two tube ends are synchronized for black: O and C (later A and D) project on the same point of the black time-axis. Reaching point B the particle leaves the pipe. The units are selected as follows: 3 squares correspond spatially to a distance of 3 m and to an interval of 10 ns on the time-axis! Importantly: One is free to select only one of the two scales, the other then being fixed by the speed of light. We read: The transit lasts for black OB = OA = 50 ns, while only OE = 30 ns applies for red.

That is the view of black. Now we consider the point of view of red.

For red the pipe OC moves through space-time to AD. This requires a time of OA = CD = OB = 30 ns. Red measures the length of the pipe to be OE = FO = OC • cos(φ) = OC • 0.6 = 7.2 m. Red knows that the clock of black indicates 50 ns at point D. Red says nevertheless that the whole transit required the time OG = FA = OA • cos(φ) = OB • cos(φ) = 30 ns • 0.6 = 18 ns for black. Black measures 50 ns, because its rear clock (the one that moves on segment CD) exhibits a constant advance of EC = GD = 32 ns over the other one moving on OA. This is the desynchronization of black's clocks as stated by red.

Carefully compare this presentation with

**B6**and convince yourself that we can read all results correctly from the diagrams without the need to do any calculations!

You can easily practice using Epstein diagrams: download here a program appropriate for your operating system!