1.

Since the reference frame of the rotating Earth is not an inertial reference frame, a correct relativist analysis of the Michelson-Morley experiment requires the use of an inertial frame moving with the Earth, but not rotating with it. In such a reference frame, what is the time taken by a light beam to travel a distance L eastward along one arm of the interferometer? Westward? What is the time taken for a light beam to travel a distance L northward along the other arm? Southward? Is there a difference in the round trip travel time for these light beams? [Hint: The lengths L are defined in the reference frame of the rotating Earth; take their length contraction into account.]

2.

Consider a closed rectangular (or, more precisely, trapezoidal) path on the surface of the Earth, consisting of four short segments: an eastward segment, followed by a northward segment, followed by a westward segment, and followed by a southward segment. Mirrors placed at an angle at the corners permit light to travel around this path. Show that the difference between the travel times for counterclockwise and clockwise light signals around this path is approximately 4 A ?sin ?/c ² in Q/c ², where A is the area enclosed in the path, ? the angular velocity of rotation of the Earth, and ? the latitude at the position of the path. What is the magnitude of the time difference...