Moving Through Curved Spacetime

Blau replies: This letter speaks to issues considered by Jack Wisdom, so we contacted him for a response.

Wisdom comments: Geoffrey Landis is correct that, in Newtonian gravity, cyclic changes in the shape of an extended body can work against the gravity gradient to effect certain changes in the orbital parameters. For example, tidally induced shape changes of a synchronously rotating natural satellite can damp the orbital eccentricity of the satellite. However, he is incorrect in identifying that effect with swimming in spacetime.

Cyclic changes in the shape of a body in the curved spacetime of Schwarzschild geometry can lead to net translation of the body. The swimming effect depends on curvature; it does not occur in the flat space of Newtonian gravity. It is a geometric effect: The amount of the translation does not depend on how fast the shape cycle is executed. In the Newtonian effect that Landis cites, there is no translation of the center of mass for fast cycles. That the swimming effect is a relativistic one is apparent in its dependence on the speed of light.