Locality and nonlocality in the interaction-free measurement

We present a paradox involving a particle and a mirror. They exchange a non local quantity, modular angular momentum L-z mod 2h, but there seems to be no local interaction between them that allows such an exchange. We demonstrate that the particle and mirror do interact locally via a weak local current < L-z mod 2h >(w). In this sense, we transform the "interaction -free measurement" of Elitzur and Vaidman, in which two local quantities (the positions of a photon and a bomb in the two arms of a Mach-Zehnder interferometer) interact nonlocally, into a thought experiment in which two nonlocal quantities (the weak modular angular momentum of the particle and of the mirror) interact locally.