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## Homework 3

Special Relativity, Spring '10

Homework 3

Since the reading this week was sooooo long (two whole chapters, one of which is actually ... finally ... technical) the HW is a little shorter than usual. Of course, really, that's not true, because the main part of your HW is after all to read and then re-read and then carefully scrutinize Chapter 3 and 4, and that will take some time.

1. Summarize (in about one paragraph) the main claim of chapter 3 and what the argument/evidence for it consists of.

2. Show that Equation (4.4) indeed follows from Equation (4.3).

3. A ball moves to the right, relative to the train, with a speed of 3/5 c. The train moves to the right, relative to the tracks, with a speed of 4/5 c. What is the speed of the ball relative to the tracks? (Hint: it's not 7/5 c.)

4. Mermin's whole derivation of Equation (4.2) from the two basic postulates uses this "race" between a ball and a photon. Draw two spacetime diagrams representing all the important features of this race: one using the train frame of reference, and one using the track frame of reference. (In class, we'll use these to go through the whole derivation over again, making sure to label all the funny distances and times -- D, T

Homework 3

Since the reading this week was sooooo long (two whole chapters, one of which is actually ... finally ... technical) the HW is a little shorter than usual. Of course, really, that's not true, because the main part of your HW is after all to read and then re-read and then carefully scrutinize Chapter 3 and 4, and that will take some time.

1. Summarize (in about one paragraph) the main claim of chapter 3 and what the argument/evidence for it consists of.

2. Show that Equation (4.4) indeed follows from Equation (4.3).

3. A ball moves to the right, relative to the train, with a speed of 3/5 c. The train moves to the right, relative to the tracks, with a speed of 4/5 c. What is the speed of the ball relative to the tracks? (Hint: it's not 7/5 c.)

4. Mermin's whole derivation of Equation (4.2) from the two basic postulates uses this "race" between a ball and a photon. Draw two spacetime diagrams representing all the important features of this race: one using the train frame of reference, and one using the track frame of reference. (In class, we'll use these to go through the whole derivation over again, making sure to label all the funny distances and times -- D, T

_{0}, T_{1}, etc. -- on the diagrams, so that every last tiny step in the derivation becomes crystal clear. You don't have to do this before class... but, if you want to start in on it, it certainly wouldn't hurt.)Last modified: Monday, December 19, 2011, 9:18 AM