The Michelson-Morley experiment is known as a second orderexperiment because the observed effect depends on (v/c)^2. Considerthe following first order experiment:
At time t = 0, observer a sends a signal to observer b at adistance L away. b records the arrival time. Assume that the systemis moving through the ether with speed v in the direction shown(left). Suppose the laboratory is then rotated 180 degrees withrespect to the velocity, reversing the positions of a and b. Attime t = T, a sends a second signal to b.
a. Show that the interval b observes between the arrival of thesignals is T + (delta)T, where
(delta)T = (2Lv)/(c^2)
to order (v/c)^3.
b. Assume that the experiment is done between the clock on theground and one on the satellite overhead. For an orbit with a 24hour period, l = 5.6R (radius of Earth). Present atomic clocksapproach a stability of 1 part in 10^14. What is the smallest valueof v that this experiment could detect using such clocks?
The Michelson-Morley experiment is known as a second orderexperiment because the observed effect depends on (v/c)^2. Considerthe following first order experiment:
At time t = 0, observer a sends a signal to observer b at adistance L away. b records the arrival time. Assume that the systemis moving through the ether with speed v in the direction shown(left). Suppose the laboratory is then rotated 180 degrees withrespect to the velocity, reversing the positions of a and b. Attime t = T, a sends a second signal to b.
a. Show that the interval b observes between the arrival of thesignals is T + (delta)T, where
(delta)T = (2Lv)/(c^2)
to order (v/c)^3.
b. Assume that the experiment is done between the clock on theground and one on the satellite overhead. For an orbit with a 24hour period, l = 5.6R (radius of Earth). Present atomic clocksapproach a stability of 1 part in 10^14. What is the smallest valueof v that this experiment could detect using such clocks?
