1. Two balloons sit on the physics lecture hall desk, at the left and right edges. The balloon at the left edge bursts, and 2 seconds later the balloon at the right edge bursts. The spacetime interval between these events is A] spacelike B] lightlike C] timelike

2. Two balloons sit on the physics lecture hall desk, at the left and right edges. The balloon at the left edge bursts, and 2 seconds later the balloon at the right edge bursts. In what reference frame are these events simultaneous? A] in a frame moving rightward at V = deskwidth / 2 s B] in a frame moving leftward at V = deskwidth / 2 s C] in no frame

3. Two balloons sit on the physics lecture hall desk, at the left and right edges. The balloon at the left edge bursts, and 2 seconds later the balloon at the right edge bursts. In what reference frame are these events in the same place? A] in a frame moving rightward at V = deskwidth / 2 s B] in a frame moving leftward at V = deskwidth / 2 s C] in no frame

4. There is always some reference frame in which a timelike interval is purely time separated (no spatial separation.) If  x=0, then  t must assume its smallest possible value. The smallest time interval is the “proper time” between two events, i.e. the time between those events in their own frame. There is always some reference frame in which a spacelike interval is purely space separated (simultaneous.)

5. Lightning strikes N & S Sandia Peaks at the same time, according to earthbound observers. For what reference frame would the strike on the N Peak occur first? A] a north-moving frame B] a south-moving frame C] no reference frame For what reference frame would the strikes occur at the same place? C

6. How do the barn doors appear to the pole vaulter? A] the exit door opens before the entrance door closes B] the entrance door opens before the exit door closes C] both doors open and close before he enters the barn D] both doors open and close after he leaves the barn

7. For which reference frame shown is the pole the shortest? A B C (our frame) D E (the pole’s frame)

8. For which reference frame shown is the pole the longest? A B C (our frame) D E (the pole’s frame) Note! The length of the pole is NOT given by a single spacetime interval. Different observers make different observations of the ends. This is subtly different from measuring time, for example, a muon lifetime.

11. To the spaceship captain, what is the spacetime interval?

12. When the accident investigation team finds the shattered, stopped ships clock, what time does it show? A] 3 years B] 4 years C] 5 years D] 6.4 years E] 9 years

13. So: doesn’t this prove that the spaceship really did have the “slow” clock, and the earth and planetary clocks are faster? NO! While the spaceship is in motion, the earth and planetary clocks are mis-synchronized, the planet’s clock being ahead.

14. What happens if the spaceship, instead of crashing, turns around. When he returns to earth, he expects that they will have aged less than himself, as their clocks have been running slowly the whole trip. But according to earth, the spaceship clocks run slowly.

15. Earth sends signals every 4 years. Spaceship receives the first signal after about 10 years, then computes (using c) when the signal was sent. SS finds signal was sent at 5 years. Earth clocks run slow.

16. After the turn, the spaceship receives the 3rd (“12 year”) signal. The spaceship clock shows about 18 years. The spaceman knows light travels at speed c, and calculates when Earth must have sent the 12 year signal. (He has implicitly assumed he has been in an inertial frame!) He finds that the signal was sent more than two years before he left (false!)

17. When the spaceman treats his own frame as inertial, he finds (erroneously) that the signals from earth were sent at bizarre times. This jump in the apparent time makes up for the slowing of the earth’s clocks. Special relativity works for inertial frames.