### Assignment 11

1. Text, problem 15.6.
2. Text, problem 15.10. Draw a space-time diagrams showing worldline of observer, worldline of clock, events A and B, worldlines of light to observer, and relevant intervals. One diagram should be the rest frame of the observer, the other, the rest frame of the clock.
3. Text, problem 15.57. Also find the separate energies of the Bi and the He. Before substituting numbers, do it for a general mass M at rest decaying into m1 and m2. Draw a 4-momentum space diagram of the process, showing the mass hyperbolas for m1 and m2.
4. The problems from the gentleman who feels you are being misled by relativity are not very challenging, but I promised you one, so here it is. He writes:
"if large rockets were attached to a 747 and mirrors attached to the wingtips so the pilot can use light pulses and an accurate clock to monitor the distance out to each wingtip as the aircraft approaches the speed of light, time dilations will affect those measurements. As the 747 reaches relativistic speeds, the pilot will begin to measure less and less time passing on the aircraft while each successive light pulse travels out to each wingtip and back, so the pilot will have to conclude that either the wings on that aircraft are contracting or the speed of the light pulses is increasing, and whichever explanation is chosen, this will be a problem for the existing theory."
This is not unlike the situation we (and the book) discussed last week. You can therefore easily find what the error is. In fact, two phrases (parts of a sentence) in the quoted passage are incorrect. Which ones? ("existing theory" means special relativity. Don't worry about the accelerating phase of the aircraft's motion, treat just the case when it is traveling uniformly close to the speed of light.)
5. Text. problem 15.75. Use invariants!