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?
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.
It’s been two decades since I took fluids and had to whip out the ol’ Navier-Stokes equation but I believe it boils down to the idea that a “time-symmetric” motion does something, and then does the opposite of that something. So whatever effect the “something” had, the “opposite something” does the exact opposite of it, undoing the effect. Like taking a step forward, then a step backwards.
Per the example, if a scallop shell closes quickly, creating a jet that launches it forward, it would then need to open again, pushing it backwards, and if the motion were truly symmetric, it would end up right back where it started.
The Reynolds Number and Newtonian Fluid bit has to do with the viscosity of the liquid, basically, if the viscosity can *change* over time, then one motion or the other might have a bigger impact and they wouldn’t be a pair of perfectly undoing forces anymore, one would end up stronger and the object would end up moving.