SR, Spring '10

Homework 10, covers Mermin Chapter 12 (and other stuff)

1. The main result of this chapter is that if two clocks are situated a (vertical) distance D apart in a uniform gravitational field g, the higher one will tick faster than the lower one by a factor (1 + gD/c^2).

(a) Summarize the argument for the qualitative claim that higher-up clocks should tick faster than lower-down clocks.

(b) Summarize the derivation of the actual formula for how much faster they tick.

(c) Plug in numbers to calculate the difference in clock rates between Brattleboro and here. How many years would you have to live, to have your life extended by one day by living in Brattleboro instead of here? (The difference in altitude for the two places is about D = 171 meters.)

2. Do the one that carried over from last week. It amounts to: work out the equations for the "Lorentz transformations" from scratch, by (say) working out what Bob (on the train moving at speed v) will say the spatial and temporal coordinates are for some event (like the exploding of a time-bomb) to which Alice assigns coordinates X and T.