Abstract
We present a paradox involving a particle and a mirror. They exchange a nonlocal quantity, modular angular momentum Lz mod 2ћ, 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 〈Lz mod 2ћ〉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.
Highlights
We present a paradox involving a particle and a mirror
EPJ Web of Conferences barrier, while its grin tunnels through to the other side. We apply this continuous Cheshire Cat separation to the “interaction-free measurement" (IFM) of Elitzur and Vaidman [6], where it challenges us to reconsider whether the effect—a paradigm of quantum nonlocality—is nonlocal after all
A detector records which path the photon takes through the interferometer, interference disappears and the photon may leave the interferometer in either direction
Summary
-called “weak values" [1] have taken their place alongside eigenvalues and expectation values as possible measured values in quantum mechanics. While an ordinary ensemble suffices for measuring eigenvalues and expectation values, weak values require a “pre- and post-selected" (PPS) ensemble. If the interaction is weak enough, the result of measuring an operator A is the weak value A w of A: Aw=. In this way, weak values enable us to answer questions about quantum systems that we otherwise cannot even ask. Barrier, while its grin tunnels through to the other side We apply this continuous Cheshire Cat separation to the “interaction-free measurement" (IFM) of Elitzur and Vaidman [6], where it challenges us to reconsider whether the effect—a paradigm of quantum nonlocality—is nonlocal after all
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