Classical Forces in Aharanov-Bohm Effects

Our recent experimental and theoretical work will be reported on Aharanov-Bohm type effects [1]. This includes the experimental demonstration that the Matteucci-Pozzi phase shift is a result of a classical force [2], in contradiction to earlier claims that it is a Type-II Aharonov-Bohm effect [3]. This result is part of a larger discussion that is centered around a classical paradox. Aharonov and Rohrlich point out that this paradox is ``{\ldots} crucial for clarifying the entirely \textit{quantum} interactions of `fluxons' and charges [4].'' Surprisingly, the Lorentz force acting on an infinite solenoid in the presence of an approaching charge is neglected [4]. Inclusion of the Lorentz force, along with the electromagnetic field momentum, leads to conservation of momentum. This motivates further investigation of the dual of the Aharanov- Bohm effect in which a neutral magnetic moment passes a charged wire. The question of sorting out which phase shifts are accompanied by classical force and which ones are not is still a topic of much debate and we report on our efforts to settle the argument. \\[4pt] [1] Batelaan H and Tonomura A 2009~\textit{Phys. Today}~\textbf{62}~38--43\\[0pt] [2] Shawn A Hilbert~\textit{et al}~2011~\textit{New J. Phys.}~\textbf{13}~093025\\[0pt] [3] Matteucci G and Pozzi G 1985~\textit{Phys. Rev. Lett.}~\textbf{54}~2469\\[0pt] [4] Aharonov Y and Rohrlich D 2005~\textit{Quantum Paradoxes: Quantum Theory for the Perplexed}~(Weinheim: Wiley)