Summary Assignment for Chapter Three Name:______Key_________

In this experiment Dean sends a light flash from the front of the bus to the back of the bus where Chuck is located. The bus moves at 0.6 ft/ns, just like the bus in the experiments described in detail in Chapter Three. This experiment begins when Dean is adjacent to Bev and launches the light flash toward Chuck. As usual, the start of the experiment is defined to be at the point where X_bus = X_Earth = 0 and T_bus = T_Earth = 0. The experiment ends when the flash reaches Chuck who is adjacent to Anne at that instant.

The data collected by Anne, Bev, Chuck, and Dean for this experiment are analogous to the data collected in the Chapter Three experiment. The goal is to draw two spacetime diagrams, one from the perspective of Anne and Bev and the other from the perspective of Chuck and Dean.

Since Chuck and Dean are doing the experiment, it is easier to start with their spacetime diagram. Use the graph paper labeled Chuck and Dean for this spacetime diagram.

1. When the experiment begins what is the value of X_bus for Dean? X_bus = 0

When the experiment begins what is the value of X_bus for Chuck? X_bus = -100 feet

2. Draw their worldlines on the Chuck and Dean Spacetime Diagram.

3. Label the spacetime point where the experiment begins as A.

4. Use point A to draw the worldlines of the laser flash and Bev.

5. Label the point where the flash reaches Chuck as B.

6. Use point B to draw Anne’s worldline.

7. According to Chuck and Dean, what is X_bus for Anne at the start of the experiment?

X_bus = -40 feet

Now it is time to draw the spacetime diagram from the perspective of Anne and Bev. Use the graph paper labeled Anne and Bev to draw this spacetime diagram.

8. When the experiment begins, what is X_Earth for Bev? X_Earth = 0

9. Label the point where the experiment begins as A.

10. Use point A to draw Dean’s worldline.

11. According to Bev, when the experiment begins, T_Earth = 0, where is Chuck located at that instant? X_Earth = -80 feet (Remember Chuck is at the back of the bus and according to Anne and Bev, how long is the bus when it is moving at 0.6 ft/ns?)

12. Use Chuck’s location at T_Earth = 0 to draw his worldline.

13. Now draw the worldline of the laser flash as it travels from Dean to Chuck.

14. Label the point where the flash reaches Chuck as B.

15. Use point B to draw Anne’s worldline.

16. Use the spacetime diagram to find X_Earth for Anne. X_Earth = -50 feet

Now we can use the two spacetime diagrams to check the conclusions that Anne, Bev, Chuck, and Dean reached about the behavior of space and time in Chapter Three.

17. According to Anne and Bev, how far apart are they standing during this experiment?

50 feet

18. According to Chuck and Dean, how far apart are Anne and Bev standing during this experiment? 40 feet

19. Explain whether or not your answer to questions 17 and 18 are consistent with the conclusions reached by Anne, Bev, Chuck, and Dean in Chapter Three?

Yes, it is consistent because C & D measure the proper distance between Anne and Bev as 80% of its value according to A & B. This is the expected shrinkage factor for a bus moving at 0.6 ft/ns.

20. Bev’s watch read zero at the start of the experiment when she was adjacent to Dean. When Bev and Chuck were adjacent, they compared times on their respective watches.

What was the time on Bev’s watch? T_Bev = 400/3 = 133 1/3 ns

What was the time on Chuck’s watch? T_Chuck = 500/3 = 166 2/3 ns

21. Explain whether the times in question 20 are consistent with the conclusions reached by Anne, Bev, Chuck, and Dean in Chapter Three?

Yes they are consistent. Bev’s watch traveled from Dean to Chuck. The “moving” watch ought to tick off less time than the two stationary watches with which it is being compared. For a relative speed of 0.6 ft/ns, the moving watch should tick off 80% as much time as T_Chuck – T_Dean, 500/3 – 0, and 80% of 500/3 is 400/3!

22. During this experiment, Chuck was adjacent to Anne and then at a later time was adjacent to Bev. When he was adjacent to Anne his, watch read T_Chuck,1 = 100 ns. At that same instant, Anne’s watch read T_Anne = 50 ns.

23. When Chuck was adjacent to Bev, his watch read T_Chuck,2 = 500/3 ns. At that same instant, Bev’s watch read T_Bev = 400/3 ns.

24. According to Chuck, 500/3 – 100 = 200/3 nanoseconds ticked off his watch during the time interval between Anne and Bev passing him by.

25. According to Anne and Bev, Chuck’s trip took 400/3 – 50 = 250/3 nanoseconds.

26. Explain whether or not your answers to questions 24 and 25 are consistent with the conclusions reached by Anne, Bev, Chuck, and Dean.

Yes they are consistent. In this case it is Chuck’s single watch that moves from Anne to Bev and ought to tick off less time when compared to their two watches. And 80% of 250/3 is the exact time it took, 200/3 ns, it took for him to move from Anne to Bev.