A Search and Discovery piece by Steven K. Blau (Physics Today, June 2003, page 21) discusses Jack Wisdom's work showing that the position of an object can be changed when that object modifies its shape by extending and retracting across a Schwarzschild metric. Although this result may be new to theorists, it is already known to rocket scientists.
In a paper presented in 1990, I showed that by changing the length of a tether in a gravitational gradient--that is, in curved spacetime--one can modify the orbit, even to the extent of making the object climb away from the planet without expenditure of reaction mass.1 In 1987, Manuel Martinez-Sanchez and Sarah Gavit had calculated similar results.2 One can't push on flat spacetime, but in a region of curved space--or, if you prefer, tidal forces--one can use the difference in force to push against gravity.
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.
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