Download Theoretical Foundation of the AB Effect E. Comay Charactell Ltd. PO

Theoretical Foundation of the AB Effect
E. Comay
Charactell Ltd.
P.O. Box 39019, Tel Aviv 61390
Israel
Abstract:
It is explained why the AB effect requires that the source of the potential behaves
like an inert object. This requirement is satisfied in the case of the experimental
demonstration of the magnetic AB effect. The inert behavior of the source justifies
the single particle approach of the first AB paper. It is also shown that the magnetic
AB effect does not prove that topology is an inherent property of quantum mechanics.
Furthermore, a thought experiment shows that the magnetic effect disappears in a
case where the external vector potential is associated with a classical, non-inert,
source. Another thought experiment disproves the existence of the electric AB effect.
(The last issue is illustrated in the following pages).
Energy Nonconservation and the Electric AB Effect
(A)
(B)
(C)
Figure 1: Three instants of the electric AB effect (see text).
Fig. 1 describes a minor variation of the standard presentation of the electric
AB effect. Two pairs of plates are made of an insulating material and the surface of
each plate is covered uniformly with electric charge, as shown. Thus, the self energy
of each plate does not change during the experiment. The actual size of the plates
is much larger than the distance between them and the distance between the plates
of each pair is infinitesimal. An electronic wavepacket moves (quite slowly) from left
to right. Before reaching the plates, it is split into two sub-packets as shown by the
black circles. When the lower subpacket is inside the plates’ region and quite far from
their edge (see (B)), the positively charged plates move adiabatically and take the
position described in (B). (In this presentation, the additional lower pair of plates
ensures that, except for edge effects, the plates’ related potential vanishes outside the
volume defined by the four plates.) Later, when the subpackets reach the position
described in (C), the positively charged plates return to their original position. Thus,
the subpackets leave the plates’ region and interfere on a screen (not shown in the
figure). The experiment is designed so the the two electronic subpackets move in a
field free region throughout the entire process. AB compare the interference pattern
obtained in the case where the plates do not move at all to the pattern obtained in the
experiment described above. They argue that the two patterns are different because
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in the experiment described above, the upper subpacket moves in a null potential
whereas the lower subpacket moves in a (field free) nonvanishing potential.
A crucial argument used in the proof of the electric AB effect is that the plates’
energy is independent of the electronic subpackets (see their 1961 paper). Assuming
that this claim holds, one can construct a counterexample and arrive at a serious
contradiction.
Let us examine a variation of this experiment. Here the plates remain in the
position described in (B) until the electronic subpackets are very far from them.
At this time, the plates return to the position described by (A). The subpackets
enter a region of magnetic field. The upper subpacket is directed by this field to its
original position on the left hand side of the plates. On the other hand, the inner
subpacket is ejected by the plates’ negative potential and acquires a higher kinetic
energy. This additional kinetic energy is removed and the lower subpacket joins the
upper subpacket on the plates’ left hand side. A part of the additional energy is
used for a compensation of the very small amount of radiation emitted by the slowly
moving electron.
This example proves the if the electric AB effect exists then energy conservation
is violated.
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