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## Homework 4

Special Relativity, Spring '10

Homework 4 (covering Mermin chapter 5)

1. Summarize, in a qualitative way, the argument for the claim that two clocks that are synchronized (i.e., two events that are simultaneous) in one frame, will fail to be synchronized (simultaneous) in another frame. In particular, assume that Alice lives on the train and arranges things as in Mermin's discussion: she puts a lamp at the center of the train, and then pushes a button on the lamp so it sends flashes of light toward the two ends of the train, and the two flashes arrive at the two ends simultaneously because they went the same distance at the same speed. Now explain qualitatively how Bob (who lives on the tracks) will analyze all of this and in particular why he'll say that the one flash of light arrives at the back of the train before the other flash of light arrives at the front of the train.

2. Draw 2 spacetime diagrams for this same sequence of events, one using Alice's frame and one using Bob's frame. Label as many of the relevant distances and times as you can, using the same notation that Mermin uses in all the equations on pages 50-51. Really, what I'm asking you to do here is work super-carefully through the derivation leading up to equation 5.5, using space-time diagrams to assist you.

3. This question is based on the discussion from the last class about the (alleged?) distinction between "c" (thought of as the speed of *light*) and "c" (thought of as the speed that is somehow an intrinsic property of spacetime structure or whatever). Think about equation 5.5, which captures the essence of this chapter. Which kind of "c" is it that appears in that equation? If somebody says that the amount by which two events (simultaneous in one frame) fail to be simultaneous in another frame is a property, not of anything having to do with *light* per se, but rather having to do with "space-time structure"... how would you respond?

Extra Credit: What is the (mathematical) relationship between L and D (from pages 50-51)?

Homework 4 (covering Mermin chapter 5)

1. Summarize, in a qualitative way, the argument for the claim that two clocks that are synchronized (i.e., two events that are simultaneous) in one frame, will fail to be synchronized (simultaneous) in another frame. In particular, assume that Alice lives on the train and arranges things as in Mermin's discussion: she puts a lamp at the center of the train, and then pushes a button on the lamp so it sends flashes of light toward the two ends of the train, and the two flashes arrive at the two ends simultaneously because they went the same distance at the same speed. Now explain qualitatively how Bob (who lives on the tracks) will analyze all of this and in particular why he'll say that the one flash of light arrives at the back of the train before the other flash of light arrives at the front of the train.

2. Draw 2 spacetime diagrams for this same sequence of events, one using Alice's frame and one using Bob's frame. Label as many of the relevant distances and times as you can, using the same notation that Mermin uses in all the equations on pages 50-51. Really, what I'm asking you to do here is work super-carefully through the derivation leading up to equation 5.5, using space-time diagrams to assist you.

3. This question is based on the discussion from the last class about the (alleged?) distinction between "c" (thought of as the speed of *light*) and "c" (thought of as the speed that is somehow an intrinsic property of spacetime structure or whatever). Think about equation 5.5, which captures the essence of this chapter. Which kind of "c" is it that appears in that equation? If somebody says that the amount by which two events (simultaneous in one frame) fail to be simultaneous in another frame is a property, not of anything having to do with *light* per se, but rather having to do with "space-time structure"... how would you respond?

Extra Credit: What is the (mathematical) relationship between L and D (from pages 50-51)?

Last modified: Monday, December 19, 2011, 9:18 AM