How can a physical force (be it fictitious or real) be zero in one frame S, but non-zero in another frame S' identical, but a few feet away? Even for exactly the same particle behavior the expression r θ θ ˙ ˙ 2 is different in every frame of reference, even for very trivial distinctions between frames. In short, if we take r θ θ ˙ ˙ 2 as "centrifugal force", it does not have a universal significance: it is unphysical.