Is it possible to "swim" in a vacuum, taking advantage of relativity, and make a useful amount of headway?

Question

This article that it is possible:

His situation seems hopeless. However, he remembers the lessons he received as rookie astronaut on swimming in empty space. By applying a weird degenerative form of breaststroke the astronaut slowly moves toward the spaceship and makes it safely back before he runs out of oxygen.

Science 20 cites and MIT paper by Jack Wisdom in support of the claim, although the latter makes no mention of astronauts.

My question is: could an astronaut doing a space 'walk' in space move their center of mass by a useful amount (or even a detectable amount) by moving their arms about by taking advantage of relativity?

Background: On this page is this comment (by the user "Skyler") that was upvoted twice:

In fact, you can "swim" in a vacuum, taking advantage of relativity: science20.com/hammock_physicist/swimming_through_empty_space. However, this is a very subtle effect, and takes hours to move a foot or two.

Similar to this question (except for asking whether an astronaut could really make enough headway to save his own life as claimed by Science 20 and Skyler).

Answer 1

The idea that an astronaut could 'swim' a noticeable amount in a vacuum is not supported by the MIT paper by Jack Wisdom http://web.mit.edu/wisdom/www/swimming.pdf because it says "The curvature of spacetime is very slight, so the ability to swim in spacetime is unlikely to lead to new propulsion devices. For a meter-sized object performing meter-sized deformations at the surface of the Earth, the displacement is of order (sic) $10^{-23}$ m."

In plain English, that means that the astronaut would have moved his body, after a trillion strokes (which at one stroke per second would take just over $30,000$ years), less than a millionth of a millimeter.

So even if the MIT paper is correct in every way and is one day verified by experiments, forget about swimming to safety in a vacuum.

Regarding whether Jack Wisdom's idea violates the law of conservation of momentum, in his paper he does not mention momentum, except to say that angular momentum (not the same thing at all) is conserved. I'm not sure what to make of that. The math and relativity theory in the paper is way above my head.