Classical mechanics, like geometry, can yield surprising results in a non-Euclidean space. One such result, recently discussed in the journal Science by MIT planetary scientist Jack Wisdom, concerns the motion of a composite object as it undergoes a cyclic series of changes in body shape. 1 Consider, for example, a person making the precise, regular motions of an Olympic swimmer. In empty Euclidean (flat) space, the swimmer’s center of mass wouldn’t move; water in the pool, of course, provides the external reaction force that propels real swimmers. The curved-space surprise is that a swimmer executing an appropriate cycle of internal changes can move, even without external forces.

The ability to swim in a curved space suggests that swimming should be possible in four-dimensional curved spacetime as well. But results that are true for spatial surfaces aren’t always true for spacetime. In his Science article, Wisdom considered a particular spacetime, called...

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