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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).

jng224
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Matthew Christopher Bartsh
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    More directly relevant is the paper istelf: http://web.mit.edu/wisdom/www/swimming.pdf rather than a circuitous link through a magazine that is pay-walled. – DKNguyen Apr 23 '21 at 20:56
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    Possible duplicates: https://physics.stackexchange.com/q/886/2451 and links therein. – Qmechanic Apr 23 '21 at 21:01
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    I’m voting to close this question because it asks for a critical review of a published paper without specifying which passage the OP had difficulty following. – WillO Apr 23 '21 at 22:46
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    @WillO The question does not ask for a critical review of any paper. It simply asks whether an astronaut really could save his own life as claimed by Skyler and by Science 20 website. – Matthew Christopher Bartsh Apr 24 '21 at 03:13
  • If one could expel air out from the space suit (or let smelly air out) and considering there is no air resistance in vacuum an astronaut could propel towards the spaceship by momentum conservation with classical mechanics, if not too far away. – anna v Apr 24 '21 at 06:16
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    @MatthewChristopherBartsh: You say the question "simply asks whether an astronaut really could save his own life as claimed". But the answer to that question is in the paper. So presumably there is something in that paper you don't understand, or that you believe is wrong. If you don't specify what passage in the paper is bothering you, then you are implicitly asking people to comment on the correctness of every part of the paper. The name for that is a critical review. – WillO Apr 24 '21 at 12:22
  • @WillO Which paper are you referring to? – Matthew Christopher Bartsh Apr 25 '21 at 04:05
  • Does this answer your question? Swimming in Spacetime - apparent conserved quantity violation – Michael Seifert Apr 27 '21 at 20:08
  • @MichaelSeifert Which question are you referring to? – Matthew Christopher Bartsh Apr 27 '21 at 20:12
  • The question you've asked, which (as far as I can tell) is "Can an astronaut move on their own in curved spacetime, even though this would seem to violate conservation of momentum?" If I've misunderstood your question, I apologize; feel free to edit what you've written for clarity. – Michael Seifert Apr 27 '21 at 20:16
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    @WillO It looks like you aren't going to answer my question. I mean, "Which paper are you referring to?". I'll take a guess that by 'the paper' you mean the MIT paper. The MIT paper is cited by the Science 20 article as evidence that an astronaut could swim to safety in a vacuum. Astronauts are not mentioned in the MIT paper. It is a long paper and I eventually was able to figure out that one statement in the paper can be used to deduce that an astronaut could not swim to safety in a vacuum. I used that to answer the my own question. – Matthew Christopher Bartsh Apr 28 '21 at 14:06

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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.

Matthew Christopher Bartsh
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