The twins and the bucket: How Einstein made gravity rather than motion relative in general relativity

In publications in 1914 and 1918, Einstein claimed that his new theory of gravity somehow relativizes the rotation of a body with respect to the distant stars (a stripped-down version of Newton’s rotating bucket experiment) and the acceleration of the traveler with respect to the stay-at-home in the twin paradox. What he showed was that phenomena seen as inertial effects in a space-time coordinate system in which the non-accelerating body is at rest can be seen as a combination of inertial and gravitational effects in a (suitably chosen) space-time coordinate system in which the accelerating body is at rest. Two different relativity principles play a role in these accounts: (a) the relativity of non-uniform motion, in the weak sense that the laws of physics are the same in the two space-time coordinate systems involved; (b) what Einstein in 1920 called the relativity of the gravitational field, the notion that there is a unified inertio-gravitational field that splits differently into inertial and gravitational components in different coordinate systems. I provide a detailed reconstruction of Einstein’s rather sketchy accounts of the twins and the bucket and examine the role of these two relativity principles. I argue that we can hold on to (b) but that (a) is either false or trivial.