Eli5: In physics, the scallop theorem states that a swimmer that exhibits time-symmetric motion cannot achieve net displacement in a low-Reynolds number Newtonian fluid environment. But why?

Question

Eli5: In physics, the scallop theorem states that a swimmer that exhibits time-symmetric motion cannot achieve net displacement in a low-Reynolds number Newtonian fluid environment. But why?

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Answer 1

The point is the time-symmetric, symmetric being the issue.

If you lay in water arms open, floating, and pull them fast to the body, you go forward. If you now pull them back fast, you go backwards (assuming not raising above water)

But if you pull them fast, let it drift forward, and then open them really slowly, you’ll NOT return to where you were, because opening slowly creates less resistance than fast, so less impulsion.