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The first presentation of the AB effect [1], treats the phase as a single particle
property. This approach is unjustified. The phase is related to the action (measured
in units of hbar). The action depends on all dynamical coordinates
of the system.
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In a later paper [2] AB claim that their argument also holds for a quantum mechanical
treatment of the entire system (see also [3], p. 365). They conclude that the
macroscopic source is affected quadratically by its relatively small interaction
with the traveling electron. This argument is incorrect. The interaction of the
source with the traveling electron obeys the fundamental law of electrodynamics
where the interaction takes a 2-body bilinear form.
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The AB single particle treatment holds in cases where the source behaves as an inert
object throughout the process. This requirement holds in the Tonomura experiment.
For a discussion,
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Assume that the AB approach where the source is not affected by
the traveling electron is adopted.
Under this condition, a counter argument proves that
the electric AB effect leads to violation of energy conservation.
For a discussion,
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References:
[1] Y. Aharonov and D. Bohm,
Phys. Rev. 115, 485 (1959).
[2] Y. Aharonov and D. Bohm,
Phys. Rev. 123, 1511 (1961).
[3] S. Olariu,
Phys. Lett. A138, 363 (1989).
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