On the relation between the Feynman paradox and Aharonov-Bohm effects

TL;DR

This paper analyzes the dynamics of Aharonov-Bohm and Aharonov-Casher effects, predicting that only one part accelerates in unconstrained motion, linking these effects to the Feynman paradox and discussing implications for quantum mechanics and electromagnetism.

Contribution

It provides a new analysis of the equations of motion for A-B and A-C systems, predicting selective acceleration and introducing a time-dependent electromagnetic momentum concept.

Findings

Only one part accelerates in unconstrained motion

Momentum conservation involves time-dependent electromagnetic momentum

Quantum phase shifts are unaffected by constraints

Abstract

The magnetic Aharonov-Bohm (A-B) effect occurs when a point charge interacts with a line of magnetic flux, while its dual, 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 A-B effects which is central to both quantum mechanics and electromagnetism may be possible.