# The two airplane version of the twin paradox: is General Relativity involved?

(See the twin paradox for an introduction.) “We were discussing proof of special relativity/time dilation in class and used, as an example, the idea of a clock being taken on a fast plane having time run slower than an identical clock left on the ground. The suggestion was made, however, that this plane would really be accelerating (circling the earth) and would therefore be in a non-inertial frame of reference and we would need to use general relativity!” Yes, you’re right. The fast plane (the one going East) is subject to General Relativity (GR) corrections (a) because of its variable altitude in the Earth’s gravitational field and (b) because of the centripital acceleration. For the plane going West, the centripital acceleration is much smaller: roughly speaking, it stays between the Earth and the sun while the Earth rotates below it. (at temperate latitudes this is possible). The gravitational field term would be rougly the same for both, but not exactly, because East and West boun