Scallop Theorem

In physics, the scallop theorem states that a swimmer moving through a highly viscous fluid at low Reynolds number can't achieve any net displacement by performing a reciprocal motion, meaning a sequence of body shapes followed by that same sequence reversed back to the starting shape. Edward Mills Purcell stated the theorem in his 1977 paper Life at Low Reynolds Number, naming it for a scallop's motion, since the animal's simple hinge opening and closing gives it only one degree of freedom, not enough to produce migration in a viscous environment. The result explains why microorganisms swimming at low Reynolds number must use more complex, non-reciprocal strokes in order to move at all.