Conservation of momentum and the Aharonov-Bohm Effect

The Aharonov-Bohm Effect serves as an example of a purely quantum mechanical phenomenon in which classical forces on the electron are thought to vanish. The presence of forces is still an ongoing debate [1,2]. Surprisingly, a complete special relativistic treatment of the forces in the electron-solenoid system has never been done [3]. We present our ongoing theoretical work on the issue, and explore a connection between Feynman's well-known example [3] of two moving point charges and the Aharonov-Bohm Effect. The relation between this theoretical work and our earlier experimental results [4] is also discussed. [1] T.H. Boyer, J. Phys. A. \textbf{39, } 3455 (2006). [2] G.C. Hegerfeldt and J.T. Neumann, [quant-ph] arXiv:0801.0799v1 (2008). [3] Y. Aharonov and D. Rohrlich, \textit{Quantum Paradoxes: Quantum Theory for the Perplexed} (Wiley-VCH, Weinheim, 2005). [4] \textit{The Feynman Lectures on Physics}. Vol. II, pp. 26-2-26-5 (1964). [5] A. Caprez, B. Barwick, and H. Batelaan. Phys. Rev. Lett. \textbf{99}, 210401 (2007).