## C9    Problems and Suggestions

1. Draw an Epstein diagram of an airplane B thundering over the head of A at 3240 km/h.
2. Solve problems 6, 7 and 11 from B7 using Epstein diagrams.
3. How fast does an Einstein train of 260 m proper length have to travel, so that it fits completely into a tunnel of proper length 240 m? In which system are we thinking, when we formulate the question in this way?
4. Positive pions are so fast that their radioactive half-life is quadruple in comparison to the value one measures of slow pions. Determine the speed of these pions a) computationally and b) graphically.
5. The famous problem of the 6 m long car and the 6 m long garage, which is provided with a door in the front and in the back: The car races with 0.8 • c through the garage. At the beginning the front door is opened and the back closed. As soon as the car is completely in the garage the front door closes. How long is the car completely in the garage? Which length does it have in the system of the garage? When, at the latest, does one have to open the back door?
6. Look again at problem 5, but this time from the point of view of the car, over which the strange garage tube is racing. How long is the tube? Why do the people in the system of the garage think they could for a certain time completely lock the car up?
7. 4 space stations, each at rest relative to the others, are to form a large square whose sides have length 1 light second. An observer X flies exactly along the diagonal AC with velocity 0.8 • c.
a) What shape does the square have for X? (calculation and picture)
b) How long does this flight from A to C last from the view of the square inhabitants?
c) The square inhabitants know that for the duration of the flight X measures another value. What is the value, and what is the reason for it from the view of the square inhabitants?
d) X actually measures this value, however his justification for it is completely different. How?
e) The inhabitants of the square synchronized their clocks in A, B, C and D. For X however only 2 of these clocks is synchronized. Which?
f) Which false synchronization do the clocks of A and B exhibit for X?
8. Since the Big Bang about 14 billion years (see cartoon in I2 !) have past. How old is a galaxy today for us, which since the Big Bang has been moving away from our Milky Way with 0.9 • c? And when was the light sent by this galaxy, if it reaches us today? Draw an Epstein diagram!
9. B flies with his space scooter in a straight line past the earth A with 0.8 • c. On his high precision wrist-watch B ascertains 30 minutes after the earth flyby that he passes a space station C. At this point he sends a radiogram to the earth. C and A are at rest relative to each other and their clocks are synchronized.
a) What distance do A and C have for B?
b) What duration do the people in A and C measure for the flight of B over this distance?
c) How many minutes after the flyby of B at A does the radiogram of B arrive at A?
Try using an Epstein diagram!
10. Simple spacetime-diagrams of the Epstein type can be mapped onto spacetime-diagrams of the widely known Minkowski type by means of a certain projection. If you are interested follw this link ! The text is in German, but the illustrations show most of the idea.