HW1

1. (a) Assuming that classical physics ideas of the addition of velocities according to Galilean relativity are valid, derive the difference between the times light travelled in both arms of a Michelson-Morley interferometer (before its recombination at point A) that results from turning the apparatus by 90 degrees from the arrangement shown in slide 15 to the arrangement shown in slide 17 of the lecture notes. Note that the magnitude of the vector v in slide 17 has not changed as a result of this rotation, but the direction of the "ether drift" is now upwards instead of to the right (as it is in slide 15) . 2 points

(b) Under the same assumptions, what is the approximate expression for the time difference for the zero and 90 degrees rotation settings? 2 points (Use binomial expansion to get an approximate expression.) 2 points

(c) Do the results of (a) and (b) change for rotations of 90 degrees clockwise and anticlockwise? 1 point

 

2. (a) Show that for vanishing speeds, the Lorentz transformations are well approximated by the Galilean transformations. 2 points.

(b) What speed is necessary in order to observe a length contraction by 1 % of a meter stick that flies past you? 2 points (c) If you were to be riding on that very stick while it is moving with that velocity with respect to a stationary observer, would you also observe this length contraction? 1 point