# On Aharonov–Bohm effect

Aharonov–Bohm effect in brief is due to some singularities in space. In books it's infinite solenoid most of the time, which makes some regions of space not simply connected.

What intrigues me is the fact that in real experiment we can't use infinite solenoid. So even if we use one and say that locally it's good approximation it doesn't change the fact that whole space is still simply connected. But the fact is that the effect was experimentally observed.

So the question arises - how one should describe this effect in more rigorous manner (or maybe not rigorous but possible in real world)?

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It's indeed difficult to experimentally realise an infinite solenoid, but this is not the main point. The key point is to have a configuration when $B=0$ whereas $A \neq 0$. This can be done with superconductors, which screen the magnetic field for instance. The experiments are there: –  FraSchelle Apr 25 '13 at 22:26
-> A. Tonomura, T. Matsuda, R. Suzuki, A. Fukuhara, N. Osakabe, H. Umezaki, J. Endo, K. Shinagawa, Y. Sugita and H. Fujiwara, Observation of Aharonov-Bohm effect by electron holography, Phys. Rev. Lett. 48(21), 1443-1446, (1982). -> A. Tonomura, N. Osakabe, T. Matsuda, T. Kawasaki, J. Endo, S. Yano and H. Yamada, Evidence for Aharonov-Bohm effect with magnetic field completely shielded from electron wave, Phys. Rev. Lett. 56(8), 792-795, (1986). –  FraSchelle Apr 25 '13 at 22:27
-> N. Osakabe, T. Matsuda, T. Kawasaki, J. Endo, A. Tonomura, s. Yano, and H. Yamada, Experimental confirmation of the Aharonov-Bohm effect using a toroidal magnetic field confined by a superconductor, Phys. Rev. A34(2), 815-822, (1986) –  FraSchelle Apr 25 '13 at 22:29

The original A-B effect discuss the possibility to observe an interference pattern related to the gauge vector $A$ without magnetic field present along the charge path. So, in this sense, it requires infinite solenoid, since it is the only configuration when $A \neq 0$ but $B=0$. –  FraSchelle Apr 25 '13 at 22:23