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The magnetic Aharonov–Bohm (A–B) effect occurs when a point charge interacts with a line of magnetic flux, while its reciprocal, the Aharonov–Casher (A–C) effect, occurs when a magnetic moment interacts with a line of charge. For the two interacting parts of these physical systems, the equations of motion are discussed in this paper. The generally accepted claim is that both parts of these systems do not accelerate, while Boyer has claimed that both parts of these systems do accelerate. Using the Euler–Lagrange equations we predict that in the case of unconstrained motion, only one part of each system accelerates, while momentum remains conserved. This prediction requires a time-dependent electromagnetic momentum. For our analysis of unconstrained motion, the A–B effects are then examples of the Feynman paradox. In the case of constrained motion, the Euler–Lagrange equations give no forces, in agreement with the generally accepted analysis. The quantum mechanical A–B and A–C phase shifts are independent of the treatment of constraint. Nevertheless, experimental testing of the above ideas and further understanding of the A–B effects that are central to both quantum mechanics and electromagnetism could be possible.

In 1985, Matteucci and Pozzi (1985 Phys. Rev. Lett. 54 2469) demonstrated the presence of a quantum mechanical phase shift for electrons passing a pair of oppositely charged biprism wires. For this experimental arrangement no forces deflect the electrons. Consequently, the result was reported as a non-local type-2 Aharonov–Bohm effect. Boyer (2002 Found. Phys. 32 41–50; 1987 Nuovo Cimento B 100 685–701) showed theoretically that the Matteucci–Pozzi effect could be associated with a time delay caused by a classical force. We present experimental data that confirm the presence of a time delay. This result is in contrast to the situation for the original magnetic Aharonov–Bohm effect. On similar theoretical grounds, Boyer has also associated classical forces and time delays with the magnetic Aharonov–Bohm effect. Recently, we reported the absence of such observable time delays. The contrast with our current work illustrates the subtle nature of Aharonov–Bohm effects.

The Aharonov-Bohm effect was first proposed in 1959, and has stimulated discussion and controversy since the start. Seen by many as a purely quantum mechanical effect, it nevertheless involves such issues as gauge invariance and relativistic dynamics. This multi-faceted nature has led it to be considered a keystone of modern quantum theory. Over the past half-century, interest has remained strong in what many believe is still an open debate as to the purely quantum nature. Additionally, discovery of similar effects for particles other than electrons has further driven curiosity. To better understand the issues such as electromagnetic mass and relativistic effects involved in the Aharonov-Bohm effect, a theoretical study of a simpler two particle system was done. The goal was to understand the manner in which mass of the system behaved strictly classically as compared to a relativistically. As a result of this, a Gedanken experiment is presented which serves as a test for covariance. The two particle system was extended to a spherical shell interacting with a single particle, and a second thought experiment put forth to explore a coupling between electromagnetism and gravitation. In the course of searching for simpler systems which involved the same issues as the Aharonov-Bohm effect, a system presented in the Feynman Lectures of Physics was found to be appropriate. We conduct a complete relativistic analysis of this system as a step towards a full relativistic analysis of the Aharonov-Bohm effect. Given the history and significance of the Aharonov-Bohm effect, it is perhaps surprising that relevant experimental tests had not been completed. For the first time, we searched for time delays as an electron passes a macroscopic solenoid. Such time delays are characteristic of classical forces acting on the electron. No such delays were found, seemingly confirming the standard viewpoint. It is still possible a classical explanation may exist for microscopic solenoids, tho

We demonstrate a wide-angle electron beam splitter capable of producing 1 cm beam separation at the detection plane. The beam splitter utilizes a nanofabricated periodic grating in combination with a bi-prism element. In contrast to devices utilizing only bi-prism elements, the use of the periodic grating causes amplitude, and not wavefront, splitting. Even at maximum separation, beam profiles remain undistorted, providing evidence that coherence is intact. This is a step towards the realization of a large area electron interferometer using such a grating bi-prism combination.